DESIGN AND IMPLEMENTATION OF MARX …...The first Marx generator with eight stages, can deliver 64...
Transcript of DESIGN AND IMPLEMENTATION OF MARX …...The first Marx generator with eight stages, can deliver 64...
Republic of Iraq
Ministry of Higher Education and Scientific Research
University of Technology
Laser and Optoelectronics Engineering Department
DESIGN AND IMPLEMENTATION OF
MARX GENERATOR FOR LASER
APPLICATIONS
A Thesis Submitted to
The Laser and Optoelectronics Engineering Department,
University of Technology in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Laser Engineering
By
Eng.
Sarmad Fawzi Hamza B. Sc. Electrical and Electronic Eng. / Laser Eng. 2003
Supervised by
Dr. Naseer Mahdi Hadi Dr. Kadhim Abid Hubeatir
February 2008 A. D. Safer 1429 A. H.
جمھورية العراق
مي لوزارة التعليم العالي والبحث الع الجامعة التكنولوجية
قسم ھندسة الليزر والبصريات االلكترونية
مجهزماركس لتطبيقات بناءتصميم و
الليزر
إلىرسالة مقدمة ةـولوجيـالجامعة التكن ةـريات االلكترونيـزر والبصـة الليـم ھندسـقس
علوم فيمن متطلبات نيل درجة الماجستير كجزء الليزرھندسة
تقدم بھا
المھندس
سرمد فوزي حمزة 2003ھندسة الليزر/ لكترونيةاألوالھندسة الكھربائية
بإشراف
كاظم عبد حبيتر. د نصير مھدي ھادي . د
ھ1429صفر م 2008شباط
الخالصة
وقمة .منظومات الليزر الغازية ذات عرض نبضة خرج قصير إن
طاقة عالية تحتاج إلى نبضات تفريغ كھربائي بمواصفات خاصة مثل محاثة
مجھز قدرة نوع وان .معدل تكرارية للنبضة وزمن نھوض سريع , واطئة
ماركس واطئ المحاثة ممكن أن يوفر ھذا النوع من نبضات التفريغ لتشغيل
. الليزرات الغازية بكامل مواصفاتھا
األول . تم تصميم وبناء وتشغيل نوعين من مجھز قدرة ماركس
ذو ثمانية مراحل تضخيم يمكن أن يوفر فولتية خرج مجھز قدرة ماركس
كيلو فولت وحصلنا 2تم شحن فولتية أولية . كيلو فولت كحد أقصى 64لغاية
666كيلو فولت بنبضة ذات زمن نھوض 12على فولتية خرج فعلية
أما المجھز الثاني فكان , %75وكفاءته مايكرو ھنري 11اثة نانوثانية ومح
كيلو فولت 400مجھز قدرة ماركس ذو عشرة مراحل تضخيم ممكن أن يوفر
كيلو فولت وحصلنا على فولتية خرج 4 تم شحنه بفولتية أولية , كحد أقصى
نانوثانية ومحاثة 50كيلو فولت بنبضة ذات زمن نھوض 38فعلية بحدود
. %95وكفاءته يكرو ھنريما 4.2
األولى , تم تصميم نوعين من دوائر القدح لنوعي مجھز ماركس
ذو دائرة قدح باستخدام مصباح وميضي مع محولة قدح لمجھز ماركس
دائرة مع) إشعال ملف(والثانية باستخدام محولة قدح ثمانية مراحل
.ذو عشرة مراحل لمجھز ماركس ) MOSFET(ترانزستور نوع
لوميضي حوالي اتم الحصول على نبضة فولتية من دائرة المصباح
بينما دائرة القدح , ثانية مايكرو 2 كيلو فولت وعرض نبضة حوالي 4.5
. مايكرو ثانية 40 وعرض نبضة حوالي تكيلو فول 7.5الثانية حوالي
II
Abstract
Gas laser systems with high peak power and short pulse duration
requires special properties of high voltage discharge pulses; i.e. low
inductance, high pulse repetition rate and fast rise time. Low inductance
Marx generator power supply can offer this kind of discharge pulses for the
gas lasers optimum operation.
Two types of Marx generators have been designed, built and tested.
The first Marx generator with eight stages, can deliver 64 kV maximum
output, is charged up to 2 kV and the high voltage output was 12 kV with
pulse rise time of 666 ns and inductance 11 µH and efficiency of 75% .
The second Marx generator with ten stages, can deliver 400 kV maximum
output, is charged up to 4kV and the high voltage output is 38 kV with
pulse rise time 50 ns, inductance 4.2 µH and efficiency of 95%.
Many types of trigger circuits have been designed and implemented
for triggering of two Marx generator systems. The first trigger is built
circuit using Xenon flash lamp with a trigger transformer. The second
trigger has been built using automobile ignition coil as a trigger transformer
with a MOSFET driver .The Xenon flash trigger circuit of high voltage
output pulse (4.5 kV) and pulse width of 2µs while the automobile ignition
coil high voltage output pulse is 7.5 kV and pulse width of 40 µs.
Appendices
APPENDIX (A)
no+ n+ = total electrons from cathode .
Electron Multiplication equation. d
a enn α0=
………… ……………………………………….(1 )d
oa ennn α)( ++=
…………………………………………… . ..(2)
where γ : cathode yield in electrons per incident ion. γ+
+ =+−nnnn oa )(
)()()( +++ +−+=+− nnennnnn o
dooa
α
)1( −=+ dda e
enn ααγ
……………………………..………………….(3)
from eq.(2): )1( −
= d
da
a eenn α
α
γ
γ+
+ +=−n
nnn oa )(
⎥⎦
⎤⎢⎣
⎡ +=− + γ
γ1)( nnn oa
……
( )( )( )
( …………………………………...……..….(4)
substitute eq.(4)to eq.(3):
)γ
γ+−
=∴ + 1oa nnn
11 −+−
= d
doa
a eenn
n α
α
γ
( )( )
( )( ) ad
da
d
do n
een
een
−−+
=−+ 1111 α
α
α
α
γγ
( )
( )11 −+−= d
ad
ad
o enenen ααα γ
( )1−−+−= daa
da
da
do ennenenen αααα γ
Appendices
( )11 −−= d
d
oa eenn α
α
γ
( )
11 −−= d
d
oa eeII α
α
γ
Appendices
APPENDIX (B)
L1 R1G
C2 C1 R2
Circuit arrangement
V/s
1/C1s L1s R1
R2 1/C2s
V(s)
Transform circuit
21
2.)(zz
zsVsV
+=
Where;
111
11 RsLsC
Z ++=
sCR
sCR
Z
22
22
2 1
1*
+=
Appendices
11122
2
22
2
11.
1..)(RsL
sCsCRR
sCRR
sVsV
++++
+=
sCsCRsCRsCRsCRsCLsCRsCR
sCRR
sVsV
122
2211222
112212
22
2
)1()1()1(.1
1..)(
+
+++++++
=
2
121
2
2
1221
3
121
2 1RRsCRs
RLsCLs
CRCCss
V
++++++=
122121221
1
111
1
22
23 1111LRCCCLRCL
RCL
DLR
RCDD +⎥
⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡+++⎥
⎦
⎤⎢⎣
⎡++
1.V=
Appendices
APPENDEX (C)
( )122
21
αα
αα
−−
=−−
TeeEV
tt
Differential equation for found maximum time:
[ ]tt eeT
E12
12122
_)(
0 αα αααα
−−
−=
tt 1122 lnln
tt ee 12
12αα αα −− =
)ln()ln( 1212
tt ee αα αα −− =
α − α = α − α
)(
)ln(
12
1
2
.max αααα
−=t
Appendices
APPENDIX (D)
112221221
1
111
1
22
23 11111.
LCCRCLRCLR
CLD
LR
RCDD
V+⎥
⎦
⎤⎢⎣
⎡+++⎥
⎦
⎤⎢⎣
⎡++
=
221222
1
11
22
121
3 1111.
RCCCRCR
CDR
RCL
DLDV
+⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡+++⎥
⎦
⎤⎢⎣
⎡++
= V(s)
Where inductance L1=zero, D =s
221122
1
11
2 1)11(
1.
RCCCRCR
CsRs
V++++
=
1
212
12
212
121122
122
1
1
2
4)()11(
RRCC
RRCC
CRCRCRCRC
RC
s−
++++
−=m
Therefore
1
2
2
1
1
2
21
12
212
121122
2
])1(
[411)(
RRR
CC
RCRC
RCCCRCRCR
++−±
++
−s =
21
2
2
1
1
2
21
12
2
1
1
2
2,1 2
)1(
411)1(
CRRR
CC
RCRC
RR
CC
S
++−±++−
=
Where s is α
Appendices
APPENDIX (E)
1/C1s Ls R
1/C2s
V(s) =Vo
Vi/s
,
where: 21
111CCC
+= ,CLR 4
=
sCsC
LsR
sCs
VV i
12
2
11
1
+++=°
sCLsRs
CsC
CVi
1
1
22 ++=
])1(
1[2
2
2
CLsRss
LssRsC
CVi
++
+−=
)1
4(
4
22
2
22
sRC CRss
sRCRs
++
+=
2)2(
4
CRs
RCs
+
+=
222⎟⎠⎞
⎜⎝⎛ +
+⎟⎠⎞
⎜⎝⎛ +
⇒
RCs
B
RCs
A
Appendices
1=A
BRC
sRC
s ++=+24
RCB 2=
)])2(2
(1[22
RCs
B
RCs
AsC
CVV i
++
+−=°
)]2(1[22
2
RCtt
RCi eRC
teC
CV −−+−=
])21(1[2
2
tRCi et
RCCCV −
+−=
Appendices
Appendix (F)
When L =zero
1/C1s
1/C s
R
2Vi/s
sCsCRsC
sV
V io
21
2
11
1
++×=
CsRsC
sVi
1
12
+× =
CRssRC
i 1
12
+×V =
CRsCRs
CCi
1
1
2 +×
V =
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+−
+
+⎟⎠⎞
⎜⎝⎛
CRsCRs
CRsC
CVi
11
1
11
2
=
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
+−
CRssCCVi
111
2
=
⎥⎦
⎤⎢⎣
⎡−
−CR
ti e
CCV
12
=
Appendices
Appendix (G)
GBG VVV −=2
VV G −=
VVV BG +=
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
+++
=321
31CCC
CCVBH
V
VCCC
CCVV G +⎥⎦
⎤⎢⎣
⎡++
+=
321
312
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+++
+=32
31
1
1CCC
CCVV
Chapter One General Introduction 1
Chapter One
General Introduction
1.1 Marx Generator Power Supply:
A Marx Generator is a clever way of charging a number of
capacitors in parallel, then discharging them in series. Originally it was
described by Erwin Marx in 1924. Marx generators offer a common way of
generating high voltage impulses that are higher than the available supply
charging voltage. Discharge capacitors can also be kept at relatively lower
voltages, usually less then 200 kV, to avoid bulky and very expensive
capacitors as well as engineering problems associated with extremely high
DC voltages. A charging circuit diagram of simple 3-stage Marx generator
during charging state is shown in figure (1-1). When the charging voltage is
applied to the system, each stage capacitor is eventually charged to the
same applied voltage through the charging resistors [1].
Fig. (1-1) Simple Marx generator charging circuit [2].
With fully charged of the system (capacitors), either the lowest gap
is allowed to breakdown from overvoltage or it is triggered by an external
source, if the gap spacing is greater than the charging voltage breakdown
spacing. The erected capacitance, a common specification, is the stage
Chapter One General Introduction 2
capacitance divided by N-stages. After (erecting) the Marx bank, the
capacitors are momentarily switched to a series configuration refer to
figure (1-2). This allows the Marx to produce a voltage pulse that is
theoretically N-stages times the charging voltage. The output switches in
figure (1-1) and figure (1-2) are used to isolate the load while the Marx is
charging, and to insure full Marx erection before the energy is transferred
to the load [1].
Fig. (1-2) Simple Marx generator discharging circuit [2].
Chapter One General Introduction 3
Charging resistors are chosen to provide a typical charging time
constant of several seconds. The charging resistors also provide a current
path to keep the arc in the spark gaps alive. The discharge through the
charging resistors sets an upper bound on the impulse fall time, although
the impulse fall time is set by external resistors in parallel with the load or
the load itself. If the gaps in the Marx generator don't fire at exactly the
same time, the leading edge of the impulse will have steps and glitches as
the gaps fire. These delays also result in an overall longer rise time for the
impulse [1].
Jitter is the variation of time delay between shots given similar
electrical stimulus. If the jitter in the gaps is reduced, the overall
performance is improved. The traditional Marx generator operating in air
has all gaps in a line with the electrodes operating horizontally opposed.
This allows the Ultra Violet (UV) from bottom gap to irradiate the upper
gaps, and due to photoelectric effects, reducing the jitter [1].
Various Marx generator designs are available in the open literature.
A selection are shown in table (1-1). Table (1-1) shows a selection of these
generators, also the specification of these generators as, the designer and
year of production, maximum voltage, relative size, storage energy, rep-
rate frequency of the system, and the load. Some basic analysis of the
energy density (J/kg) is conducted with the resulting graph of the design for
each generator shown in figure (1-3). The weights of the systems are
approximated using a density of 1000 kg/m3 if the weight is not given. The
graph shows a large range of energy density for the various designs mainly
due to the diverse overall sizes and the uses for each system by using Excel
programer. However, the graph separates systems that marking the
repetitive systems.
Chapter One General Introduction 4
Table (1-1) Comparison of Various Marx Generators
Author/Year
V
max
(kV)
size(m3) Joules
(J)
Rep-
rate(Hz) Load (Ω)
M.T. Buttram 1988 [3] 440 0.634×10-3 6000 1-10 10 Ω soap water
J. D. Sethian 1989 [4] 840 7. 56×10+1 350000 No 100 nH pinch load
Yu.A.Kotov 1995 [5] 200 9. 82 ×10-2 25 50 100
J. Hammon 1997 [6] 1000 1. 58× 10-1 62. 5 10 800
F. E. Peterkin 1999 [7] 1000 2. 9× 10-2 80 20 100
A. J. Dragt 2001 [8] 400 3. 22× 10-3 40 1 100
M.B.Lara,et.al.2005[9] 40 0.0135 33 200 50
Laura K.Heffernan 2005 [10] 1000 12. 82 ×10-2 7200 No 300 Ω dummy load
Kirk Slenes, et.al. 2006 [11] 500 0.4823 150 10 50
J.R.Mayes, et.al. 2006 [12] 40 3.37×10-2 100 100 267 nH
Jong-Hyun Kim,et.al 2007[13 120 0.59796 10800 1000 1000
0
5
10
15
20
M.T. Buttra
m 1988
J. D. S
ethian 1989
Y.A.Kotov 1995
J. Hammon 1
997
F. E. P
eterk in 1999
A. J. D
ragt 2
001
Laura K.He ffe
rnan 2005
M.B.La ra etl.2005
Kirk S lenes etl
. 2006
J.R.M
ayes 2006
Jong-Hyun K im
2007
J/Kg
Author and years
Fig. (1.3) The ratio J/kg of various Marx designs.
Recent work with compact Marx generators is moving this
technology from the traditional energy storage, pulse charging supply to a
Chapter One General Introduction 5
direct microwave generation device. With voltage pulse rise times
decreasing down to hundreds of picoseconds and peak powers reaching
several gigawatts, these compact generators are finding their niche [14].
Typical applications of the Marx generator have been used with
pulse charging circuits. In essence, the generator is used as an energy
storage element, at relatively low voltages, and when fired, the pulse
charges the transmission line to a high voltage. Typical applications are
seen in high power microwave and accelerators. Generators in this role
tend to be large, as well as slow devices.
Smaller versions of the Marx generator have filled the role of
trigger generator for larger systems. These generators are typically
characterized by their low pulse energies with several hundreds of kV. The
main attraction to these pulses lies in their rise time and compact geometry
[2].
Improvements have made Marx generator an essential part of
todays pulsed power systems. Their capabilities have been improved
dramatically by developments in Marx circuit that allow low prefire rates
and low –jitter triggering. These improvements, which are the main subject
of this chapter, allow for construction and reliable operation of large,
multimodule, synchronized Marx systems [15].
1.2 Spark Gaps:
The spark gap is a conceptually simple device. It consists of two
electrodes separated by an insulating material. The insulating material may
be a gas, liquid, or solid, but a gas is the most commonly used material. So
this research will consider only gas-filled spark gaps. A voltage is applied
across the spark gap, lower than the breakdown voltage for the gas. Then a
trigger pulse is applied and the gas breaks down. The trigger often consists
simply of applying a momentary over voltage between the electrodes. Then
the gas breaks down and a current flows across the gap.
Chapter One General Introduction 6
The required breakdown voltage depends on the nature of the gas,
its pressure, the shape and separation of the electrodes. For plane electrodes
spaced one centimeter apart with gas pressure of one atmosphere, the
breakdown voltage is 1.3 kV for neon, 3.4 kV for argon, 12 kV for
hydrogen, 22.8 kV for nitrogen and 23 kV for air. These values are reduced
for pointed electrodes [16].
1.3 Trigger Circuits:
External triggering uses a high voltage trigger pulse to create a thin
ionized streamer between the anode and cathode within the spark gap.
Ionization starts when gas adjacent to the gap is excited by the voltage
gradient induced by the high voltage pulse from the trigger device. The
trigger pulse width is important because a finite amount of time is required
for the ionized streamer to propagate down the space of the spark gap. The
trigger rise time has a decisive effect on the commutation time of the tube;
fast rising pulses of high peak amplitudes cause the device ( spark gap,
krytron or thyratron) to break down in a shorter time due to the over
voltage function. Three major driver features will strongly affect the
switching performance [17]. They are (1) trigger jitter (2) trigger output
delay time and (3) trigger rise time. Where;
Delay time: is the time taken between the application of a trigger
pulse and the commencement of conduction between the primary
electrodes.
Jitter time: is the variation of time delay between shots which
gives similar electrical stimulus [18].
Four types of trigger circuits have been used in triggering the
discharge circuit as illustrated bellow [17]:
Chapter One General Introduction 7
1.3.1 Switching By Using Thyristor Trigger Circuit:
The circuit consists of a trigger transformer with a capacitor and a
Silicon Control Rectifier (SCR) (Thyristor) in the primary. When the
capacitor is charged, a high voltage is generated at the secondary which
breaks down the switch as shown in figure (1-4) [17].
Fig. (1-4) Thyristor trigger diagram [17].
1.3.2 Switching Using Krytron Trigger Circuit:
In this circuit a Krytron type KRP-20 (Krytron Pac; A Krytron
have been associated with trigger transformer into one miniature package,
from EG&G). Figure (1-5) shows the Krytron circuit diagram, the Krytron
will be triggered by the SCR (Thyristor) when it is discharging the
capacitor into the grid making the Krytron in the on case, this will
discharge the capacitor into the trigger, the thyratron or the spark gap
[18] as shown in Figure (1-5).
GSC
PSC
Chapter One General Introduction 8
Fig. (1-5) Krytron circuit diagram [17].
1.3.3 Switching By Using Thyratron Trigger Circuit:
The major requirements of the thyratron circuit are to deliver high
quality trigger pulse with adequate voltage and current to turn on the switch
(thyratron or spark gap). To meet these requirements, selection of fast
switching to trigger the thyratron must be done. The circuit diagram is
shown in Figure (1-6) [17]. The Thyratron is triggered by two ways; first
by using Thyristor and pulse transformer as in figure (1-4) and second by
using krytron and pulse transformer as in figure (1-5).
Fig. (1-6) Schematic diagram for thyratron trigger diagram [17].
Chapter One General Introduction 9
1.3.4 Switching by using Commercial Trigger Module:
Instead of the three trigger circuits, there is a commercial trigger
module type (TM-11A, EG&G) which have been used. It is a compact
versatile laboratory instruments designed to produce a high voltage trigger
pulse of fast rise time. It provides a trigger pulse of 30 kV that can be
utilized for initiating commutation in trigger spark gaps and to provide an
ignition type pulse for fast triggering. A control voltage provides variable
output pulse from 20 kV to 30 kV; figure (1-7) shows the trigger module.
The output voltage pulse rise time is about 70 ns [17].
Fig. (1-7) EG&G trigger circuit module [17].
Chapter One General Introduction 10
1.4 Gas Laser Discharge:
The power supplies for continuous-wave gas lasers are similar in
design to those used in direct-current power supplies. Gas laser power
supplies tend to be current-limited regulated DC power supplies. The
designs are basically the same for all gas-discharge devices. The details
depend on the particular voltage-current characteristics of the gas and the
configuration of the laser. Three essential elements are used in the design
of all gas laser power supplies these are the starter or ignition circuit, the
operating supply and a current-limiting element. Many gas lasers such as
CO2, metal vapor, and excimer are operated in a pulsed mode. These lasers
pose great problems in power-supply design because the impedance of the
gas is changing rapidly during the laser pulse [16].
1.4.1 Electrical Characteristics of Gas Discharge:
In pulsed lasers, the impedance of the gas is changing over a very
large range. As the gas breaks down and begins to conduct, the impedance
drops rapidly. This makes the design of power supplies difficult. It
becomes hard to control the current rapidly enough.
This section explains power supply requirements for several types
of gas lasers, beginning with the common He-Ne laser, and also describing
power supplies for carbon dioxide lasers, metal vapor lasers and excimer
lasers.
Most gas lasers are pumped by an electrical discharge that flows
through the gas mixture between electrodes. Collisions between electrons
in the electric discharge and the molecules in the gas transfer energy from
the electrons to the energy levels of the molecules. In this process, the
upper levels of the laser transition become populated. To describe the
requirements of the power supplies needed to drive the gas discharge, the
present study begins with a discussion of the nature of the discharge and its
initiation [16].
Chapter One General Introduction 11
Electrical discharge in gases is characterized by current-voltage
characteristics as shown in Figure (1-8). The exact characteristics of
course, depend on the nature of the gas, its pressure, length and diameter of
the discharge. At low values of applied voltage to the gas, there is no
current flow. As the voltage is increased, the current remains essentially
zero until some relatively high voltage is reached. This is denoted as point
(A) in the figure. At this point a very small current begins to flow because
of a small amount of ionization that is always present. This small amount
of ionization is provided by the presence of natural radioactivity and
cosmic rays. The small current is referred to as the pre-breakdown current.
The value of the current in this region may be a few nanoamperes.
Fig. (1- 8) Relation between current-voltage and gas discharge [16].
The pre-breakdown current increases slowly until a point called the
breakdown voltage is reached point B in the figure (1-8). This is the value
at which a large number of gas molecules become ionized. The
conductivity of the gas is increased and the electrons are accelerated to
velocities at which they can transfer enough energy to ionize more
molecules through collisions. Thus as the current increases, the resistance
of the gas decreases and the voltage required to sustain the discharge
Chapter One General Introduction 12
actually decreases with increasing current (region C in the figure). This
condition called negative resistance. It is the behavior that would be
predicted by Ohm’s law with a value of resistance less than zero.
The current would continue to increase, through region D
(amperes) to thousands of amperes (region E), with less and less voltage
required to sustain it. Figure (1-8) shows ranges of current, from
nanoamperes to kiloamperes, along the abscissa. Devices operating at
various valves of current are indicated above the curve.
The requirements for power supplies for gas lasers will be derive
from the characteristics curve in Figure (1-8).The exact design for a
particular gas laser power supply will depend on the specific current-
voltage curve for the gas mixture that is being excited, but three essential
elements for any gas laser power supply are [16]:
i. A starter circuit. This portion of the power supply provides an
initial voltage pulse. The peak value of the voltage pulse must exceed the
breakdown voltage of the gas. The pulse drives the gas past point B i.e.
reach region C.
ii. Operating supply. This part of the power supply provides a
steady current flow through the gas mix, after the gas has reached region C.
It must operate at the appropriate voltage and current levels to sustain the
current in the particular gas.
iii. Current limiter. This limits the current through the gas to a
desired value and prohibits the unbounded increase of current. It usually
takes the form of a ballast resistor in series with the discharge.
The characteristics of the gas discharge as shown in Figure (1-8)
lead to challenges in the design of power supplies to drive gas lasers. It
becomes difficult to control the voltage across the gas because the voltage
depends on the current after the discharge begins [16].
Chapter One General Introduction
13
1.5 Aim of the Work:
The aim of this project is to design and implement a pulsed power
supply type Marx generator with its triggering circuits, which is suitable for
pumping gas lasers and also to achieve the following characteristics:
1- Fast discharge pulse durations ns to µs.
2- Pulse rise time of few ns.
3- High discharge voltage about 40 kV DC.
4 - Output energy of Marx generator is suitable for any application.
Chapter Two Theoretical Concepts 14
Chapter Two Theoretical Concepts
2.1 Gas Breakdown:
The details of gas-insulated gaps depend strongly upon the
breakdown mechanisms of the gas involved. There are typically two stages,
avalanche and streamer formation, although a thorough analysis includes
more complex stages.
J.S. Townsend (Electricity in Gases, 1914) did the basic work in
this area. A sidelight to his work was the discovery of cosmic rays in order
to account for the observed condition in gases. When an electric field
exists in a gaseous medium, a small current will be observed due to
available free electrons resulting from ionizing radiation. As the field is
increased, electrons begin to acquire enough energy between collisions
with gas molecules to produce secondary ionization upon impact [19], as
shows in figure (2-1).
Fig. (2-1) Discharge characteristic in Townsend region [20].
Chapter Two Theoretical Concepts 15
Townsend defined α as the number of ionizing collisions per
centimeter in the field direction produced by a single initiating electron
[15]. Thus leads to [20]:
………………………………………………………..... (2.1) doa enn α=
)
as the description of the current reaching the anode.
As the field is further increased, a second mechanism takes effect;
generation of electrons at the cathode due to positive ion bombardment.
This has a coefficient that relates ion current to electron generation. When
this term added to the upper relation [19], then we get: [21] [Appendix A]
( 110 −−= d
d
eeII α
α
γ………..……………………….……………… (2.2)
when n related to I by taking into account the electronic charge of each
electron. At some point, the denominator approaches zero so that:
( ) 011 =−− deαγ , or approximately
when then: 1⟩⟩de α
1=deαγ .
When the term eαd is about the order of 20, transition from
avalanche to streamer takes place [22].
One consequence of this is that the dielectric strength for small
(less than 1 centimeter) spacing is greater than for larger gaps.
Figure (2-2) is a typical voltage-current relationship for a gas in a
uniform field. The behavior, after reaching breakdown, depends upon the
gas. In general, a sharp drop in voltage occurs. Figure (2-3) represents the
growth of a single electron in avalanche mode with transition to streamer
mode. Note that a negative space charge builds up due to the relatively
immobile ions. Eventually, a virtual cathode forms out in space, and it
tends to produce secondary structures. A physical difference between
avalanche and streamer mode is that avalanche is invisible, but streamers
Chapter Two Theoretical Concepts 16 marked by photoionization and photoemission and are brightly luminous.
In addition, the velocity of propagation is different. A velocity of
( 107 cm / s) is accepted for avalanche, (108 cm / s) or greater is a typical
velocity of streamers [19].
Fig. (2-2) V-I characteristic for a gas in a uniform electric field [19].
Chapter Two Theoretical Concepts 17
Fig. (2-3) Breakdown in avalanche to streamer [19].
There are two other mechanisms of importance to consider in gas
breakdown: electro-negativity and the Penning effect. Some monovalent
gases, such as fluorine, and some more complex gaseous molecules, such
as SF6, have outer rings deficient in one or two electrons. These tend to
capture or attach free electrons to form negative ions.
The low mobility of such ions effectively removes the electron
from the avalanche process and reduces the first Townsend coefficient (α ).
If this attachment coefficient given by n, the breakdown criterion becomes
[20]:
( )[ 11)(
n =−−
− den
α
α]γα ……………..…………………..……………… (2.3)
The Penning effect, on the other hand, reduces breakdown strength.
If, for example, trace (1 percent) of argon added to neon, a large reduction
in breakdown strength occurs. Several mixtures exhibit this effect including
helium-argon, neon-argon, helium-mercury, and argon-iodine.
The Paschen curve for several gases is shown in figure (2-4). Note
the Penning effect on neon, also the minimum point. For a given spacing,
Chapter Two Theoretical Concepts 18 as pressure drops, so does the probability of an electron-gas molecule
collision. A point is reached where mean free paths correspond to electrode
separation, and the drops. At this point, the apparent dielectric strength
increases again [19].
Fig. (2-4) Paschen curve- typical breakdown voltage curves for different
gases between parallel–plate electrodes [19].
2.2 Transient Voltage:
An impulse voltage is a unidirectional voltage, which rises rapidly
to a maximum value and then decays slowly to zero. The wave shape is
generally defined in terms of the times t1 and t2 in microseconds, where t1 is
the time taken by the voltage wave to reach its peak value and t2 is the total
time from the start of wave to the instant when it has declined to one-half
of the peak value. The wave then referred to as t1/t2 wave. The exact
method of defining the impulse voltage, however, is specified by various
international standard specification which define the impulse voltage in
terms of nominal wave front and wave tail durations. Figure (2-5) shows
Chapter Two Theoretical Concepts 19 the shape of an impulse wave where the nominal wave front duration
t1 specified as [23]:
211 25.1 TTt = ……………………………………………..………….. (2.4)
Where: OT1 = time for the voltage to reach 10% of the peak voltage,
OT2 = time for the voltage to reach 90% of the peak voltage.
The point O1 where the line CD intersects the time axis defined as
the nominal starting-point of the wave. The nominal wave tail is the time
between O1 and the point on the wave tail where the voltage is one-half the
peak value, i.e. .The wave is then referred to as a t1/t2 wave
according to the standard specified in B.S. 923 (British Standard) A 1/50 μs
wave is then standard wave. The specification permits a tolerance of up to
± 50% on the duration of the wave front and ± 20% on the duration of the
wave tail [23].
2t
412 TOt =
Fig. (2- 5) General shape of an impulse voltage [23].
Chapter Two Theoretical Concepts 20
In the corresponding American specification, the nominal wave
front is defined as 1 and the standard wave is a 1.5/40 μs. The
tolerances allowed on the wave front and the wave tail is ±0.5 μs and ±10
μs respectively [23].
215. TT
2.2.1 Single- Stage Impulse Generator Circuit:
An impulse generator essentially consists of a capacitor, which is
charged to the required voltage and discharged through a circuit, the
constants of which can be adjusted to give an impulse voltage of the
desired shape. The basic circuit of a single- stage impulse generator is
shown in fig (2-6(a)) where the capacitor C1 is charged from a direct
current source until the spark gap G breaks down. A voltage is then
impressed upon object under test of capacitance C2 [23].
The wave shaping resistors R1 and R2 control respectively the front
and the tail of the impulse voltage available across C2 [23].
The resistor R1 will primarily damp the circuit and control the front
time T1. The resistor R2 will discharge the capacitors and therefore
essentially controls the wave tail. The capacitance C2 represents the full
load, i.e. the object under test as well as all other capacitive elements,
which are in parallel to the test object (measuring devices; additional load
capacitor to avoid large variations of t1/t2, if the test objects are changed).
No inductances are assumed so far, and are neglected in the first
fundamental analysis, which is also necessary to understand multi-stage
generators. This approximation is in general permissible, as the inductance
of all elements has kept as low as possible [24].
It is important to mention the most significant parameter of impulse
generators. Which is the maximum stored energy: ( )2max121 oMarx VCE =
Chapter Two Theoretical Concepts 21 within the discharge capacitance C1. As C1 is always much larger than C2,
this figure determines mainly the cost of a generator [24].
An analysis of the simple circuit, presented by Draper [23] is as
follows. Figure (2-6(b)) represents the Laplace transform circuit of the
impulse generator of fig. (2-6(a)) and the output voltage given by the
expression:
(a) Circuit arrangement
(b) Transform circuit
Fig. (2-6) Single-stage impulse generator [23].
Chapter Two Theoretical Concepts 22
v(s)21
2
ZZZ
sV
+= Where 1
11
1 RsC
Z += , sCR
sCZ
22
2
2
2 1+=
R
By substitution:
v(s) )1(
1)1(
22
2
11
22
2
+++
+=
sCRR
sCR
sCRR
sV
( ) 2221
1
2
11 RsCRsCR
Rs
V
++×⎟⎠⎞⎜
⎝⎛ +
=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛ +++
=
++++=
2121212211
221
211
22
1221
2
11111
1
CCRRsCRCRCRsCRV
RRCCR
sCsCRR
RsV
or v(s)bassCR
V++
= 221
1 where ⎟⎟⎠
⎞⎜⎜⎝
⎛++=
212211
111CRCRCR
a and
⎟⎟⎠
⎞⎜⎜⎝
⎛=
2121
1CCRR
b
v(s) ⎥⎦
⎤⎢⎣
⎡−
−−−
=212121
111ssssssCR
V
Where and are the roots of the equation s2+ as + b = 0 and both
will be negative. From the transform tables:
1s 2s
[ ])exp()exp()(
)( 212121
tstsssCR
Vt −−
=υ
Chapter Two Theoretical Concepts 23
In a practice R2 is much greater than R1 and C1 much greater than
C2 and an approximate solution is obtained by examining the auxiliary
equation: 01111
2121212211
2 =⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛+++
CCRRs
CRCRCRs
Where the value of (1/R1C1+1/R2C2) is much smaller than 1/R1C2.
The equation then becomes: 011
212121
2 =⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛+
CCRRs
CRs
And the roots are: 21
11CR
−≈s , 12
21CR
−≈s and 21 s⟩⟩s
The equation for the output voltage then becomes [19]
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−−⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
2112
expexp)(CRt
CRtVtυ …………………………………….(2.5)
And the graph of the expression is shown in figure (2-7).
Fig. (2-7) The impulse voltage and its components [23].
Chapter Two Theoretical Concepts 24
The above analysis shows that the wave shape depends upon the
values of the generator and the load capacitances and the wave-control
resistances. The exact wave shape will be affected by the inductance in the
circuit and the stray capacitances. The inductance depends upon the
physical dimensions of the circuit and is kept as small as possible [23].
A theoretical analysis have presented for the single-stage impulse
generator and the load circuit. The simplified circuit is shown in figure
(2-8(a)) [23].It shows that, after the discharge of the condenser C1, the
variation in the voltage V, across the load, capacitance C2 can be analyzed
by extremely tedious methods involving a quartic differential equation. If
L2 is neglected or in effect combined with L1, the equation reduces to one
involving only the third and lower powers and it takes the form,[23]
[Appendix B] ,
01111
22111121212
1
221
123 =⎥⎦
⎤⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛+++⎟⎟
⎠
⎞⎜⎜⎝
⎛++
RCCLCLCLCLRR
DRCL
RDDV ….….….(2.6)
Chapter Two Theoretical Concepts 25
(a)
(b)
Fig. (2-8) Simplified circuit of impulse generator and load. (a)
Circuit showing alternative positions of the wave-tail control resistance, (b)
Circuit for calculation of wave front [23].
The wave-tail resistance can be either on the load side or on the
generator side. If the wave-tail resistance is in position , the parameters
are slightly different but the equation remains in the same form. An
expression of this form is of little more than mathematical interest as the
stray capacitances, inductances distributed throughout the circuit, and no
precise values can be assigned to them.
'2R
Chapter Two Theoretical Concepts 26
In most cases, it is desirable to simplify the calculations by
assuming that the circuit of figure (2-8(a)) is non-inductive. Taking the
case where R2 is on the generator side of R1, it can be shown that the roots
1α− and 2α− of the differential equation for V are
( ) ⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
++−±
++= 2
12
12
2
1221 /1
/4112
/1TTX
TTT
TTXor αα
and )( 122
1
21
αα
αα
−−
=−−
TeeVV
tt
C ……..………………………….………….(2.7)
where : X=C2/C1, T1=C1R2, T2=C2R1
The actual time for the voltage V to rise to its peak value given by:
[Appendix C]
( )12
12logαααα
−= e
actualt ………………………………..……………………..(2.8)
The efficiency (η) of the generator is given by V /VC1, i.e.
)( 122
1211
ααη
αα
−−
=−−
Tee tt
……………………………...……………………(2.9)
If R 2is on the load side of R1, the roots of the equation are: [Appendix D]
( ) ⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
++−±
++= 2
12
12
2
1221 /1
/4112
/1XTTX
TTT
XTTXorαα
The position of R2 greatly affects the voltage efficiency of the
system and it will be apparent from figure (2-8(a)) that when R2 is on the
load side of R1, the resistors R1 and R2 from a potential divider and the
output voltage is reduced. No such reduction in voltage takes place when
R2 is on the generator side of R1. Edwards et al [23] had shown how the
efficiencies of the two arrangements vary with the ratioC2/C1.
Chapter Two Theoretical Concepts 27
Figure (2-9) shows the effect of position of R2 on voltage efficiency
of the generator. For low values of C2/C1 the efficiency is very low when R2
is on the load side of R1 , but when the circuit is arranged so that R2 is on
the generator side , the efficiency is highest when the load is zero and
decreases gradually with increase in the ratio C2 /C1. For any value of the
ratio C2 /C1, the voltage efficiency is higher when the resistance R2 is on the
generator side of R1 [23]. In the simplified arrangement of figure (2-8(b)),
the critical resistance R for the circuit to be non-oscillatory is given by:
CLR 4
= where 21
111CCC
+=
The voltage V across the load capacitance is then given by:
[Appendix E]
2C
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ +−= − CRtC e
CRt
CCVV /2
2
1 211 ……….……….……..………..…..(2.10)
If the inductance is reduced to zero, then: [Appendix F]
( )CRtC eC
CVV /2
2
1 1 −−= ………….…….………………………..……(2.11)
Chapter Two Theoretical Concepts 28
Fig. (2-9) Effect of position of wave-tail resistance on voltage
efficiency, (a) Resistor R 2on generator side of R1, (b) Resistor R 2on load
side of R1 [23].
The “nominal wave front “as defined in B.S. 923 (1940) is equal to
2.75 CR when L is zero and to 2.1CR when the circuit is critically damped.
Neglecting the inductance, the nominal wave tail is approximately equal to
0.72 R1 (C1 + C2). The resistance values calculated in the following
sequence.
The value of R1 required to make the circuit shown in fig (2-8(a))
non-oscillatory is first calculated ignoring R2. Then the value of R1
(> CL4 ) required to give the desired wave front is computed. Finally, the
value of R2 is calculated to give the required wave tail when R2 is on the
generator side of the R1 in the arrangement shown in the figure (2-8(a)).The
efficiency of the generator can then be approximately estimated when [C1/
(C1+C2)] multiplied by factor which is about 0.95 for a 1/50 μsec wave
[23].
Chapter Two Theoretical Concepts 29
The maximum value of (I) the current in the undamped discharge
circuit of a generator into a short circuit can be calculated from the energy
equation: 1/2LI2 =1/2C1V2 i.e. [23]
LCVI 1= ……………………………….……………………………..(2.12)
If the circuit is critically damped, the current will be given by an
expression [23]:
LC
eVI 1= ………………………………………….………………… (2.13)
An analysis have been made of impulse generator circuits of
various types and presented the values of the constants corresponding to the
most commonly used waveforms. This treatment may be extended to
evaluate the constants for any desired wave shape. [23]
The analysis showed that, the wave shape of the impulse generator
is largely affected by the circuit parameters. Has analyzed the influence of
wave front resistance, the series inductance and the load capacitance in
modifying the shape; the results are shown in figure (2-10). These relations
show that for values of the series resistance higher than a critical value,
(i.e. CL4 ) the wave front duration increases with increasing values of the
resistance and the magnitude of the peak voltage decreases. With
increasing the series inductance and load capacitance the wave front
increases but the magnitude of the peak value varies little for the chosen
range of inductance and capacitance.
The lengthening of the wave front by increasing these parameters
provides a convenient method of generation of long-front impulse voltages
suitable for carrying out tests [23].
Chapter Two Theoretical Concepts 30
Fig. (2-10) Effect of varying circuit parameters on voltage wave
shape [23].
2.2.2 Multistage Impulse Generator Circuit:
The one-stage circuit is not suitable for higher voltages because of
the difficulties in obtaining high direct current voltages. In order to
Chapter Two Theoretical Concepts 31 overcome these difficulties, Marx suggested an arrangement, which is
described below [23].
2.3 Marx Generator:
A Marx generator is a clever way of charging a number of
capacitors in parallel through resistances, then discharging them in series
through spark gaps [23] as show in figure (2-11).
Fig. (2-11) Marx Generator
(a) Charging (b) Discharging.
The essence of the Marx principle is the transient series connection
of a number of electrostatic energy stores. The eponymous Erwin Marx
described his original generator [25].Marx generators are probably the most
common way of generating high voltage impulses for testing of insulations
Chapter Two Theoretical Concepts 32 when the voltage level required is higher than available charging supply
voltages.
A typical circuit presented in figure (2-12) which shows the
connections for a five-stage generator. The stage capacitors C charged in
parallel through high-value charging resistors R. At the end of the charging
period, the points A,B,…,E will be at the potential of the D.C sources, e.g.
+V with respect to earth, and the points F,G,…,M will remain at the earth
potential. The discharge of the generator initiated by the breakdown in the
spark gap AF, which followed by simultaneous breakdown of all the
remaining gaps.
When the gap AF breaks down, the potential on the point A
changes from +V to zero and that on point G swings from zero to -V owing
to the charge on the condenser A.G. If for the time being the stray
capacitance C` is neglected, the potential on B remains +V during the
interval of the gap AF sparks over. A voltage 2V, therefore, appears across
the gap BG that immediately leads to its breakdown. This breakdown
creates a potential difference of 3V across CH; the breakdown process,
therefore, continues and finally the potential on M attains a value of -5V.
In effect, the low voltage plates of the stage capacitors are
successively raised to -V, - 2V…,-NV, if there are N stages. This
arrangement gives an output with polarity opposite to that of the charging
voltage.
Chapter Two Theoretical Concepts 33
Fig. (2-12) Basic circuit of a five-stage impulse generator [23].
The above considerations suggested that a multistage impulse
generator should operate consistently irrespective of the number of stages.
In practice for a consistent operation it is essential to set the first gap ( )
for breakdown only slightly below the second gap ( ). A more complete
analysis shows that voltage distribution across the second and higher gaps
immediately after the breakdown of the lowest gap ( ) is governed by the
1G
2G
1G
Chapter Two Theoretical Concepts 34 stray capacitances and gap capacitances shown in dotted lines in figure
(2-12). The effect of stray capacitances on voltage across immediately
after breakdown of which may be estimated as follows:
2G
1G
Assume the resistors as open circuits and stray capacitances
negligible in comparison with the stage capacitors. Let (A) in figure (2-12)
be charged to (+V). After breakdown of the point G initially at earth will
assume a potential –V, but the potential of B is fixed by the relative
magnitudes of and and is given by [24]:
1G
21 ,CC 3C
⎜⎜⎝
⎛++
+=
321
31
CCCCC
VVBH ⎟⎟⎠
⎞………………………………………………….(2.14)
hence the voltage across the gap (G ): 2
⎟⎟⎠
⎞
3C
3C
⎜⎜⎝
⎛++
++=
21
312 1
CCCC
VVG
≈
………………………………………………..(2.15)
[Appendix G].
If C 2 = 0, VG2 reaches its maximum value of 2V. If both and
are zero, will equal to V, i.e. its minimum value.
1C 3C
2GV
It is apparent, therefore, that the most favorable conditions for the operation
of the generator occur when the gap capacitance is small and the stray
capacitances and are large. The conditions set by the above expression
are transient, as the stray capacitors start discharging.
2C
1C
The practical stray capacitors are of low values, consequently the time
constants are relatively short μsec or less. 110−
For consistent breakdown of all gaps, the axes of the gaps should
be in same vertical plane so that the ultraviolet illumination from spark gap
in the first gap irradiates the other gaps. This ensures a supply of electrons
in the gaps to initiate breakdown during the short period when the gaps are
subjected to the over voltage. The consistency in the firing of the first stage
spark gap improved by providing trigger circuits [23].
Chapter Two Theoretical Concepts 35
The wave-front control resistors, in a multistage generator, can be
connected either externally to the generator or distributed within the
generator, also it may partly connected in or outside it. In the best
arrangement, about half of the resistance is outside the generator. An
advantage of distributing the wave-front resistors within the generator is
that, it reduces the need for an external resistor capable of withstanding the
impulse voltage. If all the series resistances distributed within the
generator, the inductance and capacitance of the external leads and the load
form an oscillatory circuit [23].
An external resistance, therefore, becomes necessary to damp out
these oscillations. The method of placing part of the wave-front control
resistance in series with each gap serves to protect against disruptive
discharge as well as to damp out any generator internal oscillation. Wave-
tail control resistances generally used as the charging resistors within the
generator.
The circuit shown in figure (2-13) commonly used to obtain high
efficiency with distributed series resistors. The value of is made large
compared with and which are made as small as is necessary to obtain
the required length of the wave tail. Under some conditions the current
through does not flow through and so does not reduce the initial
generator output voltage, no matter how small or how large may be. In
a practical generator employing this circuit, the voltage drop in is made
less than 1% of the output voltage by selecting suitable values of the
parameters. The stage capacitance was 0.2 μF, is about 40 Ω and the
wave-tail resistance required for a 5 μsec wave tail is about 25 Ω. is
made nearly 10 k Ω [23].
3R
1R 2R
2
2R 1R
2R 1R
1R
1R
R 3R
Chapter Two Theoretical Concepts 36
Fig. (2-13) Multi-stage generator with distributed series resistors [23].
2.3.1 Charging Of the Marx Generator:
In N-stages Marx bank, the output voltage available at any instant
is theoretically the sum of the individual stage voltages. Thus, there is an
RC line in each, except for the first stage, all forcing functions are time and
position dependent. Two solutions are conveniently available. One
relationship, according to Fitch as in figure (2-14) [19], is: 2NCRT ooCH = ………………………………………………….……… (2.16)
Fig. (2-14) Marx bank charging performance [19].
Chapter Two Theoretical Concepts 37
The second relationship is shown in figure (2-14), presents a power
series analysis that he takes to the limit as N goes to infinity. In an LC
circuit, recourse can be taken to the PFN a characteristic .ideally, such a
network has characteristic time is given by:
………………………….…….………………...... (2.17) MARXMARXCH CL=τ
The discharging into matched impedance requires a time τ2 . In
mismatched cases, oscillations occur that extend this time. More
commonly, some command charge system employed in which an external
inductor, large with respect to the Marx inductors, is resonated against the
total network capacitance. Charging usually accomplished in a half cycle of
the resonant frequency, leading to [19]:
MARXTOTALCH CLπτ = …………………………….……………….…… (2.18)
2.3.2 Discharging of the Marx Generator:
The inefficiencies of charging have a matching set of inefficiencies
associated with the discharge. Figure (2-15) reveals that, in general, a stage
capacitor is paralleled by two charging impedances, . In the resistive
case, the self-time constant is just:
oZ
2oo
DISCHCR
=τ ………………………….……………………………… (2.19)
Fig. (2-15) Marx bank discharge relationships [19].
This time must be long compared to the output pulse for good
efficiency. When inductances used as charging impedances, the behavior is
Chapter Two Theoretical Concepts 38 similar except for the appearance of resonance in place of the simpler RC
case.
The analysis in is straightforward and summarized here. A given
mesh will attempt to resonate with a current given by[19]:
LCt
LCVi NLC sin= …………..………….………………..…………..(2.20)
For good efficiency the self-ring period, T chosen much greater
than the discharge period, τ. Thus, the sine of the angle can be replaced
with the angle and:
LCt
LCVi NLC ≅
LtVN= ……………………..…………………….. (2.21)
Because the process terminates when the bank is discharged. If the
Marx discharges into matched impedance, the Marx current is:
N
N
ZNV2
I1 = …………………………………….……………………….. (2.22)
and the efficiency can be related by the ratio of ( i ). 1I/LC
When the first gap fires, all voltages around the loop must add up as before,
and equal zero, by Kirchhoff``s Law. (Gaps are opposite in sense to
capacitors.)
gapi NVNV = Initially …………………………..………………………(2.23)
( ) gapi VNNV 1−= One gap fired ……………..…………………………(2.24)
( ) gapi VNNV 2−= Two gaps fired ……………….……………………(2.25)
or, alternatively, the voltage across an unfired gap should be:
1nNNViVGap −
= .…………………….……….…………..………(2.26)
2.4 Trigger Spark Gap:
The trigger spark gap was invented in the early 1940`s to serve as a
switch in high-power modulators for radar [26]. The spark gap consists of
three electrodes in a hermetically sealed pressurized envelope. Specific
Chapter Two Theoretical Concepts 39 applications fall into two general areas, both involving capacitor switching
at low impedance levels follows:
(i) Protective device, where the gap is used to crowbar energy storage
elements such as filter capacitors and PFN`s, providing shunt protection of
RF tubes and other circuitry.
(ii) Series switch, where energy is discharged rapidly into loads include,
Marx Generators, Kerr Cells, Pockel Cells, flash tubes for pumping gas,
liquid and solid lasers and also gas lasers, such as UV Nitrogen, TEA-CO2
and metal vapors [27].
2.4.1 Electrical Operation:
The triggered spark gap is a unique switch, able to change quickly
from a near-perfect insulator to a low impedance conductor in response to
voltage applied to the electrodes. The two main electrodes carry the load
current after trigger electrode initiates conduction. Triggered spark gaps
generally characterized by peak current capability of tens of thousands of
amperes, delay times of tens of nanoseconds, arc resistance of tens of
milliohms, inductance of 5 to 30 nanohenries and life of thousands to
millions of shots depending on the application. Typical current pulse
widths are in the range of one to tens of microseconds [27].
Different spark gaps designed to employ one particular method to
create the main anode to cathode discharge, figure (2-16) shows spark gap
types. The different methods are following the triggered spark gap
electrode configurations:
1- Field distortion: three electrodes; employs the point discharge (actually
sharp edge) effect in the creation a conducting path.
2- Irradiated (laser trigger switches): three electrodes; spark source creates
illuminating plasma that excites electrons between the anode and cathode.
3- Swinging cascade: three electrodes; trigger electrode nearer to one of the
main electrodes than the other.
Chapter Two Theoretical Concepts 40 4- Mid plane three electrodes, basic triggered spark gap with trigger
electrode centrally positioned.
5- Trigatron: trigger to one electrode current forms plasma that spreads to
encompass a path between anode and cathode.
The triggered Spark gap may be filled with a wide variety of materials, the
most common are: (1) Air (2) SF6 (3) Argon (4) Oxygen.
Often a mixture of the above materials is employed. However, a
few spark gaps actually employ liquid or even solid media fillings. Solid
filled devices are often designed for single shot use (they are only used
once- then they are destroyed) Some solid filled devices are designed to
switch powers of 10 TWatts such as are encountered in extremely powerful
capacitor bank discharges, except (obviously) in the case of solid filled
devices, the media is usually pumped through the spark gap.
Spark gaps often designed for use in a certain external environment
(e.g., they might be immersed in oil). A system for transmitting the media
to the appropriate part of the device may sometimes be included. Common
environments used are: (a) Air (b) SF6 (c) Oil. Make miniature triggered
spark gaps specially designed for defense applications. These devices are
physically much smaller than normal spark gaps (few cm typical
dimensions) and designed for use with exploding foil Slapper type
detonators.
Laser switching of spark gaps, the fastest way to switch a triggered
spark gap is with an intense pulse of Laser light, which creates plasma
between the electrodes with extreme rapidity. There have been quite a few
designs employing this method, chiefly in the plasma research area.
Triggered spark gaps tend to have long delay times than Thyratrons (their
chief competitor, at least at lower energies) However once conduction has
started it reaches a peak value exceptionally rapidly (couple of
nanoseconds commutation).
Chapter Two Theoretical Concepts 41
Fig. (2-16) Trigger spark gap types, (a) the trigatron gap, (b) the laser
triggered gap, and (c) the field distortion gap [28].
Chapter Two Theoretical Concepts 42 2.4.2 Ratings and Operating Characteristics:
The transfer characteristic curve in figure (2-17) and the voltage-
current waveform in figure (2-18) show the ratings and behavior of a
triggered spark transfer to the main electrode, or more correctly, to cause
the trigger spark to initiate complete gap breakdown and condition of
current between the main electrodes.
When minimum trigger voltage required to initiate a complete
breakdown is plotted versus main electrode (E-O-E) voltage, a typical
curve of all triggered spark gaps shown in figure (2-17). This curve defines
a region on the left where firing does not ordinary occur, called the cut-off-
region, a central region called the normal operating region and a region on
the right above the point marked static breakdown voltage where the gap
self-fires simply form over-voltage on the main electrodes.
Triggered spark gaps should always operate well above the
minimum trigger voltage and above the cut-off voltage portions of the
curve to avoid the possibility of a random misfire and they should always
operate well below the static breakdown voltage point to avoid the chance
of prefire [27]. The important parts of the transfer characteristic curve are:
V T (min)-Minimum Trigger Voltage
The minimum open circuit triggers voltage for reliable triggering.
Spark Gaps should operate well above minimum trigger voltage, if
possible.
E-E (co)-Cut-Off Voltage
The main electrode (E-E) voltage marked by a sudden rise in
minimum trigger voltage as E-E voltage reduced. Operating near cut-off
should always avoid, particularly near the knee of the transfer
characteristics curve.
Chapter Two Theoretical Concepts 43 E-E (min)-Minimum Operating Voltage
The minimum main electrode voltage for reliable operation
represents approximately 1/3 of maximum operating voltage.
E-E (max)-Maximum Operating Voltage
Typically represents 80% of self-breakdown voltage (SBV), and it
is a value chosen to prevent random prefires.
SBV- Static Breakdown Voltage
The point where the gap will self-fire with no trigger voltage
applied. Pressure fill and electrode spacing determine this point [27].
Fig. (2-17) Transfer characteristics for spark gap [27].
Chapter Two Theoretical Concepts 44
Fig.(2-18) Typical-current waveform characteristics [27].
2.4.3 Range:
It is the area between minimum and maximum operating voltages.
Normal gap operating range typically has a 3:1 ratio (i.e. maximum to
minimum operating voltage). For the most reliable operation with
minimum delay time and jitter, triggered spark gaps should usually
operated at the high end of the range, between 60% and 80% of SBV.
Operation at 50% to 70% of SBV may give longer useable life at high
energy, if delay time is not critical [27].
Chapter Two Theoretical Concepts 45
Fig. (2-19) Paschen curves for triggered spark gaps [29].
Figure (2-19) shows the preferable operating range of a 3- electrode
spark gap. The operating range is in the middle distance (A) between the
voltage of automatic breakthrough and a lower limit where no spontaneous
breakthrough can be enforced, even by a triggering spark of extremely high
energy. This operating point indicated in figure (2-19), which even in the
case of fluctuations offers sufficient space on both sides [29].
2.4.4 Trigger Mode:
There are actually four transfer characteristics curves for any given
trigger spark gap, depending on the trigger mode, a term applied to the
relative polarities of the opposite, adjacent, and trigger electrodes, these
mode designations shown in figure (2-20).
Chapter Two Theoretical Concepts 46
Fig.(2-20) Gap mode designations [27].
Generally, with the large gaps, the widest operating range and
shortest delay times are obtained with mode (A) operation, that is, with the
opposite electrode negative and the trigger electrode positive with respect
to the adjacent electrode. When mode of operation is not possible or
practical, usually voltage range is reduced severely with an increase in
delay time. The smaller gaps, with smaller electrode spacing, often have
the widest operating range in Mode C. In this mode both the opposite
electrode and trigger electrode are positive with respect to the adjacent
electrode [27].
Chapter Two Theoretical Concepts 47 2.4.5 Delay Time and Jitter:
Delay time (tad) is measured between trigger voltage breakdown
and main gap conduction as shown in figure (2-18). Delay time is a
function of E-E voltage, trigger wave shape, and trigger mode. Minimum
delay time achieved at the upper end of the E-E range with a fast trigger
applied with the suitable mode polarity shown in figure (2-20). Delay time
of the gap will generally be much less than that due to rise time and delay
in the trigger circuitry [27].
Total jitter (tj) is the shot-to-shot variation in delay time plus the shot-to-
shot variation in trigger breakdown time. Jitter may be minimized by using
a fast-rising trigger pulse with trigger voltage in excess of minimum
specified trigger voltage.
2.4.6 Recovery Time:
Recovery time of gas-filled gaps is about several milliseconds
depending on peak current, current reversal, and voltage recharge rate. To
achieve proper turnoff of the gap, the discharge circuit should slightly
under damped, with voltage reversal of 5% or less. For a gap to properly
recover after discharge the gap current go to zero and the voltage across the
gap must be reduced to less than 30 volts. Recharging of the energy storage
capacitor must take place slowly, preferably from an inductive, resonant
LC, or command triode charging source. RC charging, for example, is not
conductive to short recovery time, but may be used if charging currents are
less than 5 mA DC [27].
2.5 Inductor:
The role of an inductor in the Marx generator is to charge high
voltage capacitors (C1 - Cn) in charging mode and isolate DC input voltage
and high voltage pulse in high voltage pulse generation mode .The
charging time (TCH) in charging mode can be calculated as :
Chapter Two Theoretical Concepts 48
242
4tChtCh
CH
CLCLTTππ
=== ….…….………………..……….(2.27)
To meet maximum pulse repetition rates (fmax.), the charging time
should be less than Tmax. (=1/fmax.). So maximum inductance of LCh is
obtained as follows;
max
.max 12 f
CL tCh ≤π ………….…………………………(2.28)
The current of an inductor LCh has a maximum value in high
voltage pulse generation mode. To limit maximum current of an inductor
LCh, the minimum inductance of LCh is calculated as follows [30]:
.max,
.max.max,.min
LL I
TLΔΔ
≥ ν …………………………...………………….(2.29)
2.6 Power Supply of Gas Lasers:
A gas laser is a laser in which an electric current is discharged
through a gas to produce light. The first gas laser, the Helium –neon, was
invented by an Iranian physicist Ali Javan 1960 [31]. [
2.6.1 Power Supply for TEA CO2:
A common variety of pulsed carbon dioxide laser is the TEA laser
(Transversely Excited at Atmospheric pressure). This is inherently a pulsed
device rather than a continuous laser. In contrast to most carbon dioxide
lasers that operate at total gas pressures much less than one atmosphere, the
TEA laser operates near one atmosphere gas pressure. This allows
extraction of relatively large amounts of energy per pulse. The energy in a
pulse from a carbon dioxide laser that is pulsed in the microsecond regime
increases as the square of the gas pressure (E ά P2). Thus it became
desirable to increase the gas pressure and operate at a pressure near one
atmosphere, a convenient value. But at these pressures, the uniform
electrical discharge tends to transform into an arc discharge. The discharge
voltage pulse range from (~ 300 ns - 500 ns) and the discharge current
Chapter Two Theoretical Concepts 49 pulse (~ 150 – 300 ns) while the output laser pulse ~ 100 ns ( main pulse)
plus ~ 200- 400 ns ( pulse tail).
The electrical discharge breaks down into a narrow streamer,
similar to a lightning bolt. This does not excite the whole gas volume
uniformly. To avoid this undesirable effect, the devices are operated in a
relatively short pulse regime, and a number of other measures are used,
including preionization and special shaping of the electrodes [16].
2.6.2 Power Supply for Metal Vapor Laser:
Pulsed metal vapor lasers first were developed around 1966 but
were slow. The technology of these lasers has been difficult, primarily
because of the high temperature at which the laser tube must be operated to
keep the metal in vapor form at a reasonable pressure (around 1500 C in
the case of gold). Because these lasers offer desirable wavelengths, they
have been developed to commercial status and are now reliable, robust
commercial products.
A metal vapor laser may consist of a ceramic tube with pellets of
metal (such as gold or copper) positioned inside. The tube is surrounded by
a cooling water jacket. An electrical discharge through a gas (neon) in the
tube heats the metal and produces a low-pressure vapor. The laser is
essentially a pulsed device with a high pulse repetition rate (0.5 - 5 kHz) so
that the beam appears continuous to the eye. The applied voltage depends
on the dimensions of the active medium (~ 5-20 kV for copper vapor laser).
The beam diameters are typically 1 cm or more, larger than those of most
familiar visible lasers.
Commercial pulsed metal vapor lasers are copper (511- and 578-
nm wavelengths) and gold (628 nm). Experimental demonstrations have
included lead (723 nm), manganese (534 nm), and barium (1500 nm). The
availability of these wavelengths from small devices with short pulse
duration has allowed development of a number of novel applications, such
Chapter Two Theoretical Concepts 50 as photodynamic therapy in medicine and high-speed photography.
Although such lasers are still not common, they are beginning to be used
for industrial material processing.
The short wavelength and high peak power allow high irradiance
to be delivered to a small area on a work piece. Of the metal vapor lasers,
copper is the most highly developed [16].
2.6.3 Power Supply for Excimer Laser:
Excimer lasers have used two main methods of excitation: pulsed
electric discharges or high-energy electron beams. Development of excimer
lasers has branched into two channels that represent the two excitation
methods. Electron-beam-excited devices are capable of producing very
high energy pulses. Electron-beam excitation involves large, expensive
sources of high-energy electrons. Such devices can be scaled to very large
size and are capable of reasonably high efficiency, potentially in the 5- to
10-percent range.
Devices have been constructed with energy in the kilo joules range,
and amplifiers with energy-extraction capability in the hundred-kilo joule
range appear possible. Electric-discharge Excimer lasers may be much
smaller and less expensive.
Their energy-extraction capabilities are much lower than those of
the electron-beam devices. Typical characteristics for commercial models
are pulse energy of from a few tenths of a joule to a few joules per pulse
and pulse repetition rates of tens to hundreds of hertz, with average power
in the range of one hundred watts. Because of the unstable nature of the
chemical species in an excimer laser, it is available only as a pulsed device
with short pulses, typically in the 200-nanosecond regime. The problems
with the changing impedance of the gas during the discharge become more
severe. The change is much faster and covers a greater range than is the
case for carbon dioxide laser gas mixtures.
Chapter Two Theoretical Concepts
51
Excimer lasers require short excitation pulses with half widths less
than 100 ns with rise time less than 50 ns and currents in the range of
kiloamperes. Also some means for preionizing the gas between the
electrodes is required. The usual approach has been a two-stage circuit in
which charge is stored on a storage capacitor, and then transferred by a
thyratron switch to an array of secondary capacitors, called peaking
capacitors.
The basic idea is to be able to store the charge in one portion of the
circuit, where the process can be relatively slow, and then to perform the
discharge in another portion of the circuit, which can be much faster.
The charge is transferred across preionization spark gaps that
introduce some charge into the gap between the electrodes and prepare the
gas for the main discharge [16].
Chapter Three Experimental Work 52
Chapter Three
Experimental Work 3.1 Introduction:
A homemade high voltage DC power supply up to 4 kV, two
trigger circuits (one with camera flash igniter and the other with MOSFET
transistor) where designed and implemented, two Marx generators (eight
stages and ten stages) have been designed and tested as a high voltage pulse
generator devices.
3.2 Design Principles:
The major requirements of the project are shown in the following
block diagram figure (3-1).
Fig. (3-1) Block diagram for the major requirements.
Chapter Three Experimental Work
53
3.3 Variable High Voltage Supply:
A homemade variable 4kVDC power supply is developed for
charging the Marx capacitors as shown in figure(3-2), it is consist of a
variac (0-220VAC, 5Amp), high voltage transformer (220V/4kV), current
limiter resistor 330 Ω, high voltage diodes 6kVDC for rectification (it
works as a half wave rectifier), capacitor (0.1µF-25kV) and 100kΩ
charging resistor.
Fig. (3-2) A homemade high voltage power supply.
3.4 External Trigger Generator Circuits:
In order to trigger the spark gap for first stage of the Marx
generator two trigger circuits were developed for this purpose, first camera
flash lamp trigger circuit figure (3-3), it consists of a relaxation oscillator to
generate a high voltage trigger impulse to initiate the spark at the first gap
and the second trigger circuit is the ignition coil driver circuit figure (3-4).
Chapter Three Experimental Work 54
Fig. (3-3) Camera flash lamp trigger circuit.
Fig. (3-4) Ignition coil driver circuit.
Chapter Three Experimental Work 55
3.4.1 Xenon Camera Flash lamp Triggering Circuit: A small xenon camera flash lamp liner (300V max. applied
voltage) with commercial trigger transformer (TR) 200V max. input and 20
kV max output. The resistor (Rt ) and capacitor (Ct) are used to form the
trigger generator circuit as shown in figure(3-5). The breakdown action in the xenon flash lamp occurs when the
voltage across the lamp is 256 VDC. The (10nF) capacitor (Ct) is charged
through (Rt) as the flash lamp breaks down discharging (Ct) into the
primary coil of the trigger transformer to produce an output high voltage
pulse on the secondary (~8 kV DC) which is used to trigger the first gap of
the Marx generator (8-stage).
Ω
Fig. (3-5) Xenon flash lamp trigger circuit.
Chapter Three Experimental Work 56
3.4.2 Ignition Coil Switching Trigger Circuit: The car coil circuit consists of two parts, first the dc power supply
circuit and second the ignition coil driver circuit as in figure (3-6).
12V
15V
Fig.(3- 6) Ignition coil switching trigger circiut.
A variable DC power supply is used to get an input voltage to
supply the primary ignition coil with a 12 volt DC, also a 15 volt DC is
used to supply the IC 555 trigger circuit which is used as a stable oscillator.
The IC 555 oscillates at frequency up to 4 Hz depending on the variable
resistors VR, R3 and capacitor C4.The calculations for IC 555 time on (Ton )
and time off (Toff ) and the duty cycle are :
TON = 0.7x VR x C4
= 0.7 x 50 x 103 x 0.1 x 10-6
=3.5msec
Chapter Three Experimental Work 57
TOFF = 0.7 x R3 x C4
= 0.7 x 70 x 103 x 0.1 x 10-6 = 4.9 msec
Duty Cycle with Diode = TON/ ( TOFF + TON )
= 416 msec
The output from the IC 555 directly drives a high current switching
power MOSFET transistor which switches the current through the primary
coil of the coil transformer and the output at the secondary coil is
approximately (20kVDC).
The IC 555 is a in stable operation with the output high (pin3) the
capacitor C4 is Charged by current flowing through VR and R3 .
The threshold (pin6) and trigger (pin2) inputs monitor the capacitor
voltage and when it reaches 2/3 Vs (threshold voltage ) the output becomes
low and the discharged (pin7) is connected to 0 V, when the voltage falls to
1/3 Vs ( trigger voltage ) the output becomes high again and the discharge
(pin7) is disconnected allowing the capacitor to start charging again a
pushbutton switch is connected between (pin2) and capacitor C4 to control
the trigger pulse, also to achieve a duty cycle of less than 50% .A diode
(D1) is added in parallel with R3 as shown in the diagram, this will bypasses
R3 during the charging part of the cycle so that the space time or off time
depending only on VR and C4.
An ignition coil is essentially an autotransformer with a high ratio
of secondary to primary windings. "Autotransformer", means that the
primary and secondary windings are not actually separated but they share
a few of the windings.
The ratio of secondary to primary turns in an ignition coil is
somewhere around 100:1. However, the ignition coil does not work like an
ordinary transformer. An ordinary transformer will produce output current
at the same time of input current is applied. An ignition coil actually does
most of its work as an inductor. When the ignition coil is connected to the
Chapter Three Experimental Work 58
supply, the inductor is 'charged' with current. It takes a few milliseconds for
the current to build up the magnetic field; this on account of reverse voltage
caused by the increase in magnetic field. An output high voltage trigger
pulse (12kV) is produced to trigger the first gap.
3.5 Marx Generators:
A typical Marx generator consists of (N) number of stages (eight
and ten stages), each stage consisting of resistors, capacitor and spark gap
which is the switching device. All modules are connected together such
that the capacitors are charged in parallel with spark gaps.
The Marx generator is a capacitive energy storage circuit which is
charged to a given voltage level and then quickly discharged delivering its
energy quickly to a load at very high voltage levels. Two Marx generators
were designed and implemented in this work.
A variable (4kVDC) power supply is used for this purpose when all
the capacitors are charged up to the desired voltage, first spark gap is
triggered by trigger generator circuit this makes the rest of the gaps to be
overvoltage and causing self break down, all the capacitors are thus
connected in series resulting an output voltage N times the charging
voltage, two trigger generators circuits were developed one for an eight
stages Marx generator and another for a ten stages Marx generator.
3.5.1 Marx generator (8 – stage):
A compact repetitive Marx generator has been designed, built and
tested. The generator of 8 stages is an R-C ring that consists of 8 capacitors
(4.7 nF per capacitor) and 14 resistors (2 MΩ per resistor). The generator is
charged quickly to 2kV within a charging time less than 0.52 second by a
DC charging source. The trigger system is constructed for repetitively
triggering the first discharging spark gap (There are 8 discharging spark
gaps in the generator). Due to the limited capacity of the DC charging
source the generator is tested at single pulse discharge with an output
Chapter Three Experimental Work 59
voltage about 12 kV (efficiency 75%). The outlook of Marx generator is
shown in the figure (3-7).
Fig. (3-7) Marx generator (8-stage).
The Marx generator consists of an array of Resistances,
Capacitances & Spark Gaps (R, C & S.G.).
The elements of Marx Generator are; C= 4.7 nF, R = 2MΩ and the
input power supply voltage = 0 - 4 kVDC, as shown in figure (3-8).
Fig. (3-8) Circuit diagram for Marx generator (8-stage).
The spark gap is formed with a tinned copper wire with a diameter
of 1.5 mm and the gaps should be initially set to about 1.5mm as shown in
figure (3-9).
Chapter Three Experimental Work 60
Fig. (3-9) Copper wire spark gap.
The distance between the spark gaps depend on input voltage and
number of stages. The measured output voltage pulse of Marx generator (8-
stage) is (12kVDC) for an input voltage 2kV high voltage probe also the
trigger pulses and the current pulses were measured, figure (3-10) shows
the gaps glow discharge.
Chapter Three Experimental Work 61
Fig. (3-10) Gaps glow discharge.
3.5.2 Marx Generator (10 - Stage):
A ten-stage Marx generator is built with the following parameters;
ten homemade spark gaps, (18) resisters each (100kΩ), ten ceramic
capacitors (2400 pF, 40kV), twenty wiring copper sheets , two Perspex
rulers, one Bakelite base and base holder as shown in figure (3-11).
Chapter Three Experimental Work 62
(a) Front view. (b) Side view.
Fig. (3-11) Marx generator (ten stages).
The spark gaps are designed and machined from brass metal
depending on commercial spark gap which is produced from lumenics
corporation arranged as shown in figure (3-12) with the following
dimensions, Diameter = 2.5 cm and Length = 4cm.
Chapter Three Experimental Work 63
Fig. (3-12) Spark gap arrangements.
The curvature of the gap is the most important parameter which
governed the uniformity of the discharge between the two electrodes. The
spark gap electrodes are designed using Chang profile, Chang showed that
the gradient (i.e. the E field strength) between the electrodes is greater than
Chapter Three Experimental Work 64
the gradient outside the plane portion. The equations for the uniform field
electrode (Chang`s family of profiles) are [32]:
)sinh()cos( uvKux o+=
)cosh()sin( uvKvy o+=
x and y are space coordinates and Ko(<<1) is a parameter controlling the
electrode width (chang 1973). For the π/2 profile the electrode surface is
defined by
ux = ; )cosh()2/( uKy O+= π
The field is greatest in the center region between the plates and less
everywhere else. If the making of the electrode follow the calculated
contour, the breakdown voltage between the electrodes will be the same as
if the field is infinitely uniform.
The ten- stage Marx generator was tested for an input voltage 4 kV.
The obtained output voltage was 38 kV, the circuit is operated using
ignition coil trigger circuit to obtain a trigger pulse on the first stage spark
gap as shown in figure (3-13).
Chapter Three Experimental Work 65
Fig. (3- 13) First trigger spark gap.
Figures (3-14) and (3-15) show the system arrangement for the
Marx generator with measuring instruments during testing operation.
Chapter Three Experimental Work
66
Fig. (3-14) Marx generator system (10- stage) experiment.
Fig. (3-15) Marx spark gaps discharge operation test.
Chapter Four Result & Discussion 67
Chapter Four Results and Discussion
4.1 Introduction:
The output results for the Marx generator eight stages and the Marx
generator ten stages are the voltage pulse, current pulses and trigger pulse
for the trigger circuit. Theoretical and experimental inductance calculations
were achieved for the two Marx systems.
4.2 Marx Generator (8-stage):
4.2.1 Xenon Flash Lamp Trigger Circuit:
Output voltage pulse from camera xenon flash lamp trigger circuit
is measured by using high voltage probe (P6015, 1000X, 3pF, 100mega
ohms DC, 20kV max. DC cont., 40kV peak pulse, Tektronix Inc) and a 100
MHz oscilloscope (Oscillation Tektronix 2221A, 100 MHz Digital Storage
Oscilloscope). Figure (4-1) shows the output trigger pulse delivered from
the circuit shown in figure (3- 3).
Scale (1V, 5µs)
Fig.(4-1) Output voltage trigger pulse 4.5kV.
Chapter Four Result & Discussion 68 4.2.2 Current Pulse for Marx Generator (8-stage):
Marx generator (8-stage) current pulse was measured using current
probe (Termination for P6021 AC Current Probe, Tektronix ® 011-0105-
00, LP3db ≈ 450Hz, Tc ≈ 0.35ms). Figure (4-2) shows the current pulse for
variable input voltages.
Scale (5V, 0.2 µs) Fig. (4-2) Marx generator (8-stage) current pulse.
The Xenon trigger circuit shown in figure (3-5) was tested with
different voltage from zero volt up to its maximum which is found to be ~
(256 volts). This voltage pulse has been used to trigger the first stage of
Marx generator.
Eight stages Marx generator current pulse is measured using
current probe directly mounted to the output section of the generator, the
current probe signals are shown in figures (4-2). The current calculations
are:
Chapter Four Result & Discussion 69
I Max. = 225 mA
IR = 140 mA= 0.14 A
I Min. = 85 mA= 0.085 A
T = 300 ns
The Marx is charged up to (2 kV), the energy is:
EMarx = 1/2 C V2
= 75.2 mJoule.
The eight stages Marx generator charged about (2kV) using the
homemade variable power supply and then triggered by the xenon flash
lamp, the output voltage pulses shown in figures (4-4) and (4-5).
Scale (1V, 2µs) Scale (1V, 10 µs) (a) Full voltage pulse. (b) Selected voltage pulse (first)
Figure (4-4) Voltage pulse for Marx generator - third stage 4.5 kV.
Chapter Four Result & Discussion 70
Scale (1V, 10 µs) Scale (2V, 10 µs) (a) Full voltage pulse (fifth stage). (b) Full voltage pulse (eight stages). t r≅ 666 ns , Pulse width 4.5µs ≅
Figure (4-5) Voltage pulse for Marx generator stages. 4.3 Marx Generators (10-stage):
Marx generator ten stages charged from variable high voltage
power supply up to 4 kVDC. The Marx output voltage pulse shown in
figure (4-6) is (38 kV). Figure (4-7) shows the voltage pulse for trigger
circuit with car ignition coil shown in figure (3-6).
Chapter Four Result & Discussion 71
Scale (5V, 0.2 µs)
Fig. (4-6) Marx generator (ten stages) voltage pulse. Pulse width = 450 ns, rise time = 50 ns.
(a) 5.9 kV (b) 7.5 kV Scale (1V, 0.1 ms)
Fig. (4-7) Trigger circuit high voltage output pulse about 7.5 kV (ignition coil).
Chapter Four Result & Discussion 72 4.4 Measurements and Calculations:
One of the most important parameters affecting the Marx output
pulse is the inductance. Calculations have been done using two methods,
first by measuring it with LCR meter device (PM 6303 RLC meter Philips)
for the whole components of the Marx generator, second by direct
calculations from the Marx generator output pulses.
4.4.1 LCR meter measurements method:
Inductance: L S.G.s = 2.6 µH L Stripes = 2.5 µ H L Capacitor = 20 nH
Then, Marx generator ten stages: L Marx = L S.G.s + L Stripes + L Capacitances = 2.6 µ H + 2.5 µ H + 200 n H
= 5.4 × 10 -6
= 5.4 µ H. 4.4.2 Marx generator (10-stage) output pulse calculation method:
For ten stage Marx generator the inductance calculations
depending on the Marx output pulse is done depending on the
measurements from figure (4-6).
⇒ Rise time t r 50 ns ≅ ⇒ f =
T1 =
ns501 = 2× 107 Hz.
f = TLC
121π
2× 10 7 =CL 10
121
×π
Chapter Four Result & Discussion 73
L = 2.64 nH. Decay time t de ⇒ ≅ 2 s 610−× ⇒ f =
T1 = 5×105 Hz
⇒ L = 4.2 µ H.
⇒ Pulse width ≅ 450 ns ⇒ f =
T1 = 2.1×106 Hz.
L=2.3×10 -7 H. ∴L Total = L Rise Time + L Decay Time
= 2.64 nH +4.2 µ H = 4.2 µH. L Pulse Width = 2.3×10 -7 H.
4.4.3 Marx generator (8-stage) output pulse calculation method:
For eight stages Marx generator the inductance measured from the
measurements from figure (4-5 (b)):
Rise time t r 6.66 ⇒ ≅ ×10 -7s
⇒ T
f 1= = 1.5 ×106 Hz.
⇒ L = 2.99 × 10 -7 H. ⇒ Decay time t de ≅ 4 × 10- 6 s ⇒ f =
T1 = 2.5 ×105 Hz.
⇒L = 1.07897×10-5 H.
Chapter Four Result & Discussion 74 ⇒ Pulse width ≅ 4.5×10 -6s ⇒ f =
T1 = 2.222× 105 Hz
⇒ L = 1.3658×10-5 H.
∴L Total = L Rise Time + L Decay Time
= 11.0887µH
L Pulse Width = 1.3658×10-5 H.
Table (4-1) shows the inductance results for the eight and ten stage
Marx generators.
Table (4-1)
L Pulse width Ldecay Lrise 1.36×10-5 H 1.07×10-5 H 2.99 × 10 -7 H 8 - stage 2.3×10 -7 H 4.2 µ H 2.64 nH 10 - stage
Chapter Four Result & Discussion 75 4.5 Characteristic Marx generator (10-stage):
The calculated results are listed in table (4-2) for the 10-stage Marx
to show the all parameters which affected the Marx output pulse width.
Table (4-2)
Unit Value Description Parameter
kV 400 Open circuit voltage V Open
stage 10 Number of stage N
pF 2400 Stage capacitance max.
voltage 40 kV C Stage
10-10 F 2.4 Erected capacitance C eq. or C Marx
kV 40 Maximum charging voltage VMax. Ch
kV 4 Real charging voltage VCh
Hµ 4.2026 Erected series inductance L Marx or L eq.
10-7H 4.2026 Stage inductance L Stage
ohm 132.328505Marx impedance Z Marx
10 8watt3.03 Power peak P Peak
mJ 192 Energy stored in marx E Marx
s 0.0216 Charging time T Ch
Hz 46 Maximum Repetition rate f RR
ns 50 Rise time t r
µs 2 Decay time t de
watt 8.8 Average power P ave
% 95 Efficiency into a load η
mA 40 Charging current ICharge
From table (4-2) the first important parameter is the output pulse
rise which is 50 ns; this result is close to the aim for the designed Marx
which is around 10 nsec. The second parameter is the pulse repetition
Chapter Four Result & Discussion 76 frequency which is 46 Hz, this parameter is very important for the gas laser
which work with high repetition frequency like Excimer and nitrogen laser.
Table (4 -3) Dimensions of the Marx generator (`10- stage)
Unit Value Diameter Parameter
cm 75 Marx length L Marx
cm 7.5 Marx width W Marx
cm 11 Marx hight H Marx
Chapter Four Result & Discussion 77
4.6 Characteristic Marx Generator (8-stage):
The calculated results are listed in table (4-4) for the 8-stage Marx
to show the all parameters which affected the Marx output pulse width.
Table (4 -4)
Unit Value Description Parameter
kV 64 Open circuit voltage (typical) V Open
stage 8 Number of stage N
nF 4.7 Stage capacitance, max.
voltage 8kVDC
C Stage
10-10F 5.875 Erected capacitance Ceq. or C Marx
kV 8 Maximum charging voltage VMax.Ch
kV 2 Real charging voltage VCh
Hµ 11.0887 Erected series inductance L Marx or L eq.
Hµ 1.3860875Stage inductance L Stage
ohm 137.38407Marx impedance Z Marx
MW 7.453 Peak power P Peak
mJ 75.2 Energy stored in marx E Marx
s 0.5264 Charging time T Ch
Hz 1.8996 Maximum repetition rate f RR
ns 666 Rise time t r
sµ 4 Decay time t de
watt 0.1428 Average power P ave.
% 75 Efficiency into a load η
mA 1 Charging current ICharge
From table (4-4) the first important parameter is the output pulse
rise which is 666 nsec; this result is far from the aim of the designed Marx
which is around 10 nsec. The second parameter is the pulse repetition
Chapter Four Result & Discussion
78
frequency which is 1.8996 Hz; this parameter was less than the expected
which is about 10 Hz.
Table (4-5) Dimensions of the Marx generator (8- stage)
Unit Value Diameters Parameters
cm 38 Marx length L Marx
cm 5.5 Marx width W Marx
cm 4 Marx height H Marx
Chapter Five Conclusions And Recommendations For Future Work
79
Chapter Five
Conclusions And Recommendations For Future Work 5-1 Conclusions:
From the present work, we can conclude the following:
1- The spark gap design imposes great effect on the discharge output pulse
width and rise time. Spark gap also affected the Marx generator inductance
and impedance because it adds an imaginary stray capacitance which
causes increasing in the inductance of whole system.
2- The components of the Marx generator (capacitors, resistors and wiring
connections type) play an important role in determining the impedance and
inductance of the whole system. To design and build Marx generator with
low inductance and fast rise time pulse, it must use low inductance
capacitors and special resistors (e.g. silicon carbide type).
3- The trigger circuit is affecting the discharge properties for the first spark
gap of the Marx, which will in parallel affect the whole gaps discharge too,
so one must determine the trigger pulse properties such as; pulse width, rise
time, fall time and peak power depending on the Marx generator spark gap
design and properties.
4- High voltage pulses with short pulse width and fast rise time depends
greatly on the earthing system used in the laboratory, because bad earthing
system will increase the pulse duration and change all the signal properties
even if the system is well designed and implemented.
5- The open circuit voltage for 8 stage Marx generator is 64 kV but the real
measured output voltage was 12 kV because the primary charging voltage
is 2 kV and it is possible to reach the Marx maximum output voltage if the
laboratory earthing system is well designed and implemented.
6- The open circuit voltage for 10 stage Marx generator is 400kV but the
real Measured output voltage was 38 kV because the primary charging
Chapter Five Conclusions And Recommendations For Future Work
80
voltage is 4 kV and it is possible to reach the Marx maximum output
voltage if the laboratory earthing system is well designed and implemented.
7- The inductance for the two Marx supplies from table (4-1) is 13.6 µH for
the 8-stage and 0.23 µH for the 10-stage, the inductance difference between
the two systems is duo to the kind of capacitors, resistors, spark gaps
design and wiring. For the 8-stage, capacitors was commercial type (cheap)
and the spark gaps were made from curved copper wire, but for the 10-
stage the capacitors were ceramic type (low inductance ~ 20 nH) and the
spark gaps were well designed (Chang profile), which decreases the
inductance for the 10-stage system.
5-2 Recommendations for Future Work:
The suggested future work to improve the present research and to
obtain more advanced results is the following:
1-Decreasing the jitter time and pulse width by enhancement of the Marx
generator components (low inductance materials).
2- Design and construction of Marx generator with different spark gaps
design.
3- Design and construction of solid state Marx generator using solid-state
switches.
4- Design and construction of circuit for a pair of Marx stages.
5- Design and construction of a compact, low inductance repetitive Marx
generator.
6- Design and construction of an atmospheric and pressurized spark gap
filled with N2 or SF6 gas for Marx generator operation.
III
Contents Acknowledgment I
Abstract II
Contents III
List Of Abbreviation VI
List Of Symbols VII
1. Chapter One: General Introduction 1
1.1 Marx Generator Power Supply. 1
1.2 Spark Gaps. 5
1.3 Trigger Circuits. 6
1.3.1 Switching By Using Thyristor Trigger Circuit. 7
1.3.2 Switching By Using Krytron Trigger Circuit. 7
1.3.3 Switching By Using Thyratron Trigger Circuit. 8
1.3.4 Switching By Using Commercial Trigger Module. 9
1.4 Gas Laser Discharge. 10
1.4.1 Electrical Characteristics Of Gas Discharges. 10
1.5 Aim Of The Work. 13
2. Chapter Two: Theoretical Concepts 14
2.1. Gas Breakdown 14
2.2. Transient Voltage 18
2.2.1 Single -Stage Impulse Generator Circuit 20
2.2.2 Multistage Impulse Generator Circuit 30
2.3 Marx Generator 31
2.3.1 Charging of Marx Generator 36
2.3.2 Discharging of the Marx Generator 37
2.4 Trigger Spark Gap 38
2.4.1 Electrical Operation 39
IV 2.4.2 Ratings and Operating Characteristics 42
2.4.3 Range 44
2.4.4 Trigger Mode 45
2.4.5 Delay Time and Jitter 47
2.4.6 Recovery Time 47
2.5 Inductor 47
2.6 Power Supply of Gas Lasers 48
2.6.1 Power Supply for TEA CO2 48
2.6.2 Power Supply for Metal Vapor Laser 49
2.6.3 Power Supply for Excimer Laser 50
3. Chapter Three: Experimental Work 52
3.1 Introduction 52
3.2 Design Principles 52
3.3 Variable High Voltage Supply 53
3.4 External Trigger Generator Circuits 53
3.4.1 Xenon Camera Flash lamp Triggering Circuit 55
3.4.2 Car Coil Switching Trigger Circuit 56
3-5 Marx Generator 58
3-5-1 Marx generator (8 – stage) 58
3-5-2 Marx Generator (10 – Stage) 61
4. Chapter Four: Results and Discussion 67
4-1 Introduction 67
4-2 Marx generator (8-stage) 67
4-2-1 Xenon Flash Lamp Trigger Circuit 67
4-2-2 Current Pulse For Marx Generator 68
4.3 Marx Generator (10-stage) 70
4-4 Measurements and Calculations 72
V 4-4-1 LCR meter calculation method 72
4-4-2 Marx generator (10-stage)output pulse calculation
method 72
4-4-3 Marx generator (8-stage) output pulse calculation
method 73
4.5 Characteristic Marx generator (10-stage) 75
4.6 Characteristic Marx Generator (8-stage) 77
5.Chapter Five: Conclusions And Recommendations For Future
Work 79
5-1 Conclusion 79
5-2 Recommendations For Future Work 80
6. References 81
7. Appendices i
Appendix(A) i
Appendix(B) iii
Appendix(C) v
Appendix(D) vi
Appendix(E) vii
Appendix (F)
Appendix (G)
ix x
VI
List of Abbreviations Symbol CGS Grid storage capacitance.
CPS Anode storage capacitance.
EPS Anode supply voltage.
PFN Pulse forming network.
RGC Grid charging resistor.
RKA Keep alive resistor.
RPC Anode charging resistor.
SBV Self- breakdown voltage.
SBV Static. Breakdown voltage.
SCR Silicon controlled rectifier.
U.V. Ultra violet.
VII
List of Symbols Symbol Unit
C Capacitance for LC circuit. F
C1 Discharge Capacitance of generation. F
C2 Capacitance of the load. F
Co Charge capacitance. F
Ceq. , C Marx Erected capacitance. F
C Stage Stage capacitance. F
Ct Total capacitance. F
d Distance between electrodes. cm
e Damping factor.
E Marx Energy stored in Marx. J
E-E(CO) Cut off voltage. V
E-E(max.) Maximum operating voltage. V
E-E(min.) Minimum operating voltage. V
f Max. Maximum pulse repetition rate. Hz
G Spark gap.
H Marx Marx height. cm
I Current arrive to anode. A
I1 Marx current. A
ICharge Charging of current. A
iLC Current for LC circuit. A
IMax. Maximum current pulse. A
IMin. Minimum current pulse. A
Io Current arrive to cathode. A
IR Next peak current pulse. A
K o Aspect ratio.
%
L Inductance for LC circuit. H
VIIIL1 Internal inductance of generation. H
L2 External inductance of load or connection. H
LCh Charge inductor. H
L Marx , L eq. Erected series inductance. H
Lmin. Minimum inductance. H
L Stage Stage inductance. H
n Attachment coefficient. cm-1
N Number of stage. stage
n a Numbers of electron arrive to anode. cm-1
n o Number of elec. incident to cathode due to external radiation .
cm-1
n+ Number of elec. incident to cathode by secondary emission
cm-1
n1 Number of fired gaps.
P Peak Peak power. W
P ave. Average power. W
R1 Resistance controlling the wave front. Ω
R2 , '2R Resistance controlling the wave tail. Ω
Ro Charge resistance. Ω
t Maximum of time. sec.
T Period. sec.
t ad Delay time. sec.
t J Jitter time. sec.
t1 Nominal wave front duration. sec.
t2 Nominal wave tail duration. sec.
tactual Actual time. sec.
t r Rise time. sec.
t dec Decay time. sec.
TCH Time of charge. sec.
u Flux function.
ν Potential function.
IXVC1 Voltage to which C1 is charged. V
VCh Maximum charge voltage. V
VGap Voltage across the gap. V
Vi Initial voltage. V
VL max. Maximum high voltage. V
VN Stage voltage. V
V Open Open circuit voltage. V
VT(min.) Minimum trigger voltage. V
W Marx Marx width. cm
x Space coordinates of x-axis.
y Space coordinates of y- axis.
Z Marx Marx impedance. Ω
ZN Stage impedance. Ω
Zo Impedance. Ω
α Townsend coefficient. cm-1
γ Cathode yield in electrons per incident ion. cm-1
ΔILMax Maximum current of an inductor. A
η Efficiency. %
τ DISCH Discharge period. sec.
References 81
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