Behaviour of

Coupling of Electromagnetic Fields from

Intentional High Power Electromagnetic

Sources with a Buried Cable and an

Airborne Vehicle in Flight

A Thesis

Submitted for the Degree of

Doctor of Philosophyin the Faculty of Engineering

By

Sunitha K

Department of Electrical Engineering

Indian Institute of Science

Bangalore - 560 012

India

September 2012

Acknowledgements

I consider this acknowledgement as one of the few opportunities in life when I get to reflect

back on my actions and realize the contributions of those people who have made a tremendous

impact in all my endeavors. I believe this thesis is not just about getting a doctorate degree,

but it contains the guidance, encouragement, motivation, advice and blessings of several

people and everytime I open this thesis, I would have the greatest pride to have interacted

with such wonderful people at some point of time.

Today, I find immense pleasure in extending my heartfelt gratitude and sincere thanks

to all of you who have made this thesis possible.

At the forefront, I would like to express my deepest gratitude to my research supervisor,

Dr. Joy Thomas M. for his willingness to consider me as his student and more importantly

for agreeing to pursue research on the present topic . I would remain indebted to him for

the amount of efforts and time he had spent all these years in trying to generate research

facilities to pursue this research work and also for his patient hearing to all associated

problems. His nature of being more of a friend rather than a supervisor has always provided

extra energy in my research efforts. I would always cherish the valuable time spent with

him over long discussions related to both research and non-research interests. His constant

encouragement, continuous support and help during the duration of my stay in IISc have

always been a tremendous source of motivation for me. Thank You, Sir for everything you

did for me.

When I write this acknowledgement, I cannot forget Dr.D.V.Giri, Protech, Alamo, CA

who had helped me through out my research work and had given valuable suggestions for

improving the quality of the work. Besides my research supervisor, he had extended me all

his support and shared all his experiences and knowledge in the area of my research topic.

This had given me lot of insight to the problem at hand and was able to do the computations.

i

ii Acknowledgements

My experimental work would not have been complete without the timely help and co-

operation extended by Mr. Riaz Ahmed, Mr. Sreedharan in the High Voltage Laboratory,

Dept. of Electrical Engineering, IISc and my special thanks goes to them.

I would like to thank the Indian Institute of Science for providing me the Institute

scholarship, the facility to stay in its beautiful campus and for the technical facilities to

pursue this research work. My sincere thanks are due to Dr.P.S.Sastry for extending the

necessary facilities in the department when he was the Chairman of the department and for

his support towards my other interests.

I do not know how to thank to all my labmates, Mr. Sisir, Mr. Venkatesulu, Mr. Sridhar

Preetha P., Joseph and who were always available to help me during my presentations in the

laboratory and also in times of need. I am going to miss you all and also the lively technical

discussions we usually have in the laboratory. Thank you so much for everything.

I am very thankful to my very dear friends, for their support and encouragement over all

these years.

Words can not help me in expressing my deep sense of gratitude to my mother, my in

laws and my husband and my daughter for their constant encouragement and moral support

throughout my research work. I will remain forever indebted to them for giving me the

support.

THANK YOU ALL

Sunitha K

Abstract

Society’s dependence on electronic and electrical systems has increased rapidly over the past

few decades, and people are relying more and more on these gadgets in their daily life because

of the efficiency in operation which these systems can offer. This has revolutionized many

areas of electrical and electronics engineering including power sector, telecommunication

sector, transportation and many other allied areas. With progress in time, the sophistication

in the systems also increased. Also as the systems size reduced from micro level to nano

level, the compactness of the system also increased. This paved the way for development in

the digital electronics leading to new and efficient ICs that came into existence. Power sector

also faced a resurge in its technology. Most of the analog meters are now replaced by digital

meters. The increased sophistication and compactness in the digital system technology made

it susceptible to electromagnetic interference especially from High Power Electromagnetic

Sources. Communication, data processing, sensors, and similar electronic devices are vital

parts of the modern technological environment. Damage or failures in these devices could

lead to technical or financial disasters as well as injuries or the loss of life.

Electromagnetic Interference (EMI) can be explained as any malicious generation of

electromagnetic energy introducing noise or signals into electric and electronic systems, thus

disrupting, confusing or damaging these systems. The disturbance may interrupt, obstruct,

or otherwise degrade or limit the effective performance of the circuit. These effects can range

from a simple degradation of data to a total loss of data. The source may be any object, arti-

ficial or natural, that carries rapidly changing electrical currents, such as an electrical circuit.

The sources of electromagnetic interference can be either unintentional or intentional. The

sources producing electromagnetic interference can be of different power levels,different fre-

quency of operation and of different field strength.One such classification of these sources are

the High Power Electromagnetic Sources (HPEM) High Power Electromagnetic environment

iii

iv Abstract

refers to sources producing very high peak electromagnetic fields at very high power levels.

These power levels coupled with the extremely high magnitude of the fields are sufficient

to cause disastrous effects on the electrical and electronic systems. There has been a lot of

developments in the field of the source technology of HPEM sources so that they are now

one of the strongest sources of electromagnetic interference.

High Power Electromagnetic environment refers to the sources producing very high peak

electromagnetic fields at very high power levels. These power levels coupled with the ex-

tremely high magnitude of the fields are sufficient to cause disastrous effects on the electrical

and electronic systems. HPEM environments are categorized based on the source char-

acteristics such as the peak electric field, often called threat level, frequency coverage or

bandwidth, average power density and energy content. The sources of electromagnetic inter-

ference can be either unintentional or intentional. Some examples of unintentional sources

are the increased use of electromagnetic spectrum which generates disturbance to various

systems operating in that frequency band, poor design of systems without taking care of

other systems present nearby as well as lightning. Intentional sources are High altitude

Electromagnetic Pulse (HEMP) or Nuclear Electromagnetic Pulse (NEMP) due to nuclear

detonations, Ultra Wide Band (UWB) field from Impulse Radiating Antennas (IRA), Nar-

row band fields like those coming from High Power Microwaves (HPM), High Intensity Radio

Frequency (HIRF) sources. Of these the lightning is natural and all other sources are man-

made. The significant progress in the Intentional High-Power Electromagnetic (HPEM)

sources and antenna technologies and the easy access to simple HPEM systems for anyone

entail the need to determine the susceptibility of electronic equipment as well as coupling of

these fields with systems such as cables (buried as well as aerial), airborne vehicle etc. to

these types of threats.

Buried cables are widely used in the communication and power sectors due to their effi-

cient functioning in urban cities and towns. These cables are more prone to electromagnetic

interferences from HPEM sources. The buried communication cables or even the buried data

cables are connected to sensitive equipments and hence even a slight rise in the voltage or

the current at the terminals of the equipments can become a serious problem for the smooth

operation of the system. In the first part of the thesis the effect of the electromagnetic field

due to these sources on the cables laid underground has been studied.

The second part of this thesis deals with the study of the interaction of the EM field

from the above mentioned HPEM sources with an airborne vehicle. Airborne vehicle and its

Abstract v

payload are extremely expensive so that any destruction to these as a result of the voltages

and currents induced on the vehicle on account of the incoming HPEM fields can be quite

undesirable. The incoming electromagnetic fields will illuminate the vehicle along its axis

which results in the induction of currents and voltages. These currents and voltages will get

coupled to the internal control circuits that are extremely sensitive. If the induced voltage/

current magnitude happen to be above the damage threshold level of these circuits then it

will result in either a malfunction of the circuit or a permanent damage of it, with both of

them being detrimental to the success of the mission. This will even result in the abortion

of the mission or possible degradation of the vehicle performance. Hence it is worthwhile to

see what will be the influence of an incoming HPEM electromagnetic field on the airborne

vehicle with and without the presence of an exhaust plume.

In this work, the HPEM sources considered are NEMP, IRA and HPM. The electromag-

netic fields produced by the EMP can induce large voltage and current transients in electrical

and electronic circuits which can lead to a possible malfunction or permanent damage of the

systems. The electric field at the earths surface can be modelled as a double exponential

pulse as per the IEC standard 61000-2-9. The NEMP field incident on the earths surface

is considered as that coming from a source at a distance far away from the earths surface;

hence a plane wave approximation has been used. Impulse radiating antennas are the ones

that are used as the major source of ultra wide band radiation. These are highly powerful

antennas that use a pulsed power source as the input and this power source is conditioned

to get an extremely sharp rise time pulse. These antennas are very high power antennas

that are capable of producing a significant electromagnetic field. Impulse radiating antenna

is a paraboloidal reflector and hence is an aperture antenna. Initially the radiated field due

to this aperture needs to be found out at any observation point from the antenna. In this

thesis, the aperture distribution method is used to accurately determine the field due to the

aperture. In this method the field reflected from the surface of the reflector is first found

on an imaginary plane through the focal point of the reflector that is normal to the axis of

the reflector, by using the principles of geometrical optics, which then is extended to the

observation point. The IRA considered for the present work is the one of the most powerful

IRA as per the published literature available in the open domain. This has an input voltage

of 1.025 MV. The far field electric field measured at the boresight (at r =85 m) being equal

to 62 kV/m, and the uncorrected pulse rise time (10%-90%) is 180 ps for this IRA.

HPM sources are usually electromagnetic radiators having a reflector with a horn antenna

vi Abstract

kept at their focal point for excitation. HPM sources generally operate in single mode or at

tens or hundreds of Hz repetition rates. Many HPM radiators are developed in the world

each with their own peculiar geometry and power levels. In the present thesis, a single

waveguide (WR-975) fed HPM antenna assembly has been studied. The chosen waveguide

has a cut-off frequency of 1 GHz and a power level of 10 GW. The wavelength associated

with the waveguide is 0.3 m. The field pattern shows a definite peak in its response when

the frequency is 1GHz, the cut-off frequency of the waveguide.

The electric field coming out of the HPEM sources travel through the medium that is

either air alone or a combination of air and soil respectively depending upon whether the

circuit on which the coupling is analysed is an airborne vehicle or an underground cable.

The media plays a major role in the coupling, as the field magnitude is influenced by the

characteristic properties of the media. As height increases the magnitude of the electric field

decreases for all types of sources and also the time before which the field waveform starts is

increased. The electric field in the soil is decided by the soil properties such as its conductivity

and permittivity. The soil is modelled in such a manner that its conductivity and permittivity

values are taken as a function of frequency by giving due attention to the high frequency

behaviours of soils as the incident field has high frequency components. A soil medium

can be electromagnetically viewed as a four component dielectric mixture consisting of soil

particles, air voids, bound water, and free water. When electric field is incident on the soil,

it gets polarized. This is as a result of a wide variety of processes, including polarization of

electrons in the orbits around atoms, distortion of molecules, reorientation of water molecules,

accumulation of charge at interfaces, and electrochemical reactions. Whatever is the HPEM

source, an increase in the soil conductivity results in an increased attenuation of the field.

Also there is a significant loss of high frequency components in the GHz range in the field

due to the selective absorption by the soil. This effect causes the percentage attenuation

to be maximum for HPM and minimum for NEMP and IRA lying in between these two

extremities. Increase in permittivity of the soil causes attenuation of the electric field for

all HPEM sources. This is due to the relaxation mechanisms in the soil due to atomic- or

molecular-scale resonances.

The coupling of the electromagnetic fields due to HPEM sources is considered in the first

phase. Two cables are considered (i) buried shielded and (ii) buried shielded twisted pair

cables. The results are arrived at using the Enhanced Transmission Line model. The induced

current is more for a shielded cable than a twisted pair cable of the same configuration. The

Abstract vii

induced current magnitude depends upon the type of the HPEM source, the depth of burial

of the cable and the point on the cable where the current/ voltage is computed. Current

is maximum at the centre of the cable for a matched termination and the voltage is the

minimum at this point. The ratio of the induced current in the inner conductor with respect

to the shield current of a shielded cable is the least for an HPM, then comes the IRA and

finally the NEMP. This is due to the fact that higher frequencies are absorbed more by the

shield of the cable. This affects HPM induced current the maximum and NEMP the least

because of the presence of the lower frequency components in NEMP. Induced current in the

twisted pair cable depends upon the number of pairs of the cable and the pitching of the

cable.

The electromagnetic field from the HPEM sources propagates with less attenuation in air

due to the lower resistance this medium offers for electromagnetic wave propagation. Hence

any system in air be it electrical or electronic, will be under the strong illumination by these

electromagnetic fields. As the second part of this thesis, the influence of the electromagnetic

fields from all the three HPEM sources on an airborne vehicle in flight is analysed. For

this part of study, the EM fields radiated by all the three sources at different heights from

the earths surface have been computed. The coupling study has been done for the case of

a vehicle with plume as well as without plume. For the second case, the electromagnetic

modelling of the plume has been done taking into consideration its conductivity, which in turn

depends on the different ionic species present in the plume. The species of the exhaust plume

depends upon the chemical reactions taking place in the combustion chamber of the nozzle of

the vehicle. The presence of the alkali metals as impurity in the airborne vehicle propellant

will generate considerable ion particles such as Na+, Cl− in addition to e- in the plume

mixture during combustion which makes the plume electrically conducting. But it does not

influence the pressure, temperature and velocity of the plume. After the nozzle throat, the

exhaust plume regains the supersonic speed, so the flow of the exhaust plume is assumed

as compressible flow in the second region. The electrons have high collision frequency, high

number density, high plasma frequency and lower molecular mass and hence the highly mobile

electrons dominate the heavy ion particle in the computation of the electrical conductivity of

the plume. The plume conductivity decreases marginally from the axis till a distance equal

to the nozzle radius but the peak value increases sharply towards the exit plane edge of the

nozzle radius. The induced current is computed using Method of Moments. The induced

current depends upon the type of interference source, its characteristics, whether the plume

viii Abstract

is present or not and the type of the plume. The HPM induces maximum current in the

vehicle because of the fact that the plume has a tendency to become more conductive at

these frequencies. The induced currents due to the EM fields from IRA and NEMP comes

after the HPM. The presence of the plume enhances the magnitude of the induced current.

If the plume is homogeneous then the current induced in it is more.

Contents

Acknowledgements i

Abstract iii

Contents xii

List of Tables xiii

List of Figures xiv

1 Introduction 1

1.1 Need for Studying Electromagnetic Interference . . . . . . . . . . . . . . . . 1

1.2 High Power Electromagnetic (HPEM) Environment . . . . . . . . . . . . . . 2

1.3 Failure Rates of Electronic Components due to Electromagnetic Interference 5

1.4 Nuclear Electromagnetic Pulse (NEMP) . . . . . . . . . . . . . . . . . . . . 6

1.4.1 Origin of EMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.2 Classification of EMP Environment . . . . . . . . . . . . . . . . . . . 8

1.4.3 Characteristics of High Altitude EMP . . . . . . . . . . . . . . . . . . 9

1.4.3.1 Spatial Extent . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4.3.2 Effects of EMP . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Impulse Radiating Antenna (IRA) . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5.1 Primary Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5.2 Pulse Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5.2.1 Marx Generator [46] . . . . . . . . . . . . . . . . . . . . . . 13

1.5.2.2 Tesla Transformer . . . . . . . . . . . . . . . . . . . . . . . 16

1.5.3 Pulse Sharpening System . . . . . . . . . . . . . . . . . . . . . . . . . 18

ix

x Contents

1.5.4 Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.5.4.1 Paraboloidal Antenna . . . . . . . . . . . . . . . . . . . . . 19

1.5.4.2 Horn Antenna . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.5.4.3 Half IRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.5.4.4 Collapsible IRA . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.5.5 Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.5.6 A commercial IRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.6 High Power Microwaves (HPM) . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.6.1 Applications of HPM . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.7 Objectives of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.8 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Electric Field due to Intentional HPEM Sources 30

2.1 Electric Field from a Nuclear Burst . . . . . . . . . . . . . . . . . . . . . . . 30

2.1.1 Polarization and Ground Effects . . . . . . . . . . . . . . . . . . . . . 31

2.1.2 Modelling the NEMP field due to a High Altitude Nuclear Burst . . . 31

2.2 Impulse Radiating Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.1 Computation of Radiated Field from an IRA . . . . . . . . . . . . . . 32

2.2.2 Radiation Pattern of IRA in the Near and the Far Field . . . . . . . 37

2.2.3 Illustrative Example in Time Domain . . . . . . . . . . . . . . . . . . 45

2.2.4 Equivalence between Spectral and Temporal Characteristics of IRA . 47

2.3 Electric Field at the Different Points due to a HPM Source . . . . . . . . . . 51

2.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 Influence of the Medium on the Electric field Propagation 57

3.1 Electric Field in Different Media due to HPEM Sources . . . . . . . . . . . . 57

3.2 Electric Field in Air at Varied Heights due to HPEM Sources . . . . . . . . . 59

3.3 Electric Field Attenuation due to Soil Characteristics . . . . . . . . . . . . . 61

3.3.1 Effect of Soil Parameters on the Electric Field . . . . . . . . . . . . . 61

3.4 Response of the Soil to the Field Excitation from HPEM Sources . . . . . . 64

3.4.1 Variation of the Conductivity of the Soil on the Response Characteristics 66

3.4.2 Variation of the Permittivity of the Soil on the Electric Field Behaviour 67

Contents xi

3.4.3 Influence of the Depth of Penetration of the Field in the Soil on its

Spectral and Temporal Characteristics . . . . . . . . . . . . . . . . . 69

3.5 Case Study of Typical Types of Soils . . . . . . . . . . . . . . . . . . . . . . 71

3.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4 Induced Voltage and Current in a Buried Cable due to HPEM Sources 77

4.1 Theory and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.2 Underground Cable Getting Illuminated by HPEM Sources . . . . . . . . . . 78

4.3 Coupling with the Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.4 High Frequency Electromagnetic Field Coupling to Buried Cables . . . . . . 81

4.5 Validation of the Proposed Method . . . . . . . . . . . . . . . . . . . . . . . 84

4.6 Induced Voltage/ Current in the Shield of the Cable due to the HPEM Sources 86

4.6.1 Response of the Cable to NEMP Field . . . . . . . . . . . . . . . . . 86

4.6.2 Response of the Cable to an IRA Field . . . . . . . . . . . . . . . . . 87

4.6.3 Response of the Cable to an HPM Field . . . . . . . . . . . . . . . . 90

4.7 Induced Current in Twisted Pair Cable due to HPEM Sources . . . . . . . . 92

4.7.1 Coupling of the EM field due to NEMP with the Twisted Pair Cables 96

4.7.2 Coupling due to IRA Electric Field . . . . . . . . . . . . . . . . . . . 97

4.7.3 Coupling due to HPM Electric Field . . . . . . . . . . . . . . . . . . 103

4.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5 Coupling of the Field from an HPEM Source with an Airborne Vehicle in

Flight 109

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.2 Review of the previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.3 Geometry of the Airborne Vehicle . . . . . . . . . . . . . . . . . . . . . . . . 110

5.4 Modeling of the Exhaust Plume . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.5 Electromagnetic Modelling of the Plume . . . . . . . . . . . . . . . . . . . . 113

5.6 Method of analysis used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.7 Validation of the Method Used . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.8 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.8.1 Coupling of NEMP with missile . . . . . . . . . . . . . . . . . . . . . 124

5.8.2 Coupling of IRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

xii Contents

5.8.3 Coupling of HPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.9 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6 Conclusions 136

References 141

List of Tables

1.1 IEME Classification Based On Bandwidth . . . . . . . . . . . . . . . . . . . 3

1.2 Susceptibility Levels of Equipments for Destruction Failure [6] . . . . . . . . 6

2.1 Range of Commencement of the Far Field for Different Frequencies of IRA . 38

2.2 Beam Width as a Function of Frequency for Different Distances . . . . . . . 44

2.3 Estimated Directive Gain vs. Frequency for a 2-arm IRA (same as for a 4-arm

IRA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.4 Directive Power Gain Of The Aperture Antennas . . . . . . . . . . . . . . . 46

5.1 Composition of the Solid Propellant . . . . . . . . . . . . . . . . . . . . . . . 113

xiii

List of Figures

1.1 Different Modes of Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 The High Power Electromagnetic Environment [6]. . . . . . . . . . . . . . . . 5

1.3 The Typical Electromagnetic Pulse. . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 EMP Ground Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.5 EMP Ground Coverage for High Altitude Bursts at 100 and 200 km. . . . . 11

1.6 EMP Energy from the High Altitude Burst [36]. . . . . . . . . . . . . . . . . 11

1.7 The Block Diagram Showing the Different Components of an IRA [44]. . . . 14

1.8 Capacitive Energy Storage [46]. . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.9 A Capacitor Assembly [46]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.10 Marx Generator [46]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.11 Dual Trigatron Switch of a Low Jitter type Pulse Generator [45]. . . . . . . 17

1.12 Tesla Transformer [45]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.13 Pulse Sharpening System [43]. . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.14 Different Antennas (a) Paraboloidal antenna (b) Horn antenna (c) Half reflec-

tor IRA (d) Collapsible IRA [43]-[70]. . . . . . . . . . . . . . . . . . . . . . . 21

1.15 Hydrogen Switch [45]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.16 Different Forms of the Equivalent Circuit for the JOLT Hyperband System [45]. 24

1.17 Photograph of the JOLT Hyperband System [45]. . . . . . . . . . . . . . . . 24

1.18 The Basic Block Diagram for an HPM Generator. . . . . . . . . . . . . . . . 27

1.19 Elements of a Single Waveguide feed system [71]. . . . . . . . . . . . . . . . 27

1.20 A Single Reflector fed by a Feed Horn [71]. . . . . . . . . . . . . . . . . . . . 27

2.1 Variations in High - altitude EMP Peak Electric Field [36]. . . . . . . . . . . 33

2.2 Frequency Domain Waveform of the Input NEMP Field at the Earths surface. 33

xiv

List of Figures xv

2.3 Time Domain Waveform of the Input NEMP Field at the Earths Surface. . . 33

2.4 Reflector Geometry and the Aperture plane [79]. . . . . . . . . . . . . . . . . 36

2.5 Orientations of the Various Unit Vectors [79]. . . . . . . . . . . . . . . . . . 36

2.6 x - Component of the Aperture Field . . . . . . . . . . . . . . . . . . . . . . 36

2.7 y - Component of the Aperture Field . . . . . . . . . . . . . . . . . . . . . . 36

2.8 Logarithmic Plot of Antenna Radiation Pattern at 5 m. . . . . . . . . . . . . 40

2.9 Logarithmic Plot of Antenna Radiation Pattern at 100 m. . . . . . . . . . . 41

2.10 Polar Plot of Antenna Radiation Pattern at 5 m. . . . . . . . . . . . . . . . 42

2.11 Polar Plot of Antenna Radiation Pattern at 100 m. . . . . . . . . . . . . . . 43

2.12 A Parabolic Reflector type IRA. . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.13 Spectral Response of the Output Voltage of the Pulser. . . . . . . . . . . . . 48

2.14 Temporal Response of the Output Voltage of the Pulser. . . . . . . . . . . . 48

2.15 Spectral Response of the Radiated Electric Field from the IRA at Different

Distances along the Boresight. . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.16 Frequency Domain Waveform of the Measured Field from the JOLT IRA along

the Boresight at a distance of 304 m [45]. . . . . . . . . . . . . . . . . . . . . 49

2.17 Temporal Response of the Radiated Electric Field from the IRA at Different

Distances Along the Boresight. . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.18 Time Domain Waveform of the Measured Field from a JOLT IRA Along the

Boresight at a distance of 304 m [45]. . . . . . . . . . . . . . . . . . . . . . . 49

2.19 Spectral Response of the Electric Field in the Waveguide. . . . . . . . . . . . 53

2.20 Time Response of the Electric Field in the Waveguide. . . . . . . . . . . . . 53

2.21 The Aperture Field Distribution. . . . . . . . . . . . . . . . . . . . . . . . . 53

2.22 Spectral Response of the Electric Field due to HPM Source at Different Points

at 100 m Away From the Source. . . . . . . . . . . . . . . . . . . . . . . . . 55

2.23 Time Response of the Electric Field due to HPM Source at Different Points

at 100 m Away From the Source. . . . . . . . . . . . . . . . . . . . . . . . . 55

2.24 Mesh Plot of the Time Response of the Electric Field due to HPM Source at

Different Points at 100 m Away from the Source. . . . . . . . . . . . . . . . 55

3.1 Schematic Diagram for Field Propagation Air and Soil. . . . . . . . . . . . . 58

3.2 Fresnel Vertical Reflection Coefficient, Rv. . . . . . . . . . . . . . . . . . . . 60

3.3 Fresnel Vertical Transmission Coefficient,Tv . . . . . . . . . . . . . . . . . . . 60

xvi List of Figures

3.4 Fresnel Vertical Reflection and Transmission Coefficients for an Incident Angle

of 900. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5 Frequency Domain Waveform of the Electric Field Due to NEMP at Different

Heights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.6 Time Domain Waveform of the Electric Field Due to NEMP at Different Heights. 62

3.7 Frequency Domain Waveform of the Electric Field due to an IRA at Different

Heights above the Ground. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.8 Time Domain Waveform of the Electric Field due to an IRA at Different

Heights above the Ground. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.9 Frequency Domain Waveform of the Electric Field due to HPM Source at

Different Heights from the Earths Surface. . . . . . . . . . . . . . . . . . . . 62

3.10 Time Domain Waveform of the Electric Field due to HPM Source at Different

Heights from the Earths Surface. . . . . . . . . . . . . . . . . . . . . . . . . 62

3.11 Attenuation Constant in Soil for Different Soil Conductivities. . . . . . . . . 65

3.12 Phase Constant of the Soil for Different Soil Conductivities. . . . . . . . . . 65

3.13 Ratio of the Conduction Current to Displacement Current at Different Soil

Conductivities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.14 Skin Depth in Soil for Different Conductivities. . . . . . . . . . . . . . . . . 65

3.15 Frequency Domain Waveform of the NEMP Field in Soil at Different Conduc-

tivities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.16 Time Domain Waveform of the NEMP Field in Soil at Different Conductivities. 68

3.17 Frequency Domain Waveform of the Electric Field at the Cable Location for

Different Earth Conductivities for an Incident IRA Field. . . . . . . . . . . . 68

3.18 Time Domain Waveform of the Electric Field at the Cable Location for Dif-

ferent Earth Conductivities for an Incident IRA Field. . . . . . . . . . . . . 68

3.19 Frequency Domain Waveform of the Electric Field at the Cable Location for

Different Earth Conductivities for an Incident HPM Field. . . . . . . . . . . 68

3.20 Time Domain Waveform of the Electric Field at the Cable Location for Dif-

ferent Earth Conductivities for an Incident HPM Field. . . . . . . . . . . . . 68

3.21 Frequency Domain Waveform of NEMP Field in Soil at Different Permittivities. 70

3.22 Time Domain Waveform of NEMP Field in Soil at Different Permittivities. . 70

3.23 Frequency Domain Waveform of the Electric Field at the Cable Location at

Different Earth Permittivity for an Incident IRA Field. . . . . . . . . . . . . 70

List of Figures xvii

3.24 Time Domain Waveform of the Electric Field at the Cable Location at Dif-

ferent Earth Permittivity for an Incident IRA Field. . . . . . . . . . . . . . . 70


Different Earth Permittivity for an Incident HPM Field. . . . . . . . . . . . 70


ferent Earth Permittivity for an Incident HPM Field. . . . . . . . . . . . . . 70

3.27 Frequency Domain Waveform of NEMP Field in Soil at Different Depths. . . 72

3.28 Time Domain Waveform of NEMP Field in Soil at Different Depths. . . . . . 72


Different Depths of Burial of the Cable. . . . . . . . . . . . . . . . . . . . . . 72


ferent Depths of Burial of the Cable. . . . . . . . . . . . . . . . . . . . . . . 72

3.31 Frequency Domain Waveform of the Electric Field from an HPM Source at

the Cable Location at Different Depths of Burial of the Cable. . . . . . . . . 72

3.32 Time Domain Waveform of the Electric Field from an HPM Source at the

Cable Location at Different Depths of Burial of the Cable. . . . . . . . . . . 72

3.33 Frequency Domain Waveform of NEMP Field in Soil for Different Soil Con-

ditions for 1m Depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.34 Time Domain Waveform of NEMP Field in Soil for Different Soil Conditions

for 1m Depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.35 Frequency Domain Waveform of the Electric Field for an IRA at the Cable

Location for Different Soil Conditions at 1m Depth. . . . . . . . . . . . . . . 74

3.36 Time Domain Waveform of the Electric Field for an IRA at the Cable Location

for Different Soil Conditions at 1m Depth. . . . . . . . . . . . . . . . . . . . 74

3.37 Frequency Domain Waveform of the Electric Field for an HPM Source at the

Cable Location for Different Soil Conditions at 1m Depth. . . . . . . . . . . 74

3.38 Time Domain Waveform of the Electric Field for an HPM Source at the Cable

Location for Different Soil Conditions at 1m Depth. . . . . . . . . . . . . . . 74

4.1 Schematic of the HPEM Sources Illuminating a Buried Cable Along with the

Cable Termination and other Details. . . . . . . . . . . . . . . . . . . . . . . 79

4.2 Equivalent Circuit Representation of the External and Internal Circuits of a

Cable used for Coupling Analysis [100]. . . . . . . . . . . . . . . . . . . . . . 79

xviii List of Figures

4.3 Schematic Representation of the External and Internal Circuits of a Cable

used for Coupling Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.4 Transfer Impedance of a Shielded Coaxial Cable. . . . . . . . . . . . . . . . . 79

4.5 Segmentation of the Cable for Coupling Studies. . . . . . . . . . . . . . . . . 85

4.6 Induced Current at the Midpoint of a Wire by Frequency Domain Analysis. . 85

4.7 Induced Current at the Midpoint of a Wire by NEC Computation. . . . . . . 85

4.8 Cross Section of the Buried Cable. . . . . . . . . . . . . . . . . . . . . . . . 85

4.9 The Observation Points on the Cable where the Induced Current and the

Voltage is Plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.10 Frequency Domain Waveform of the Induced Current on the Shield due to

NEMP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.11 Time Domain Waveform of the of Induced Current in the Shield. . . . . . . . 88

4.12 Mesh Plot of the Induced Current on the Shield. . . . . . . . . . . . . . . . . 88

4.13 Time Domain Waveform of the Induced Voltage on the Shield. . . . . . . . . 88

4.14 Mesh Plot of the Induced Voltage on the Shield. . . . . . . . . . . . . . . . . 88

4.15 Time Domain Waveform of the Induced Current on the Inner Conductor. . . 88

4.16 Mesh Plot of the Induced Current on the Inner Conductor. . . . . . . . . . . 89

4.17 Time Domain Waveform of the Induced Voltage on the Inner Conductor. . . 89

4.18 Mesh Plot of the Induced Voltage on the Inner Conductor. . . . . . . . . . . 89

4.19 Induced Current on the Shield at Different Points of a Cable due to EM field

from an IRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.20 Mesh Plot of the Induced Current on the Shield due to EM field from an IRA. 89

4.21 Induced Voltage on the Shield at Different Points of the Cable due to EM

field from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.22 Mesh Plot of the Induced Voltage on the Shield due to the EM field from an

IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.23 Induced Current on the Inner Conductor at Different Points of the Cable due

to the EM field from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.24 Mesh Plot of the Induced Current on the Inner Conductor due to the EM field

from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.25 Induced Voltage on the Inner Conductor at Different Points of the Cable due

to the EM field from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . 91

List of Figures xix

4.26 Mesh Plot of the Induced Voltage on the Inner Conductor due to the EM field

from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.27 Frequency Domain waveform of the Induced Current on the Shield due to EM

field from an HPM source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.28 Induced Current on the Shield at Different Points of the Cable due to EM

field from an HPM source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.29 Frequency Domain waveform of the Induced Current on the Inner Conductor

of the Cable due to EM field from an HPM source. . . . . . . . . . . . . . . 93


to EM field from an HPM source. . . . . . . . . . . . . . . . . . . . . . . . . 93

4.31 Induced Current on the Inner Conductor at Different Points of the Cable due




4.33 Bifilar Helix Configuration of a Twisted Pair Cable used for Computation

Purposes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.34 Induced Current on the Cable Shield for 1 Pair due to NEMP. . . . . . . . . 98

4.35 Induced Current on the Cable Inner Conductor for 1 Pair due to NEMP. . . 98

4.36 Induced Voltage in the Cable Shield for 1 Pair due to NEMP. . . . . . . . . 98

4.37 Induced Voltage on the Cable Inner Conductorfor 1 Pair due to NEMP. . . . 98

4.38 Induced Current on the Cable Shield for 2 Pairs due to NEMP. . . . . . . . 98

4.39 Induced Current on the Cable Inner Conductor for 2 Pairs due to NEMP. . . 98

4.40 Induced Voltage on the Cable Shield for 2 Pairs due to NEMP. . . . . . . . . 99

4.41 Induced Voltage on the Cable Inner Conductor for 2 Pairs due to NEMP. . . 99

4.42 Induced Current on the Cable Shield for 25 Pairs due to NEMP. . . . . . . . 99

4.43 Induced Current on the Cable Inner Conductor for 25 Pairs due to NEMP. . 99

4.44 Induced Voltage on the Cable Shield for 25 Pairs due to NEMP. . . . . . . . 99

4.45 Induced Voltage on the Cable Inner Conductor for 25 Pairs due to NEMP. . 99

4.46 Induced Current on the Cable Shield for 100 Pairs due to NEMP. . . . . . . 100

4.47 Induced Current on the Cable Inner Conductor for 100 Pairs due to NEMP. 100

4.48 Induced Voltage on the Cable Shield for 100 Pairs due to NEMP. . . . . . . 100

4.49 Induced Voltage on the Cable Inner Conductor for 100 Pairs due to NEMP. . 100

xx List of Figures

4.50 Effect of the Pitching on the Induced Current in a Twisted Pair Cable due to

NEMP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.51 Induced Current on the Cable Shield for 1 Pair due to EM field from an IRA. 101

4.52 Induced Current on the Cable Inner Conductor for 1 Pair due to EM field

from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.53 Induced Voltage on the Cable Shield for 1 Pair due to EM field from an IRA. 101

4.54 Induced Voltage on the Cable Inner Conductor for 1 Pair due to EM field

from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101


from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.56 Induced Current on the Cable Inner Conductor for 2 Pairs due to EM field

from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.57 Induced Voltage on the Cable Shield for 2 Pairs due to EM field from an IRA. 102

4.58 Induced Voltage on the Cable Inner Conductor for 2 Pairs due to EM field

from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.59 Induced Current on the Cable Shield for 25 Pairs due to EM field from an IRA.102


from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.61 Induced Voltage on the Cable Shield for 25 Pairs due to EM field from an IRA.102


from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102


from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.65 Induced Voltage on the Cable Shield for 100 Pairs due to EM field from an

IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


EM field from an IRA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.68 Induced Current on the Cable Shield for 1 Pair due to EM field from an HPM

Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

List of Figures xxi

4.69 Induced Current on the Cable Inner Conductor for 1 Pair due to EM field

from an HPM Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.70 Induced Voltage on the Cable Shield for 1 Pair due to EM field from an HPM

Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105



4.72 Induced Current on the Cable Shield for 2 Pairs due to EM field from an HPM

Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105



4.74 Induced Voltage on the Cable Shield for 2 Pairs due to EM field from an HPM

Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106



4.76 Induced Current on the Cable Shield for 25 Pairs due to EM field from an

HPM Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106




HPM Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106



4.80 Induced Current on the Cable Shield for 100 Pairs due to EM field from an

HPM Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107




HPM Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107




EM field from an HPM Source. . . . . . . . . . . . . . . . . . . . . . . . . . 107

xxii List of Figures

5.1 Airborne Vehicle with the Exhaust Plume. . . . . . . . . . . . . . . . . . . . 111

5.2 Solid Propellant Rocket with a Nozzle. . . . . . . . . . . . . . . . . . . . . . 111

5.3 Mesh Plot of the Conductivity along the Axial and Radial Direction. . . . . 119

5.4 Conductivity of the Exhaust Plume along the Axial Position. . . . . . . . . . 119

5.5 Thin Wire Model of the Vehicle with the Exhaust Plume for Coupling Analysis.119

5.6 Computed Induced Current in the Missile Without Plume at Different Wave-

lengths of the Incoming Field for the Canonical example. . . . . . . . . . . . 122

5.7 Induced Current in the Missile Without Plume at Different Wavelengths of

the Incoming Field for the Canonical example [154]. . . . . . . . . . . . . . . 122

5.8 Computed Induced Current in the Missile with Plume at Different Wave-

lengths of the Incoming Field for the Canonical example. . . . . . . . . . . . 122

5.9 Induced Current in the Missile with Plume at Different Wavelengths of the

Incoming Field for the Canonical example [154]. . . . . . . . . . . . . . . . . 122

5.10 Computed Induced Current in the Missile With and Without Plume for an

Electrically Short Missile for the Canonical example. . . . . . . . . . . . . . 122

5.11 Induced Current in the Missile With and Without Plume for an Electrically

Short Missile for the Canonical example [154]. . . . . . . . . . . . . . . . . . 122

5.12 Computed Induced Current in the Missile with and without Plume for the

Vehicle Length equal to its Resonance Length for the Canonical example. . . 123

5.13 Induced Current in the Missile with and without Plume for the for the Vehicle

Length equal to its for the Canonical example [160]. . . . . . . . . . . . . . . 123

5.14 Coupling of the Fields due to HPEM Sources with an Airborne Vehicle . . . 123

5.15 The Observation Points for the Computation of the Induced Current in a

Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.16 Induced Current at the Nose due to an NEMP Electric Field. . . . . . . . . . 126

5.17 Induced Current at the Tail due to an NEMP Electric Field. . . . . . . . . . 126

5.18 Induced Current at the Midpoint of the Vehicle due to an NEMP Electric Field.126

5.19 Variation of the Induced Current along the Length of the Missile and its Plume

due to an NEMP Electric Field. . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.20 Derivative of Induced Current at the Nose due to an NEMP Electric Field. . 127

5.21 Derivative of Induced Current at the Tail due to an NEMP Electric Field. . 127

5.22 Derivative of Induced Current at the Midpoint of the Vehicle due to an NEMP

Electric Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

List of Figures xxiii

5.23 Induced Voltage Between the Endpoints due to an NEMP Electric Field. . . 127

5.24 Induced Current at the Nose due to an IRA Electric Field. . . . . . . . . . . 129

5.25 Induced Current at the Tail due to an IRA Electric Field. . . . . . . . . . . 129

5.26 Induced Current at the Midpoint of the Vehicle due to an IRA Electric Field. 129

5.27 Variation of the Induced Current along the Length of the Missile and Plume

due to an IRA Electric Field. . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.28 Derivative of Induced Current at the Nose due to an IRA Electric Field. . . 130

5.29 Derivative of Induced Current at the Tail due to an IRA Electric Field. . . . 130

5.30 Derivative of Induced Current at the Midpoint of the Vehicle due to an IRA

Electric Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.31 Induced Voltage Between the Endpoints due to an IRA Electric Field. . . . . 130

5.32 Induced Current at the Nose due to an HPM Electric Field. . . . . . . . . . 133

5.33 Induced Current at the Tail due to an HPM Electric Field. . . . . . . . . . . 133

5.34 Induced Current at the Midpoint of the Vehicle due to an HPM Electric Field. 133

5.35 Variation of the Induced Current along the Length of the Missile and Plume

due to an HPM Electric Field. . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.36 Derivative of Induced Current at the Nose due to an HPM Electric Field. . . 134

5.37 Derivative of Induced Current at the Tail due to an HPM Electric Field. . . 134

5.38 Derivative of Induced Current at the Midpoint of the Vehicle due to an HPM

Electric Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.39 Induced Voltage Between the Endpoints due to an HPM Electric Field. . . . 134

Chapter 1

Introduction

1.1 Need for Studying Electromagnetic Interference

Society’s dependence on electronic and electrical systems has increased rapidly over the

past few decades, and people are relying more and more on these gadgets in their daily life

because of the easiness and efficiency in operation which these systems can offer. This has

inturn revolutionized many areas of electrical and electronics engineering including power

sector, telecommunication sector, and many other allied areas. As time progressed, the

sophistication in the systems also increased. As we are moving from a micro level to a nano

level in system size, the compactness also increased hence forth. This paved the way for

the development in digital electronics and new and efficient ICs came into existence. Power

sector also faced a boom in its technology. Most of the analog meters are now replaced by

digital meters that have enhanced the customer appreciation to such equipments. on the

other hand, this increased sophistication and compactness in the system technology made it

susceptible to electromagnetic interference. Communication, data processing, sensors, and

similar electronic devices are vital parts of the modern technological environment. Damage

or failures in those devices could lead to technical or financial disasters as well as injuries or

the loss of life [1]-[5].

Electromagnetic Interference (EMI) can be explained as any malicious generation of

electromagnetic energy introducing noise or signals into electric and electronic systems, thus

disrupting, confusing or damaging these systems. The disturbance may interrupt, obstruct,

or otherwise degrade or limit the effective performance of the circuit [6]-[13]. These effects

can range from a simple degradation of data to a total loss of data. The source may be

any object, artificial or natural, that carries rapidly changing electrical currents, such as an

1

2 Chapter 1. Introduction

electrical circuit. The sources of electromagnetic interference can be either unintentional or

intentional. Intense Electromagnetic (EM) signals in the frequency range of 200 MHz to 5

GHz can cause upset or damage in electronic systems. This induced effect in an electronic

system is commonly referred to as Intentional Electro-Magnetic Interference (IEMI).Some

examples of unintentional sources are the increased use of electromagnetic spectrum which

generates disturbance to various systems operating in that frequency band, poor design of

systems without taking care of other systems present nearby. These include electric power

transmission lines, electric motors, thermostats etc. Electrical power being turned off and

on rapidly is a potential source of EMI. The spectra of these sources generally resemble that

of synchrotron sources, stronger at low frequencies and diminishing at higher frequencies,

though this noise is often modulated, or varied, by the creating device in some way. Included

in this category are computers and other digital equipments as well as televisions. The rich

harmonic content of these devices means that they can interfere over a very broad spectrum.

The sources producing electromagnetic interference can be of different power levels,different

frequency of operation and of different field strength. One such classification of these sources

are the High Power Electromagnetic Sources (HPEM) High Power Electromagnetic environ-

ment refers to sources producing very high peak electromagnetic fields at very high power

levels. These power levels coupled with the extremely high magnitude of the fields are suf-

ficient to cause disastrous effects on the electrical and electronic systems. There has been a

lot of developments in the field of the source technology of HPEM sources so that they are

now one of the strongest sources of electromagnetic interference.

1.2 High Power Electromagnetic (HPEM) Environment

HPEM threat environments can be categorized based on the technical attributes of the

source and also based on the way the fields from these sources couples with any system on

its pathway [6]-[12].Based on the technical attributes of the sources HPEM environment is

classified according to:

• Peak electric field, often called threat level

• Frequency coverage or bandwidth classification

• Average power density

1.2. High Power Electromagnetic (HPEM) Environment 3

• Energy content

Based on the peak electric fields there are low field sources, moderate field and high field

sources. These depends upon the circuits used to get the required field from these sources.

Another way of classifying the HPEM environments is based on the frequency content or

their bandwidth. This classification is on the basis of the frequency content of their spectral

densities according to which there are narrowband, moderate band, ultra-moderate band

and hyper band sources. To characterize these environments, we consider the band ratio,br

of the EM spectrum.

br =fhfl

(1.1)

where fh is the higher frequency content in the spectrum anf fl is the lower frequency

content. This classification is shown in table 1.1 [6].

Table 1.1: IEME Classification Based On Bandwidth

Band Type Percentage Bandwidth (pbw) Band ratio (br)

Narrow (hypo) < 1 < 1.01

Moderate (Meso) 1 pbw < 100 1.01 <br< 3

Ultra−moderate 100 pbw< 163.64 3 <br < 10

(ultra meso or sub hyper)

Hyper band 163.64 pbw < 200 br 10

This terminology is consistent with IEC 61000-2-13 Standard, titled EMC, Highpower

electromagnetic (HPEM) environments – radiated and conducted. There are several HPEM

generators that employ current and emerging technologies, that fall in each of the categories

listed in table 1.1. The above classification is useful in describing potential HPEM environ-

ments. In the case of HPEM waveforms, we stipulate the lower frequency limit to be 1 Hz

if there is a large dc content in the spectrum.

In addition, the HPEM environments are characterized by the coupling mechanism. The

fields from the HPEM sources can be either radiated or conducted, that is based on the

medium used for propagation. In the radiated environments air forms the medium of prop-

agation and in the conducted environments the wire, cable etc. form the medium to carry

the field from the source to the victim circuit where EMI occurs.The way the fields get into


Figure 1.1: Different Modes of Coupling

the victim circuits can be either as a front-door coupling or by back-door as shown in Fig.

1.1. In the front door coupling, the fields get into the system or the equipments by way of

the antennas, sensors etc. that are installed in the system. In the back door coupling this

field penetration occurs through holes and other cavities or slots available in any part of the

circuit.

All these characterizations are intended to provide information needed to estimate the

effects caused by HPEM environments. If one is assessing the risk that an HPEM environ-

ment causes hazardous situations in a given system one will have to focus more on aspects

like

• Likelihood of occurrence of the HPEM environment under real life conditions (i.e.

outside a laboratory)

• Ability to access the target system (i.e. come close to the target (radiated) or connect

to a cable (conducted)

• Sensitivity of the target to the specific HPEM environment

The HPEM environment is shown in Fig 1.2. It includes lightning, High altitude Elec-

tromagnetic Pulse (HEMP) due to nuclear detonations, Ultra Wide Band (UWB) field from

Impulse Radiating Antennas (IRA), Narrow band fields like those coming from HPM, HIRF

1.3. Failure Rates of Electronic Components due to Electromagnetic Interference 5

Figure 1.2: The High Power Electromagnetic Environment [6].

sources. Of these, the lightning is natural and all other sources are man-made. the sources

are dealt in details in the next sections.

1.3 Failure Rates of Electronic Components due to Elec-

tromagnetic Interference

Electromagnetic interference leads to failure of the equipments that can be either a tempo-

rary upset of one or more components in the system or a permanent failure of the system.The

failure effects in any system depends upon the breakdown failure rate (BFR) and the Destruc-

tive Failure Rate. The breakdown failure rate can be defined as the number of breakdowns

of a system, divided by the number of pulses applied to it. This does not involve a physical

damage to the system. After suitable rectification the system goes back into its normal

functioning. That value of the electrical field strength at which the BFR gets 5 % of the

maximum value is the breakdown threshold. The breakdown bandwidth (BB) is defined as

the span of the electrical field strength, in which the BFR changes from 5%to 95% of the

maximum. The Destructive Failure Rate of the device under test has been defined as the

number of destructions divided by the number of pulses applied to the system. Here there

will be physical damage of the system so that the system will not recover without a hard-


Table 1.2: Susceptibility Levels of Equipments for Destruction Failure [6]

EUT UWB in kV/m EMP in kV/m HPM in kV/m

Logic Devices 25 120 NA∗

Microcontroller 7.5 42 NA

Microprocessor Boards 4 25 0.2

PC Systems 12 NA NA

PC Networks 0.2 0.5 NA

∗ data not available.

ware repair [14]. The susceptibility levels of different equipments under an interference due

to high power sources like Ultra Wide Band Pulse (UWB), Electromagnetic Pulse (EMP)

and High Power Microwave (HPM) are shown in table 1.2.

The destruction of the devices occurs depending upon the field strengths. At lower field

strengths electronic components such as diodes or transistors on the chip will be damaged

that are mainly due to flash over effects. If the amplitude of the electromagnetic pulse

increases by about 50%, additional on chip wire destructions like smelting of PCB tracks

without flash over effects and multiple component destructions can occur. Further increase

in the amplitude leads to additional bond wire destructions, multiple components, and on

chip wire destructions. On that account it is possible to predict the destruction effects of

integrated circuits on chip level, if the proposed measurement set-up is used [15]-[21].

1.4 Nuclear Electromagnetic Pulse (NEMP)

A high altitude nuclear burst produces Nuclear Electro Magnetic Pulses (EMP) in addition

to the generation of heat, light and nuclear radiation. These electromagnetic pulses are pro-

duced at the same time as the blast itself and can illuminate a large geographical area. The

electromagnetic fields produced by the EMP can induce large voltage and current transients

in electrical and electronic circuits which can lead to a possible malfunction or permanent

damage of the systems [22]-[30] . The typical electromagnetic pulse waveform at the earth’s

surface is given in Fig. 1.3. The probability of damage of the electronic devices is higher

if their sensitivity is more. This makes it important that the electronic devices and circuits

be hardened so as to reduce the damage level due to EMP. Consequently, there is a great

1.4. Nuclear Electromagnetic Pulse (NEMP) 7

Figure 1.3: The Typical Electromagnetic Pulse.

need for laboratory simulation and measurement of EMP. The origin, classification, physics

of generation and characteristics of EMP will be presented in this chapter [22]-[30].

1.4.1 Origin of EMP

Nuclear bombs when detonated can produce electromagnetic signals and this leads to the

generation of EMP. However, the extent and potentially dangerous nature of EMP effect

were not realized for several years. Only during the atmospheric nuclear tests in the early

1950s that attention slowly began to focus on EMP as a probable cause of malfunction of

electronic equipments. Finally, around 1960, the possible vulnerability of various civilian

and military electrical and electronic systems to EMP was recognized. Although and EMP

may be caused by non-nuclear explosions as well, the present usage of the term EMP is such

that it refers to EMP of nuclear origin exclusively [31]-[36].

Nuclear explosions of all types from underground to high altitudes are accompanied

by an EMP, although the intensity and duration of the pulse and the area over which it

is effective vary considerably with the location of the burst point with respect to earth’s

surface. The strongest electric fields are produced near the burst by explosions at or near


the earth’s surface, but for those at high altitudes the fields at the earth’s surface are strong

enough to be of concern for electrical and electronic equipments over a very much larger area

[31]-[36].

Majority of the EMP energy lies within the radio frequency spectrum ranging from a few

hertz to the very high frequency (VHF) band. The pulse is characterized by electromagnetic

fields with short rise times and a high peak electric field amplitude (tens of kilovolts per

meter) [31]-[36]. A significant property of EMP is its large area of coverage; intense fields from

a single burst outside the atmosphere can cover an area of earths surface several thousand

kilometres in diameter. EMP thus differs from many other sources of electromagnetic energy,

whether natural (lightning) or man-made (such as HPM and ESD). EMPs time waveform

exhibits a higher amplitude and shorter rise time. Also, the electromagnetic radiation due

to EMP can occur almost at the same time (the limitation being the speed of light) over a

large area. Intense natural and man-made fields, on the other hand, seldom have such wide

simultaneous distribution. Also, while natural and man-made sources are usually confined

to a narrow portion of the frequency spectrum, EMP occupies a broad frequency spectrum

from a few hertz to the VHF band (> 100 MHz).

1.4.2 Classification of EMP Environment

EMPs major characteristics its time signature and spatial extent depend primarily on

the height and location of the nuclear burst relative to the point of observation [31]-[36].

EMP is thus often classified according to burst height, namely surface, air or high altitude.

A surface burst occurs on or close to the ground, and an air burst takes place between 2

and 20 kilometres above the ground. Bursts occurring above 40 kilometres are classified

as high altitude bursts. However, a burst between 0 and 2 kilometres produces an EMP

with characteristics of both surface and air bursts and those between 20 and 40 kilometres

generate EMP with characteristics of both air and high-altitude bursts.

Two regions surrounding the nuclear burst are important in EMP considerations namely

the deposition (source) region and the radiation region. The deposition region is the space

around the burst where the EMP is generated. It contains intense electric and magnetic

fields as well as a highly conducting plasma (ionized gas). The deposition region is limited

to a radius of 3 to 6 kilometers around a surface burst, about 5 to 15 kilometers around an

air burst and about 3000 kilometers for a high-altitude burst.


Depending upon the burst height, the geomagnetic field and/or asymmetries in the envi-

ronment cause the source fields to radiate well beyond the deposition region. These radiation

regions contains somewhat less intense fields and have three general characteristics, viz.,

(1) the direction of propagation is radially outward from the burst,

(2) the electric and magnetic field vectors are in a plane perpendicular to the direction

of propagation,

(3) the fields have a far-field range dependence of 1/R.

Although all three types of bursts produce a radiated pulse, they differ in time waveform

and spatial coverage. High-altitude EMP can have a strong radiated electromagnetic field

and a wide area of coverage. An air burst produces a relatively weak radiated field but

can have a large non-radiated field. Surface burst EMP is characterized by a large non-

radiated field and a significant radiated field. In the present work, a High Altitude EMP

is considered. The physics of generation of High Altitude EMP, the various models for

explaining the generation of EMP are reported in many literatures [31]-[42].

1.4.3 Characteristics of High Altitude EMP

A high altitude nuclear burst differs from the surface and air bursts in that EMP is the

major effect. There is no significant overpressure pulse and the atmosphere diminishes all

other prompt weapon effects.

The radiated fields due to high altitude EMP have very intensity; short rise times and

they cover a wide area because of the height and large extent of the source region.

The characteristics such as the spatial extent, time waveform and peak amplitude of

high altitude EMP depend on the height of burst (HOB), weapon yield, and the observer’s

location in relation to the burst [31]-[42].

1.4.3.1 Spatial Extent

The geographical coverage of high altitude EMP over the earth’s surface is determined en-

tirely by the height of burst.

As shown in Fig. 1.4, the maximum ground range (tangent radius) depends on the

tangent to the earth from the burst point and is the arc length between this tangent and the

earth’s surface directly beneath the burst (surface zero).

Assuming that the earth is spherical, the tangent radius RT (in kilometres) is


RT = RE cos−1(RE

RE +HOB) (1.2)

Where RE = 6370 kilometres is the approximate radius of the earth and HOB is the

burst height in kilometres. The total surface area AT (in square kilometres) covered by a

high-altitude burst is given by

AT =2πR2

EHOB

(RE +HOB)(1.3)

Figure 1.8 shows the area of coverage for India for bursts of 100, 300 and above 300

kilometres over the central India for a 1 MT burst.

1.4.3.2 Effects of EMP

The primary effect of an EMP is to illuminate a system or portion of it with an electromag-

netic wave. Secondary effects are the time-varying induced currents and voltages on cables,

wires, antennae, transmission lines like power lines, telecommunication lines etc., and in gen-

eral any metallic or good conducting element in the path of the pulse or an aperture through

which it penetrates. Possible succeeding effects are mainly physical, such as thermal heating

effects, sparking, insulation breakdown and other non-linear saturation and or overloading

effects. Permanent damage or burn out of circuit components can occur as a result of the

above physical processes. Certain semiconductors, capacitors and metal film resistors are

particularly susceptible to damage. Operational upset of the system also can occur, caused

by the presence of an interfering signal [22]-[30].

Fig. 1.6 shows the energy of the electromagnetic pulse at various stages of its generation

as well as on the surface of the earth for a one megaton nuclear burst at a height of 100 km.

The energy density at the surface of earth for this case is about 3 J/m2. In order to achieve

the desired level of confidence that a system is designed and implemented properly for the

EMP hardness, some experimental verification is required. Since it is unrealistic to verify

the EMP hardness of a system in a true nuclear environment laboratory simulation of the

EMP environment for test purposes becomes a necessity. In addition, because of the intense

field of the EMPP for an extremely short duration, appropriate sensors, instrumentation and

measurement technology also become necessary for EMP tests.

The EMP simulator is a test tool or system designed to produce a known electromagnetic

field which can be used to illuminate a system under test the same way as real EMP does.


Figure 1.4: EMP Ground Coverage

Figure 1.5: EMP Ground Coverage for High Altitude Bursts at 100 and 200 km.

Figure 1.6: EMP Energy from the High Altitude Burst [36].


Therefore an idealized EMP facility should produce a wave shape, similar to the double

exponential waveform shown. It should also have some over test capability (in higher magni-

tudes of E and H fields). The facility should have the capability of orienting the test object

to account for polarization and direction of arrival. Also, an ideal EMP simulator should

produce plane waves with a ratio of E/H equal to 120π. In addition, the fields produced by

such a facility should not be unduly affected by the test object. In practice, however, there

is no facility which achieves all the desirable characteristics.

1.5 Impulse Radiating Antenna (IRA)

Impulse radiating antennas are powerful and highly efficient antennas which are used as a

major source of Ultra Wide Band (UWB) radiation. These antennas uses a pulsed power

source as input and this power source is conditioned to get an extremely sharp rise time

pulse [43]-[44]. These antennas are capable of producing an intense electromagnetic field.

Impulse radiating antennas are driven by high voltages with very sharp rise times. these

high voltages generate the field that gets reflected from the antenna used in the IRA so that

the net electric field at the required observation point has the characteristics of a sharp rise

time, impulse nature and very high peak electric field.Typically the rise time is of the order

of pico-seconds and the voltage rating will be in kilovolts and the electric field will be of

the order of kV/m. there are very powerful IRA’s like JOLT that operate with a million

volts input voltage at pico-second rise time which gives electric fields of about 100’s of kV/m

magnitude. The major components of an Impulse Radiating Antenna (IRA) are as shown

in the block diagram of Fig. 1.7 and includes a primary energy storage, a pulse generator,a

pulse sharpening system and an antenna.

IRA has a number of applications including underground object detection, periscope

detection, to determine the characteristics of rocks, for atmospheric studies and so on.

1.5.1 Primary Energy Storage

the energy required for driving the entire power circuit of the IRA comes from the primary

energy storage. this consists of either a capacitor or an inductor that can store energy in its

electric/magnetic field respectively. If inductors are used as energy storage there are chances

of more losses occurring by way of leakage. This seriously affects the performance of the

1.5. Impulse Radiating Antenna (IRA) 13

circuit. Hence it is not possible to get the required high voltage and the sharp rise time.

Since the major characteristics of IRA includes its sharp rise time and high peak electric

field,inductors are not a good choice for energy storage.

The primary energy storage commonly used are capacitors that store energy in its electric

field. Such an energy storage device is shown in Fig. 1.8. The energy stored in these

capacitors are given to the load which is the antenna through a series of circuit components.

There can be losses occurring in this process of energy transportation of this energy. Hence

if a single capacitor is used it may not be able to handle the total energy that is to be needed

by the circuit. Hence in all commercial IRA’s, instead of using a single capacitor, a number

of capacitors are stacked together so that the net energy storage is increased. The number

of capacitors stacked are a function of the magnitude of the output voltage required [44].

In the case of stacked capacitors, there should be proper insulation of the entire unit

else it can lead to a failure at the pulsed voltage levels. A co-axial geometry is usually

chosen so as to get a minimum inductance. The capacitors are mainly ceramic capacitors

mounted between the inner and outer aluminium conductors.these capacitor assembly is kept

in dielectric boxes that are made out of thick acrylic. Suitable elastomers are added to give

the dielectric protection. One such elastomer is silicone which is used in the most powerful

IRA known as JOLT [46].

1.5.2 Pulse Generator

The major part of an IRA is the pulse generator. This receives the enrgy from the primary

energy storage and it has a number of circuits including the capacitors, inductors transform-

ers and spark gaps that finally helps in building the voltage levels to the required magnitude

that is to be used by the antenna. To generate high voltage pulses with voltage amplitudes

of several 100 kV ′s there are two major technologies known, Marx Generators, and Tesla

Transformer.

1.5.2.1 Marx Generator [46]

A Marx generator is an efficient impulse generator, where charging and discharging of ca-

pacitors are used to get the required impulse voltage. the capacitors are charged in parallel

and discharged in series. Usually these impulse generating circuits are meant for generating

impulses with a rise time of the order of µs. But in an IRA the voltage must be either in


Figure 1.7: The Block Diagram Showing the Different Components of an IRA [44].

Figure 1.8: Capacitive Energy Storage [46].

Figure 1.9: A Capacitor Assembly [46].


tens or hundreds of kV or even more with rise time of the order of pico- seconds. Hence the

Marx generator circuit uses capacitors rated in nano farads or even in pico farads. The stray

inductance of the circuit should be as minimum as possible. The major draw back of using

Marx generator in IRA application involves the number of switches required to produce the

required output waveform. So operation of large number of switches in this case can cause

jitter in the performance which can seriously damper the efficiency of the IRA. So this jitter

must be avoided. There are several methods used to avoid jitter in the operation. They are:

• A compact, lightweight, and portable design of Marx generator that is housed in a

tubular containment pressure vessel.In this case the Marx generator works in an atmo-

sphere of pressurized dry air. this improves the pulse repetation rates of the IRA.

• A configurable output polarity using a single polarity charging source

• A modular construction that allows setting the output voltage and pulse width as

desired

• Utilization of corona-stabilized (or field enhanced) spark gap switches for high PRR

operation

• Optical coupling of spark gap switches to reduce system jitter

• A triggering scheme that allows for a subnanosecond command trigger to output jitter

• Parallel resonant charging using a series inductance and resistance in each stage to

support high pulse repetation rate operation

Low jitter triggering of the Marx generator requires a bipolar trigger input. The con-

ventional Marx generator used a trigatron switch in the first stage and only the first stage

switch was triggered. In the case of a bipolar trigger input,a dual pulsed trigatron switch

is used to improve the performance. Fig. 1.11 shows schematically the new dual-pulsed

trigatron switch configuration as it would be employed in the first two stages of a Marx

generator. The circuit in Fig. 1.11 is quite similar to a standard trigatron circuit. However,

the positive going output of trigger transformer T1 is coupled through trigger capacitor Ct

to the anode of the first stage switch. When the trigger pulse is first applied, almost the full

potential drop occurs across the trigger gap T-K which rapidly breaks down. This is because


the capacity of the trigger gap is much smaller than the series combination of capacitors Ct

and Cp. When the trigger gap closes, the full transformer potential is rapidly applied to the

switch anode and heater capacitor Cp. This circuit achieves a simultaneous UV illumination

of gas molecules in the gap and over-voltage of the gap potential. The heater capacitor Cp

rapidly heats the discharge channel and switch closure causes the large potential to appear

on the cathode of the following stage [45].

Because of the lower efficiency of the Marx generator , Tesla transformers are used as a

better option for pulse generation [43]-[48].

1.5.2.2 Tesla Transformer

Tesla transformers are air cored transformers that are highly efficient in the transfer of energy

from its primary side to the secondary high voltage side. They operate based on the principle

of resonance in either primary or the secondary side. The Tesla Transformer technology is

widely used in IRA because of the following reasons:

• Compact size

• Low input voltage on primary side

• Low energy requirements of the pulser

• Capability to run easier on higher repetition rates

• Only one single switch

The low pulse energy requirements for the generation of UWB pulses with rise times

<500 ps and pulse width < 1 ns gave the Tesla Transformer an advantage against the Marx

Generator. Fig. 1.12 shows the Tesla Transformer. For sharp rise times needed for the

input voltage to IRA, the tesla transformer operates in the pressurized gas atmosphere so

that the switchings and the transfer of energy is more efficient. For optimum performance of

the Tesla Transformer the resonance frequency of the primary side and the secondary side

should be very close, therefore all stray capacitance and inductivities must be considered

while designing the system [45].


Figure 1.10: Marx Generator [46].

Figure 1.11: Dual Trigatron Switch of a Low Jitter type Pulse Generator [45].

Figure 1.12: Tesla Transformer [45].


1.5.3 Pulse Sharpening System

The pulse sharpening system is used when a transient pulse of fast rise time is required

[43]-[44]. Pulse sharpening system mainly uses a spark gap and the switching speed of the

spark gap decides the rise time attained by the pulse at the output of the pulse sharpening

circuit.

A pulse sharpening system of three sections, charge line, pulse line, and load line as

shown in Fig. 1.13. Each line is separated from the other by a discharge gap. The charge

line is connected to the output of the pulse generator circuit. It actually decides the charging

rate of the spark gaps and also decides a higher switching rate or a normal switching rate is

required based on the rise time required. Pulse line actually produces the pulse which has

the required rise time and is fed to the load line where fine tuning of the rise time and the

field occurs so that at the output of the load line the pulse has the required magnitude and

rise time for the electric field. The characteristic impedances of all the three sections must

be properly designed to get the required output characteristics.

Spark gaps being the important component in a pulse sharpening system, the size, the

gap distance and the type of the spark gaps plays an important role in its efficient operation.

As rise time of the odder os pico-seconds are necessary for IRA , the spark gaps are needed to

operate in an atmosphere where the switching can be done faster. Usually highly pressurized

hydrogen gas is used so that the required rise times can be obtained.The generation of pulse

rise times less than 500 ps at pulse amplitudes above 100 kV is normally done by fast over

charging a spark gap. The gap will then see a higher voltage as the switching is done faster

than at a low charging rate, this causes a higher electrical field strength between the gaps.

By placing several gaps in series, the leading edge of the pulse could be sharpened.

Figure 1.13: Pulse Sharpening System [43].


1.5.4 Antennas

UWB systems need special antennas for receiving or transmitting short pluses with risetimes

less than 1 ns. Ordinary wideband antennas are generally not able to transmit short pulses,

because of the dispersion. There are several antenna designs for transmitting ultra short

pulses [43]-[70]. The typical antennas are:

• Paraboloidal Antenna

• TEM horn antenna

• Half IRA

• Collapsible IRA

1.5.4.1 Paraboloidal Antenna

A parabolic reflector (or dish or mirror) is a reflective device used to collect or project energy

such as light, sound, or radio waves. It has a circular paraboloid shape. The parabolic

reflector transforms an incoming plane wave travelling along the axis into a spherical wave

converging toward the focus. Conversely, a spherical wave generated by a point source placed

in the focus is transformed into a plane wave propagating as a collimated beam along the axis.

In IRA it is the second principle that is used. This is the most directive type of antenna.

A parabolic antenna is a high-gain reflector antenna used for radio, television and data

communications, and also for radio location (radar), satellite television, extensive terrestrial

microwave links, such as those between cellphone base stations, and wireless WAN/LAN

applications have also proliferated this antenna type,ground-based and airborne radar and

radio astronomy.A parabolic reflector antenna is shown in Fig. 1.14a.

1.5.4.2 Horn Antenna

A horn antenna is essentially an open-ended wave guide, of increasing cross-sectional area,

which radiates directly in a desired direction or feeds a reflector that forms a desired beam.

Horn antenna has an E-plane and an H-plane where the field is either electric or magnetic

respectively. A very wide range of beam patterns may be formed by controlling horn dimen-

sions and shapes, placement of the reflector, and reflector shape and dimensions. A horn

antenna is shown in Fig. 1.14b.


1.5.4.3 Half IRA

The major task of the antenna design is to minimise the frequency and spatial dispersion,

and to increase the capability of operating voltage. For compact UWB source a half IRA

design has same advantages when connecting the source to the antenna. The basic idea

behind the half IRA is to operate only with one half of the antenna and to use the electrical

symmetry plane at ground potential as a mirror for the electrical field below the antenna

. The cylindrical electrical field distribution of the pulse line is converted by the two feed

arms into a plane electrical field which is transmitted by the mirror. A compact gas switched

UWB source and the half IRA is shown in Fig. 1.14c.

1.5.4.4 Collapsible IRA

It is a wideband antenna that could be used by ground troops and is of lightweight and

portable. This IRA shown in Fig. 1.14d., that is made of conducting fabric. This antenna

can fold up like an umbrella. It can perform efficiently from high frequency to X-band [64].

1.5.5 Switches

Switches are a necessary part of the IRA system.The switches are designed so that they are

compact,lower probabilities of bulk and surface breakdown. the material used for making

switches should have the necessary properties such as durability, high mechanical end elec-

trical strength to withstand a breakdown and so on. There are lot of materials with desirable

electrical and mechanical properties that are capable of making switches. The different types

of switches used are [43]-[58]:

• High pressure hydrogen switch

• Triggered gas switches

• Oil Switches

• Solid-State Switching

High Pressure hydrogen switches are the most commonly used category of switches for

IRA’s. This is because they are capable of withstanding voltages upto 1 MV at repetation

rates of 100s of Hz. The switch is composed of copper tungsten electrodes with a coaxial


(a) (b)

(c) (d)

Figure 1.14: Different Antennas (a) Paraboloidal antenna (b) Horn antenna (c) Half reflector

IRA (d) Collapsible IRA [43]-[70].


Figure 1.15: Hydrogen Switch [45].

pressurized housing. Pulse repetition rates in the 100s of Hz are achieved by using moderate

hydrogen pressures as the insulating medium. The electrodes are shaped with a Rogowski

profile to produce a uniform field distribution [49]. The high pressure hydrogen gas will

give some amount of insulation. Additional insulation can be provided by using dielectric

oils.This switch is shown in Fig. 1.15

Triggered gas switches are used for precision switching that will allow the full exploitation

of UWB radiation for a wide range of applications. These switches are having less jitter.

Oil switches has a liquid dielectric as the switching medium and it doesnot have mechanical

parts that are required in the case of a high pressurized switch.Also, whereas the electrical

breakdown field in gases scales with the pulse width of the charging waveform as, in liquids,

the breakdown field scales. Thus, a fast-charging waveform, coupled with the intrinsically

higher electrical breakdown fields, allows for very high inter electrode electric fields. The

typical liquid used is transformer oil, but its drawback is that switch firing leaves behind

particles of carbon residue that limit rep rate and will eventually short out the switch. Solid

state switches uses semiconductor materials for switching and is based on the principle of

avalanche breakdown.


1.5.6 A commercial IRA

A commercial IRA is the JOLT antenna [45] which is the most powerful half-IRA. It has

a paraboloidal reflector antenna with a 3.05 m diameter, that is cut in half and flanged

for attachment to the ground plane.A transient energy source is located at the focal point

of this reflector that launches a near-ideal TEM spherical wave on to the reflector through

a polypropylene lens to be reflected as a collimated beam. Each TEM feed line has a

characteristic impedance of 170 Ω(in oil) against the image plane, resulting in a net antenna

impedance of 85 Ω for all frequencies, as long as TEM launch condition is maintained. The

antenna system can be thought of as an 85Ω load energized by the pulser. The energy is

stored in a capacitor and is then switched out to the antenna which is seen as load by the

pulser, as indicated in Fig. 1.16. A line schematic diagram and a photograph of the JOLT

system are shown in Fig. 1.17.

The ground plane creates rigidity for the upper surface of the modular frame and serves

as the ground reference and an image plane for the impulse radiating antenna (IRA). It also

provides the lower containment for SF6, which insulates the dome and feed arms. The ground

plane also creates a shielded volume under it for the placement of sensitive components of

the pulser. The gas containment bag is constructed from flexible, UV-stabilized PVC film.

This film is surrounded by a gas tight zipper which fastens the bag to the edges of the

ground plane and the perimeter of the antenna. The gas is filled from the back side of

the antenna and the pressure is monitored by a sensitive pressure gauge. The gas system

supplies the high-pressure hydrogen gas to both the trigatron switch and the transfer switch.

The system is charged using high pressure, sealable quick-disconnects which are connected

to an external hydrogen gas cylinder. When the switches are charged to the correct pressure,

a valve is closed to trap the gas in the system. The line pressure is then vented and the

quick-disconnect released.

There is a polypropylene lens at the focal point to ensure a near-ideal spherical TEM

wave launch on to the conical transmission lines formed by the feed arms. The spherically

shaped (for mechanical ease of construction) feed-point lens with a radius of 0.457 m serves

three purposes.

• It ensures a near- ideal spherical TEM launch on to the reflector

• Because of its polypropylene construction, it provides the necessary insulation between


Figure 1.16: Different Forms of the Equivalent Circuit for the JOLT Hyperband System [45].

Figure 1.17: Photograph of the JOLT Hyperband System [45].

1.6. High Power Microwaves (HPM) 25

the feed arms and the ground plane

• It provides an inner containment dome for the high-velocity transformer oil, which is

used to clear debris from the peaker switch

The electric fields inside the lens are held-off by the oil insulating medium. However,

outside the spherical lens medium, SF6 gas is present at 1 atmosphere pressure and the

electric field has hot spots or field maxima around the feed arm conductor protruding out

of the lens. The interface between the lens and the outside gas medium could have two

dielectric discontinuities (oil/container and container/gas).

All these circuits except the primary energy source are kept in a polypropylene container

called pulser,since this container has the same dielectric constant as that of the dielectric oil.

The closing of the high pressure hydrogen gas switch in the pulser generates a TEM wave

that gets out of the pulser towards the reflector, where it gets reflected and hence is available

at the observation point. The electric field at any observation point has a prepulse and an

impulse that are characteristic features of the distance of the observation point from the

antenna and also on the characteristics of the voltage in the pulser.

1.6 High Power Microwaves (HPM)

HPM sources are usually electromagnetic radiators having a reflector with a horn antenna

kept at their focal point for excitation. HPM sources generally operate in single mode or at

tens or hundreds of Hz repetition rates. Many HPM radiators are developed in the world each

with their own peculiar geometry and power levels. The frequencies ranging between 300

MHz to 300 GHz are usually named as the microwave frequencies, whose wavelengths vary

from 1 m to 1 mm. A microwave transmission consists of a microwave source, a wave guide,

a transmitting antenna, a propagation path, a receiving antenna, another wave guide and

finally a receiver. Microwave generation can be accomplished in different ways depending

upon the different varieties of the sources used such as klystrons, magnetrons, gyratrons

etc. Basically, the kinetic energy of the charged particle which is electrons in a beam is

converted into microwave energy in all these sources. Hence wave particle interaction is the

fundamental principle which results in the generation of high power microwaves [71]-[77].

HPM sources are transient generators that produces a short burst of energy, lasting for

about a microsecond or less. The basic block diagram for an HPM generator is shown in


Fig. 1.18.

HPM radiating systems consists of an HPM source with a single rectangular wave guide

feeding an evacuated feed horn through a series of vacuum flanges as shown in Fig. 1.19.

The output of this system is connected to an offset Cassegrain system as shown in Fig.

1.20. This gives a directed HPM radiation. The radiation coming out of the antenna can

cause severe electromagnetic interference. The power to this antenna assembly is fed from

evacuated rectangular wave guides, the number of wave guides depending upon the power

level required. In the present study a single WR-975 wave guide fed HPM antenna assembly

has been considered. This has a dominant H1,0 mode at the cut-off frequency of 1 GHz and

power level of 10 GW. The peak electric field of the wave guide is 25 MV/m. The wavelength

associated with the wave guide is 0.3 m.

1.6.1 Applications of HPM

• Particle accelerators

• Wireless power transmission

• Controlled fusion reaction

• Plasma heating for magnetic confinement fusion

• High power and high resolution radars

• Military defense applications to disrupt or destroy offensive electronic systems like high

power jammers

1.7 Objectives of the thesis

Study of different Intentional HPEM sources:

The different HPEM sources considered are NEMP, IRA and HPM. The characteristics

of these sources are to be studied and the way the electromagnetic field is generated from

these sources are analysed.

Computation of electromagnetic field due to HPEM sources: The electromag-

netic fields due to the HPEM sources is to be determined at a given distance from the source

in the case of IRA and HPM sources and at earths surface in the case of NEMP source.

1.7. Objectives of the thesis 27

Figure 1.18: The Basic Block Diagram for an HPM Generator.

Figure 1.19: Elements of a Single Waveguide feed system [71].

Figure 1.20: A Single Reflector fed by a Feed Horn [71].


Effect of the ambient media on the propagation of the electromagnetic field:

The effect of the properties of the media such as air and the soil affects the propagation

characteristics of the electromagnetic field. This knowledge is essential before proceeding to

study the coupling of the field with a buried cable and an airborne vehicle.

Coupling of the electromagnetic fields due to HPEM sources with a buried

cable:

Computation of the induced current and voltage in a buried shielded and twisted pair

cables due to the incoming electromagnetic field due to HPEM sources. This involves the

analysis of the cable parameters, the method of coupling adopted and finally computation

of the induced current and voltage.

Coupling of the electromagnetic fields due to HPEM sources with an airborne

vehicle in flight:

Electromagnetic modelling of the plume of an airborne vehicle, and computation of the

induced current and voltage in the vehicle in the presence and absence of the plume to

determine the effect of the plume on the coupling phenomenon.

1.8 Organization of the thesis

The thesis is organized as follows:

Chapter 1: Introduction:

The effect of the HPEM sources on the different systems are presented.The different

HPEM sources considered are NEMP, IRA and HPM. The characteristics of these sources

are presented and the way the electromagnetic field is generated from these sources are

discussed.

Chapter 2: Electric field due to HPEM Sources:

The electromagnetic fields due to the HPEM sources is determined at a given distance

from the source in the case of IRA and HPM sources and at earths surface in the case of

NEMP source.

Chapter 3: Effect of the ambient media on the electric field from IEMI

sources:

Two types of media are considered in this chapter- air and the soil. The characteristic

properties of both these media are considered. The effect of the properties of the media such

as air and the soil affects the propagation characteristics of the electromagnetic field. This

1.8. Organization of the thesis 29

knowledge is essential before proceeding to the coupling of the field with a buried cable and

an airborne vehicle.

Chapter 4: Coupling on a buried cable:

The cable is considered to be buried in the soil. Computation of the induced current and

voltage in a buried shielded and twisted pair cables due to the incoming electromagnetic

field due to HPEM sources. This involves the analysis of the cable parameters, the method

of coupling adopted and finally computation of the induced current and voltage.

Chapter 5: Coupling of the field due to IEMI with an airborne vehicle in

flight:

Electromagnetic modelling of the plume of an airborne vehicle, and computation of the

induced current and voltage in the vehicle in the presence and absence of the plume to

determine the effect of the plume on the coupling phenomenon has been presented in this

thesis .

Chapter 6: Conclusion: The conclusion and the scope for future work are presented

in this chapter, along with a summary of the chapters 2 to chapter 5.

Chapter 2

Electric Field due to Intentional

HPEM Sources

2.1 Electric Field from a Nuclear Burst

The radiated fields due to a high altitude EMP incident on the earths surface could be

modelled locally by a plane electromagnetic wave, where the ratio of the magnitude of the

electric field strength E (V/m) to the magnitude of the magnetic field strength H (A/m) is

the impedance of free space [36].

E

H= 377 Ω (2.1)

Since the motion of the Compton electrons depends on the orientation of geomagnetic

field, the incident EMP fields vary significantly (in peak amplitude, rise time and duration)

over the large area affected by the EMP. The maximum peak electric field Emax occurs just

south of surface zero and can be as high as 50 kV/m depending upon the height of burst and

the weapon yield. The peak field observed at any other location is some fraction of Emax.

The variations in peak electric fields on the earths surface for high-altitude bursts ranging

in height from 100 to 500 km is shown in Fig. 2.1.

In addition to the orientation and dip of the geomagnetic field, geometric factors based

on the observer’s position in relation to the burst also cause spatial variations of the EMP

field strength. The maximum peak fields are found at 2 x HOB south of surface zero. The

EMP time waveform also varies considerably over the area of coverage. Near surface zero,

the EMP has a rise time of about 5 ns (10 to 90% of the peak field) and a time to half value

of 20 ns. In the region of maximum peak fields, the rise time is just under 10 ns with a time

30

2.1. Electric Field from a Nuclear Burst 31

to half-value of about 50 ns. Finally, near the tangent radius due south of the burst, the rise

time is somewhat longer than 10 ns and the time to half-value is about 200 ns.

2.1.1 Polarization and Ground Effects

The polarization of the EMP is also a significant factor in its coupling to communication

facility and to the external structures that service it like power lines, communication cables,

microwave towers etc. The polarization depends on the locations of both the burst and the

observer and on the orientation of the geomagnetic field.

The EMP fields described up to now are only incident fields. The total fields at any point,

however also include the reflection of these fields from the ground plane. The total fields

can be larger or smaller than the incident fields depending upon polarization. For a point

directly beneath the burst (assuming that the ground is a good conductor), the reflected

field reduces the total electric field and increases the total magnetic field.

2.1.2 Modelling the NEMP field due to a High Altitude Nuclear

Burst

The electric field at the earths surface can be modeled as a double exponential pulse according

to IEC standard 61000-2-9 [78]. The NEMP field incident on the earths surface is considered

as that coming from a source at a distance far away from the earths surface, hence a plane

wave approximation has been used. This field is modeled as the electric field component of

the incident NEMP and can thus be taken as

E(t) = 65000(exp(−at)− exp(−bt)) (2.2)

Where,

a = 4× 107s−1 (2.3)

b = 6× 108s−1 (2.4)

The incident NEMP waveform is shown in frequency and time domains in Fig. 2.2

and Fig. 2.3 respectively. This incident electric field component from the nuclear burst is

32 Chapter 2. Electric Field due to Intentional HPEM Sources

assumed to be arriving at a certain angle of incidence. The field is assumed to have vertical

polarization.

2.2 Impulse Radiating Antenna

A paraboloidal reflector is an aperture antenna. There are two methods to analyze the

radiation characteristics of reflector antennas:

(a) Current Distribution Method

Current distribution method which uses the distribution of the surface current on the

reflector. This current density is then integrated over the surface of the reflector to get the

radiated fields. If the feed pattern is asymmetrical or placed off-axis then the integration

along the surface of the reflector would be tedious and time consuming. In this work the

aperture distribution method is considered [79].

(b) Aperture Integration Method

In this method the field reflected from the surface of the reflector is first found on a plane

that is normal to the axis of the reflector by using the principles of geometrical optics [79].

This plane is the aperture plane which is considered through the focal point of the reflector.

This plane is then considered to have equivalent sources that are assumed to be zero outside

the projected area of the reflector along the aperture plane [79]. These equivalent sources

form the source for computation of the radiated fields. Aperture method is advantageous in

that the integration over the aperture can be done with relative ease for any feed position

[79].

2.2.1 Computation of Radiated Field from an IRA

If the aperture plane at the focal point of the reflector had a constant E-field denoted by Ea,

the far field is simply given by an integration of the aperture field over the aperture which

can be written as [79].

Efar(r, λ) =EaA

rλ=ωEaA

2πrc(2.5)

Where,

A = area of this aperture

r = distance along the boresight where the field is to be computed

2.2. Impulse Radiating Antenna 33

Figure 2.1: Variations in High - altitude EMP Peak Electric Field [36].

104

105

106

107

108

10−4

10−3

10−2

Frequency (Hz)

Ele

ctric

fiel

d m

agni

tude

(V

/m/H

z)

Figure 2.2: Frequency Domain Waveform of the Input NEMP Field at the Earths surface.

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

45

50

Time (ns)

NE

MP

ele

ctri

c fi

eld

(kV

/m)

Figure 2.3: Time Domain Waveform of the Input NEMP Field at the Earths Surface.


λ = wavelength of the mono-chromatic illumination,

c = speed of light in vacuum.

ω =angular frequency in rad/s.

This simple equation demonstrates the differentiating character of an aperture. In other

words, the far field is a spatial integration of the aperture field combined with its temporal

derivative, since (jω) in frequency domain translates to (∂/∂t) in time domain. Clearly,

a step function aperture field results in an impulse-like far field with its rich hyper band

characteristics. Thus an intimate knowledge of the aperture fields is both sufficient and

necessary in computing the far fields.

The geometry of the antenna used for the computation is a paraboloidal reflector antenna.

An aperture plane is considered and the electric filed at this plane is initially computed. This

field then form input to further computation of the field along any observation point from

the antenna. Consider the parabolic antenna shown in Fig. 2.4. The field from this antenna

is computed using the aperture integration method whose basic theory is outlined by Balanis

[79]. Consider an excitation source to be located at the focal point of the antenna. For the

given source at the focal point, let the gain function be Gf (θ1, φ1). All the angles are shown

in Fig. 2.5. The incident field on the antenna, with the direction perpendicular to the radial

distance, can be written as,

−→Ei(r1, θ1, φ1) = ei C1

√Gf (θ1, φ1)

exp(−j−→k .−→r1 )

r1(2.6)

Where,

C1 =µ

ε

0.25 Pt2π

0.5

(2.7)

Gf = gain function of the source

r1 = distance between the centre of the projected cross sectional area to the source

position on the surface of the reflector

(θ1, φ1) = co-ordinates of the source point along the reflector

Pt = total radiated power of the source

Where the unit vectors are as shown in Fig. 2.5. On the surface of the reflector, the

current density vector is given by


−→Js = 2

√ε

µ

√Gf (θ1, φ1)

exp(−j−→k .−→r1 )

r1u (2.8)

The unit vector u can be written from Fig. 2.5 as

ux = −ax sin θ1 sinθ12

cosφ1 (2.9)

uy = ay cosθ12

(sin2 φ1 cos θ1 + cos2 φ1) (2.10)

uz = −az cos θ1 sinθ12

sinφ1 cosφ1 (2.11)

u =ux + uy + uz√

1− sin2 θ1 sin2 φ1

(2.12)

To find the aperture field at a plane through the focal point, the reflected fields Er at r1

is first found. This is of the form

−→Er = er C1

√Gf (θ1, φ1)

exp(−j−→k .−→r1 )

r1(2.13)

Where er is the unit vector depicting the polarization of the field. For the given geometry

er becomes

er =ax sinφ1 cosφ1 (1− cos θ1)− ay (sin2 φ1 cos θ1 + cos2 φ1)√

1− sin2 θ1 sin2 φ1

(2.14)

Hence on any plane passing through the focal point, the reflected field is given by

−→Eap = er C1

√Gf (θ1, φ1)

exp(−j−→k r1 (1 + cos θ1))

r1 (1 + cos θ1)(2.15)

Hence,

−→Eap = ax Eax + ay Eay (2.16)

Where Eax and Eay are the x and y components of the reflected field over the aperture,

and the unit vectors are shown in Fig. 2.5. These aperture fields are a function of the

position along the aperture at which it is computed. These x and y components of the

aperture fields are plotted in Fig. 2.6 and Fig. 2.7 respectively. These plots indicate that


Figure 2.4: Reflector Geometry and the Aperture plane [79].

Figure 2.5: Orientations of the Various Unit Vectors [79].

Figure 2.6: x - Component of the Aper-

ture Field .

Figure 2.7: y - Component of the Aper-

ture Field .


the field varies depending upon the co-ordinates along the aperture plane. This necessitates

that to get the total field it is required to carry out an integration of the contribution due

to aperture field at each and every point along the aperture plane, that can be done only

using a numerical integration method which gives proper weightage to the contribution due

to the aperture field at any given point for the computation of the radiated field. From the

general radiation equation, the electric field at any observation point at a distance r from

the focal point can be written as

−→Eθs =

−jk exp(−j−→k .−→r (Lφ + ηNθ)

4πr(2.17)

−→Lφ =

∫∫[−Mx sinφ+My cosφ] exp(−j

−→k .−→r cosψ ds′ (2.18)

Where ψ is the angle between r and r1. Hence the net radiated field is given by

−→Eθs =

−jke(−j−→k .−→r ) (1 + cos θ)

4πr

∫∫(Eax cosφ+ Eay sinφ)ejk (x′ sin θ cosφ+y′ sin θ sinφ)dx′dy′

(2.19)

2.2.2 Radiation Pattern of IRA in the Near and the Far Field

For the JOLT HIRA under consideration, the half paraboloidal antenna [45],has the following

specifications

The diameter, D of the IRA = 3.05 m

The ratio of the focal length, F to the diameter, D = 0.33.

If, λ is the wavelength of the radiated field,then the range at which the far field starts is

a function of the frequency of the radiated field. It can be shown that the far field starts at

df = 2D2

λ(2.20)

The commencement of the far field for different frequencies is tabulated in table 2.1. It

can be seen that the far field starts close to the antenna at 1 MHz, where as it is 61.93 m

if the frequency rises to 1 GHz. To see the effect of this range variation with frequency on

the radiated electric field, the electric field is plotted at two representative distances from

the antenna, one in the near field which is at 5 m and other in the far field of 100 m with


Table 2.1: Range of Commencement of the Far Field for Different Frequencies of IRA

Frequency The distance of commencement of

(MHz) the far field from IRA (m)

1 0.06

5 3.09

100 6.19

200 12.37

500 30.97

1000 61.93

1500 92.90

10000 618.99

the frequency varied from 1 MHz to 10 GHz. The electric field is computed along the E

plane as a function of the spot frequencies and also with respect to the off boresight angle.

These computations are done with φ assumed to be a constant and the resultant variation

of the field with respect to θ is estimated using equation 2.19 . This field is then normalized

with respect to the maximum electric field intensity occurring along the boresight. The

integration is done numerically in MATLAB along the x and y coordinates of the aperture

plane.

The radiated electric fields are plotted at the spot frequencies of 1 MHz, 50 MHz, 100

MHz, 500 MHz, 1 GHz and 10 GHz for the observation point of 5 m and are shown in Fig.

2.8. The wavelengths for which the computations have been made are 300 m, 6 m, 3 m,

0.6 m, 0.3 m and 0.03 m. The antenna diameter D in terms of wavelength (D/λ) has the

values of 0.01, 0.51, 1.02, 5.08, 10.17 and 101.67. The spot frequencies are 1 MHz, 50 MHz,

500 MHz, 1 GHz, 2 GHz and 10 GHz for the observation point of 100 m and the respective

wavelengths are 300 m, 6 m, 0.6 m, 0.3 m, 0.2 m and 0.03 m respectively. The antenna

diameter D in terms of wavelength (D/λ) has the values of 0.01, 0.51, 1.02, 5.08, 10.17 and

101.67. The change in the spot frequency pattern for 5 m and 100 m is due to the fact

that for the observation point at 5 m, for any frequency after 50 MHz, the field approaches

the far field characteristics whereas for the 100 m point the far field starts only after 1500

MHz. Hence to get the radiated field plots in the far field as well as in the near field, the

frequencies are chosen in the above manner.


The frequency range chosen extends from the medium frequency to the X-band. The

computed field radiation patterns at various frequencies are shown in Fig. 2.8 to Fig. 2.11.

Fig. 2.8 and Fig. 2.10 are the logarithmic and the polar radiation patterns for the observation

point of 5m and Fig. 2.9 and Fig. 2.11 are the respective figures for observation point at

100 m.

The radiation pattern characteristics are purely a function of the location of the obser-

vation points, whether in the near field or in the far field, apart from being a function of

the frequency of the radiated field. For higher frequencies, the field radiation pattern starts

to have disturbances after a particular frequency caused due to the fact that for higher fre-

quencies the wavelength of the radiated field will be less, which leads to the fields having

more spatial dependence.

At very low-frequency of 1 MHz, the radiation pattern is that of a dual dipole with a

near cardioid pattern having a very broad beam width. Also very few oscillations are seen

in the radiation patterns at low frequencies and these oscillations steeply increases with

frequency. This analysis can also be obtained from [63]. At very low frequencies, (kx 1),

the integral becomes nearly a constant and the cardioid or [1+ cos (θ )] becomes apparent. If

the observation point is in the near field of the antenna which is at 5 m, then for a frequency

of 56 MHz, the far field starts at 5 m. It is 8.95 m if the frequency is 100 MHz. Hence for any

frequency higher than 56 MHz, 5 m point is considered as a near field point for the radiated

fields and for frequencies lesser than 56 MHz, this point is in the far field zone. This results

in the disturbances in the radiated field pattern in Fig. 2.8 and Fig. 2.10 for frequencies of

100 MHz and above and a rather smooth cardiod pattern for lower frequencies.

The same phenomenon is repeated for 100 m point which is in the far field of the antenna.

For this point, if the frequency of the radiated field is 1119 MHz, the far field becomes 100 m

which is the observation point that is considered. Hence for all frequencies above 1119 MHz,

the radiated field will assume 100 m as if in the near field zone and results in a field pattern

that has a noisy pattern which is evident from Fig. 2.9 and Fig. 2.11. If the frequency is less

than this value, then 100 m comes in the far field zone which results in a smooth pattern for

the radiated fields.

The beam widths for these two observation points are tabulated in table 2.2. The far field

point (100 m) gets a more narrowed beam than for 5m which is in the near field zone. As

the frequency increases due to the constriction of the field pattern, the beam width reduces.

It is evident that all the frequencies have their peak radiation on boresight. One can say


−150 −100 −50 0 50 100 150−80

−70

−60

−50

−40

−30

−20

−10

0

Angle with respect to boresight(deg.)

Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de(d

B)

1 MHz.

−150 −100 −50 0 50 100 150−80

−70

−60

−50

−40

−30

−20

−10

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de(d

B)

50 MHz.

−150 −100 −50 0 50 100 150−140

−120

−100

−80

−60

−40

−20

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de(d

B)

100 MHz.

−150 −100 −50 0 50 100 150−80

−70

−60

−50

−40

−30

−20

−10

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de(d

B)

500 MHz.

−150 −100 −50 0 50 100 150

−80

−70

−60

−50

−40

−30

−20

−10

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de(d

B)

1000 MHz.

−150 −100 −50 0 50 100 150

−100

−80

−60

−40

−20

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de(d

B)

10000 MHz.

Figure 2.8: Logarithmic Plot of Antenna Radiation Pattern at 5 m.


−150 −100 −50 0 50 100 150−80

−70

−60

−50

−40

−30

−20

−10

0

Angle with respect to boresight (deg.)

Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de

(dB

)

1 MHz.

−150 −100 −50 0 50 100 150

−80

−70

−60

−50

−40

−30

−20

−10

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de (

dB)

50 MHz.

−150 −100 −50 0 50 100 150−100

−80

−60

−40

−20

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de (

dB)

500 MHz.

−150 −100 −50 0 50 100 150−100

−80

−60

−40

−20

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de

(dB

)

1000 MHz.

−150 −100 −50 0 50 100 150−100

−80

−60

−40

−20

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de (

dB)

2000 MHz.

−150 −100 −50 0 50 100 150−100

−80

−60

−40

−20

0


Rel

ativ

e el

ectr

ic fi

eld

mag

nitu

de (

dB)

10000 MHz.

Figure 2.9: Logarithmic Plot of Antenna Radiation Pattern at 100 m.


0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

1 MHz. 50 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

100 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

500 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

1000 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

10000 MHz.

Figure 2.10: Polar Plot of Antenna Radiation Pattern at 5 m.


1 MHz. 50 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

500 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

1000 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

2000 MHz.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

10000 MHz.

Figure 2.11: Polar Plot of Antenna Radiation Pattern at 100 m.


that this is somewhat fortuitous, since when this antenna was originally designed, the low

frequency performance has not been considered. Later analyses showed that even at very

low frequencies where the antenna can be characterized by a pair of dipole moments (electric

and magnetic), the resultant radiation is in the boresight direction.

The field patterns at various frequencies shown in Fig. 2.8 Fig. 2.11are just that they

are not indicative of the relative strength of the fields at various frequencies, but only the

variation in the off boresight axis, after normalizing the fields to the peak value on boresight

at each frequency. The relative strengths of each sinusoidal component and the relative

phases depend on many factors such as the excitation voltage spectrum, antenna size etc.

The directive gain or the gain along the boresight of the IRA as a function of frequency is

easy to derive.

Table 2.2: Beam Width as a Function of Frequency for Different Distances

Frequency Bandwidth (Deg.) Bandwidth (Deg.)

(MHz) for 5m for 100m

1 131 124

50 95 90

100 47 45

200 24 20

500 9.5 9

1000 4.8 4

1500 2.5 2

10000 1.5 1

On the boresight, the directive gain becomes

G = limr→∞

[4πZinZ0

] [rE

Va]2 (2.21)

Where Va is the voltage input. In the far field r →∞

rE

Va=

D

2λfg2(2.22)

G =πD2

fg2λ2

(2.23)


Where D is the reflector diameter and fg2 = Zin/Zo. For a 2-arm IRA, the numerical

parameters are D=3.66 m and fg2 = 400 Ω / 377 Ω = 1.061, and its directive gain is listed

in table 2.3.

Table 2.3: Estimated Directive Gain vs. Frequency for a 2-arm IRA (same as for a 4-arm

IRA)

Frequency Wavelength, D/λ Directive Gain Directive Gain

(MHz) λ (m) (Numerical) dB

1 300 0.01 4.2 x 10−4 -67.5

50 6 0.61 1.1 -0.8

100 3 1.22 4.4 12.9

200 1.5 2.44 17.6 24.9

500 0.6 6.10 110 40.9

1000 0.3 12.21 442 52.9

1500 0.2 18.30 991 59.9

10000 0.03 122.00 44048 92.9

The gain is seen to increase as (frequency) 2 or 20 dB per decade. In practice, however,

the gain does not arbitrarily increase and will cut off at some high frequency due to feed

imperfections. It is also observed that for a 4-arm IRA, the radiated field is larger by a factor

of√

2 resulting in twice the radiated power of a 2-arm IRA. But, in this case the input power

is also increased by a factor of 2. Consequently, the directive gain remains unchanged. The

gains of the aperture antennas are summarised in table 2.4.

2.2.3 Illustrative Example in Time Domain

To get the temporal characteristics of the JOLT IRA, the reflector is considered to be fed by

a transverse electromagnetic wave structure energized by a pulser source. This source has

the following characteristics [45]:

The far field electric field measured in the boresight at r = 85 m being equal to 62 kV/m,

The uncorrected pulse rise time (10%-90%) equal to 180 ps.

This parabolic IRA reflector is shown in the Fig. 2.12. The following analytical model

has been used to describe the output voltage, according to which the pulser output voltage,


Table 2.4: Directive Power Gain Of The Aperture Antennas

Type of Aperture Antenna Directive Power Gain

A circular aperture (diameter D) with a uniform π2D2/λ2

aperture field or the perfect aperture

2-arm IRA of diameter D (π/fg2)(D2/λ2)

4-arm IRA of diameter D (900 feed arms) (2fg4/fg2)(π/fg2)(D2/λ2)

Directive Gain is same as the 2-arm case, since (π/fg2)(D2/λ2)

both the radiated and input powers are

increased by a factor of 2 fg2 = 2fg4

4-arm IRA of diameter D 20 % higher than a 4-arm IRA

(600 feed arms) (900 feed arms) or a 2-arm IRA

its derivative and the Fourier Transform can be written as [61]:

V (t) = V0 e(−β |t|

td)[1

2erfc(

√π|t|td

)] t < 0 (2.24)

V (t) = V0 e(−β |t|

td)[1− 1

2erfc[

√π|t|td

]] t > 0 (2.25)

V (ω) =V0td

(β + jωtd)e

14π

(β+jωtd)2

(2.26)

The pulser feeding the IRA, has the following specification [45]

V0 = 1.025 MV

td = 180 ps

β = 0.036

(dV/dt)max = 5.556×1015 V/s.

The peak amplitude of the voltage waveform is slightly less than V0. We find that with

V0 of 1.025 MV, the peak amplitude turns out to be 1 MV. The above depicted model for

voltage is plotted in frequency and time domains in Fig. 2.13 and Fig. 2.14 respectively.

This voltage is used for the computation of the electric field. One can compute the boresight

temporal field at various distances using a closed form expression developed in [59],[80]-[81].

It is also possible to calculate the fields in frequency domain as described in the previous

section and do an inverse Fourier transform to get the temporal fields. The results are the


same and the spectral and temporal fields are plotted in Fig. 2.15 and Fig. 2.17 respectively

which are computed from the aperture integration method of the previous section combined

with Fourier inversion. The far field can be shown to start at a range r given by [45]

r ≥ D2

2ctd(2.27)

This range turns out to be 85 m. The computation have been validated by comparing it

with the measured electric field at the observation point at a boresight range of 304 m. The

measured electric field at this observation point as taken from the literature [45] are shown

in Fig. 2.16 and Fig. 2.18 which shows a close similarity with the computed results.

2.2.4 Equivalence between Spectral and Temporal Characteristics

of IRA

The equivalence is based on the fundamental principle of Fourier or Laplace transformation.

For simplicity, let us write the Fourier transform pair of integrals.

f(t) =1

2π

+∞∫−∞

F (ω)ejωtdω (2.28)

F (ω) =

+∞∫−∞

f(t)e−jωtdt (2.29)

Note that is a real function of a real variable t while F (ω) is a complex function of

a real variable . One has to know the temporal function for all times to get the spectrum

and conversely, one has to know the spectral function for all frequencies to get the temporal

function. In measurement scenarios, this creates a problem since the data is either band

limited or time limited. Nevertheless the equivalence is straight forward. By setting t = 0

and ω = 0, observe that

f(0) =1

2π

+∞∫−∞

F (ω)dω (2.30)

F (0) =

+∞∫−∞

f(t)dt (2.31)


Figure 2.12: A Parabolic Reflector type IRA.

106

107

108

109

1010

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Frequency (Hz)

Vol

tage

(V

/Hz)

Figure 2.13: Spectral Response of the Output Voltage of the Pulser.

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Time (ns)

Vo

ltag

e (M

V)

Figure 2.14: Temporal Response of the Output Voltage of the Pulser.


106

107

108

109

1010

10−9

10−8

10−7

10−6

10−5

10−4

Frequency (Hz)

Ele

tric

fiel

d in

tens

ity (

V/m

/Hz)

40m60m80m100m200m

Figure 2.15: Spectral Response of the

Radiated Electric Field from the IRA at

Different Distances along the Boresight.

Figure 2.16: Frequency Domain Wave-

form of the Measured Field from the

JOLT IRA along the Boresight at a dis-

tance of 304 m [45].

0 1 2 3 4 5 6 7 8

0

50

100

150

Time (ns)

Ele

ctri

c fi

eld

inte

nsi

ty (

kV/m

)

40m60m80m100m200m

Figure 2.17: Temporal Response of

the Radiated Electric Field from the

IRA at Different Distances Along the

Boresight.

Figure 2.18: Time Domain Waveform of

the Measured Field from a JOLT IRA

Along the Boresight at a distance of 304

m [45].


Both of these quantities (initial value in time domain and DC content in frequency

domain) need to be zero if we are dealing with a radiated electric field. The reasons being;

1) there cannot be a radiated signal before the signal can get there and 2) antennas do not

radiate DC into the far field. Ensuring these vanishing quantities in a measurement can be

a good check on the measurement schemes. In the context of an IRA, it is observed that it

can be excited by a transient pulse that contains many frequencies or by a single frequency

sinusoidal voltage. If we apply a CW sinusoidal voltage to the IRA, the far field is the

derivative of the sinusoid or simply a co-sinusoid everywhere. What is changing with the

observer location is the amplitude and phase of that co-sinusoid. The amplitude is changing

with the off boresight angle as is estimated in Fig. 2.8 to Fig. 2.11 at various frequencies.

The amplitude on the boresight will depend on the antenna size, frequency and the antenna

impedance. If we use the IRA in a pulsed mode, the voltage pulse has many frequencies.

They all get radiated from the same focal point of the reflector (hence the antenna is non-

dispersive). However, each frequency has a different radiation pattern as shown in Fig. 2.8

to Fig. 2.11 at various frequencies . If we measure the radiated field at any arbitrary position

in front of the antenna, we get a temporal waveform of the field, as in Fig. 2.16. This has

a definite relationship with the applied voltage. It is important to realize that this field

when Fourier transformed will have many frequencies with varying amplitudes and phases.

Phase is a frequency domain concept and is equivalent to a delay in time domain. A time

domain signal, radiated electric field as in the case of Fig. 2.16, is merely a collection of

many sinusoids, each with a different amplitude and phase.

Gain and beam-width of the IRA is calculated in section 3 as a function of the frequency.

In time domain the precise definitions of gain and beam-width are yet to be standardized.

We have chosen to define the temporal beam-width as the angular points where the peak

power of the temporal waveforms is 70%of their boresight value. This is simply a matter of

convenience at this time. Suffice it to say that in front of the pulse-excited IRA, one has a

temporal waveform of the electric field at any arbitrary observation point and this waveform

can be Fourier transformed to observe its spectral content. It does not make sense to talk

of side lobes in time domain. One can also assert that the high frequencies have the highest

directive gain and hence the pulse on boresight will have the shortest rise time. The radiated

pulse becomes smaller and fatter as, one goes off the boresight. It is likely that standardized

definitions of gain and beam-width will evolve in the future for pulsed antennas.

2.3. Electric Field at the Different Points due to a HPM Source 51

2.3 Electric Field at the Different Points due to a HPM

Source

In the present study, a single waveguide (type WR-975) fed HPM antenna assembly has

been considered. The dimensions of this waveguide are a = 247.65 mm and b = 123.83 mm

having a propagation frequency of 1 GHz and nominal frequency range of 0.75-1.12 GHz

[71]-[77]. The peak electric field in the waveguide is taken as 25 MV/m. The spectral and

temporal response of the waveguide field is plotted in Fig. 2.19 and Fig. 2.20.

This has a cut-off frequency of 1 GHz and a power level of 10 GW. The wavelength

associated with the waveguide is 0.3 m. The field pattern shows a definite peak in its

response when the frequency is 1 GHz, the cut-off frequency of the waveguide. On the lower

side of the cut-off frequency, the field magnitude is constant and on the higher side it sharply

drops as the frequency increases. The average power, Pavg in the rectangular waveguide is

[71]-[77].

Pavg =E2

0

2ζ0

ab

2(1− λ

2a2)0.5 (2.32)

where

E0 = peak electric field in the waveguide

ζ0 = characteristic impedance of the free space

λ = operating wavelength

a = inside larger dimension of the waveguide

b = inside smaller dimension of the waveguide

Hence the peak electric field, Epeak in the waveguide can be written as

Epeak = E0 =√

2pavgz1,0 (2.33)

where

z1,0 = ζ0 (1− λ

2a2)0.5 (2.34)

Because of its dominant H1,0 mode of propagation, the field will have only that component

and all other components will be zero in this mode of propagation. The power in this

waveguide is fed to the evacuated pyramidal feed horn. The peak electric field intensity in

the horn aperture is given by,


Epeak(horn) = Epeak(waveguide)ab

a′b′(2.35)

where,

a = the width of the horn

b = the height of the horn

Hence the net field along the aperture will be given by,

Ex = Epeak(horn) cosπy

ae−jk[ x

′22lE

+ y′22lH

](2.36)

The field along the aperture of the horn depicted by the above equation is a function

of the distance from the centre of the horn. This field is plotted in Fig. 2.21. This figure

shows bell type characteristics that peak at the centre of the horn with no variation along

its width. Since the aperture field is a function of the coordinates along the aperture of the

pyramidal horn, it is non-uniform in nature. This is typical of the H1,0 mode of propagation.

The peak electric field intensity is 2.93 MV/m. The waveguide field response also has an

identical characteristics and the response is given by equation 2.33. This aperture field serves

as an input parameter for computing the field from the pyramidal horn antenna. The output

field from the horn antenna can be either in a reactive near field, radiating intermediate field

or Fresnel region and in a radiating far field or Fraunhofer region. The Fresnel region is

important to analyze the dielectric interface required at the reflector so that there is no

breakdown occurring at the region close to the reflector. Fraunhofer fields are the basic

source in the assessment of the reflector illumination.

The electric field from a pyramidal horn antenna at any distance r from it can be written

as:

−→E (x, y, z) =

1

4π

∫∫ −→E (x′, y′) e

−jkrr [(jk +

1

r) cos θ + jk] dx′ dy′ (2.37)

Where E (x′, y′) is the aperture field, Ex that is obtained from equation 2.36. θ is the

angle off the boresight at the observation point considered. A non uniform aperture field

causes the integrand to be evaluated at each and every points, hence numerical integration

is required to tackle this situation. This field of the pyramidal horn antenna serves as input

to the offset Cassegrain reflector antenna. Using equation 2.37 the net field at the reflector

input can be computed and this field forms the input for determining the radiated field

output from the reflector antenna.

2.3. Electric Field at the Different Points due to a HPM Source 53

106

107

108

109

1010

10−20

10−15

10−10

10−5

100

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

Figure 2.19: Spectral Response of the Electric Field in the Waveguide.

0 1 2 3 4 5−15

−10

−5

0

5

10

15

20

25

Time (ns)

Ele

ctric

fiel

d (M

V/m

)

Figure 2.20: Time Response of the Electric Field in the Waveguide.

01

23

4

0

5

100

1

2

3

Distance along the width (m)

Distance along the height (m)

E−f

ield

(M

V/m

)

0.5

1

1.5

2

2.5

Figure 2.21: The Aperture Field Distribution.


For the present work the parameters of the horn and the reflector are [71]-[78]: horn

aperture height = 3.5λ and reflector area = 20 m2. The peak electric field at the horn

aperture is obtained as 2.93 MV/m from Fig. 2.21. The peak field at the reflector surface

came out to be 335 kV/m, as per 2.35. Using this field, the radiated field output at 100

m from the antenna assembly is plotted in Fig. 2.22 and Fig. 2.23 in frequency and time

domains. The mesh plot of the electric field is shown in Fig. 2.24

These figures bring out the fact that the field is dominant at 1 GHz, the cut-off frequency

of the waveguide. The maximum field is 410 kV/m and the delay time of 333 ns corresponds

to the travel time from the antenna to the observation point.

2.4 Chapter Summary

The electric field is computed at different points from the HPEM sources, based on the

characteristic properties of the sources. NEMP field at earths surface is modeled using

the IEC standard 61000-2-9. The radiation pattern is calculated for the IRA using the

aperture integration using the aperture field which is shown in the chapter. The HPM field

is computed at the observation point using the non uniform aperture field. The following

inferences are arrived at:

• The electric field at any point is a function of the type of the source and the charac-

teristics of the source.

• The maximum electric field occurs at the boresight.

• For an IRA, the shape of the radiation pattern of the electric field is decided by the

frequency, and also whether the observation point is in the near or the far field with

respect to the antenna.

• Polar plot of the radiation pattern has no side lobes till the frequency is 50 MHz if the

observation point is at 5m but after wards it changes to irregular patterns with side

lobes. Polar plot is having no sidelobes till 1500 MHz if the observation point changes

to 100 m. This is decided by the range of commencement of the far field for a given

frequency.

• Beam width of the radiation pattern decreases with an increase in the frequency for

any observation point.

2.4. Chapter Summary 55

106

107

108

109

1010

10−20

10−15

10−10

10−5

100

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

Figure 2.22: Spectral Response of the Electric Field due to HPM Source at Different Points

at 100 m Away From the Source.

358 360 362 364 366 368−300

−1000

100

300

500

Time (ns)

Ele

ctric

fiel

d (K

V/m

)

346 348 350 352 354 356−300

−1000

100

300

500

Time (ns)

Ele

ctric

fiel

d (K

V/m

)

330 335 340−300

−1000

100

300

500

Time (ns)

Ele

ctric

fiel

d (K

V/m

)

358 360 362 364 366 368−300

−1000

100

300

500

Time (ns)

Ele

ctric

fiel

d (K

V/m

)

Figure 2.23: Time Response of the Electric Field due to HPM Source at Different Points at

100 m Away From the Source.

Figure 2.24: Mesh Plot of the Time Response of the Electric Field due to HPM Source at

Different Points at 100 m Away from the Source.


• The gain of the antenna increases as square of the frequency with each increase in the

frequency.

• The electric field at the boresight of an IRA has a prepulse that lasts for 8 ns which

accounts for the time taken by the pulse to traverse the reflector diameter before it is

felt at the given observation point.

• For an HPM, the field has a centre frequency of 1 GHz, which is the centre frequency

of the waveguide field.

• The aperture field along the pyramidal horn antenna is mainly cosine in nature with

a maximum field at the centre of the horn cross section.

• The electric field at any observation point is decided by the dimensions of the horn,

the dimension of the reflector antenna that finally radiates the field and also the char-

acteristics of the waveguide field.

Chapter 3

Influence of the Medium on the

Electric field Propagation

The electric field coming out of the HPEM sources travels through the media that could be

either air alone or a combination of air and soil respectively depending upon whether the

system on which the EM coupling process is analysed is an airborne vehicle or an underground

cable. The intervening medium plays a major role in the coupling process and the magnitude

of the coupled field is influenced by the characteristic properties of the medium. This chapter

deals with the effect of the air medium as well as the combination of air and soil media on

the electric field coming out of these sources.

3.1 Electric Field in Different Media due to HPEM

Sources

The electric field reaching the earth’s surface will suffer reflection from the earth and only a

percentage of the incoming field will be able to penetrate into the soil. This percentage of the

field transmitted into the soil is a function of the characteristic properties of the soil. The soil

is characterized by its dielectric permittivity and conductivity. To quantify the above soil

parameters two coefficients are used which actually determines the exact magnitude of the

field either in soil or in the air. These are the earth’s reflection and transmission coefficients

known as the Fresnel coefficients. A schematic diagram for field propagation in air or soil is

shown in Fig. 3.1.

The electric field at any height, h above the earth can hence be written as:

E(x, 0, h) = Einc + Eref (3.1)

57

58 Chapter 3. Influence of the Medium on the Electric field Propagation

Figure 3.1: Schematic Diagram for Field Propagation Air and Soil.

where

Eref = EincRv (x sinψ cosφ + y sinψ sinφ + z cosψ)ejk(−x cosψ cosφ+y cosψ sinφ−z sinψ) (3.2)

and Rv is the Fresnel reflection coefficient, which can be written as [95]

Rv =((εr(1 + σg

jωε0εr) sinψ)− (εr(1 + σg

jωε0εr))− cos2 ψ)0.5

((εr(1 + σgjωε0εr

) sinψ) + (εr(1 + σgjωε0εr

))− cos2 ψ)0.5(3.3)

Here Einc is the incident field due to HPEM sources, either in time or frequency domain.

These fields are given in detail in the previous chapter. ψ and φ are the angles of incidence,

εr is the relative permittivity of the soil and σg is its conductivity. Similarly at any depth d

below the soil, the net field will be due to the field transmitted into the soil, which can be

written as

E(x, 0, d) = Et (3.4)

where

Eref = EincTv (x sinψt cosφ − y sinψt sinφ + z cosψ)ejk(−x cosψt cosφ+y cosψt sinφ−z sinψ) (3.5)

Where Tv is the Fresnel transmission coefficient, which can be written as [95]

3.2. Electric Field in Air at Varied Heights due to HPEM Sources 59

Tv =2Z0g sinψ

Z0 sinψ + Z0g sinψt(3.6)

sinψt =

√1 + (

k cosψ

γg)2 (3.7)

Here is the transmitted angle which is a function of the characteristic properties of the

soil. All these angles are shown in the Fig. 3.1. These Fresnel reflection and transmission

coefficients are a function of the angles of incidence of the field with the earth’s surface.

These coefficients are plotted as a function of the angles of incidence in Fig. 3.2 to Fig. 3.4.

The values of the reflection and the transmission coefficients approaches a constant value

asymptotically, such that their sum is equal to 1.This constant value is 0.53 if the angle of

incidence is 900, and the transmission coefficient approaches asymptotically to 0.47 at this

same angle of incidence.

3.2 Electric Field in Air at Varied Heights due to HPEM

Sources

The electric field at the earth’s surface due to a high altitude nuclear electromagnetic pulse

is taken 50 kV/m according to the standard. Using this field at the earth’s surface, the

electric field at any height above the earth’s surface can be obtained after getting the earth’s

reflection coefficient at the frequencies of interest of NEMP. The NEMP field as a function

of frequency and item is plotted in Fig. 3.5 and Fig. 3.6. As height increases the field drops

29 kV/m to 3 kV/m as the height increases from 100 m to 1000 m in steps of 100 m. The

shift in the time domain is a function of the height at which the field is computed. The IRA

field at different heights is plotted in frequency and time domain for the source discussed

in section 2.2.2 in Fig. 3.7 and Fig. 3.8 respectively. The field varies from 24.8 kV/m to 5

kV/m for the above height range with the time delay a function of the height. The HPM

field shows a variation from 160 kV/m to 20 kV/m for this height range as can be seen from

Fig. 3.9 and Fig. 3.10.

The variation of the field with height is a function of the type of the source and also the

characteristics of the medium which is air. The frequency domain waveforms for the field

at different heights for these sources show that as the source varies from NEMP to IRA to


Figure 3.2: Fresnel Vertical Reflection Coefficient, Rv.

Figure 3.3: Fresnel Vertical Transmission Coefficient,Tv .

106

107

108

109

1010

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Frequency (Hz)

Fre

snel

co

effi

cien

ts

Vertical reflectioncoefficient

Vertical transmissioncoefficient

Figure 3.4: Fresnel Vertical Reflection and Transmission Coefficients for an Incident Angle

of 900.

3.3. Electric Field Attenuation due to Soil Characteristics 61

HPM, the variation in the magnitude of the fields with height is less noticable, which means

the graphs are more crowded at higher heights.

3.3 Electric Field Attenuation due to Soil Character-

istics

The electric field from the sources of HPEM has to travel through soil medium before it

encounters with the buried cable. Hence the characteristics of the field at the cable are

largely dependent upon the electrical and magnetic characteristics of the soil. But electrical

parameters are more important than the magnetic properties for coupling studies. As such,

it is worthwhile to analyse the effect of the soil electrical parameters on the electric field

intensity due to different HPEM sources. The equation given in section 3.1 can be used for

the determination of the electric field in the soil.

3.3.1 Effect of Soil Parameters on the Electric Field

The electric field reaching the soil will suffer attenuation once it enters the soil due to

the effect of the soil properties. When the field passes through the soil, the amount of the

attenuation it suffers can be mathematically represented in terms of the attenuation constant

of the soil. The attenuation constant is the real part of the complex propagation constant.

Fig. 3.11 and Fig. 3.12 show the attenuation constant and the phase constant as a function

of the frequency contents in the field, for different electrical conductivities of the soil. The

attenuation constant rises linearly with frequency at low frequencies and reaches a constant

value asymptotically at higher frequencies. The point at which this shift in the attenuation

from linearity to steady state increases as the soil conductivity increases which are 5 MHz,

10 MHz, 100 MHz, 1 GHz and 10 GHz respectively for conductivities 0.001 S/m to 10 S/m.

So with every 10 times increase in conductivity, the change over frequency also shifts by 10

times. The attenuation coefficient is dependent upon the nature of the soil and the energy of

the incoming electromagnetic field. If the energy of the incoming electromagnetic radiation

is higher on account of the higher energy of the incident photons, and if the material is less

dense, then lower will be the attenuation coefficient. The phase constant follows a linear

variation with frequency but has two linear variations, the initial one having a slope of

3.5/decade for the conductivity of the soil of 1 S/m, but finally approaches asymptotically


104

105

106

107

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

Frequency (Hz)

Ele

ctri

c fi

eld

inte

nsi

ty (

kV/m

/Hz)

100 m200 m300 m400 m500 m600 m700 m800 m900 m1000 m

Figure 3.5: Frequency Domain Waveform

of the Electric Field Due to NEMP at Dif-

ferent Heights.

0 20 40 60 80 1000

20

40

60

80

100

Time (ns)

Ele

ctri

c fi

eld

(kV

/m)

100 m200 m300 m400 m500 m600 m700 m800 m900 m1000 m

Figure 3.6: Time Domain Waveform of the

Electric Field Due to NEMP at Different

Heights.

106

107

108

109

1010

10−9

10−8

10−7

10−6

10−5

10−4

10−3

Frequency (Hz)

Ele

tric

fiel

d in

tens

ity (

V/m

/Hz)

100 m200 m300 m400 m500 m600 m700 m800 m900 m1000 m


of the Electric Field due to an IRA at Dif-

ferent Heights above the Ground.

1000 1500 2000 2500 3000 3500 4000−5

0

5

10

15

20

25

30

Time (ns)

Ele

ctric

fiel

d (k

V/m

)

100 m200 m300 m400 m500 m600 m700 m800 m900 m1000 m

Figure 3.8: Time Domain Waveform of the

Electric Field due to an IRA at Different

Heights above the Ground.

106

107

108

109

1010

10−8

10−7

10−6

10−5

10−4

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z) 100 m200 m300 m400 m500 m600 m700 m800 m900 m1000 m


of the Electric Field due to HPM Source at

Different Heights from the Earths Surface.

500 1000 1500 2000 2500 3000 3500 4000−200

−100

0

100

200

300

400

500

Time (ns)

Ele

ctric

fiel

d (k

V/m

)

100 m200 m300 m400 m500 m600 m700 m800 m900 m1000 m


the Electric Field due to HPM Source at

Different Heights from the Earths Surface.

3.3. Electric Field Attenuation due to Soil Characteristics 63

to another linear variation having 32/decade slope. Attenuation in the soil is decided by the

moisture content of the soil. Higher the moisture content, more will be the absorption of the

field by these molecules which cause lesser field to be penetrated into the soil.

Another characteristic that is of importance is the ratio of the conduction current to the

displacement current in the soil. The conduction current to displacement current ratio gives

an idea about how good a dielectric is the soil. This is plotted in Fig. 3.13. Conduction

current is more at low frequencies where as the displacement current takes an upper hand

as the frequency increases, causing the ratio to fall down. As the conductivity of the soil

increases, any given value of this ratio will be attained only at higher frequencies; or rather

there is a shift in the frequency response of this ratio, and also the magnitude of the ratio

increases with conductivity at a given frequency [82]-[92]. This typical response is due to the

chemical and physical properties of the soil such as soil structure, texture, bulk density, the

chemistry of the soil, the state of the soil, the distribution of pore spaces and of course the

most important being the water content in it. The percentage variation of these different

constituents of the soil alters the distribution of the mobile electrical charges in the soils

which exponentially increases with the increase in the water content [82]-[92].

Kaatze observed that when water is present in any dielectric material it brings about

large changes in its dipole moment due to the rupture and reformation of hydrogen bonds.

Hence, whenever the electric fields at different wavelengths strike the surface of the soil,

these different properties of the soil try to resist its onward propagation in the soil. This

gets reflected as the attenuation. As a result, fields can penetrate in the soil depending upon

the skin depth in the soil. This is plotted in Fig. 3.14. The skin depths at 1 MHz are 15.9

m, 5 m, 1.8 m, 0.3 m and 0.1 m respectively for the soil conductivities of 0.001 S/m, 0.01

S/m, 0.1 S/m, 1 S/m and 10 S/m respectively. Higher the conductivity of the soil, lesser will

be the skin depth which is due to the fact that the soil layers are highly conducting which

cause a horizontal propagation of the fields rather than the onward propagation through the

soil layers to the inner most part of it. This horizontal spread out of the field is prominent

at higher conductivities for a given frequency and also for higher frequencies at a given

conductivity. Hence the skin depth drops with either increase in conductivity of the soil or

increase in frequency. Thus the skin depth of the soil depends on the nature of the field, its

frequency content and the complex frequency dependent properties of the soil [90].

A soil medium can be electromagnetically viewed as a four component dielectric mixture

consisting of soil particles, air voids, bound water, and free water. Bound water refers to


the water molecules contained in the first few molecular layers surrounding the soil particles;

these are tightly held by the soil particles due to the influence of osmotic forces [82]-[92].

The forces acting on the water molecules decrease rapidly with the distance away from the

surface of the soil, hence the water molecules located several molecular layers away are able

to move within the soil medium with relative ease, and hence becomes free water. Because of

the action of the high intensity of forces, a bound water molecule interacts with an incident

electromagnetic wave which is quite different from that of a free water molecule, thereby

showcasing a dielectric dispersion spectrum that is extremely dissimilar from that of free

water. The percentage of water molecules present in the first few molecular layers adjoining

the soil is directly proportional to the total surface area of the soil particles contained in a unit

volume. The total surface area of the particles is, in turn, a function of the soil particle size

distribution and mineralogy. The complex dielectric constants of bound and free water are

each functions of the electromagnetic frequency, the physical temperature, and the salinity

of the soil. Hence, the dielectric constant of the soil mixture is, in general, functions of the

above parameters and also that of the total volumetric water content, the relative fractions

of bound and free water, which are related to the soil surface area per unit volume, the

bulk soil density, the shape of the soil particles, and the shape of the water inclusions. For

slow variation of electromagnetic entities, a hysteresis type behaviour may occur. For direct

current or very slow variations of electromagnetic entities, humidity migration phenomena,

including electro osmosis and effects of temperature heterogeneity may take place, which

cannot be dealt with only by means of local soil parameters. For fast transients, namely

those associated with HPEM fields, the soil behaviour is important for a reasonably wide

frequency range, typically up to tens of GHz. Hence it is worth while to see the effect of the

different types of HPEM fields on the soil and how the soil reacts to those kinds of excitation

sources [82]-[92].

3.4 Response of the Soil to the Field Excitation from

HPEM Sources

HPEM sources generates the electric field that eventually penetrates the soil before reaching

the cable. The soil through which the field passes influences a lot on the field propagation.

For this, the effect of conductivity of the soil, permittivity of soil and the depth of penetration

is analysed for all the above HPEM sources.The soil modeling is based on the frequency of

3.4. Response of the Soil to the Field Excitation from HPEM Sources 65

106

107

108

109

1010

10−2

10−1

100

101

102

103

104

Frequency (Hz)

Atte

nuat

ion

(dB

/m/H

z)

10 S/m1 S/m.1 S/m.01 S/m.001 S/m

Figure 3.11: Attenuation Constant in

Soil for Different Soil Conductivities.

106

107

108

109

1010

10−2

10−1

100

101

102

103

Frequency (Hz)

Pha

se c

onst

ant

10 S/m1 S/m.1 S/m.01 S/m.001 S/m

Figure 3.12: Phase Constant of the Soil

for Different Soil Conductivities.

106

107

108

109

1010

0

20

40

60

80

100

Frequency (Hz)

Co

nd

uct

ion

cu

rren

t to

dis

pla

cem

ent

curr

ent

10 S/m1 S/m.1 S/m.01 S/m.001 S/m

Figure 3.13: Ratio of the Conduction

Current to Displacement Current at

Different Soil Conductivities.

106

107

108

109

1010

0

2

4

6

8

10

12

14

16

Frequency (Hz)

Ski

n D

epth

(m

)

10 S/m1 S/m.1 S/m.01 S/m.001 S/m

Figure 3.14: Skin Depth in Soil for Dif-

ferent Conductivities.


the incident field and the percentage of water content. Hence the modelling technique used

should be applicable for a broad spectrum so as to incorporate all the frequency components

in the incident field. Several soil models have been reported in the literature, some of them

are the Scott model, Eberle model, Jaycore model, Kings model, Longmire model and Messier

model [82]-[92]. The Scott model is derived from the measurements of the electrical resistivity

and which is used to determine the electrical conductivity and the dielectric constant. These

parameters hence derived are functions of the frequency and the water content. This model is

suitable for Nuclear Electromagnetic pulse coupling studies where the frequency encountered

is in MHz. The next three models are slight variation from Scott model. Generally, the

independent measurements of these earth parameters over a broad frequency spectrum will

lead to non causal transient solution especially if the frequency encountered is very high.

This lead to the development of other models so as to take care of this situation. Of these

models, Messier model is the one suited for high frequency applications, and hence is adopted

in this work. According to Messier model the effective dielectric constant and the effective

soil conductivity of any soil can be computed by the following expressions:

εeff (ω) = ε∞ +

√2σ0ε∞ω

(3.8)

σeff (ω) = σ0 +√

2σ0ε∞ω (3.9)

Where ε∞ is the high frequency dielectric constant and σ0 is the DC conductivity. Both

these parameters are a function of the percentage water content. Using this εeff and σeff ,

the impedance of the soil and the propagation constant of the soil can be derived whose

equations are already given in [82]-[92].

3.4.1 Variation of the Conductivity of the Soil on the Response

Characteristics

NEMP electric field is mainly predominant in the MHz frequency range. Fig. 3.15 to Fig.

3.20 show this variation of field with the conductivity of the soil. Fig. 3.15 and Fig. 3.16

show the field variation with the conductivity for NEMP, similarly Fig. 3.17 and Fig. 3.18

show the field variation with the conductivity for IRA and Fig. 3.19 and Fig. 3.20 show the

field variation with the conductivity for HPM. The depth at which the field is computed is 1


m. The permittivity of the soil is taken as 10. As the conductivity of the soil increases, the

magnitude of the field comes down. Also the field is having a delay time, which corresponds

to the delay time for a propagation of 1m distance down the soil if the soil has a conductivity

of 0.001 S/m. But as the conductivity of the soil increases, the delay time increases, which is

on account of the fact that the dipole moments in the water molecules causes a definite time

for the rupture and reformation of the hydrogen bonds, due to which the field takes a definite

time to get itself felt at any given observation point. If the excitation field is an ultra wide

band field coming from an IRA, then for conductivities of 0.001 S/m and 0.01 S/m, the field

pattern is the same as the field in air, except for the reduction in the magnitude owing to the

soil attenuation. But at 0.1S/m, the field has some higher frequency components missing,

but in the lower frequency range the field is more or less of the same shape as the input

UWB field. As the conductivity rises above this value, the field pattern changes altogether

and it is possible to identify a single cut-off frequency of 0.1 GHz. For HPM electric field

also the field follows the pattern of the input HPM field at conductivities till 0.1 S/m. For

higher conductivities, the field is mainly composed of frequency components up to 0.3 GHz

and afterwards the field is drooping drastically in nature.

The above response of the soils of varied conductivity to the HPEM fields of different

impulse characteristics involving frequency components from MHz to tens of GHz range

shows that the field characteristics depends upon the characteristics of the source and the

conductivity of the soil. For a given conductivity of the soil, higher frequency components

in the field are more attenuated as compared to the lower frequency components so that

NEMP field will be able to penetrate the soil with lesser resistance than an HPM or UWB.

But for a given source of HPM field, higher the conductivity of the soil more will be the

attenuation in the soil.

3.4.2 Variation of the Permittivity of the Soil on the Electric Field

Behaviour

Permittivity of the soil has a similar effect on the field propagation. Fig. 3.21 to Fig. 3.26

plots this variation in the field with the permittivity of the soil. Fig. 3.21 and Fig. 3.22

show the field variation with the permittivity for NEMP, similarly Fig. 3.23 and Fig. 3.24

show the field variation with the permittivity for IRA and Fig. 3.25 and Fig. 3.26 show

the field variation with the permittivity for HPM. The electric field at different permittivity


104

105

106

107

108

10−7

10−6

10−5

10−4

10−3

10−2

Frequency (Hz)

Ele

ctric

fiel

d m

agni

tude

(V

/m/H

z)

10 S/m1 S/m.1 S/m.01 S/m.001 S/m


form of the NEMP Field in Soil at Dif-

ferent Conductivities.

0 1 2 3 4 50

0.5

1

1.5

Time (µs)

Ele

ctric

fiel

d in

tens

ity (

kV/m

)

10 S/m1 S/m0.1 S/m0.01 S/m0.001 S/m

Figure 3.16: Time Domain Waveform

of the NEMP Field in Soil at Different

Conductivities.

106

107

108

109

1010

10−10

10−9

10−8

10−7

10−6

10−5

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z) 10 S/m1 S/m.1 S/m.01 S/m.001 S/m


form of the Electric Field at the Cable

Location for Different Earth Conductiv-

ities for an Incident IRA Field.

674 675 676 677 678 679 680 681 682−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (ns)

Ele

ctric

fiel

d (

kV/m

)

10 S/m1 S/m.1 S/m.01 S/m.001 S/m


the Electric Field at the Cable Location

for Different Earth Conductivities for an

Incident IRA Field.

106

107

108

109

1010

10−15

10−10

10−5

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

10 S/m1 S/m0.1 S/m0.01 S/m0.001 S/m



Location for Different Earth Conductiv-

ities for an Incident HPM Field.

672 672.5 673 673.5 674 674.5 675 675.5 676−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Time (ns)

Ele

ctric

fiel

d (k

V/m

)

10 S/m1 S/m0.1 S/m0.01 S/m.001 S/m



for Different Earth Conductivities for an

Incident HPM Field.


is plotted for conductivity of soil taken as 10-3 S/m. When the permittivity of the soil

is low i.e., when it is 5, the electric field magnitude is 39 kV/m, 19 kV/m and 53 kV/m

respectively for NEMP, IRA and HPM. But as the permittivity rises above this, the field

drops down drastically. This is due to the relaxation mechanisms in the soil due to atomic-

or molecular-scale resonances. This may be attributed to the soil structure which consists

of a definite percentage of water, as well as to the interfacial phenomena by rotational

orientation of the water molecule which occurs in the frequency range of about 10 GHz in

free water. When the electric field is incident on the soil, it is polarized that is as a result of

a wide variety of processes, including polarization of electrons in the orbits around atoms,

distortion of molecules, reorientation of water molecules, accumulation of charge at interfaces,

and electrochemical reactions. Relaxation contribution is very small at low frequencies and

becomes large at high frequencies. This is due to the fact that at higher frequencies, the

molecular forces impeding the dipole orientation dominate, and the dipole become unable to

follow the changes, hence at these frequencies the orientation of permanent dipoles no longer

contributes to the dielectric constant. There is also some phase lag between the external

electric field and the dipole orientation, which enables the material to draw energy from the

source and dissipate it in the form of heat. This leads to increased attenuation for higher

permittivity.

3.4.3 Influence of the Depth of Penetration of the Field in the Soil

on its Spectral and Temporal Characteristics

The depth of burial of cable influences a lot on the electric field at that point. As the depth

of burial of the cable increases, the field has to penetrate more diatance through the soil

medium, hence suffering from increased opposition due to soil particles. Which ever source

is being considered, whether it is NEMP, IRA or HPM, the soil behaviour follows a similar

pattern. Fig. 3.27 to Fig. 3.32 show this variation of field with depth of burial of cable. Fig.

3.27 and Fig. 3.28 show the field variation with depth for NEMP, similarly Fig. 3.29 and

Fig. 3.30 show the field variation with depth for IRA and Fig. 3.31 and Fig. 3.32 show the

field variation with depth for HPM. In all the above cases, the depth of burial is varied from

20 cm to 20 m. The permittivity of the soil is taken as 10 and the conductivity is 10−3 S/m.

For NEMP, the percentage variation in field with depth is less, whereas for IRA, by the time

the depth approaches 3m, the field has lost most of its magnitude so that further increase


104

105

106

107

108

10−6

10−5

10−4

10−3

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z) 5101220


form of NEMP Field in Soil at Different

Permittivities.

0 1 2 3 4 50

5

10

15

20

25

30

35

40

Time (µs)

Ele

ctric

fiel

d in

tens

ity (

kV/m

)

5101220


of NEMP Field in Soil at Different

Permittivities.

106

107

108

109

1010

10−10

10−9

10−8

10−7

10−6

10−5

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

5101220



Location at Different Earth Permittiv-

ity for an Incident IRA Field.

675 676 677 678 679 680

0

5

10

15

20

Time (ns)

Ele

ctri

c fi

eld

(kV

/m)

5101215



at Different Earth Permittivity for an

Incident IRA Field.

106

107

108

109

1010

10−10

10−8

10−6

10−4

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

5101520



Location at Different Earth Permittiv-

ity for an Incident HPM Field.

672 672.5 673 673.5 674 674.5 675 675.5 676−60

−40

−20

0

20

40

60

Time (ns)

Ele

ctric

fiel

d (k

V/m

)

5101520



at Different Earth Permittivity for an

Incident HPM Field.

3.5. Case Study of Typical Types of Soils 71

in depth leads to a very feeble field having no significant magnitude. Also as the depth

increases, the IRA field pattern changes from its basic shape at low depths and is found

to have predominantly a centre frequency around 0.1 GHz. This prominence in the field at

that frequency is on account of the selective absorption by soil on some of the frequencies

present in the IRA field. In the case of HPM, the field magnitude is negligibly small, once

the depth increases above 2 m. Also the field doesn’t have any prominent centre frequency

at higher depths of penetration. The soil characteristics described in the previous sections

are actually a function of the percentage water content that varies steadily with increase in

the depth. This variation in the soil characteristics leads to the fields being attenuated more

and more as the depth increases.

3.5 Case Study of Typical Types of Soils

In the previous sections, we have seen the influence of soil conductivity, permittivity and

the depth of burial of the cable on the electric field characteristics from different HPEM

sourceshave been presented and discussed. In this section, a case study is conducted on

the different types of soils available and hence to see what will be the characteristics of the

fields from the different HPEM sources in these soil varieties. The soil samples taken are

pertaining to different regions.

(a) City industrial area soils ε∞=3, σ0 = 10−4

(b) Soils in mountainous regions ε∞=5, σ0 = 5×10−3

(c) Soils in the dry sandy area ε∞=10, σ0 = 4×10−3

(d) Rich agricultural lands with soils ε∞=15, σ0 = 10−2

(e) Pastoral hills with soils ε∞=20, σ0 = 4×10−2

(f) Highly moist ground soils ε∞=30, σ0 = 5×10−2

The electric field is plotted at a depth of 1 m from the earth’s surface, with the soils of

the above characteristics taken into consideration, so that the effect of variation of the soil

medium on the electric field can be analysed

The plot of the electric field intensity for an NEMP source is shown in Fig. 3.33 and

Fig. 3.34. The frequency domain plot of the electric field shows that the field pattern match

exactly at lower frequencies for all the different soil varieties. But as the frequency rises

above 1 MHz, there is a variation in the electric field plots between different soils, and this


104

105

106

107

108

10−6

10−5

10−4

10−3

10−2

10−1

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z) 0.2 m0.5 m1 m1.5 m2 m3 m5 m10 m20 m


form of NEMP Field in Soil at Different

Depths.

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

3.5

Time (µs)

Ele

ctric

fiel

d (k

V/m

)

0.2 m0.5 m1 m1.5 m2 m3 m5 m10 m20 m


NEMP Field in Soil at Different Depths.

106

107

108

109

1010

10−10

10−9

10−8

10−7

10−6

10−5

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

0.2 m0.5 m1 m1.5 m2 m3 m5 m10 m20 m



Location at Different Depths of Burial

of the Cable.

700 750 800 850 900

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (ns)

Ele

ctri

c fi

eld

(kV

/m)

0.2 m0.5 m1 m1.5 m2 m3 m5 m10 m20 m


of the Electric Field at the Cable Loca-

tion at Different Depths of Burial of the

Cable.

106

107

108

109

1010

10−12

10−10

10−8

10−6

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

0.2 m0.5 m1 m2 m5 m


form of the Electric Field from an HPM

Source at the Cable Location at Differ-

ent Depths of Burial of the Cable.

680 700 720 740 760 780 800−5

0

5

Time (ns)

Ele

ctric

fiel

d (k

V/m

)

0.2 m0.5 m0.7 m1 m1.5 m2 m3 m5 m10 m


of the Electric Field from an HPM

Source at the Cable Location at Differ-

ent Depths of Burial of the Cable.

3.5. Case Study of Typical Types of Soils 73

shift goes own increasing with further increase in the frequency. This behaviour of the field

is due to the fact that at low frequencies the soil has a higher skin depth, owing to the lesser

resistance offered by the soil.

At low frequencies, it is the input field that dominates rather than the soil characteristics.

Hence even though the characteristics of the soil are different, the electric field will not be

able to differentiate between the individual soils. But as the frequency increases, there is a

selective attenuation by the soil on the field which is purely dependent upon the soil nature.

Hence, any difference in the nature of the soil will be easily reflected in the magnitude of the

field, and that is why there is a significant difference in the field plots due to different soils.

Also, the peak value of the electric field is 2.7 kV/m, 2.4 kV/m, 1.5 kV/m, 0.6 kV/m, 0.3

kV/m and 0.1 kV/m for the soils (a) to (f) respectively.

The field from an IRA in the soil of different conditions is plotted in Fig. 3.35 and Fig.

3.36. The field does not have variations in the low frequency range till 0.2 GHz. But for

frequencies above that the field pattern is highly dependent on the soil characteristics. For

soils in the city industrial area, the attenuation is less and also the field characteristics has a

significant horizontal portion, which goes on reducing and finally for the highly moist ground

the field pattern is as if there is a cut-off frequency at 2 GHz. The peak values of the field

are 1.5 kV/m, 1 kV/m, 0.75 kV/m, 0.38 kV/m, 0.15 kV/m and 0.05 kV/m respectively

for soils from (a) to (f). The pre-pulse time of the field in the soil is a function of the soil

characteristics. The more moist the ground is, lesser will be the pre-pulse time and broader

is the impulse region.

The field due to HPM suffers a greater attenuation than that of IRA and NEMP fields.

This plot is shown in Fig. 3.37 and Fig. 3.38. The wave shape of the field is identical to

that of the field in the earth’s surface for soils (a), (b), and (c). For the remaining three soil

categories, there is a shift in the waveform at low frequencies. Also the cut-off frequency

reduces as the soil becomes more and more wet. This can be seen from the reduction in

the shift of the cut-off frequency as the soil pattern changes from (a) to (f). This can

be attributed to the geometrical spreading of the field in soils of higher conductivity that

prevents significant amount of field from getting deeper into the soil. Hence there is a

reduction of skin depth at higher frequencies.


104

105

106

107

108

10−6

10−5

10−4

10−3

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)

City industrial areaMountainsDry sand coastal landRich agricultural landPastoral Hills,Rich soilHighly moist ground


form of NEMP Field in Soil for Different

Soil Conditions for 1m Depth.

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

Time (µs)

Ele

ctric

fiel

d (

kV/m

)



of NEMP Field in Soil for Different Soil

Conditions for 1m Depth.

106

107

108

109

1010

1011

10−10

10−8

10−6

10−4

10−2

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z) City industrial areaMountainsDry sand coastal landRich agricultural landPastoral Hills,Rich soilHighly moist ground


form of the Electric Field for an IRA

at the Cable Location for Different Soil

Conditions at 1m Depth.

676.5 677 677.5 678 678.5 679 679.5

0

0.5

1

1.5

Time (ns)

Ele

ctri

c fi

eld

(kV

/m)



of the Electric Field for an IRA at the

Cable Location for Different Soil Condi-

tions at 1m Depth.

106

107

108

109

1010

10−12

10−10

10−8

10−6

Frequency (Hz)

Ele

ctric

fiel

d in

tens

ity m

agni

tude

(V

/m/H

z)



form of the Electric Field for an HPM

Source at the Cable Location for Differ-

ent Soil Conditions at 1m Depth.

673 674 675 676 677 678 679 680 681

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (ns)

Ele

ctric

fiel

d in

tens

ity (

kV/m

)



of the Electric Field for an HPM Source

at the Cable Location for Different Soil

Conditions at 1m Depth.


3.6 Chapter Summary

The electric fields in the air and in the soil for different characteristic properties of these

media have been computed, by taking into account the reflection and transmission coefficients

from the soil. The following conclusions can be drawn from the results presented:

• The electric field propagation in any medium is influenced by the properties of the

medium, whether it is air or soil.

• As the height increases the magnitude of the electric field decreases for IRA and HPM

sources and also the time before which the field waveform starts is increased.)

• For low soil conductivities the attenuation constant of the soil saturates fast, but if the

conductivity increases the attenuation constant saturates at higher frequencies.

• For low soil conductivities, the conduction current to displacement current is low and

it increases at higher conductivity. However, the skin depth follows a reverse trend.

• A soil medium can be electromagnetically viewed as a four component dielectric mix-

ture consisting of soil particles, air voids, bound water, and free water.

• When electric field is incident on the soil, it is polarized that is as a result of a wide

variety of processes, including polarization of electrons in the orbits around atoms,

distortion of molecules, reorientation of water molecules, accumulation of charge at

interfaces, and electrochemical reactions.

• Whatever is the HPEM source, an increase in the soil conductivity results in more

attenuation of the field. Also there is a significant loss of high frequency components

in the GHz range in the field due to selective absorption by the soil. This effect cause

the percentage attenuation to be maximum for HPM and minimum for NEMP and

IRA lying in between these two extremities. This is because HPM is mainly a narrow

band source with high frequency components in the GHz range, IRA and NEMP are

wideband sources and has spectral content in the MHz range.

• Increase in permittivity of the soil causes more attenuation of the electric field for all

HPEM sources. This is due to the relaxation mechanisms in the soil due to atomic- or

molecular-scale resonances.


• As the depth of burial of the cable increases, the field has to penetrate more through

the soil medium, hence suffering from increased opposition due to soil particles. Hence

the field magnitude drops at higher depths.

• Soils in the city industrial areas have a higher field penetration and soils in the moist

wet lands provides the maximum attenuation.

Chapter 4

Induced Voltage and Current in a

Buried Cable due to HPEM Sources

4.1 Theory and Background

Buried cables are used in different applications: such as in communication, power transmis-

sion and distribution, as control cables and so on. Underground cables are widely used in

the communication and power sectors due to their efficient functioning in urban cities and

towns. As such, it is important that the cable system should perform its intended func-

tion as it may be connected to some sensitive equipment at the sending and receiving ends.

Of these the communications sector has an extensive network of low power cables that are

running here and there. On account of this, these cables are more prone to electromagnetic

interferences from HPEM sources. The buried communication cables or even the buried data

cables are connected to sensitive equipment, even a slight rise in the voltage or the current

at the terminals of the equipments can become a serious problem for the smooth operation

of the system. In this aspect, it is worthwhile to determine the effect of the electromagnetic

field due to these sources on the cables laid underground.

In the previous chapters, the electromagnetic field from these HPEM sources in the air

and in the soil is computed taking into consideration the soil dielectric properties. Thus it

turns out that the soil characteristics has a lot to do with the coupling of the field with the

cable. Treating this as an electromagnetic compatibility problem, the victim circuit becomes

the cable, the source of interference being the electric field from the HPEM sources and the

air and soil forms the path of propagation of the interference signal to the victim circuit.

Having known the electromagnetic field from the HPEM sources, the problem that is to be

tackled is to find the induced voltage and current in the cables, and also the computational

77

78 Chapter 4. Induced Voltage and Current in a Buried Cable due to HPEM Sources

method adopted for the same.

4.2 Underground Cable Getting Illuminated by HPEM

Sources

The Fig. 4.1 gives the schematic of a cable getting illuminated by the electromagnetic fields

due to the different HPEM interference sources. The earth plane is considered to be of infinite

extent. The cable is buried such that the midpoint of the cable is aligned with the boresight

of the antennae in the case of IRA and HPM sources. In this work, only direct radiation

from IRA and HPM sources are considered. The NEMP field is present uniformly in the

region surrounding the cable so that the cable has a homogeneous illumination throughout

its length due to NEMP field. The IRA and HPM sources are located at a distance of 100

m above the earth’s surface. Different types of soils are considered in the last chapter and

also some case studies are also presented. For the present work, to find the coupling with

the cable, it is assumed that the cable runs in a dry sandy land. This type of soil has

characteristic properties that will lead to an induced voltage which is neither too low nor

too high. The conductivity of this soil is 0.001 S/m and the relative dielectric constant is

10.

4.3 Coupling with the Cable

HPEM electric field coupling with the cable is done in two stages [93]-[98]:

• Coupling to the external circuit, and

• Coupling to the internal circuit

The detailed circuit configuration of the two circuits is given in Fig. 4.2. The equivalent

circuit representation is shown in Fig. 4.3. The external circuit consists of the soil whose

impedance is Zsoil and admittance is Yg [95], the outer layer of the cable shield whose

impedance is Zsh and the outer dielectric layer which has a series impedance of Zins and a

capacitance of Xc. The internal circuit consists of the inner layer of the shield of impedance

Zss., inner insulation of impedance Zind and admittance of Yins as well as conductor of

4.3. Coupling with the Cable 79

Figure 4.1: Schematic of the HPEM Sources Illuminating a Buried Cable Along with the

Cable Termination and other Details.

Figure 4.2: Equivalent Circuit Representation of the External and Internal Circuits of a

Cable used for Coupling Analysis [100].

Figure 4.3: Schematic Representation of

the External and Internal Circuits of a Ca-

ble used for Coupling Analysis.

106

107

108

109

10−10

10−8

10−6

10−4

10−2

100

Frequency (Hz)

Tra

nsfe

r im

peda

nce(

ohm

s/m

/Hz)

Figure 4.4: Transfer Impedance of a

Shielded Coaxial Cable.


impedance Zwire. The two circuits are coupled by means of the shield transfer impedance,

Zt.

The value of Zt is computed using Schelkunoffs equation [95]. According to this equation

transfer impedance can be written as :

ZT =1

2πaσT

(1 + j)Tδ

sinh(1 + j)Tδ

(4.1)

The transfer impedance for the shielded cable that is used for the present work is shown

in Fig. 4.4. The transfer impedance is a function of the type of the cable, the frequencies of

the field that is going to excite the cable and also that of the shield thickness. This varies

with the frequency and is tens of milli-ohms per meter at low frequency. It also drops with

frequency. The incident electric field reaching the cable will induce voltage in the shield.

This can be determined by assuming the shield as a single core conductor with an outer

layer of insulation. At all the points along the length of the shield, there is an excitation due

to the field. This is a case of the distributed excitation and hence the current is induced at

every point on the cable at the same time.

The terminal characteristics of the cable matters has to be considered in the induced

voltage computation, because the net voltage or current on the cable is influenced by the

type of cable termination used. This can be attributed to the concept of travelling waves,

as the net voltage/current at any point is the sum of the travelling wave components of

the voltages / currents coming from either sides of the observation point. These travelling

wave components have a transmitted part and a reflected part, the reflected wave being a

function of the terminal impedance of the cable. Hence the nature of the termination is

critical in the evaluation of the induced parameters. In the present case, both the shield

and the inner conductor are terminated respectively by their own characteristic impedances

as shown in the Fig. 4.1. In this case, there are no reflections of the shield current from

the ends and likewise there is no reflection of the current in the inner conductor from the

ends of the cable. These currents propagate to either ends of the cable and get terminated

because of the matching impedances connected at the end points. The method of analysis

should accommodate for these effects. Several methods are used in practice to find the

coupling. Most of them are based on the transmission line model of the cable [95]. Since

the frequency encountered in the HPEM sources coupling varies from MHz to GHz range,

the method used for coupling should accommodate for these huge frequencies involved. At

4.4. High Frequency Electromagnetic Field Coupling to Buried Cables 81

these frequencies the transverse dimension of the line and the return path is more than the

significant wavelength of the exciting electromagnetic field. Hence scattering theory needs

to be adopted for such problems. In the present work, these electrodynamic corrections are

incorporated in the basic Transmission Line Approximation [95] and was found to be suitable

for such a case and hence is adopted in this work.

4.4 High Frequency Electromagnetic Field Coupling to

Buried Cables

The equivalent circuit for studying the field to cable coupling is divided into external and

internal circuits as explained in the previous section. Hence the coupling process is first

studied for the external circuit and then the study of interaction with the internal circuit is

taken up. For the coupling study, it is assured that the total tangential electric field is zero

for a horizontal wire. The technique for studying the coupling is adopted from [97]

According to this method, the total electric field,−−→Etot is given as

−→ex ·−−→Etot = −→ex · (

−−→Eexc +

−−→Escat) = 0 (4.2)

where −→ex is the unit vector along the x direction, Eexc is the excitation components of the

electric field and Escat is the scattered component of the electric field which is the reaction

field of the wire to the excitation field. Eexc is given by,

−−→Eexc =

−→Etr (4.3)

Where, Etr is the transmitted component of the electric field which is dealt in detail in

chapter 2.

−−→Escat = −jω

−→A −∇φ (4.4)

where A is the vector potential and φ is te scalar potential

−−→Escat = −jω µ0

4π

L∫0

−→exI(x′)g(x, x′)dx′ −∇φ (4.5)

g(x, x′) = g0(x, x′)−Rv gi(x, x

′) (4.6)


where I(x′) is the induced current along the line, g(x, x′) is the Green′s function and

g0(x, x′) is the Green′s function for the lossy medium and gi(x, x

′) is the image component

of the Green′s function and Rv is the Fresnel reflection coefficient the equation for which is

given in the previous chapter. Hence, g0(x, x′) is given by

g0(x, x′) =

e−jkR1

R1

(4.7)

and gi(x, x′) is given by

gi(x, x′) =

e−jkR2

R2

(4.8)

where k is the propagation constant in the soil, R1 and R2 are the distances from the

source point in the ground to the corresponding image point in air and is given by

R1 =√

((x− x′)2 + a2) (4.9)

R2 =√

((x− x′)2 + 4d2) (4.10)

To get the scattered electric field, the equation of continuity is to be used , which gives

the charge density and hence the current distribution that is related as per the given formula,

q =1

jω

∂I

∂x(4.11)

Hence,

φ(x) =1

4πεeff

L∫0

∂I(x′)

∂x′g(x, x′)dx′ (4.12)

Escat = −jω µ

4π

L∫0

I(x′)g(x, x′)dx′ +1

j4πωεeff

∂

∂x

L∫0

∂I(x′)

∂x′g(x, x′)dx′ (4.13)

The excitation field depends upon the sources considered that can be obtained from the

source characteristics of the respective sources. Hence

Eexc + Escat = 0 (4.14)

4.4. High Frequency Electromagnetic Field Coupling to Buried Cables 83

Solving the above equation gives the induced current at any point on the wire. According

to the standard TL theory, the scattered voltage is,

Vs(x) = −ds∫0

Ez(z, x)dz (4.15)

where Ez(z, x) is the vertical electric field at the given depth

Vs(x) = φ(d, x)− φ(0, x) (4.16)

But

φ(0, x) = 0 (4.17)

Or,

dVs(x)

dx+ jω

µ0

4π

L∫0

I(x′)g(x, x′)dx′ = Eexc(d, x) (4.18)

d

dx

L∫0

I(x′)g(x, x′)dx′ + jω4πε0Vs(x) = 0 (4.19)

Solving the above equations for the external circuit, we can get the current and voltage

induced at all the desired locations on the cable. For example, the net current at any point

is the sum of all the currents reaching that point. If there are n+1 points on the cable, then

I(x = p) = −p−1∑x=0

I(x) + I(x = p) +x=n∑x=p+1

(4.20)

These n+1 points are shown in Fig. 4.5. along with the direction of the travelling waves

of voltages and currents. In the above equation the first term refers to the current flowing

from the left hand side of the desired point and the last term refers to the net current

flowing from the right hand side. The middle term is the contribution to the current due to

the induced current at the point of interest itself. So depending upon where the observation

point is located, the relative contribution from either side of the observation point varies.

This causes variation in the characteristics of the current at that point. A similar explanation

holds good for the induced voltage also.


The current induced in the shield gets coupled to the inner circuit. Only a small portion

of this shield current gets coupled to the inner circuit, which is given as Zt ∗ I(x), where

Zt is the transfer impedance of the cable. This voltage term forms the excitation term to

a similar set of transmission line equations as in equation 4.18 and equation 4.19. Solving

these equations will give the induced current and voltages on the inner conductor of the

cable.

4.5 Validation of the Proposed Method

The method used for computing the induced voltage/current is validated by taking one of the

HPEM sources and computing the induced current in a wire buried at a depth of 1 m in soil.

HPM is taken as the excitation source and the current is computed at the midpoint of the

wire with HPM antenna at a distance of 1 km from the earth’s surface. The induced current

so obtained is plotted in Fig. 4.6 and Fig. 4.7. The current obtained by the proposed method

is validated by computing the induced current using the full wave model incorporating the

Sommerfeld Integral using the commercially available NEC software. The data used for

validation are as follows:

• SIMULATION PLATFORM : NEC V-4

• Number of segments: 801

• Frequency points: 1 MHz-2300 MHz step: 1 MHz

• Lossy ground model: Sommerfeld Integral

• Time domain solution: IFFT transformation

The result shows close similarity to the induced current computation using the Enhanced

Transmission Line Model (ETLM). All the transition points match closely at the respective

frequencies in both the figures. And the shape is maintained too, except for an additional

jump in the waveform occurring at 3.4 GHz, in the falling portion of the waveform for the

induced current. Because of the close matching, this method (ETLM) is used for computing

the induced current/ voltage in the cable in this work.

4.5. Validation of the Proposed Method 85

Figure 4.5: Segmentation of the Cable for Coupling Studies.

108

109

1010

10−14

10−12

10−10

10−8

Frequency (Hz)

Indu

ced

curr

ent (

A/H

z)

Figure 4.6: Induced Current at the Mid-

point of a Wire by Frequency Domain

Analysis.

Figure 4.7: Induced Current at the Mid-

point of a Wire by NEC Computation.

Figure 4.8: Cross Section of the Buried

Cable.

Figure 4.9: The Observation Points on the

Cable where the Induced Current and the

Voltage is Plotted.


4.6 Induced Voltage/ Current in the Shield of the Ca-

ble due to the HPEM Sources

The method of induced current computation is explained in one of the previous section 4.2

to 4.4. Also the method so used is validated against a full wave current model and the results

using both the methods matched well. Using this method, the induced voltage and current

on a buried shielded cable is computed for the three HPEM sources, NEMP, IRA and HPM.

The cable is a shielded cable, the shielding of which is done by using tape wound galvanized

steel with negligible spacing between the turns. The cable is buried at a depth of 1m below

the earth’s surface. The length of the cable is taken as 10 m. The outer insulation and the

inner insulation used is PVC. The inner conductor is made of copper. The dimensions of

the cable is shown in Fig. 4.8. The cable is buried in a dry sandy soil having a permittivity

of 10 and conductivity of 10−3 S/m.

The electric field from the HPEM sources will travel initially through the air and then

get into the soil media where the field behaves in an entirely different fashion rather than in

the air. This behavioural mechanism is already given in chapter 3.

The response of the cable to the electric field from these sources is decided by how much

voltage and current is induced in it when the electric field due to these sources strike the

cable. The induced current and voltage is plotted at four points along the cable length.

These observation points are shown in the Fig. 4.9.In all the induced current and voltage

plots the labels a and d show the end points of the cable, b shows the observation point ant

a distance of 2m from the point a, and c shows the midpoint of the cable.These observation

points are marked in Fig. 4.9

4.6.1 Response of the Cable to NEMP Field

The induced current in the shield due to the electric field from an NEMP is shown in Fig.

4.10 to Fig. 4.18. The spectral characteristics of the induced current show a peak in the value

of the current at a frequency close to 1 MHz and the drop in current after this frequency

is more than the other side, where current slowly increases with rise in the frequency. This

drop in the current is attributed to the higher attenuation constant of the soil once the

frequency increases. The induced current has a peak value of 65 A at the midpoint of the

cable. There is a gradual reduction in the magnitude of the current from the midpoint of

4.6. Induced Voltage/ Current in the Shield of the Cable due to the HPEM Sources 87

the cable to the endpoints. The induced voltage in the shield is zero at the midpoint and

gradually rises to the ends. Also, the polarity of the voltage is different on either side of the

midpoint with a peak voltage of 4.8 kV at the endpoint of the cable. The current and the

voltage in the shield start after a delay time,

td = 1 / propagation velocity in soil = 10 ns

In both the current and voltage waveforms, the basic wave shape of the NEMP field,

i.e., the double exponential nature is preserved. In the inner conductor, the current has a

peak value of 1 A and the voltage has a peak magnitude of 80 V. The current in the inner

conductor starts after a delay time of 10 µs.

4.6.2 Response of the Cable to an IRA Field

The induced current and voltage in a shielded cable due to an IRA generated field can be

computed in the following manner. The IRA source is considered to be located at a distance

of 100 m from the earth’s surface. The field at the cable location is identified using the source

characteristics. For this the IRA source is so located that the boresight of the antenna strikes

exactly at the midpoint of the cable. This configuration gives a maximum field at the centre

of the cable. Now the field at all the points of the cable is taken as the source for computing

the induced parameters in the cable, by taking due consideration of the cable parameters.

The current thus computed in the cable shield is plotted in Fig. 4.19 to Fig. 4.20.

These figures show that the induced current in the cable shield is maximum at the centre

of the cable, where the electric field is the maximum. This peak magnitude of the current

is 150 A. The wave shape of the current has a prepulse followed by an impulse as expected

for an IRA type field. But once the observation point shifts from the centre of the cable

to the sides, i.e., to left or to the right of the centre, the current magnitude drops almost

exponentially with the distance, so that the magnitude of the current is 100 A and 75 A

respectively at observation points 2 m and 0 m, which corresponds to a distance of 3 m and

5m from the centre of the cable to the ends of the cable. The similar pattern is repeated

at both the sides from the centre, as the cable is symmetrical with respect to the field and

also there are no reflections from the endpoints. Fig. 4.20 shows a mesh plot of the current

along the cable, which shows the variation of the current along the cable. The current at

the midpoint of the cable starts after a delay time which is given by,

td = (100 m / velocity of propagation of the field in air) + (1/ velocity in soil) =


104

105

106

107

108

10−7

10−6

10−5

10−4

Frequency (Hz)

Indu

ced

curr

ent

(A/H

z)


form of the Induced Current on the

Shield due to NEMP.

0 2 40

10203040506070

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

10203040506070

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

10203040506070

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

10203040506070

Time (µs)

Indu

ced

curr

ent (

A)

a b

c d


the of Induced Current in the Shield.

0

5

10 05

10

0

20

40

60

80

100

Time (µs)Distance along the

length of the cable (m)

Indu

ced

curr

ent

(A)

10

20

30

40

50

60

70

80

Figure 4.12: Mesh Plot of the Induced

Current on the Shield.

0 2 4

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4−1

−0.5

0

0.5

1

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 40

1

2

3

4

5

Time (µs)

Indu

ced

volta

ge (

kV)

a b

c d


the Induced Voltage on the Shield.

05

10 02

46−10

−5

0

5

10

Time (µs)Distance along the

length of the cable (m)

Indu

ced

volta

ge (

kV)

−6

−4

−2

0

2

4

6


Voltage on the Shield.

0 50 100 150−1

−0.5

0

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100 150−1

−0.5

0

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100 150−1

−0.5

0

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100 150−1

−0.5

0

0.5

Time (µs)

Indu

ced

curr

ent (

A)

a

c

b

d


of the Induced Current on the Inner

Conductor.


0

2

4 50

100150

200250

−1.5

−1

−0.5

0

Time (µs)

Distance along the length of the cable (m)

Indu

ced

curr

ent (

A)

−1

−0.8

−0.6

−0.4

−0.2

10 0


Current on the Inner Conductor.

0 50 100 1500

20

40

60

80

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 1500

20

40

60

80

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−80

−60

−40

−20

0

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−80

−60

−40

−20

0

Time (µs)

Indu

ced

volta

ge (

V)

(a) (b)

(c) (d)

a

c

b

d


of the Induced Voltage on the Inner

Conductor.

0

5

10 0100

200300

−100

−50

0

50

100

Time (µs)


Indu

ced

Vol

tage

(V

)

−60

−40

−20

0

20

40

60


Voltage on the Inner Conductor.

300 400 500 600−100

0

100

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−100

0

100

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500−100

−50

0

50

100

150

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−100

−50

0

50

100

150

Time (ns)

Indu

ced

curr

ent (

A)

a b

c d

Figure 4.19: Induced Current on the

Shield at Different Points of a Cable due

to EM field from an IRA .

0

5

10 300 350 400 450 500 550

−100

−50

0

50

100

150

Time (ns)


Indu

ced

curr

ent (

A)

−50

0

50

100


Current on the Shield due to EM field

from an IRA.


343 ns

But as we move to the end points, the delay time increases due to the time it takes for

the field to get itself felt at that point, which triggers the current to get induced at these

points.

A similar effect is seen for the voltages which are plotted in Fig. 4.21 and Fig. 4.22 which

show the voltage magnitudes of 11 kV, 8 kV and 5.5 kV at the midpoint, at 2m point and

at the endpoint of the cable respectively . The voltage waveshape has opposite polarity on

either sides of the midpoint on account of the reversal of the travelling waves at either sides

of the midpoint. This is clearly seen from the mesh plot of the voltage at Fig. 4.22. The

spike at the centre of the cable corresponds to the self excitation at the centre due to the

field, which gradually drops down as the distance to the endpoint increases.

In the cable centre conductor the induced current magnitudes are 2.5 A, 1.7 A and 1.2

A respectively and the voltages are 85 V, 130 V and 170 V respectively at the midpoint,

2m and 0m points which are shown in Fig. 4.23 to Fig. 4.26. The induced current peaks

at the midpoint of the cable where as the voltage is the lowest at this point. This is due to

the fact that the travelling waves of the voltages coming from either sides of the midpoint

tend to combine in such a way that the net voltage becomes the least at the midpoint and

the highest at the endpoint, which is on account of the zero reflection of the travelling waves

from the ends because of the matched termination used. This is clear from the mesh plot of

the voltage shown in Fig. 4.26.

4.6.3 Response of the Cable to an HPM Field

As in the case of an IRA, an HPM source is considered such that it is at a distance of 100

m from the earth’s surface, and the boresight of the antenna touches the mid point of the

cable. This source gives an induced current on the shield whose spectral characteristics is

shown in Fig. 4.27. The time domain waveforms of the induced current and voltage are

plotted in Fig. 4.28 and Fig. 4.29 respectively. This shows that the 1 GHz cut-off frequency

is maintained in the spectrum of the induced current. The corresponding temporal response

shows a peak value of the current to be 520 A, which drops exponentially to 400 A at 2m

point and again dropping exponentially to 260 A at the end points of the cable. The current

preserves the basic shape and characteristics of an HPM pulse.

The same is applicable to the induced voltage in the shield that is 40 kV, 32 kV and 20


300 400 500 600 700−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

300 400 500 600 700−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

300 400 500 600 700−10

−5

0

5

10

Time (ns)

Indu

ced

volta

ge (

kV)

300 400 500 600 700−10

−5

0

5

10

Time (ns)

Indu

ced

volta

ge (

kV)

a

c d

b

Figure 4.21: Induced Voltage on the

Shield at Different Points of the Cable

due to EM field from an IRA.

0

5

10 300 350 400 450 500 550

−10

−5

0

5

10

15

Time (ns)

Indu

ced

volta

ge(k

V)


−5

0

5

10


Voltage on the Shield due to the EM

field from an IRA.

200 400 600 800 10001200

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

a

dc

b

Figure 4.23: Induced Current on the In-

ner Conductor at Different Points of the

Cable due to the EM field from an IRA.


Current on the Inner Conductor due to

the EM field from an IRA.

200 400 600 800 10001200−170

−100

−50

0

50

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 80010001200−170

−100

−50

0

50

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200−50

0

50

100

170

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200−50

0

50

100

170

Time (ns)

Indu

ced

volta

ge (

V)

a b

c d

Figure 4.25: Induced Voltage on the In-


Cable due to the EM field from an IRA.


Voltage on the Inner Conductor due to

the EM field from an IRA.


kV respectively at the endpoint of the cable, at 2 m and at the midpoint of the cable. The

polarity reversal between the induced voltages in either sides of the midpoint of the cable

is also clear from the Fig. 4.29. The time delay incurred before the current is felt at the

midpoint of the cable is 334 ns as in the case of IRA.

The induced current and voltage in the inner conductor of the cable are plotted in Fig.

4.30 to Fig. 4.32. In the inner conductor of the cable, the induced current characteristics

is such that the current drops very fast and almost by 100 MHz, the current is reduced sig-

nificantly. The high frequency components have vanished from the waveform of the induced

current waveform on the inner conductor that were present in the current induced on the

shield. This can be attributed due to the transfer impedance of the cable which is negligibly

small at frequencies close to GHz range. This can also be seen from the Fig. 4.30. The

induced current occurring on the inner conductor is 8 A, 6 A and 4 A at the midpoint, at

2 m and at the ends of the cable respectively. Also the induced voltage in the conductor is

600 V, 400 V and 300 V at the ends, at 2m and at the midpoint of the cable respectively.

4.7 Induced Current in Twisted Pair Cable due to HPEM

Sources

The present day communication cables are mostly twisted pair cables, because of the ad-

vantage of lower attenuation of the signals transmitted through these cables [98] as well

as their excellant performance in low to medium speed data transmission applications. The

twisted-pair cable is used extensively because of its low-loss, low-cost, and low-coupling char-

acteristics. At low frequencies, the coupling among cables is generally related to the magnetic

field that is produced in proximity to driven cables. A twisted-pair transmission line is a pair

of wires with circular cross-section, coated uniformly with a dielectric, and twisted about

each other with a uniform pitch. The wires are typically copper, and the dielectric is gen-

erally one of many plastics, depending upon the application. Multiple twisted-pairs can be

grouped together and encased in an insulating jacket, and twisted-pair transmission lines

can be either shielded or unshielded. There are thin, flexible cables that are easy to string

between walls. These cables can have more lines running through the same wiring ducts

and hence costs less per meter than any other type of LAN cable, electrical noise going into

or coming from the cable can be prevented and cross-talk is minimized. But at the same

time twisted pair’s are susceptible to electromagnetic interference that greatly depends on

4.7. Induced Current in Twisted Pair Cable due to HPEM Sources 93

108

109

1010

10−14

10−13

10−12

10−11

10−10

10−9

10−8

Frequency (Hz)

Indu

ced

curr

ent (

A/H

z)

Figure 4.27: Frequency Domain wave-

form of the Induced Current on the

Shield due to EM field from an HPM

source.

368 370 372 374 376 378−400

−200

0

200

400

600

Time (ns)

Indu

ced

curr

ent (

A)

354 356 358 360 362 364−400

−200

0

200

400

600

Time (ns)

Indu

ced

curr

ent (

A)

340 345 350−400

−200

0

200

400

600

Time (ns)

Indu

ced

curr

ent (

A)

368 370 372 374 376 378−400

−200

0

200

400

600

Time (ns)

Indu

ced

curr

ent (

A)

c

a b

d


Shield at Different Points of the Cable

due to EM field from an HPM source.

106

107

108

109

1010

10−20

10−15

10−10

10−5

Frequency (Hz)

Indu

ced

curr

ent (

A/H

z)

Figure 4.29: Frequency Domain wave-

form of the Induced Current on the In-

ner Conductor of the Cable due to EM

field from an HPM source.

368 370 372 374 376 378−40

−20

0

20

40

Time (ns)

Indu

ced

volta

ge (

kV)

354 356 358 360 362 364−40

−20

0

20

40

Time (ns)In

duce

d vo

ltage

(kV

)

340 345 350−40

−20

0

20

40

Time (ns)

Indu

ced

volta

ge (

kV)

368 370 372 374 376 378−40

−20

0

20

40

Time (ns)

Indu

ced

volta

ge (

kV)

a

dc

b



Cable due to EM field from an HPM

source.

400 600 800−8

−6

−4

−2

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−8

−6

−4

−2

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−8

−6

−4

−2

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−8

−6

−4

−2

0

Time (ns)

Indu

ced

curr

ent (

A)

a b

c d

Figure 4.31: Induced Current on the In-



source.

300 400 500 600

−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

300 400 500 600

−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

300 400 500 600

−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

300 400 500 600

−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

a

c

b

d




source.


the pair twisting schemes. Also in video applications that send information across multiple

parallel signal wires, twisted pair cabling can introduce signalling delays.

It is worth while to see the effect of HPEM interference on a shielded twisted pair cable

so as to analyse the performance of these cables under an electromagnetic interfering envi-

ronment. The performance of twisted pair cables depends upon the number of twisted pairs

in the cable has and the pitch. Hence in this section the twisted pair cables are analysed

based on the above two aspects. For the analysis the twisted pair is considered to be wound

into a bifilar-helix configuration as shown in Fig. 4.33. This allows a convenient analysis

of the geometrical shape, including the relative orientation of the wires with respect to the

illuminating electromagnetic field. Accordingly, the cartesian coordinates of points along the

bifilar helix are as follows:

x1 = R0 cosαl (4.21)

y1 = R0 sinαl (4.22)

x2 = −R0 cosαl (4.23)

y2 = −R0 sinαl (4.24)

z1 =αpl

2π(4.25)

z2 =αpl

2π(4.26)

α = (R20 + (

p

2π)2)−0.5 (4.27)

Where p is the pitch, R0 is the radius of the helix, l is the arc length (wire length).

If the pitch of the turns and wavelength are considered to be much greater than the wire

separation, then the inductance and capacitance per unit length, as well as the characteristic

impedance, are essentially the same as that occurring for an untwisted pair.

Four different twisted pair cables are considered: 1 pair, 2 pairs, 25 pairs and 100 pairs

cables. The cable dimensions for these pairs are as follows:


Figure 4.33: Bifilar Helix Configuration of a Twisted Pair Cable used for Computation

Purposes.

1 pair:

Conductor dimension = 0.5 mm

Insulated conductor diameter = 0.9 mm.

Jacket thickness = 0.65 mm.

Outer cable diameter = 4.3 mm.

Shield thickness = 0.5 mm.

2 pairs:



Jacket thickness = 0.65 mm.

Outer cable diameter = 5.1 mm.


25 pairs:



Jacket thickness = 1 mm.

Outer cable diameter = 12 mm.


100 pairs:




Jacket thickness = 1 mm.

Outer cable diameter = 15 mm.


Induced current and voltage in the shield and the conductor of the cable is computed by

using the same technique as used for the shielded cables for NEMP,IRA and HPM electric

fields. In all the induced current and voltage plots the labels a and d show the end points of

the cable, b shows the observation point ant a distance of 2 m from the point a, and c shows

the midpoint of the cable.These observation points are marked in Fig. 4.9

4.7.1 Coupling of the EM field due to NEMP with the Twisted

Pair Cables

The induced current and voltage in the buried cable shield and conductor due to electromag-

netic field from an NEMP source is as plotted in Fig. 4.34 to Fig. 4.50. The peak induced

current in the cable shield is 87 A, 75 A, 66 A and 52 A respectively for 1 pair, 2 pairs, 25

pairs and 100 pairs cables respectively. With an increase in the number of pairs of the cable

that is being twisted, the induced current in the cable reduces. This can be attributed to

the effective increase in the cable size that causes more area of the cable to participate in

the current distribution, thereby causing a significant drop in the magnitude of the current.

The dimension of the cable for a 25 pairs almost matched with that of the shielded cable,

and it is seen that the current shows a slight increase in the magnitude, which is due to the

lower thickness of the outer insulation, which causes the impedance due to the insulation

to vary from that of a shielded cable. This variation in the impedance offered by the outer

insulation influences the overall impedance of the external circuit of the cable, the individual

constituents of this circuit has already been dealt in detail during the analysis of the shielded

cable. The induced voltage in the cable shield is 7.3 kV, 6.1 kV, 5 kV and 4 kV respectively

for the above number of pairs of the twisted pair cable.

In the inner circuit, the current in the cable conductor is 0.42 A, 0.39 A, 0.35 A and 0.2A

respectively for 1 pair, 2 pairs, 25 pairs and 100 pairs cables. The peak value of the current

for a shielded cable was 1 A. 25 pairs twisted pair cable, whose dimensions matches with

the shielded cable has a peak current of 0.35 A, thereby accounting for about 65% reduction


in the magnitude of the current. This reduction in the current is due to the twisting of the

conductors in a twisted pair cable that will cause cancellation of the current on account of

the inductive effects.

The change in the pitching of the twisted pair cable affects the induced current consid-

erably. The pitching is varied from one to 10 times the diameter, d and the induced current

is computed. As the diameter is varied the current increases and it saturates at 4.5d, where

d = diameter. Any further change in the pitching has negligible effect on the current. This

is because once the pitching is higher, then the twisting will not have its effect and hence

the current remains unaffected. But on the lower side, any decrease in the pitching will

make a more tightly twisted cable, which will cause the mutually coupled components of the

currents to get cancelled and hence the net current drops.

4.7.2 Coupling due to IRA Electric Field

Electric field due to IRA couples with the twisted pair cable in a manner similar to that of

NEMP. The peak current induced in the cable shield are 180 A, 160 A, 140 A and 175 A

respectively for the 1, 2, 25 and 100 pairs of cables in the shield. This plot is shown in Fig.

4.51, Fig. 4.55, Fig. 4.59 and Fig. 4.63 respectively. In the conductor these currents are 2.1

A, 2 A, 1.5 A and 1.3 A for the above pairs of the cable. These respective plots are shown

in Fig. 4.52, Fig. 4.56, Fig. 4.60 and Fig. 4.64.

The induced voltage in the cable shield is 15 kV, 12 kV, 11 kV and 9 kV respectively and

is plotted in Fig. 4.53, Fig. 4.57, Fig. 4.61 and Fig. 4.65 and in the conductor these are 160

V, 130 V, 100 V and 80 V respectively and are shown in Fig. 4.54, Fig. 4.58, Fig. 4.62 and

Fig. 4.66. The peak value of the induced current in the conductor is plotted as a function

of the pitching of the cable in Fig. 4.67. In contrast to the current due to an NEMP, where

there is a large gap between the 25 pair and 100 pair and almost equal gap between the

remaining pairs, in the IRA the gap between the current plots are almost equal. This is due

to the fact that the mutual coupling eliminates certain frequency components in the current

induced due to EM field from an IRA, which are mainly the high frequency components.

Again this is only a function of the pitching. The variation in the cable diameter affects

less as compared to NEMP because the shield thickness is the same, and only the insulation

thickness varies and because of the skin effect, this variation is only less affected in the output

current. The induced current drops by 40% for 25 pair cable from the current magnitude


0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

a

c d

b


Cable Shield for 1 Pair due to NEMP.

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

ba

dc


Cable Inner Conductor for 1 Pair due

to NEMP.

0 2 4−8

−6

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4−8

−6

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4−1

0

1

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 40

2

4

6

8

Time (µs)

Indu

ced

volta

ge (

kV)

a

c

b

d

Figure 4.36: Induced Voltage in the Ca-

ble Shield for 1 Pair due to NEMP.

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)In

duce

d vo

ltage

(V

)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

a b

c d

Figure 4.37: Induced Voltage on the Ca-

ble Inner Conductorfor 1 Pair due to

NEMP.

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

a

c

b

d


Cable Shield for 2 Pairs due to NEMP.

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

ba

c d


Cable Inner Conductor for 2 Pairs due

to NEMP.


0 2 4

−6

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4

−6

−4

−2

0

Time (µs)In

duce

d vo

ltage

(kV

)

0 2 4−1

0

1

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 40

2

4

6

Time (µs)

Indu

ced

volta

ge (

kV)

a

c

b

d


ble Shield for 2 Pairs due to NEMP.

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

a b

c d


ble Inner Conductor for 2 Pairs due to

NEMP.

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

a b

c d


Cable Shield for 25 Pairs due to NEMP.

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

a b

c d



to NEMP.

0 2 4−6

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4−6

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4−1

0

1

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 40

2

4

6

Time (µs)

Indu

ced

volta

ge (

kV)

a b

c d



0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

a b

c d



NEMP.


0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

0 2 40

50

100

Time (µs)

Indu

ced

curr

ent (

A)

a b

c d


Cable Shield for 100 Pairs due to

NEMP.

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

0 50 100−0.5

−0.25

0

0.25

0.5

Time (µs)

Indu

ced

curr

ent (

A)

a b

c d



to NEMP.

0 2 4

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4

−4

−2

0

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 4−1

0

1

Time (µs)

Indu

ced

volta

ge (

kV)

0 2 40

2

4

Time (µs)

Indu

ced

volta

ge (

kV)

a b

c d



0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

0 50 100 150−120

−60

0

60

120

Time (µs)

Indu

ced

volta

ge (

V)

a b

c d



NEMP.

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

Pitch (in diameters)

Pea

k In

du

ced

cu

rren

t (A

)

1 pair2 pair25 pair100 pair

Figure 4.50: Effect of the Pitching on

the Induced Current in a Twisted Pair

Cable due to NEMP.


300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

a

c

b

d


Cable Shield for 1 Pair due to EM field

from an IRA.

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

a b

c d



to EM field from an IRA.

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d


ble Shield for 1 Pair due to EM field

from an IRA.

200 400 600 800 10001200−200

−100

0

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200−200

−100

0

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

a

c

b

d


ble Inner Conductor for 1 Pair due to

EM field from an IRA.

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

a

c

b

d




200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent(

A)

a

c

b

d





1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d


ble Shield for 2 Pairs due to EM field

from an IRA.

200 400 600 800 10001200−200

−100

0

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200−200

−100

0

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

a

c

b

d




300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

a

c

b

d


Cable Shield for 25 Pairs due to EM

field from an IRA.

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

a b

c d




1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d



from an IRA.

200 400 600 800 10001200−200

−100

0

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200−200

−100

0

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

a

c

b

d





for a shielded cable

4.7.3 Coupling due to HPM Electric Field

Electric field due to IRA couples with the twisted pair cable in a manner similar to that

of NEMP. The peak currents induced on the cable shield are 515 A, 510 A, 505 A and 502

A respectively for the 1, 2, 25 and 100 pairs of cables in the shield. These waveforms are

shown in Fig. 4.68, Fig. 4.72, Fig. 4.76 and Fig. 4.80 respectively. On the inner conductor,

these induced currents are 8 A, 7 A, 5 A and 3.5 A for the above pairs of the cable. The

respective plots are shown in Fig. 4.69, Fig. 4.73, Fig. 4.77, and Fig. 4.81.

The induced voltage in the cable shield is 60 kV, 50 kV, 35 kV and 30 kV respectively

and are plotted in Fig. 4.70, Fig. 4.74, Fig. 4.78 and Fig. 4.82 and on the inner conductor

these are 580 V, 560 V, 540 V and 500 V respectively which are shown in Fig. 4.71, Fig.

4.75, Fig. 4.79 and Fig. 4.83. The peak value of the induced current in the conductor is

plotted as a function of the pitching of the cable in Fig. 4.84. In the case of HPM, the gap

between the currents of 1 and 2 pair is the smallest as compared to the other sources. This

is because the variation in the conductor dimension is only 0.2 mm in the outer diameter

which has negligible influence on a high frequency signal, because of the skin effect. The

percentage variation of the induced current from the shielded cable to the twisted pair cable

of 25 pair is 37.5%.

4.8 Chapter Summary

This chapter deals with the computation of the induced current and voltage in a buried

cable. Two types of cables are considered - shielded cable and twisted pair cable. For the

computation, the Enhanced Transmission Line Model has been used which is explained in

the chapter. The validation of the present model is done with the help of NEC - 4 full wave

analysis and the results are found to be closely matching. The following conclusions are

arrived from this chapter:

• The induced current is more for a shielded cable than a twisted pair cable of the same

configuration.)

• The induced current magnitude depends upon the type of the HPEM source, the depth

of burial of the cable and the point on the cable where the current/ voltage is computed.


300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

300 400 500 600−200

0

200

Time (ns)

Indu

ced

curr

ent (

A)

a

c

b

d




200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

200 400 600 800 10001200−3

−2

−1

0

1

Time (ns)

Indu

ced

curr

ent (

A)

a b

c d




1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

1600 1800 2000

−10

0

10

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d



from an IRA.

200 400 600 800 10001200−200

−100

0

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200−200

−100

0

Time (ns)In

duce

d vo

ltage

(V

)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

200 400 600 800 10001200

0

100

200

Time (ns)

Indu

ced

volta

ge (

V)

a b

c d




0 2 4 6 8 100

0.5

1

1.5

2

2.5


Pea

k In

du

ced

cu

rren

t (A

)

1 pair2 pair25 pair100 pair



Cable due to EM field from an IRA.


1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1700 1705 1710

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1685 1690 1695

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

a b

dc


Cable Shield for 1 Pair due to EM field

from an HPM Source.

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

a

c d

b



to EM field from an HPM Source.

370 375 380

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

355 360 365

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

340 345 350

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

370 375 380

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d


ble Shield for 1 Pair due to EM field

from an HPM Source.

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

a

dc

b



EM field from an HPM Source.

1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1700 1705 1710

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1685 1690 1695

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

a

c d

b


Cable Shield for 2 Pairs due to EM field

from an HPM Source.

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

a

c

b

d





370 375 380

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

355 360 365

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

340 345 350

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

370 375 380

−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d



from an HPM Source.

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

a

c

b

d




1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1700 1705 1710

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1685 1690 1695

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

a b

c d



field from an HPM Source.

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

a b

c d




370 375 380−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

355 360 365−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

340 345 350−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

370 375 380−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d



from an HPM Source.

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

a

c

b

d





1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1700 1705 1710

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1685 1690 1695

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

1710 1715 1720 1725

−500

0

500

Time (ns)

Indu

ced

curr

ent (

A)

a

c

b

d



field from an HPM Source.

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

400 600 800−10

−5

0

Time (ns)

Indu

ced

curr

ent (

A)

a

c d

b




370 375 380−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

355 360 365−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

340 345 350−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

370 375 380−50

0

50

Time (ns)

Indu

ced

volta

ge (

kV)

a

c

b

d



from an HPM Source.

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

400 600 800−600

−300

0

300

600

Time (ns)

Indu

ced

volta

ge (

V)

a

c d

b




0 2 4 6 8 100

2

4

6

8

10


Pea

k In

du

ced

cu

rren

t (A

)

1pair 2 pair25 pair100 pair




Source.


• Current is maximum at the centre of the cable for matched terminations and the

voltage is the minimum at this point.

• The percentage of the induced current in the inner conductor with respect to the shield

current of a shielded cable is the least for an HPM, then comes the IRA and finally

the NEMP. This is due to the fact that higher frequencies are absorbed more by the

shield of the cable. This affects the induced currents due to HPM the maximum and

NEMP the least because of the presence of the lower frequency components in NEMP.

• Induced current in the twisted pair cable depends upon the number of pairs of the

cable and the pitching of the cable for a given HPEM source.

• The percentage variation in the current between the induced currents in the shielded

and twisted pair cable is 67% for the NEMP, 40% for IRA and 37.5% for the HPM.

This is due to the fact that the smaller variations in the conductor dimensions are

negligible for frequencies in the GHz range.

• The twisted pair cable of pitching equal to 4.5 times the diameter shows the saturation

limit of the induced current. With decrease in the pitching below this value will cause

current to reduce proportionately. This can be attributed to the reduction of the

mutually induced currents when the twisting becomes tighter.

Chapter 5

Coupling of the Field from an HPEM

Source with an Airborne Vehicle in

Flight

5.1 Introduction

The electromagnetic field from the HPEM sources propagate with less attenuation in the air

as compared to soil due to the lower resistance this medium offers for electromagnetic wave

propagation. Hence any airborne system in its vicinity will be subjected to intense illumi-

nation by these electromagnetic fields. Hence in this chapter, the influence of the radiated

electromagnetic fields from HPEM sources on an airborne vehicle in flight is analysed.

Airborne vehicle and its payload are extremely expensive that any damage or loss of these

as a result of the voltages and currents induced on the vehicle on account of the incident

intense HPEM electromagnetic fields can be quite undesirable. The incident electromagnetic

fields will polarize the vehicle along its axis which results in the induction of currents and

voltages. These currents and voltages will get coupled with the internal control circuits that

are extremely sensitive to such transient voltage and current pulses [99]. If the induced

voltage/ current magnitude happens to be above the damage threshold level of these circuits

then it will result in either a malfunction of the circuit or a permanent damage to it with

either of them being detrimental to the vehicle. This will even result in the abortion of

the mission or possible degradation of the vehicle performance. Hence it is worthwhile to

see the effect of an incoming HPEM electromagnetic field on the airborne vehicle with and

without the presence of its exhaust plume. For this initially plume has to be modelled

electromagnetically. Then the induced current and voltage in the vehicle is computed for

109

110 Chapter 5. Coupling of the Field from an HPEM Source with an Airborne Vehicle in Flight

the electromagnetic fields from all the three HPEM sources like NEMP, IRA and HPM.

5.2 Review of the previous work

Many studies have been done on the coupling of lightning with an airborne vehicle [100]-[106].

Also studies have been reported for the electromagnetic modelling of the plume [100]. The

early studies done are on the modelling of the airborne vehicle as a right circular cylinder

and computation of its capacitance [105]-[113].

Very few studies have been done on the measurement of the plume parameters of the

vehicle [110]-[112]. This is due to the negligibly small time involved in the burning process

to accurately measure the concentration of the species of the plume and also due to the high

cost incurred for the vehicle firings. The plume parameters such as temperature, pressure,

velocity and heat transfer rate for a nozzle expansion ratio of 7.6 and nozzle half angle of 150

is dealt in [113] for a solid propellant motor. The properties of a highly turbulent, chemically

reactive low altitude rocket plume was discussed in [114]-[118]. The electrical conductivity of

the plume was analysed along with its intensive parameter distribution by [119],[120] using

the Aerochemical Low Altitude Plume Program (LAPP). Many others have also subsequently

computed the parameter distribution of the plume and also the electromagnetic modelling of

the plume using FLUENT software for analysing the exhaust plume characteristics [121],[123]

. In the present work also the electromagnetic modelling of the plume using FLUENT is

utilized. There have been reports on the microwave attenuation in the presence of the trailing

exhaust plume of the vehicle [124],[125].

The induced current on the vehicle for a lightning electromagnetic field is computed in

[100] using Finite Difference Time Domain method for a vehicle that is just lifted off the

ground with the exhaust plume either touching the ground or close to the ground.

5.3 Geometry of the Airborne Vehicle

The geometry of the airborne vehicle and the exhaust used for the present analysis is as

shown in Fig. 5.1. For the present analysis it is assumed that the vehicle is in flight at

a height of 600 m above the ground. The diameter of both the vehicle and the plume is

considered to be the same, but the respective lengths are different. In the present work

an airborne vehicle of 20 m length and diameter of 0.5 m is considered. The length of the

5.3. Geometry of the Airborne Vehicle 111

exhaust plume is considered to be 75 m.

Figure 5.1: Airborne Vehicle with the Exhaust Plume.

Figure 5.2: Solid Propellant Rocket with a Nozzle.

To get the required thrust in the airborne vehicles, propellants are used which consists of

a fuel and an oxidizer. The fuel acts as an agent for propulsion when it burns in combination

with oxygen, which is being supplied by the oxidizer. There are three types of propellants:

liquid, solid and hybrid [129]. For the present work, a solid propellant is considered, which


is HTPB/AP/Al, where HTPB is Hydroxyl Terminated Polybutadiene, AP- Ammonium

Perchlorate (NH4ClO4) and Al is Aluminium. Ammonium Perchlorate (AP) is a finely

ground mineral salt which is used as the oxidizer that constitutes approximately 60-90% of

the propellant. The fuel used is aluminium which is added along with the mixture, which

increases the density and temperature of the exhaust plume. The propellant is held together

by polymeric binders such as polybutadienes, HTPB which is also consumed as fuel. These

propellants will look like rubber in its final form. A solid propellant motor with a nozzle is

shown in the Fig. 5.2. The characteristics of this solid propellant is flame tempertaure of 34400K, density of 1854.552 kg/m3 and a metal content of 4-17 wt %. When combustion occurs,

a supersonic exhaust plume is initiated from the highly compressed air in the combustion

chamber and expands through the nozzle. The composition of the solid propellant used is

given in the table 5.1.

5.4 Modeling of the Exhaust Plume

The coupling of the HPEM electric field with the airborne vehicles requires the accurate

modelling of the exhaust plume [128]-[130]. This modeling is aimed at determining the

electrical parameters of the plume such as the electrical conductivity and permittivity. These

parameters of the plume depend upon the properties of the plume such as the pressure,

temperature, species concentration and the velocity of the exhaust plume. Hence to get

the conductivity and permittivity of the plume, these intensive properties of the plume are

computed at two different sections- one inside the combustion chamber upto the nozzle

throat and second the exterior to the nozzle which is the ambient temperature where the

plume comes out. In the first section the NASA Chemical Equilibrium with Application

(CEA) software is used. In the second region, the commercially available software, FLUENT,

is used for the modelling of the exhaust plume properties. The data obtained through

the first section is the input to the FLUENT software to be used in the second section.

The FLUENT software will give the characteristics of the plume such as the temperature,

pressure, velocity and the species concentration in the axial and in the radial directions in

the ambient atmosphere. The detailed analysis of these two sections is dealt in [100].

5.5. Electromagnetic Modelling of the Plume 113

Table 5.1: Composition of the Solid Propellant

Propellant Weight

(%)

Ammonium Perchlorate 79

HTPB 13

Al 8

5.5 Electromagnetic Modelling of the Plume

The electrical properties of the exhaust plume such as conductivity and permittivity depends

upon the following factors [140],[141]:

• Combustion chamber pressure

• Combustion chamber pressure

• Nozzle back pressure

• Propellant composition

• Impurity content in the propellant which initiates the ionic charge transport in the

exhaust

• The parameters of the plume:

– Temperature

– Pressure

– Shock wave

– Velocity

– Species concentration.

When combustion occurs the exhaust comes out from the combustion chamber through

the converging and the diverging nozzle. The region from the combustion chamber to the

nozzle throat where the Mach number of exhaust plume is less than 1 is the subsonic zone.

Here it is incompressible in nature. At the nozzle throat, the Mach number is 1, which is the


transonic zone and out of the nozzle throat it is the supersonic zone where Mach number is

more than 1. In this zone the flow is compressible in nature.

The effective electrical conductivity and permittivity of an exhaust plume can be written

as:

σe = ε0

νeω2pe

ω2 + ν2e−

∑i=Na+,Cl−

νiω2pi

ω2 + ν2i

(5.1)

εe = ε0

1−∑

i=e−,Na+,Cl−

ω2pi

ω2 + ν2i

(5.2)

where,

νe = collision frequency of electrons with the neutral species

νi = collision frequency of ions, i.e., Na+, Cl− with other neutral species

ω = incident EM field frequency

ωpe = plasma frequency of electrons

ωpi = plasma frequency of the ionized plume

The collision frequency can be written as

νk =

√8kBT

πmk

[Nsp∑j=1

Qkjnj

√1 +

mk

mj

](5.3)

where

k = e−, Na+ and Cl−

j = 1, 2, 3, ., Nsp

Nsp = total number of neutral species

m = mass/molecule

Q = cross sectional area of electrons and ions with other species.

n = number density of ions present in the plume which depends upon the

static pressure and temperature of the plume

The expression for the number density is

nj =XjP

XTkBT(5.4)

where,

Xj = mole fraction of the species

5.6. Method of analysis used 115

XT = total mole fraction of the species

P = absolute pressure distribution.

The plasma frequency ωpk of the charged particles is

ωpk =

√nkq2kmkε0

(5.5)

where

k = e−, Na+ and Cl−

q = charge of electrons and ions

When any incoming electromagnetic field interacts with the exhaust plume it reacts with

the free electrons, free ions and heavy immobile neutral species. Since the neutral particle

does not have any interaction with the field the basic interaction of the field will be with the

electrons and ions.

The conductivity has both axial and radial variation. The mesh plot of conductivity is

shown in Fig. 5.3.

The conductivity of the missile exhaust plume along the axial position is plotted in Fig.

5.4. In this plot the maximum conductivity at each radial direction is plotted as a function

of the axial position. The conductivity starts from 0.1187 S/m and drops down to 0.02

S/m at the end point. In between these two extremities the conductivity plot shows several

oscillations at points close to the nozzle throat, where as this value drops down smoothly

after 2.1 m. This can be attributed to the intense chemical reactions taking place near

the nozzle throat that causes the conductivity to behave in a random manner, whereas it

stabilizes once the plume gets out of the nozzle premises. This behavior is also reported in

[100], where the results are closely matching.

5.6 Method of analysis used

The Finite Difference Time Domain Formulation has been used to compute the coupling of

transient electromagnetic fields with the airborne vehicle. This is a computational method

in time domain. This method has lots of disadvantages when it comes to real problem:

• This formulation requires the computation of the parameters of the airborne vehicle

like the capacitance, inductance and the resistance. This imposes a restriction on


the maximum height at which the coupling can be computed. Hence this method is

suitable only for those cases where the plume is either touching the ground or at some

definite small distance from the ground.

• If the incoming field has a lower rise time then accurate representation in time domain

will involve a huge matrix that is to be solved to get the desired results. In those

cases it is better to go for frequency domain approach where it is easier to get the

response in frequency domain, by sweeping through all the frequency components that

can possibly link with the field. This is very important in such fields as IRA field where

the rise time involved is in picoseconds and HPM fields where the centre frequency is

in GHz.

• The stability and the accuracy condition for coupling analysis is as per the Courant-

Freidricks-Lewy condition which gives:

CFL ≤ 4tvp4z

(5.6)

For NEMP, HPM and IRA fields the wavelengths involved are so small that the CFL

criterion demands more number of points on the surface of the vehicle to accurately

capture the coupling phenomenon. These many spatial points along with the huge

number of time steps will make the size of the computational matrix huge which makes

it complicated to be solved.

Hence in the present work, the coupling of the incoming HPEM sources with the airborne

vehicle is computed using the method of moments as discussed in [148]. Consider a thin wire

having N short segments connected together. These N points represent an N- port network.

The wire is formed by short circuiting all these N ports. The wire impedance and admittance

can be calculated to any degree of accuracy by using the geometry of the wire. The method

of moments mainly makes use of the four equations [142]-[146]:

− Ei1 = −jωAi −

∂φ

∂l(5.7)

−→A = µ

∫axis

I(l)e−j−→k .−→R

4πRdl (5.8)


φ =1

ε

∫axis

σ(l)e−j−→k .−→R

4πRdl (5.9)

σ =−1

jω

dI

dl(5.10)

where,

l = variable measured along the wire axis

R = distance measured from a source point on the axis to the field point on

the wire surface.

A = magnetic vector potential

σ = the charge density

I = current on the wire

The airborne vehicle is considered as a thin wire [147]-[154], and the method of moments

is applied to this thin wire model. This model is the best three dimensional model suited

especially if the current propagation is mainly in the axial direction. This thin wire ap-

proximation eliminates the circulating currents on the surface of the vehicle and only the

axial current needs to be considered. This thin wire model of the airborne vehicle with the

exhaust plume is as shown in the Fig. 5.5. The vehicle and the plume are modelled as thin

wire cylinders of lengths lv and lp respectively, both of radius a. The plume has an internal

impedance of Zp along the axial length of the plume, which defines the characteristics of

the plume. Zv represents the impedance of the vehicle. The incident field is EI , which

illuminates the cable. The magnitude of the field at any point along the axis of the vehicle

can be obtained from the properties of the HPEM sources that are presented in sections 2.1,

2.2 and 2.3. So the fields at different heights from the ground computed and presented in

sections 3.2 forms the source of excitation for this vehicle.

lv/2∫z′=−(lp+lv/2)

π∫φ′=0

I(z′)e−jk0R

Rdφ′dz′ = (A cos k0z +B sin k0z)

·−j2πψ0

λE0

sinθiejk0zcosθi

·j4π2

ψ0

z∫t=−(lp+lv/2)

Zi(t)I(t)sink0(z − t)dt

(5.11)


where,

Zi(z) =Ziv, − lv/2 ≤ z ≤ lv/2

=Zip, − (lp + lv/2) ≤ z ≤ −lv/2

(5.12)

R =

√[(z − z′)2 + 4a2sin2

(φ′

2

)](5.13)

where,

k0 = propagation constant in air

ψ0 = characteristic impedance of air.

A and B are constants that are to be determined by imposing the boundary condition

that the current at the end points of the thin wire is zero as it is open circuited. This means

that, I(-(lp + lv/2))=0 and I(lv/2)=0. This equation can be solved by assuming piece wise

linear approximation [155] for each small sections of the thin wire starting from one end of

the wire, say the plume end. In each of these small sections, the current is assumed to be

constant. This process is continued till the vehicle open end is reached. By applying the

boundary conditions and the piece wise linear technique [155], a matrix of induced current

that is finally to be computed is derived.

To apply method of moments to a thin wire model, the following assumptions [154] are

used:

• Length to diameter ratio of the vehicle and plume, l = (lp + lv), is assumed to be very

large, i.e., (lp + lv)/2a1.

• The vehicle is assumed to be in the far field from the HPEM sources and also from

the ground so as to make good the assumption that the incident field is a plane wave.

This is satisfied since the vehicle is assumed to be in flight.

• The details of the junction between the vehicle and the plume are not treated in this

method.

• Plume is considered as a thin cylinder of radius a. The properties of the plume such

as the conductivity and permittivity are determined from the electromagnetic mod-

elling of the plume. In this work, the plume is treated as both homogeneous and non

homogeneous, with the respective properties.


Figure 5.3: Mesh Plot of the Conductivity along the Axial and Radial Direction.

0 1 2 3 4 5 6 7 80.02

0.04

0.06

0.08

0.1

0.12

Axial Position (m)

Co

nd

uct

ivit

y (S

/m)

Figure 5.4: Conductivity of the Exhaust Plume along the Axial Position.

Figure 5.5: Thin Wire Model of the Vehicle with the Exhaust Plume for Coupling Analysis.


5.7 Validation of the Method Used

The method of moment is used to compute the induced current in a vehicle, here referred to

as a missile, and the result so obtained is compared with the results in [154] for validation.

Here the parameters for computation are:

lp = 5.54lv

Conductivity of exhaust plume = 0.25 S/m

(lp + lv)/a = l/a = 157

Conductivity of the missile (vehicle) = 3.54×107 S/m

λE0 = 1

θi = 900

The electrical length of the missile 0.1 ≤ (lv/λ) ≤ 0.5

Considering that the plume is homogeneous, the induced current in the missile is com-

puted using equation 5.11 the above parameters. Computations were also repeated for the

case without the plume and the results are plotted in Fig. 5.6,Fig. 5.8, Fig. 5.10 and Fig.

5.12. The results are compared with the available results in the literature [154] as shown in

Fig. 5.7, Fig. 5.9, Fig. 5.11 and Fig. 5.13. Fig. 5.6 and Fig. 5.7 compares the induced

current on the missile at different wavelengths of the incoming field without the plume. Both

the results are closely matching and it is seen that the current builds up at the centre of

the missile and is zero at either ends. With the variation in the wavelength, current peaks

at the centre of the missile when lv/λ is close to 0.5. The frequency corresponding to this

wavelength causes resonance to occur and causes a rise in the current. When the plume is

present, the current at the tail end of the missile from where the plume starts, has some

current that is different from zero. This plot is shown in Fig. 5.8 and is compared with Fig.

5.9 which is taken from [154]. This is the effect of the finite conducting plume and hence

the current becomes zero at the bottom most point of the plume. The induced current in

the missile for two resonance lengths of the vehicle is plotted in Fig. 5.10 and Fig. 5.12.

This computed result is compared with that published by [154] as Fig. 5.11 and Fig. 5.12.

Two resonance lengths are considered, which are lv = 0.39 λ and lv = 0.09 λ. The major

observations are:

Electrically short missile:

5.8. Results and Discussions 121

The induced current in the missile is 0.06 mA. The presence of the plume causes an

increase in the current in the vehicle, and the current becomes 0.14 mA. The current is the

least at the tail end of the vehicle.

Vehicle with the length equal to resonance length:

For a vehicle with its length equal to the resonance length, the induced current in the

missile is 3.5 mA, which drops to 2.5 mA in the presence of the plume.

The current is the least at the centre of the total length of the plume and the missile and

maximum at the tail end of the missile.

Inferences:

The tail end of the vehicle has more induced current for an electrically short missile. This

is a disadvantage as it will lead to more current getting into the vehicle structure, through

the apertures that will lead to damaging the control circuits.

5.8 Results and Discussions

A sketch of the airborne vehicle used in the present work is as shown in the Fig. 5.5. The

length and radius of the vehicle are 20 m and 0.5 m respectively. The active length of the

exhaust plume is 75 m. The conductivity of the vehicle is taken as 3.54×107 S/m and the

conductivity of the exhaust plume is taken from Fig. 5.4, which is computed for the whole

length of the plume. Two types of exhaust plumes are considered, one is a homogeneous

exhaust plume, where the plume conductivity is same over the entire length of the plume.

This conductivity for the present work is 0.12 S/m, which is the maximum conductivity of

the exhaust plume. The effect of all the three types of HPEM sources with the vehicle is

computed using the equation 5.27. The coupling of the HPEM sources with the vehicle can

be schematically shown in Fig. 5.14. Nuclear EMP is a high altitude burst and HPM and

IRA are located at heights of 100 m above the earth’s surface. The vehicle is assumed to be

at a height of 600 m above the earth’s surface.

The induced current is computed at three different points on the vehicle:

• At the nose, at 97.5% of lv

• At the midpoint of the vehicle, at 47.5% of lv

• At the tail end of the missile, at 2.5% of lv


0.1

0.2

0.3

0.4

0.5

00.2

0.40.6

0.81

0

2

4

6

lm/lam

w/l

Mag

nit

ud

e o

f in

du

ced

cu

rren

t (

mA

)

1

2

3

4

5

Figure 5.6: Computed Induced Current

in the Missile Without Plume at Differ-

ent Wavelengths of the Incoming Field

for the Canonical example.

Figure 5.7: Induced Current in the Mis-

sile Without Plume at Different Wave-

lengths of the Incoming Field for the

Canonical example [154].

0.10.2

0.30.4

0.5

0

0.5

1

0

1

2

3

lm/lamw/l

Mag

nit

ud

e o

f in

du

ced

cu

rren

t (m

A)

0.5

1

1.5

2

2.5

Figure 5.8: Computed Induced Current

in the Missile with Plume at Different

Wavelengths of the Incoming Field for

the Canonical example.

Figure 5.9: Induced Current in the

Missile with Plume at Different Wave-

lengths of the Incoming Field for the

Canonical example [154].

0 0.1 0.2 0.3 0.4 0.5 0.60

0.05

0.1

.15

w/lam

Mag

nit

ud

e o

f in

du

ced

cu

rren

t (m

A) missile

missile with plume

Figure 5.10: Computed Induced Cur-

rent in the Missile With and Without

Plume for an Electrically Short Missile

for the Canonical example.


Missile With and Without Plume for an

Electrically Short Missile for the Canon-

ical example [154].


0 0.5 1 1.5 2 2.50

1

2

3

4

w/lam

Mag

nit

ud

e o

f in

du

ced

cu

rren

t (m

A) missile

missile with plume

Figure 5.12: Computed Induced Cur-

rent in the Missile with and without

Plume for the Vehicle Length equal to

its Resonance Length for the Canonical

example.


Missile with and without Plume for the

for the Vehicle Length equal to its for

the Canonical example [160].

Figure 5.14: Coupling of the Fields due to HPEM Sources with an Airborne Vehicle .

Figure 5.15: The Observation Points for the Computation of the Induced Current in a Vehicle

.


These three points are shown in Fig. 5.15 for the vehicle. The induced voltage computed

is the difference between the voltages at the tail and the nose end of the vehicle. The induced

current and voltage is computed for three cases:

• The vehicle alone.

• Vehicle in the presence of a homogeneous plume

• Vehicle in the presence of an inhomogeneous plume

5.8.1 Coupling of NEMP with missile

The NEMP electric field is modelled according to the IEC 61000-2-9 as explained in the

chapter 2. These currents are plotted in Fig. 5.16 to Fig. 5.18. The induced current in

the vehicle without plume is extremely oscillatory with an exponential decay in the peak

magnitude with respect to time. But when an exhaust plume is present, the characteristics

of the current waveform changes to a smooth one that almost has the double exponential

behaviour of the interfering NEMP field. The magnitude of the current increases from 7 A

peak in the case when the plume is absent to 9 A in the presence of the plume at the nose of

the vehicle (Fig. 5.16). This current is 2 A at the tail end of the vehicle without the plume

and is 35 A with the plume present (Fig. 5.17). At the midpoint of the vehicle these values

are respectively 16 A and 27 A (Fig. 5.18). There is a large shoot up in the magnitude of

the current at the tail end in the presence of the conducting plume as compared to other

points, because of the conducting species in the plume that starts from the tail end of the

vehicle which adds to the contribution of the induced current and also, it acts as a channel

that routes the current to the vehicle. These currents can easily penetrate into the inner

circuitry of the vehicle causing more destruction.

The induced current over the entire vehicle and plume is plotted in Fig. 5.19 for all the

three cases explained in the previous section. The peak currents are 10 A, 70 A and 110 A

for a vehicle without plume, for a vehicle with an inhomogeneous plume and for a vehicle

with a homogeneous plume of conductivity 0.12 S/m as in the Fig. 5.19 respectively . The

induced current in the whole structure is highest for the third case, as the plume offers a

maximum conductivity that will cause higher currents to get coupled with the vehicle and

also with the plume. In the case of a non homogeneous plume there is a gradual distribution

of the conductivity, which peaks only at the tail end of the vehicle where the plume starts.


But once it gets out of this point then the plume resistivity increases and this affects the

overall distribution of the current. It is due to this increase in the resistivity of the plume

the oscillations that are present in the induced current in the vehicle are damped out when

plume is present. The current peaks at the midpoint of the vehicle when there is no plume

and for the cases with plumes present, the peak value of the current occurs at the centre of

the vehicle plume structure.

The rate of change of the current follow a similar pattern that is oscillatory in nature

if there is no plume present and if the plume is presen as shown in Fig. 5.20 to Fig.

5.22t, then the pattern changes from the oscillatory nature to one with both negative and

positive variations this switching over takes place due to the falling and rising portions of

the induced current. The peak value of d1/dt is 40 A/s without plume and 80 A/s with a

non homogeneous plume (Fig. 5.20) at the nose of the vehicle and these are 40 A/s and 310

A/s at the tail end of the vehicle (Fig. 5.21) and are 55 A/s and 190 A/s respectively at the

midpoint of the vehicle (Fig. 5.22). Again the tail end is the more prominent region where

the rate of change of current can be too high. the induced voltage between the endpoints of

the vehicle is shown in Fig. 5.23 which shows the maximum voltage induced to be 78 V and

58 V respectively for a vehicle without plume and a vehicle with plume.

5.8.2 Coupling of IRA

The IRA is assumed to be located at a height of 100 m from the earth’s surface and the

vehicle is assumed to be at a height of 800 m above the earth’s surface. The induced

current is computed at the nose, tail and the midpoint of the vehicle under this excitation

source. These results are plotted in Fig. 5.24 to Fig. 5.26. The induced current has a peak

magnitude of 4 A and 5 A respectively without and with the plume at the nose end of the

vehicle. At the tail end these values are respectively 4 A and 92 A and at the midpoint these

are 27 A and 49 A respectively. The induced current plot for the vehicle without plume

is oscillatory and also the envelope of the current plot exponentially decays and comes to

zero, again rises to a second peak and falls off to a second zero and this continues, with the

peak value of each additional envelope themselves are exponentially decaying in magnitude.

There are mainly two frequencies of oscillation for the current, one frequency, and the larger

one corresponding to the step in the length chosen for computation, which is the frequency

for the oscillations inside the envelope. The smaller frequency corresponds to the frequency,


0 20 40 60 80 100−10

−5

0

5

10

Time (ns)

Indu

ced

curr

ent (

A)

With exhaust plumeWithout exhaust plume

Figure 5.16: Induced Current at the Nose due to an NEMP Electric Field.

0 20 40 60 80 100−40

−30

−20

−10

0

10

Time (ns)

Indu

ced

curr

ent (

A)


Figure 5.17: Induced Current at the Tail due to an NEMP Electric Field.

0 20 40 60 80 100−30

−20

−10

0

10

20

Time (ns)

Indu

ced

curr

ent (

A)


Figure 5.18: Induced Current at the

Midpoint of the Vehicle due to an

NEMP Electric Field.

0 20 40 60 80 1000

50

100

150

Distance along the missile (m)

Mag

nit

ud

e o

f in

du

ced

cu

rren

t (A

)

Vehicle with inhomogeneous plumeVehicle without exhaust plumeVehicle with homogeneous plume

Figure 5.19: Variation of the Induced

Current along the Length of the Missile

and its Plume due to an NEMP Electric

Field.


0 20 40 60 80 100−100

−50

0

50

Time (ns)

di/d

t (A

/ns)


Figure 5.20: Derivative of Induced Current at the Nose due to an NEMP Electric Field.

0 20 40 60 80 100−350

−300

−250

−200

−150

−100

−50

0

50

100

Time (ns)

di/d

t (A

/ns)


Figure 5.21: Derivative of Induced Current at the Tail due to an NEMP Electric Field.

0 20 40 60 80 100−200

−150

−100

−50

0

50

100

Time (ns)

di/d

t (A

/ns)


Figure 5.22: Derivative of Induced Cur-

rent at the Midpoint of the Vehicle due

to an NEMP Electric Field.

0 20 40 60 80 100−80

−60

−40

−20

0

20

40

60

80

Time (ns)

Indu

ced

volta

ge (

V)


Figure 5.23: Induced Voltage Between

the Endpoints due to an NEMP Electric

Field.


at which the envelopes themselves appear, which depends upon the time taken by each

travelling wave formed due to the induced current to reappear at the same point a second

time. The insertion of the non homogeneous plume causes the waveform to be smooth with

a single negative portion followed by a positive part, the negative portion being controlled

by the prepulse of the incident IRA field and the positive part by the impulse region of the

IRA field. There is an increase in the current magnitude if the plume is present, which is

mainly due to the presence of a finite conductivity exhaust gas that adds to the net current

contribution to the vehicle and also to the plume. Fig. 5.27 shows that the peak current is 20

A, 140 A and 255 A respectively for a vehicle with no plume present, with a non homogeneous

plume and for a homogeneous plume respectively. The reason for this response is the variable

conductivity of the plume in all the three cases. Also the homogeneous plume that has the

maximum conductivity causes more induced current and hence a higher interference to the

systems connected inside the vehicle. Hence the systems inside the vehicle should have

sufficient hardening to take care of this situation.

The rate of change of current also follows a similar pattern as current waveform when

there is no plume present, but in the presence of the plume the waveform is as shown in Fig.

5.28 to Fig. 5.30 for the nose, tail and the midpoint respectively. The zero crossings in the

waveform correspond to the points where induced current has minima and maxima points.

The peak magnitudes of di/dt are 34 A/ns and 45 A/ns for the missile in the absence and

presence of the plume respectively. These are respectively 34 A/ns and 720 A/ns for the

tail end of the vehicle and are respectively 200 A/ns and 450 A/ns for the midpoint of the

vehicle. A higher di/dt and current in the case of the IRA field adds to the damage potential

of this field.

The induced voltage between the endpoints of the vehicle is 140V and 160V respectively

for the vehicle without the plume and with the non homogeneous plume as in Fig. 5.31.

The waveform of the induced voltage is of the similar pattern as that of the current, and

the characteristics of the voltage is also identical. The induced voltage has a pattern similar

to that of the di/dt of the current, which indicates the reactive nature of the vehicle rather

than being resistive in nature. This nature imposes a higher induced voltage on account of

the rate of change of the magnetic field due to the currents in the vehicle structure.


2400 2450 2500 2550−10

−7.5

−5

−2.5

0

2.5

5

7.5

10

Time (ns)

Indu

ced

curr

ent (

A)

Vehicle without exhaust plumeVehicle with exhaust plume

Figure 5.24: Induced Current at the Nose due to an IRA Electric Field.

2400 2450 2500 2550−100

−75

−50

−25

0

25

50

75

100

Time (ns)

Indu

ced

curr

ent (

A)


Figure 5.25: Induced Current at the Tail due to an IRA Electric Field.

2350 2400 2450 2500 2550−50

−40

−30

−20

−10

0

10

20

30

40

50

Time (ns)

Indu

ced

curr

ent (

A)



Midpoint of the Vehicle due to an IRA

Electric Field.

0 20 40 60 800

50

100

150

200

250

300

350

400


Mag

nit

ud

e o

f in

du

ced

cu

rren

t (A

)

Vehicle without plumeVehicle with inhomogeneous plumeVehicle with homogeneous plume


Current along the Length of the Missile

and Plume due to an IRA Electric Field.


2400 2450 2500 2550−50

−40

−30

−20

−10

0

10

20

30

40

50

Time (ns)

di/d

t (A

/ns)


Figure 5.28: Derivative of Induced Current at the Nose due to an IRA Electric Field.

2400 2450 2500 2550−800

−600

−400

−200

0

200

400

600

800

Time (ns)

di/d

t (A

/ns)


Figure 5.29: Derivative of Induced Current at the Tail due to an IRA Electric Field.

2350 2400 2450 2500 2550−500

−400

−300

−200

−100

0

100

200

300

400

500

Time (ns)

di/d

t (A

/ns)




to an IRA Electric Field.

2400 2450 2500 2550−200

−150

−100

−50

0

50

100

150

200

Time (ns)

Indu

ced

volta

ge (

V)



the Endpoints due to an IRA Electric

Field.


5.8.3 Coupling of HPM

The high power microwave source is located at a height of 100 m from the earth’s surface and

the vehicle is located at a height of 800 m from the ground. The induced current is plotted

in Fig. 5.32, to Fig. 5.34 respectively for the nose, tail and the midpoint of the vehicle.

The maximum value of the induced current is 14 A and 20 A respectively for the vehicle

without plume and with plume. These currents are 14 A and 350 A at the tail end and are

100 A and 200 A at the midpoint. The waveform of the current without plume is oscillatory

with an exponential decay. The frequency of these oscillations is 1 GHz, the frequency of

the input field. If there is plume present, then the current has a waveform that is having a

shape similar to the interfering HPM field and with the frequency of GHz, but the repeated

oscillations in the case if plume is not there are absent as against the case when the plume is

present. In the case of NEMP and IRA, the oscillations in the induced current if the plume

is not there, are governed by the incremental step in the length taken, but with HPM it is

the characteristics of the field that governs the pattern of the current. The peak induced

current is 100 A, 500 A and 1400 A as shown in Fig. 5.35 for a vehicle without plume,

with a non-homogeneous plume and the vehicle with a homogeneous plume respectively. it

is reported in [100] that at a frequency of 2.29 GHz, loss tangent of the exhaust plume is

1, so the exhaust plume behaves as a good conductor for EM waves having frequency close

to 2.29 GHz. This effect is reflected in the current waveform since the HPM frequency is

1 GHz, where the plume has a tendency to be more conductive, that causes a rise in the

induced current magnitude.

The di/dt value for the vehicle without plume is 110 A/ns and is 145 A/ns with the plume

present at the nose of the vehicle. These values are respectively 110 A/ns and 2700 A/ns

at the tail end of the vehicle and are respectively 750 A/ns and 1500 A/ns at the midpoint

of the vehicle. these plots are shown in Fig. 5.36 to Fig. 5.38 The response of the induced

current follows a similar pattern as that of the current, because of its sinusoidal nature. The

di/dt values are the highest for the HPM as compared with the other HPEM sources. This

increases the destructive potential of the HPM sources to the vehicle. If there are apertures,

the HPM imposes further threat as it can easily get into the system and affect the circuits

inside.

The induced voltage in the vehicle between its endpoints is 480 V and 590V respectively

for a vehicle without the plume and a vehicle with plume as shown in Fig. 5.39. The


characteristics of the voltage waveform are similar in pattern to that of the induced current

pattern.

5.9 Chapter summary

Coupling of the EM fields due to the HPEM sources with an airborne vehicle is computed.

The airborne vehicle is in flight and is assumed to be at a height of 800 m above the earths

surface. The HPEM sources are located at a height of 100 m except NEMP, which is a high

altitude burst. Based on the electric field along the surface of the vehicle structure, at all

points on the surface along its axis, a distributed excitation system can be arrived at. This

field forms the source for the generation of the currents and voltage along the vehicle and

the plume. Based on the computations the important inferences obtained are as follows:

• The species of the exhaust plume depends upon the chemical reactions taking place in

the combustion chamber of the nozzle.

• The presence of the alkali metals as impurity in the airborne vehicle propellant will

generate considerable ion particles such as Na+, Cl− in addition to e− in the plume

mixture during combustion which makes the plume electrically conducting. But it does

not influence the pressure, temperature and velocity of the plume.

• After the nozzle throat, the exhaust plume regains the supersonic speed, so the flow of

the exhaust plume is assumed as a compressible flow in the second region.

• The electrons have high collision frequency, high number density, high plasma frequency

and lower molecular mass and hence the highly mobile electrons dominate the heavy

ion particle in the computation of the electrical conductivity of the plume.

• The plume conductivity decreases marginally from the axis till a distance equal to the

nozzle radius but the peak value increases sharply towards the exit plane edge of the

nozzle radius. In the study, the peak value of the plume conductivity is found to be

0.12 S/m and it decreases to 0.02 S/m at an axial distance of 7.5 m from the exit plane

of the vehicle.

• At a frequency of 2.285 GHz, loss tangent of the exhaust plume is 1, so the exhaust

plume in the present study behaves as a good conductor.

5.9. Chapter summary 133

2389 2390 2391 2392 2393 2394 2395 2396 2397−20

−15

−10

−5

0

5

10

15

20

Time (ns)

Indu

ced

curr

ent (

A)


Figure 5.32: Induced Current at the Nose due to an HPM Electric Field.

2389 2390 2391 2392 2393 2394 2395 2396 2397−400

−300

−200

−100

0

100

200

300

400

Time (ns)

Indu

ced

curr

ent (

A)


Figure 5.33: Induced Current at the Tail due to an HPM Electric Field.

2355 2356 2357 2358 2359 2360 2361 2362 2363 2364−200

−150

−100

−50

0

50

100

150

200

Time (ns)

Indu

ced

curr

ent (

A)



Midpoint of the Vehicle due to an HPM

Electric Field.

0 20 40 60 800

500

1000

1500

2000


Mag

nit

ud

e o

f in

du

ced

cu

rren

t (

A)

Vehicle without plumeVehicle with inhomogeneous plumeVehicle with homogeneous plume


Current along the Length of the Mis-

sile and Plume due to an HPM Electric

Field.


2389 2390 2391 2392 2393 2394 2395 2396 2397−150

−100

−50

0

50

100

150

Time (ns)

di/d

t (A

/ns)


Figure 5.36: Derivative of Induced Current at the Nose due to an HPM Electric Field.

2389 2390 2391 2392 2393 2394 2395 2396 2397−3000

−2000

−1000

0

1000

2000

3000

Time (ns)

di/d

t (A

/ns)


Figure 5.37: Derivative of Induced Current at the Tail due to an HPM Electric Field.

2355 2356 2357 2358 2359 2360 2361 2362 2363 2364−1500

−1000

−500

0

500

1000

1500

Time (ns)

di/d

t (A

/ns)




to an HPM Electric Field.

2389 2390 2391 2392 2393 2394 2395 2396 2397−600

−400

−200

0

200

400

600

Time (ns)

Indu

ced

volta

ge (

V)



the Endpoints due to an HPM Electric

Field.

5.9. Chapter summary 135

• The induced current depends upon the type of interference source, its characteristics,

whether the plume is present or not and the type of the plume.

• The HPM induces maximum current in the vehicle because of the fact that the plume

has a tendency to become more conductive at these frequencies. The IRA field and

the NEMP field follows HPM in its effect.

• The presence of the plume enhances the magnitude of the induced current. If the

plume is homogeneous then the current induced in it is more.

• The waveform of the induced current depends upon the incremental step in length if

the HPEM source is NEMP, depends upon the step in length and also the distance

travelled by the given pulse to reach the same point a second time, if the source of

interference is IRA and it depends upon the source characteristics alone if the source

is HPM.

Chapter 6

Conclusions

The HPEM sources are a major source of interference to electrical and electronic systems

that can possibly lead to a permanent damage or at least a temporary malfunctioning of the

equipments. Hence it is worthwhile to analyse the interaction of the radiated electric fields

from these sources with systems. In this thesis a buried cable and an airborne vehicle in

flight has been considered. The source characteristics are analysed from the data available

from the literature and the electric field is computed at any point from the HPEM sources,

based on their characteristic properties.

NEMP field at earth’s surface is modelled using the specifications given in the IEC

standard 61000-2-9 is used. The radiation pattern is calculated for the IRA using the aperture

integration using the aperture field which is shown in the chapter 2. The HPM field is

computed at the observation point using the non uniform aperture field. The electric field

at any point is a function of the type of the source and the characteristics of the source.

The maximum electric field occurs at the boresight. For an IRA, the shape of the radiation

pattern of the electric field is decided by the frequency, and also whether the observation

point is in the near or the far field with respect to the antenna.Polar plot of the radiation

pattern has no side lobes till the frequency is 50 MHz if the observation point is at 5m

but after wards it changes to irregular patterns with side lobes. Polar plot is having no

side lobes till 1500 MHz if the observation point changes to 100 m. This is decided by the

distance at which the far field commences for a given frequency. Beam width of the radiation

pattern decreases with an increase in the frequency for any observation point. The gain of the

antenna increases as square of the frequency with each increase in the frequency. The electric

field at the boresight of an IRA has a prepulse that lasts for 8 ns which accounts for the time

taken by the pulse to traverse the reflector diameter before it is felt at the given observation

136

137

point. For an HPM, the field has a centre frequency of 1 GHz, the centre frequency of the

waveguide field. The aperture field along the pyramidal horn antenna is mainly cosine in

nature with a maximum field at the centre of the horn cross section. The electric field at any

observation point is decided by the dimensions of the horn, the dimension of the reflector

antenna that finally radiates the field and also the characteristics of the waveguide field.

The electric field is computed in the air and in the soil for different characteristic proper-

ties of these media, by taking into account the Fresnel reflection and transmission coefficients

of the soil. The electric field propagation in any media is influenced by the properties of

the media, whether it is air or soil. As height increases the magnitude of the electric field

decreases for all types of sources and also the time before which the field waveform starts

is increased. The electric field in the soil is decided by the soil properties such as its con-

ductivity and permittivity. The soil is modelled in such a manner that its conductivity and

permittivity values are taken as a function of the frequency by giving due attention to the

high frequency behaviours of soils as the incident field has high frequency components. For

low soil conductivities the attenuation constant of the soil saturates soon, but it takes more

frequencies to saturate if the conductivity increases. For low soil conductivities, the conduc-

tion current to displacement current is low and it increases at higher conductivity. The skin

depth follows a reverse trend. A soil medium can be electromagnetically viewed as a four

component dielectric mixture consisting of soil particles, air voids, bound water, and free

water. When electric field is incident on the soil, it is polarized as a result of a wide variety

of processes, including polarization of electrons in the orbits around atoms, distortion of

molecules, reorientation of water molecules, accumulation of charge at interfaces, and elec-

trochemical reactions. Whatever is the HPEM source, an increase in the soil conductivity

results in more attenuation of the field. Also there is a significant loss of high frequency

components in the GHz range in the field due to selective absorption by the soil. This effect

cause the percentage attenuation to be maximum for HPM and minimum for NEMPand

IRA lying in between these two extremities. This is because HPM is mainly a narrow band

source with high frequency components in the GHz range, IRA has both GHz and MHz

frequencies, NEMP mainly having frequencies in the MHz range. Increase in permittivity of

the soil causes more attenuation of the electric field for all HPEM sources. This is due to the

relaxation mechanisms in the soil due to atomic- or molecular-scale resonances. As the depth

of burial of the cable increases, the field has to penetrate more through the soil medium,

hence suffering from increased opposition due to soil particles. Hence the field magnitude

138 Chapter 6. Conclusions

drops at higher depths. Soils in the city industrial areas have a higher field penetration and

soils in the moist wet lands provides the maximum attenuation.

This chapter deals with the computation of the induced current and voltage in a buried

cable. Two cables are considered - shielded cable and twisted pair cable. The results are

arrived at using the Enhanced Transmission Line model which is explained in the chapter.

The validation of the present model is done with the help of NEC V- 4 full wave analysis

and the results are found to be closely matching. The induced current is more for a shielded

cable than a twisted pair cable of the same configuration. The induced current magnitude

depends upon the type of the HPEM source, the depth of burial of the cable and the point

on the cable where the current/ voltage is computed. Current is maximum at the centre

of the cable for a matched termination and the voltage is the minimum at this point. The

percentage of the induced current in the inner conductor with respect to the shield current of

a shielded cable is the least for an HPM, then comes the IRA and finally NEMP. This is due

to the fact that higher frequencies are absorbed more by the shield of the cable. This affects

the induced voltage due to HPM the maximum and induced voltage due to NEMP the least

because of the presence of the lower frequency components in NEMP. Induced current in the

twisted pair cable depends upon the number of pairs of the cable and the pitching of the

cable for a given HPEM source. The percentage variation in the current between the induced

currents in the shielded and twisted pair cable is 67 for the NEMP, 40 for IRA and 37.5 for

the HPM. This is due to the fact that the smaller variations in the conductor dimensions are

negligible for frequencies in the GHz range. For the twisted pair cables, when the pitching

is equal to 4.5 times the diameter saturation limit of the induced current is reached. With

decrease in the pitching below this value, the current reduces proportionately. This can be

attributed to the reduction of the mutually induced currents when the twisting becomes

closer.

Coupling of the EM fields due to the HPEM sources with an airborne vehicle has also

been studied in this thesis. The airborne vehicle is in flight and is assumed to be at a height

of 800 m above the earths surface. The HPEM sources are located at a height of 100m

except NEMP, which is a high altitude burst. Based on the electric field along the surface

of the vehicle structure, at all points on the surface along its axis, a distributed excitation

system can be arrived at. This field forms the source for the generation of the currents and

voltage along the vehicle and the plume. The species of the exhaust plume depends upon the

chemical reactions taking place in the combustion chamber of the nozzle. The presence of

139

the alkali metals as impurity in the airborne vehicle propellant will generate considerable ion

particles such as Na+, Cl- in addition to e- in the plume mixture during combustion which

makes the plume electrically conducting. But it does not influence the pressure, temperature

and velocity of the plume. After the nozzle throat, the exhaust plume regains the supersonic

speed, so the flow of the exhaust plume is assumed as compressible flow in the second region.

The electrons have high collision frequency, high number density, high plasma frequency and

lower molecular mass and hence the highly mobile electrons dominate the heavy ion particle

in the computation of the electrical conductivity of the plume. The plume conductivity

decreases marginally from the axis till a distance equal to the nozzle radius but the peak

value increases sharply towards the exit plane edge of the nozzle radius. In the study, the

peak value of the plume conductivity is found to be 0.12 S/m and it decreases to 0.02 S/m

at an axial distance of 7.5 m from the exit plane of the vehicle. At a frequency of 2.285 GHz,

loss tangent of the exhaust plume is 1, so the exhaust plume in the present study behaves as

a good conductor. The induced current is computed using method of moments as it is found

to be more appropriate to an airborne vehicle in flight. The induced current depends upon

the type of interference source, its characteristics, whether the plume is present or not and

the type of the plume. The HPM induces maximum current in the vehicle because of the

fact that the plume has a tendency to become more conductive at these frequencies. The

IRA field and NEMP field follows HPM in its effect. The presence of the plume enhances the

magnitude of the induced current. If the plume is homogeneous, then the current induced in

it is more. The waveform of the induced current depends upon the incremental step in the

length if the HPEM source is NEMP, whereas it depends upon the incremental step in the

length and also the distance travelled by the given pulse to reach the same point a second

time, if the source of interference is IRA and it depends upon the source characteristics alone

if the source is HPM.

Scope of future work

The research work in this thesis can be extended further by including the following points:

• Experimental validation of the coupling of the HPEM sources with the buried cable.

• Experimental validation of the coupling with the airborne vehicle in the presence of

the exhaust plume due to HPEM sources.

• The coupling of transient electromagnetic fields with an airborne vehicle for different

140 Chapter 6. Conclusions

propellants used (such as liquid propellants instead of solid propellants as in the present

case).

References

[1] Daniel Mansson, Rajeev Thottappillil and Mats Backstrom, “Methodology for Classifying

Facilities with Respect to Intentional EMI”, IEEE Trans. on Electromag. Compat., Vol.

51, no. 1, pp. 46–52, Feb 2009.

[2] J. Delsing, , J. Ekman, J. Johansson, S. Sundberg, M. Backstrom and T. Nilsson, “Sus-

ceptibility of Sensor Networks to Intentional Electromagnetic Interference ”, Proc. 17th

Int. Zurich Symp. on Electromagn. Compat., pp. 172–175, Mar 2006.

[3] Daniel Mansson, Mats Backstrom and Rajeev Thottappillil, “Intentional EMI Against

Critical Infrastructures, a Discussion on Mitigation Philosophy”, In Proc. Asia-Pacific

Int. Symp. on Electromagn. Compat., pp. 134–137, Beijing, April 2010.

[4] Mats G. Backstrom, and Karl Gunnar Lovstrand , “Susceptibility of Electronic Systems

to High-Power Microwaves: Summary of Test Experience”, IEEE Trans. on Electromag.

Compat. , Vol. 46, no. 3, pp. 396–403, Aug 2006.

[5] Rajeev Thottappillil, Daniel Mansson and Mats Backstrom, “Response of Electrified

Railway Facilities to Intentional Electromagnetic Interference -Review of Research at

Uppsala University”, Asia-Pacific Symp. on Electromag. Compat., pp. 291–294, Singa-

pore, May 2008.

[6] Daniel Nitsch, Michael Camp, Frank Sabath, Jan Luiken ter Haseborg and Heyno Garbe,

“Susceptibility of Some Electronic Equipment to HPEM Threats”, IEEE Trans. on Elec-

tromagn. Compat., Vol. 46, no. 3, Aug 2004.

[7] William A. Radasky and Manuel. W. Wik, “Overview of the Threat of Intentional Elec-

tromagnetic Interference (IEMI)”, IEEE Int.Symp. on Electromag. Compat.,pp. 1024–

1027, May 2003.

141

142 References

[8] William A. Radasky , “The Threat of Intentional Electromagnetic Interference (IEMI) to

Wired and Wireless Systems”, Int. Zurich Symp. on Electromag. Compat., pp. 160–163,

Feb 2006.

[9] Yuri V. Parfenov, Leonid N. Zdoukhov, William A. Radasky, and Michel Ianoz, “Con-

ducted IEMI Threats for Commercial Buildings ”, IEEE Trans. on Electromagn. Com-

pat., Vol. 46, no. 3, pp. 404–411, Aug 2004.

[10] Manuel W. Wik, William A. Radasky, Robert L. Gardner ,“The Threat of Intentional

Electromagnetic Interference”, Asia-Pacific Conf. on Environ. Electromag., pp. 17–19,

Shanghai, May 2000.

[11] Van Keuren and J. Knighten, “Implications of the High-Power Microwave Weapon

Threat in Electronic System Design”, IEEE Int. Symp. On Electromag. Compat., pp.

370-371, Aug. 1991..

[12] William. A. Radasky,Edward Savage, “Intentional Electromagnetic Interference (IEMI)

and Its Impact on the U.S. Power Grid”, Tech. Rep.,Metatech Corporation, Meta- R-323,

Jan. 2010.

[13] William. A. Radasky, “Protection of Commercial Installations from the High-Frequency

Electromagnetic Threats of HEMP and IEMI using IEC standards”, Asia-Pacific Symp.

on Electromag. Compat., pp. 758–761, Beijing, May 2010

[14] D.V. Giri, and F. M. Tesche, “Classification of Intentional Electromagnetic Environ-

ments (IEME)”, IEEE Trans. on Electromagn. Compat., Vol. 46, no. 3, pp. 322–328,

Aug 2004.

[15] W. Radasky, “New Developments in Intentional Electromagnetic Interference (IEMI)

and High-Altitude Electomagnetic Pulse (HEMP) (Invited)”,Proc. Of URSI General As-

sembly, 2005.

[16] Manuel. W. Wik, and William. A. Radasky, “Intentional Electromagnetic Interference

(IEMI)-Background and Status of the Standardization Work in the International Elec-

trotechnical Commission (IEC)”,Proc. Of URSI General Assembly, 2002.

References 143

[17] William A. Radasky, Carl E. Baum, and Manuem W. Wik, “Introduction to the Special

Issue on High-Power Electromagnetics (HPEM) and Intentional Electromagnetic Inter-

ference (IEMI)”, IEEE Trans. on Electromagn. Compat., Vol. 46, no. 3, pp. 314–321,

Aug 2004.

[18] Manuel. W. Wik, and William. A. Radasky, “Development of High-Power Electromag-

netic (HPEM) Standards”, IEEE Trans. on Electromagn. Compat., Vol. 46, no. 3, pp.

439–445, Aug 2004.

[19] W. Radasky, “Progress in the Field of Intentional Electromagnetic Interference (IEMI)

Since the New Delhi General Assembly in 2005 ”,Proc. Of URSI General Assembly, 2008.

[20] Richard Hoad, William A. Radasky, “Progress in IEC SC 77C High-Power Electro-

magnetics Publications in 2009 ”, Asia-Pacific Symp. on Electromag. Compat., pp. 762–

765,Beijing, May 2010.

[21] EMP Engineering and Design Principles, Bell Telephone Laboratories Inc., Whippany,

NJ, 1975.

[22] R. N. Ghose, EMP Environment and System Hardness Design, Don White Consultants

Inc., Gainesville, Virgina, 1984.

[23] S. Glasstone and P.J. Dolan, The Effects of Nuclear Weapons, 3rd Edition, Castle House

Publication Ltd., 1980.

[24] I.N. Mindel,DNA EMP Awareness course Notes , 3rd Edition, I.I.T. Research Institute,

Chicago, Illionis, 1977.

[25] K.S.H. Lee (Ed.),EMP Interaction : Principles, Techniques and Reference Data , Hemi-

sphere Publishing Co., Washington D.C., 1986.

[26] E.J. Lerner, “Electromagnetic Pulses: Potential Crippler,”IEEE Spectrum, Vol. 18, No.

5, pp. 41–46, May 1981.

[27] J.B. Hays, “Protecting Communication Systems from EMP Effects of Nuclear Explo-

sions,”IEEE Spectrum, Vol. 1, No.5, pp. 115–122, May 1964.

[28] W.J. Broad, “Nuclear Pulse (III): Playing A Wild Card”, Science, Vol.212, No. 4500,

pp. 1248–1251, June 1981.

144 References

[29] E.J. Lerner, “EMPs and Nuclear Power,”IEEE Spectrum, Vol. 18, No. 6, pp. 48–49,

June 1981.

[30] L.W. Ricketts, J.E. Bridges and J.Mileta, EMP Radiation and Protective Techniques,

John Wiley and Sons Inc., New York, 1976.

[31] C.L.Longmire, “On the Electromagnetic Pulse Produced by Nuclear Explosions”, IEEE

Trans. on Electromag. Compat., Vol. EMC–20, No.1, pp. 3–13, Feb.1978.

[32] J.S. Forrest, “The Nuclear Electromagnetic Pulse,”IEE Review, Vol. 33, No. 7, pp.

443–444, July 1987.

[33] R.O. Lange, “Simulating the Electrical Effects of Nuclear Detonations,”IEEE Trans. on

Electromag. Compat., Vol. EMC–8, No.4, pp 197-209, Dec. 1966.

[34] C.L. Longmire, “On the Electromagnetic Pulse Produced by Nuclear Explosions”, IEEE

Trans. on Electromag. Compat., Vol. EMC–20, No.1, pp. 3–13, Feb.1978.

[35] C.E. Baum, “EMP Simulators for Various Types of Nuclear EMP Environments: An

interim categorization,”IEEE Trans. on Electromag. Compat., Vol. EMC-20, No. 1, pp.

35–53, Feb. 1978.

[36] Joy Thomas. M, “Developmental Studies of an Electromagnetic Pulse Simulator”, PhD

Thesis, Indian Institute of Science, Bangalore, India, 1993.

[37] J.C. Giles, “A Survey of Simulators of EMP outside the Source Region,”Proc. Int.

Conf. and Workshop on Electromagnetic Interference Compatibilty, Bangalore, India,

Sept. 1987.

[38] I.D. Smith and H. Aslin, “Pulsed Power for EMP Simulation,”IEEE Trans. on Electro-

mag. Compat., Vol. EMC - 20, No. 1, pp. 53–59, Feb. 1978.

[39] H.M. Shen, R.W.P. King and T.T. Wu, “The Exciting Mechanism of the Parallelplate

EMP Simulator,”IEEE Trans. on Electromag. Compat., Vol. EMC-29, No.1, pp. 32–39,

Feb. 1987.

[40] C.E. Baum, D.F. Higgins and D.V. Giri, “Pulser Test Results and Preliminary Esti-

mation of Transient Electric Field Waveforms in ATLAS 1,”ATLAS Memo No. 18, Oct.

1976.

References 145

[41] D.V. Giri, T.K. Liu,F.M. Tesche and R.W.P. King, “Parallel Transmission Line type of

EMP Simulator: A Systematic Review and Recommendations,”Sensor and Simulation

Note No. 261, April 1980.

[42] E.K. Miller, A. J. Poggio and G.J Burke, “An Integro Differential Equation Technique

for Time Domain Analysis of Thin Wire Structures”, J. Computational Physics, Vol.12,

pp.48, 1973.

[43] M. Jung, Th. H.G. G. Weise, U. Braunsberger and F. Sabath, “High Power Compact

UWB-Systems,”in Proc. Int. Conf. Pulsed Power Applications , Gelsenkirchen, Germany,

Mar. 2001.

[44] F. J. Agee and W. D. Prather, “Ultra-Wideband Transmitter Research,”IEEE Trans.

Plasma Sci., Vol. 26, June 1998.

[45] C. E. Baum, W. L. Baker, W. D. Prather, J. M. Lehr, J. P. OLoughlin, D. V. Giri, I.

D. Smith, R. Altes, J. Fockler, D. Mclemore, M. D. Abdalla, and M. C. Skipper, “JOLT:

A highly directive, very intensive, impulse-like Radiator”, Proc. IEEE, Vol. 92, pp, pp.

1096–1109, 2004.

[46] J. R. Mayes and W. J. Carey, ”The Marx Generator as an Ultra Wideband Source”

13th IEEE International Pulsed Power Conference, Las Vegas, NV, July 2001.

[47] Focia, R.J. Frost, C.A., A Compact, “Low Jitter, Fast Rise Time, Gas-Switched Pulse

Generator System with High Pulse Repetition Rate Capability”, 34 th IEEE Int. Conf.

on Plasma Science, pp. 363, June 2007.

[48] Verma R, Shyam A, Chaturvedi S, Kumar R, Lathi D, Sarkar P, Chaudhary V, Shukla

R, Debnath K, Sharma S, Sonara J, Shah K, Adhikary B, Jigna T, Piyush J., “Impulse

Electromagnetic Interference Generator”, Power Modulator Symposium, High-Voltage

Workshop. Conference Record of the Twenty-Sixth International, pp. 543–546, CA, 2004.

[49] Leland H. Bowen, Everett G. Farr, Dean I. Lawry, J. Scott Tyo ,“An Ultra-Compact

Impulse Radiating Antenna”, Sensor and Simulation Notes , Note 494, October 2004.

[50] Lanney M. Atchley, Everett G. Farr, J. Scott Tyo, Noel de la Merced, Larry L. Alt-

gilbers, “Development and Testing of a Parachute Deployable Impulse Radiating Antenna

”, Sensor and Simulation Notes, Note 465, March 2002

146 References

[51] W. D. Prather, C. E. Baum, F. J. Agee, J. P. OLaughlin, D. W. Scholfield, J. W. Burger,

J. Hull, J. S. H. Schoenberg and R. Copeland, “Ultrawide Band Sources and Antennas:

Present Technology, Future Challenges”Ultra-Wideband, Short Pulse Electromagnetics 3,

pp. 43–56, Plenum Press, NY, 1997.

[52] C. J. Buchenauer, J. S. Tyo and J. S. H. Schoenberg, “Antennas and Electric Field

Sensors for Ultra-Wideband Transient Time Domain Measurements: Applications and

Methods”Ultra- Wideband, Short Pulse Electromagnetics 3, pp. 405–422, Plenum Press,

New York, 1996.

[53] J. M. Lehr, M. D. Abdalla, F. Gruner, M. C. Skipper and W. D. Prather, “Development

of a Hermetically sealed, High-Energy Trigatron Switch for High Repetition Rate Ap-

plications,”12th IEEE International Pulse Power Conference, 1999, Monterey, CA, June

27–30, 1999, pp. 146–149.

[54] J. M. Lehr, M. D. Abdalla, J. W. Burger, J. M. Elizondo, J. Fockler, F. Gruner, M.

C. Skipper, I. D. Smith and W. D. Prather, “Design and Development of a 1 MV, Self

Break Switch for high Repetition Rate Operation,”12th IEEE International Pulse Power

Conference, 1999, Monterey, CA, June 27–30, 1999, pp. 1199–1202.

[55] William D. Prather, Carl E. Baum, Jane M. Lehr, Robert J. Torres, Tyrone C. Tran,

Jeffrey W. Burger, John A. Gaudet , “Recent Developments In Ultra-Wideband Sources

and Antennas ”, Ultra-Wideband, Short-Pulse Electromagnetics 5, Edited by P. D. Smith

and S. R. Cloude. Kluwer Academic/Plenum Publishers, 2002.

[56] W. Prather et al., “Ultra wideband sources and antennas,”UltraWideband Short Pulse

Electromagentics 4 . New York: Plenum, pp. 119–130, 1999.

[57] W. D. Prather, C. E. Baum, J. M. Lehr, J. P. OLoughlin, S. Tyo, J. S. H. Schoenberg,

R. J. Torres, T. C. Tran, D. W. Scholfield, J. W. Burger, and J. A. Gaudet, “Ultra-

Wideband Source Research”, IEEE 12th Intern. Pulse Power Conf., Vol. 1, Monterey,

CA., USA, pp. 185–189, 1999.

[58] J. S. H. Schoenberg, J. W. Burger, J. S. Tyo, M. D. Abdalla, M. C. Skipper, and

W. R. Buchwald, “Ultra-Wideband Source using Gallium Arsenide Photo Conductive

Semiconductor Switches,”IEEE Trans. Plasma Sci., Vol. 25, pp. 327–334, Apr. 1997.

References 147

[59] 59. C. E. Baum, E. G. Farr and D. V. Giri, “Impulse radiating antennas,”Ultra Wide-

band/ Short Pulse Electromagentics 2. New York: Plenum, pp. 139–147, 1993

[60] 60. E. G. Farr, Charles. A. Frost, “Development of a Reflector IRA and a Solid Lens

IRA, Part I: Design, Predictions and Construction,”Sensor and Simulation Note 396,

1996.

[61] D. V. Giri, H. Lackner, I. D. Smith, D. W. Morton, C. E. Baum, J. R. Marek, W.

D. Prather, and D. W. Scholfield, “Design, Fabrication, and Testing of a Paraboloidal

Reflector Antenna and Pulser System for Impulse like Waveforms,”IEEE Trans. Plasma

Sci., Vol. 25, pp. 318–326, Apr. 1997.

[62] E. G. Farr, C. E. Baum, and C. J. Buchenauer, “Impulse radiating antennas, Part

II,”Ultra-Wideband, Short Pulse Electromagnetics, H. L. Bertoni, L. Carin, and L. B.

Felsen, Eds. Plenum, New York 1993.

[63] D. V. Giri, J. M. Lehr, W. D. Prather, C. E. Baum and R. J. Torres, “Intermediate and

Far Fields of a Reflector Antenna Energized by a Hydrogen Spark-Gap Switched Pulser,

IEEE Trans. Plasma Sciences, Vol. 28, pp. 1631–1636, October 2000.

[64] C. E. Baum, E. G. Farr and D. V. Giri, “Review of Impulse-Radiating Anten-

nas,”chapter 16, pp 403–439, Review of Radio Science 1996-1999, Oxford University

Press.

[65] C. E. Baum, “Configurations of TEM Feed for an IRA,”Sensor and Simulation Note

327, 27 April 1991.

[66] C. E. Baum, “Variations on the Impulse Radiating Antenna Theme,”Sensor and Sim-

ulation Note 378, February 1995.

[67] E. G. Farr and C. E. Baum, “Feed-Point Lenses for Half-Reflector IRAs,”Sensor and

Simulation Note 385, November 1995.

[68] J. S. Tyo and J. S. H. Schoenberg, “Radiated Field Measurement from a 1-m Diameter

Half IRA,”Sensor and Simulation Note 471, February 1999.

148 References

[69] F. Sabath, D. Nitsch, M. Jung, Th. H. G. G. Weise, “Design and Setup of a short Pulse

Simulator for Susceptibility Investigations,”Sensor and Simulation Note 460, 1 October

2001.

[70] E. G. Farr and G. D. Sower, “Design Principles of Half-Impulse Radiating Antennas,

Sensor and Simulation Note 390, December 1995.

[71] D. V. Giri, High-Power Electromagnetic Radiators: Nonlethal Weapons and Other Ap-

plications, Harvard University Press, November 2004.

[72] W. Woo and D. V. Giri, “Directing HPM Radiation at Targets in Far Fields”, HPM

Research Note, Physics International Company, January 1988.

[73] D. V. Giri, “Preliminary Considerations for High Power Microwave Radiating Systems”,

Circuit and Electromagnetic System Design Note 40, December 28, 1990.

[74] Y.Rahmat-Samii, D.W.Duan, D.V.Giri, and L. F. Libelo, “Canonical Examples of Re-

flector antennas for High Power Microwave Applications,”IEEE Trans. Electromagn.

Compat., Vol. 34, No. 3, pp. 197–205, Aug. 1992.

[75] C. D. Taylor, D. V. Giri, High Power Microwave Systems and Effects , Taylor and

Francis, U. S. A, 1994.

[76] C. E. Baum, “Some Features of Waveguide/Horn Design ”Sensor and Simulation Note

314, 18 November 1988.

[77] E. Schamiloglu, “High Power Microwave Sources and Applications”, Microwave Sym-

posium Digest, IEEE MTT-S International, Vol.2, pp. 1001–1004, June 2004.

[78] Description of HEMP environment-radiated disturbance, IEC Standard 61000-2-9, 1996.

[79] C. A. Balanis, Antenna Theory Analysis and Design, John Wiley Sons Publishers, Inc.,

New York, 2005.

[80] 82. Oleg V. Mikheev, S. A. Podosenov, K .Y. Sakharov, A. A. Sokolov, Y. G. Svekis,

and V. A. Turkin, “New Method for Calculating Pulse Radiation from an Antenna with

a Reflector”, IEEE Trans. on Electromag. Compat., Vol. 39, no. 1, pp. 48–54, Feb 1997.

References 149

[81] C. E. Baum, “Radiation of Impulse-Like Transient Fields”, Sensor and Simulation Note

321, 25 November 1989.

[82] Jinliang He, Baoping Zhang, Rong Zeng, and Bo Zhang, “Experimental Studies of

Impulse Breakdown Delay Characteristics of Soil”, IEEE Trans. Power Delivery, Vol.

26, No. 3, pp. 1600-1607, July 2011.

[83] N. M. Nor, A. Haddad and H. Griffiths, “Determination of Threshold Electric Field,

Ec under High Impulse Currents”, IEEE Trans. Power Delivery, Vol. 20, pp. 2108–2113,

2005.

[84] Ovchinkin O.A. and Sugak, V.G., “The Influence of Soil Electric Properties upon the

Ground-Penetrating Radar (GPR) Signal Characteristics”, Telecommunications and Ra-

dio Engineering, Vol. 57, No’s 1011, pp. 101–109, 2002.

[85] Dobson, M.C., Ulaby, F.T., Hallikainen, M.T. and El-Rayes, M.A “Microwave Dielectric

Behaviour of Wet Soil. Part II: Dielectric Mixing Models”, IEEE Trans. on Geoscience

and Remote Sensing, Vol. 23, pp. 35–46, 1985

[86] Saarenketo, T., “Electrical Properties of Water in Clay and Silty Soils”, Journal of

Applied Geophysics, 40, pp. 73–88, 1998

[87] J.H.Scott, R. D. Carroll and D. R .Cunningham,”Dielectric Constant and Electrical

Conductivity of Moist Rock from Laboratory Measurements”, Sensor and Simulation

Note 116, Kirtland AFB, NM, August 1964.

[88] F. M. Tesche, “On the Modeling and Representation of a Lossy Earth for Transient

Electromagnetic Field Calculations”, Theoretical Note 367, July 9,2002.

[89] S.H. Zainud-Deen, M. E. Badr, E. M. Ali, K. H. Awadalla and H. A. Sharshar, “Effects

of Soil Physical Properties on Landmines Detection using Microstrip Antenna as a Sensor

”, Progress In Electromagnetics Research C, Vol. 7,pp.13–24, 2009

[90] Larisa Pozdnyakova, “Electrical Properties of Soils”, PhD Thesis, University of

Wyoming, Wyoming, 1999.

[91] Jackie E. Hipp, “Soil Electromagnetic Parameters as Functions of Frequency, Soil Den-

sity, and Soil Moisture”, Proc. Of IEEE, Vol. 62, No. 1, pp. 98–103 Jan 1974.

150 References

[92] Ronald. W. P. King, “The Transmission of Electromagnetic Waves and Pulses into the

Earth”, Journal of Applied Physics, Vol. 39, No.9, pp. 4444–4452, Aug 1968.

[93] E. Petrache, M. Paolone, F. Rachidi, C. A. Nucci, V. Rakov , M. Uman, D. Jordan,

K.Rambo, J. Jerauld, M. Nyffeler and J.Schoene, “Lightning induced currents in buried

coaxial cables: A frequency domain approach and its validation using rocket triggered

lightning”, J. Electrostat., Vol.65, No.5-6, pp. 322–328, May 2007.

[94] E. F. Vance, “Internal Voltages and Currents in Complex Cables”, Interaction Note 8,

June 1967.

[95] F. M. Tesche, M. Ianoz, T. Karlsson, EMC Analysis Methods and Computational Models,

Wiley – Interscience, New York, 1997.

[96] E. D. Sunde, Earth conduction effects in transmission systems, Dover, New York, 1968.

[97] Farhad Rachidi and Sergey V. Tkachenko, “Electromagnetic Field Interaction with

Transmission Lines from classical theory to HF Radiation Effects”, WIT Press, Boston,

2008.

[98] Clayborne D. Taylor, J. Philip Castillo, “On the Response of a Terminated Twisted-

Wire Cable Excited by a Plane-Wave Electromagnetic Field”, IEEE Trans. on Electro-

mag. Compat., Vol. EMC-22, No. 1, pp. 16–19, Feb 1980.

[99] D. J. Serafin , D. Dupouy, “Potential IEMI Threats Against Civilian Air Traffic”,Proc.

Of URSI General Assembly, 2005.

[100] Sisir Kumar Nayak, “Transient Lightning Electromagnetic Field Coupling with an

Airborne Vehicle in the Presence of its Conducting Exhaust Plume”, PhD Thesis Indian

Institute of Science, Bangalore, India, 2008.

[101] H. J. Christian, K. Crouch, B. Fisher, V. Mazur, R. A. Perala, and L. Ruhnke, “The

Atlas/Centaur lightning strike incident”, J. of Geophys. Res., Vol. 94, No. D11, pp.

13–169. 13 177, 1989.

[102] R. Godfrey, E. R. Mathews, and J. A. McDivit, “Analysis of Apollo 12 lightning

incident, Marshall Space Flight Center”, Tech. Rep. MSC-01540, NASA–TM–X–62894,

1970.

References 151

[103] J. A. Plumer, J. P. Moreau, and R. F. Hess, “The new aircraft lightning environment

and related test waveforms standard from SAE AE4L and EUROCAE WG31”, Proc.

International Conference on Lightning and Static Electricity , 1999–01–2395, Toulouse,

France, June 1999, pp. 383–391.

[104] M. A. Uman and V. A. Rakov, “The interaction of lightning with airborne vehicles”,

Progress in Aerospace Sciences, Vol. 39, pp. 61–81, 2003.

[105] T. R. Ferguson and R. H. Duncan, “Charged cylindrical tube”, J. of Appl. Phys., Vol.

32, No. 7, pp. 1385–1387, July 1961.

[106] W. R. Smythe, “Charged right circular cylinder”, J. of Appl. Phys., Vol. 27, No. 8, pp.

917–920, Aug 1956.

[107] W. R. Smythe, “Charged right circular cylinder”, J. of Appl. Phys., Vol. 33, No. 10,

pp. 2966–2967, Aug 1962.

[108] C. M. Butler, “Capacitance of a finite-length conducting cylindrical tube”, J. of Appl.

Phys., Vol. 51, No. 11, pp. 5607–5609, Nov 1980.

[109] L. Verolino, “Capacitance of a hollow cylinder”, Electrical Engineering, Springer-

Verlag, Vol. 78, No. 4, pp. 201–107, July 1995.

[110] E. A. Darrow and E. Lays, “Solid propellant rocket exhaust effects and methods of

attenuation”, Martin-Marietta Corporation, Denver, Colorado, Tech. Rep. NAS10-2300,

Martin–CR–65–93, Vol–I, Jan 1966.

[111] E. Lays and E. A. Darrow, “Solid propellant rocket exhaust effects and methods of

attenuation”, Martin-Marietta Corporation, Denver, Colorado, Tech. Rep. NAS10-2300,

Martin–CR–65–93, Vol–II, Jan 1966.

[112] E. Lays, “Design handbook for launch complexes from solid propellant exhaust”, Tech.

Rep. NAS10-2300, Martin–CR–66–11, March 1966.

[113] L. M. Hair and R. E. Somers, “Test data from small solid propellant rocket motor

plume measurements (FA-21)”, Tech. Rep. NASA-CR-150348, RTR–016–4, June 1976.

152 References

[114] D. E. Jensen and H. S. Pergament, “Effects of nonequilibrium chemistry on electrical

properties of solid propellant rocket exhaust plumes”, Combust. and Flame, Vol. 17, pp.

115–124, 1971.

[115] D. E. Jensen, “Competitive Reaction Kinetics in Seeded flames and Rocket Exhausts”,

Combust.and Flame, Vol. 18, pp. 217–223, 1972.

[116] D. E. Jensen and A. S.Wilson, “Prediction of rocket exhaust flame properties”, Com-

bust. and Flame, Vol. 25, pp. 43–55, 1975.

[117] D. E. Jensen and G. A. Jones, “Theoretical Aspects of Secondary Combustion in

Rockets Exhausts”, Combust. and Flame, Vol. 41, pp. 71–85, 1981.

[118] J. M. Cousins and D. E. Jensen, “On the Computation of Ionization Levels in Rocket

Exhaust Flames”, Combust. and Flame, Vol. 52, pp. 111–125, 1983.

[119] J. D. Nordgard and G. S. Smith, “A Plasma Model of Missile Exhaust plume”, Tech.

Rep. RADC–TR–77–144, 1977.

[120] J. D. Nordgard and G. S. Smith, “Electromagnetic Simulation of Missile Exhaust

Plumes”, IEEE Trans. on Electromagn. Compat. , Vol. 29, no. 2, pp. 157–168, May 1987.

[121] R. W. P. King, The Theory of Linear Antenna. Harvard University Press, Cambridge,

MA, 1956.

[122] G. Smith and K. Taylor, “Modelling of Two Phase Rocket Exhaust Plumes and other

Plume Prediction Developments”, 2000, [Online]. Available: www.cham.co.uk/Newvisitor

/cases/plume/plume.doc

[123] C. W. Dennis and P. Sutton, “Assessing Rocket Plume Damage to Launch Vehicles”,

41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit , AIAA 2005–

4163,Tucson, Arizona, July 2005.

[124] S. K. Nayak and M. J. Thomas, “Electrical Characterization of Airborne Vehicle Ex-

haust Plume”, IEEE Trans. on Dielectric and Electrical Insulation,Vol.16, No. 2, April

2009.

References 153

[125] V. Cooray, M. Zitnik, M.Rahman, and Y. Liu, “Physical model of surge-current char-

acteristics of buried vertical rods in the presence of soil ionization”, J. of Electrostatics,

Vol. 60, pp. 193–202, 2004.

[126] M. Barrere, ( Rocket Propulsion), Elsevier, Van Nostrand, New York, 1960.

[127] G. P. Sutton and O. Biblarz, Rocket Propulsion Elements, 7th ed. JohnWiely and Sons,

New York, 2001.

[128] S. Gordon and B. J. McBride, “Computer program for calculation of complex chemical

equilibrium compositions and applications-I: Analysis”, NASA Lewis Research Center,

Cleveland, OH, Tech. Rep. NASA RP–1311, Oct 1994.

[129] B. J. McBride and S. Gordon, “Computer program for calculation of complex chemical

equilibrium compositions and applications II, Users manual and program descriptions”,.

NASA Lewis Research Center, Cleveland, OH, Tech. Rep. NASA RP–1311–P2, June

1996.

[130] E. Orberk, “Internal flow analysis of a technology demonstrator rocket motor with new

CFD code”, 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,

AIAA–98–3967, Cleveland, OH, USA, 1998.

[131] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Taylor and Francis, 1980.

[132] H. K. Versteeg andW. Malalasekera, An Introduction to Computational Fluid Dynam-

ics: The Finite Volume Method, Pearson, Prentice Hall, 1995.

[133] J. O. Hinze, ( Turbulence, McGraw-Hill Publishing Co., New York, 1975.

[134] B. E. Launder and D. B. Spalding, Lectures in Mathematical Model of Turbulence,

Academic Press, London, England, 1972.

[135] V. Yakhot and S. A. Orszag, “Renormalization group analysis of turbulence: I. Basic

Theory”, J. of Scientific Computing, Vol. 1, No. 1, pp. 1–51, 1986.

[136] T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, “A New k- Eddy-Viscosity

Model for Higher Reynolds Number Turbulent Flows- Model, Development and Valida-

tion”, Computer Fluids, Vol. 24, No. 3, pp. 227–238, 1995.

154 References

[137] S. Sarkar and L. Balkrishnan, “Application of a Reynolds-Stress Turbulence Model to

the Compressible Shear Layer”, Tech. Rep. ICASE Report No. 90–18, NASA Contactor

Report 182002, NASA, Langley Research Center, Hampton, VA, Feb 1990.

[138] B. J. McBride, [Online], Available: www. galcit. caltech. edu/EDL/public/

thermo/nasadat

[139] B. J. McBride, M. J. Zehe, and S. Gordon, “NASA Glenn Coefficients for Calculating

Thermodynamic Properties of Individual Species”, Tech. Rep. NASA/TP–2002–211556,

Sep 2002.

[140] Q. Liu and P. Zhang, “Parameter identification of microwave attenuation of solid

rocket exhaust plumes”, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference

and Exhibit, AIAA–95–2591, San Diego, CA, USA, July 1995.

[141] L. D. Smoot and D. L. Underwood, “Prediction of microwave attenuation characteris-

tics of rocket exhausts”, J. Spacecraft, Vol. 3, pp. 302–309, 1966.

[142] A. T. Adams, Electromagnetics for Engineers, Ronald Press, New York, 1972

[143] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics-Vol.

2, Narosa Publishing House, New Delhi, 1998.

[144] J. D. Kraus, Electromagnetics, Mc Graw-Hill, New York, 1991.

[145] R. C. Dorf, The Electrical Engineering Handbook, CRC Press, Boca Raton, FL, 1993,

pp. 935–947.

[146] R. F. Harrington, Field Computation by Moment Methods, The Macmillan Company,

New York, 1968.

[147] C. D. Taylor, “Electromagnetic scattering by thin inhomogeneous circular cylinders”,

Radio Science, Vol. 2, No. 7, pp. 729–738, July 1967.

[148] J. C. W. Harrison and E. A. Aronson, “On the Response of Missile with Exhaust

Trail of Tapered Conductivity to Plane Wave Electromagnetic Field”, IEEE Trans. on

Electromagn. Compat., Vol. 11, no. 2, pp. 40–50, May 1969.

References 155

[149] C. D. Taylor, C.W. H. Jr, and E. A. Aronson, “Resistive Receiving and Scattering

Antenna”, IEEE Trans. on Antenna and Propagation, Vol. 15, No. 3, pp. 371–376, May

1967.

[150] J. C. W. Harrison, “Missile Circumferential Current Density for Plane Wave Electro-

magnetic Field Illumination”, IEEE Trans. on Electromagn. Compat., Vol. 13, No. 2, pp.

35–40, May 1971.

[151] D. E. Merewether, “Transient Current Induced on a Metallic Body of Revolution by

an Electromagnetic Pulse”, IEEE Trans. on Electromagn. Compat., Vol. 13, No. 2, pp.

41–44, May 1971.

[152] D. E. Rosner, “Estimation of Electrical Conductivity at Rocket Nozzle Exit Sections”,

J. Amer. Rocket Soc., Vol. 32, pp. 1602–1605, Oct 1962.

[153] G. S. Smith, J. D. Nordgard,W. A. Holm, and H. L. Bassett, “Electromagnetic Simula-

tion of Missile Exhaust Plumes, Construction and Testing of a Physical Plume Simulator

and the Predicted Results of a Theoretical Thin Wire Rocket/Plume Model”, Tech. Rep.

RADC–TR– 81–8, 1981.

[154] G. S. Smith, J. D. Nordgard, and J. Edwards, “Alteration of the Surface Current on a

Missile by the Presence of an Exhaust Plume”, IEEE Trans. on Electromagn. Compat.,

Vol. 19, No. 4, pp. 383–394, May 1977.

[155] E. A. Aronson, C. D. Taylor, “Matrix Methods for Solving Antenna Problems”, IEEE

Trans. on Antennas and Propagation, pp. 696–697, Sep 1967.

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