Research Article Technique of Coaxial Frame in...

Research ArticleTechnique of Coaxial Frame in Reflection for theCharacterization of Single and Multilayer Materials withCorrection of Air Gap

Zarral Lamia1 Djahli Farid1 and Ndagijimana Fabien2

1 Laboratory of Scientific Instrumentation Institute of Electronic FERHAT Abbess University 19000 Setif Algeria2 Laboratory of IMEP-LAHCMinatec Institute of Microelectronics Electromagnetism and Photonics38000 Grenoble France

Correspondence should be addressed to Zarral Lamia lamia zarralyahoofr

Received 6 March 2014 Revised 2 June 2014 Accepted 17 June 2014 Published 24 July 2014

Academic Editor Wenhua Yu

Copyright copy 2014 Zarral Lamia et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Techniques based on fixture probes in reflection are used in microwave reflectometry as a novel diagnostic tool for detection ofskin cancers for complex permittivity measurements on liquid samples and oil shale and for complex dielectric permittivity ofanimalsrsquo organs and tissues measurements in microwave band for the needs of modern veterinary medicine In this work we havedeveloped a technique to characterize multilayer materials in a broadband frequency range A coaxial probe in reflection has beenspecially developed for microelectronic substrate Using SMA connector loss tangent of 10minus4 and relative permittivity have beenmeasured with an error of 0145The extension of the coaxial probe in reflection technique to multilayer substrates such as Delrinand Teflon permitted to measure bilayer material provided the good knowledge of electrical parameters and dimensions of onelayer In the coaxial transmission line method a factor that greatly influences the accuracy of the results is the air gaps betweenthe material under test and the coaxial test fixture In this paper we have discussed the influence of the air gaps (using samples of05mm air gaps) and the measures that can be taken to minimize that influence when material is measured The intrinsic valuesthus determined have been experimentally verified We have described the structure of the test fixture its calibration issues andthe experimental results Finally electromagnetism simulations showed that the best results can be obtained

1 Introduction

In this paper we have developed a method using a coaxialfixture that allows the extraction of electrical parameters ofsubstrates by the reflection measurement This coaxial probeis in contact at its end with the samples and with a shortcircuit for calibration For validation we have measured theTeflon and Delrin (Pome) The validation of the method isfirst made on monolayer materials and secondly on multi-layers substrates We reversed the positions of the couple ofmaterials (Delrin Teflon) then (Teflon-Delrin) to check theirasymmetries In the multilayer measurements we use Teflonas reference material

2 Principle of the Method

Figure 1 shows the structure of the line with sample as wellas the reference plans of measurements in this method Ourmethod requires six measures to be made in a first step weperform one measure of the 11987811 parameters in open circuitand another one in short circuit for calibration In a secondstep we measure the 11987811 parameters of line without sampleterminatedwith open circuit andwith short circuit at the endIn the third and last step wemeasure the 11987811 parameters of theline with sample terminated with short circuit and with opencircuit

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 324727 9 pageshttpdxdoiorg1011552014324727

2 International Journal of Antennas and Propagation

P1 P2P0

Short circuit

SMA connector

Air

Sam

ple

Figure 1 Presentation of the coaxial reflective frame with sample

To move from plan P1 to plan P2 as shown in Figure 1we apply the following formula [1] with l being the lengthbetween P0 and P1

1198781015840

119894119895

= 119878119894119895

sdot 1198902sdot119895sdot120574119897

(1)

3 Presentation of the CoaxialFrame in Reflection

A coaxial frame is a coaxial line comprising a centralconductor and a cylindrical outer aluminum conductor Thisline is connected to the tester bymeans of an SMA connectorwhich is placed on one of its ends so as to measure the 11987811parameters in which the electrical parameters of the materialare extracted [2] On the termination of the coaxial line weconnect a short circuit or open circuit so that the materialunder test is in direct contact with the short circuit (Figure 1)

For the modeling of this frame we have calculated all theparameters of the transmission line as well as the dimensionsof the samples to be characterized before proceeding to thesimulation step

4 Electromagnetic Simulations and Validation

We simulated the structure of the frame with and withoutsample in the case of loss and lossless dielectric using CSTand HFSS111 simulators The simulation is made with thefollowing steps

41 Impedance Matching Bandwidth The test structure com-prises a radiating coaxial transmission line in a semi-infiniteenvironment with a given thickness and ended by a metalplate for short circuit The ratio of the inner diameter (2119886)and of the outer conductor (2119887) is set so that the characteristicimpedance of the transmission line is equal to 50Ω inwithoutsample

42 Extraction of the Electrical Parameters of the DielectricThe 11987811 parameters obtained by simulation allow easy accessto propagation phase 120574119897 in the presence and in the absence ofmaterial Consider

119885 (119878) = 119885119899 sdot1 + 119878

1 minus 119878 (2)

where 119885(119878) is the impedance characteristic function of 119878parameters 120574 is the propagation constant and 119897 is the lengthof the line

In the absence of the dielectric material we have

119885119888air = radic119885119888air119888119888 sdot 119885119888air119888119900

120574119897air = 119886 tanhradic119885119888air119888119888

119885119888air119888119900

(3)

In the presence of the dielectric material

119885119888mat = radic119885119888mat119888119888 sdot 119885119888mat119888119900

120574119897mat = 119886 tanhradic119885119888mat119888119888

119885119888mat119888119900

(4)

where 119885119888 is the characteristic impedance of the lineThese two measures of parameter 120574119897 [3 4] allow easy

access theoretically to parameters 120576119903

and tan 120575119889

of thedielectric material

From the line impedance in short circuit and open circuitto extract the propagation parameters of a transmission linewe can measure the 11987811 reflection parameters in two differentconfigurations namely the line in short circuit and the linein open circuit [5] Any transmission line can be representedby its propagation constant (119885119888 120574119897)

The input impedance119885in of a transmission line loaded byimpedance 119885

119877

is determined by the following expression

119885in = 119885119888119885119877

+ 119885119888 tanh (120574119897)119885119888 + 119885

119877

tanh (120574119897) (5)

In the case of a short-circuit line (119885119877

= 0) the impedanceseen at the input line is written as

119885in119888119888

= 119885119888 sdot tanh (120574119897) = 119885119899

1 + Γcc1 minus Γcc

= 119885cc (6)

where 119885119899

is the standard resistance that is equal to 50Ohmand Γ is a coefficient of reflexion

In the case of an open-circuit line (119885119877

= infin) theimpedance seen at the input of the line is

119885in119888119900

=119885119888

tanh (120574119897)= 119885119899

1 + Γ119888119900

1 minus Γ119888119900

= 119885119888119900

(7)

43 Extraction of the Complex Relative Permittivity Thecomplex relative permittivity and the loss angle are obtainedfrom

120576eff =120574119897mat + 119885119888air120574119897air + 119885119888mat

tan 120575 =120574119897mat sdot 119885119888mat120574119897air sdot 119885119888air

(8)

where 120576eff is the effective relative permittivity and tan 120575 is thedielectric losses

International Journal of Antennas and Propagation 3

Figure 2 Sample of Delrin and Teflon for 119889 = 5mm and 15mm

1 2 31

2

3

4

No air gapInner air gapTwo air gaps

Real

par

t of r

elat

ive p

erm

ittiv

ity

Frequency (GHz)

Figure 3 Real part of relative permittivity of Delrin

44 Machining of the Samples The advanced hypothesis ofthe measurement technique in coaxial line (spread of a singleTEM mode in all regions of the line) requires the completefilling of the transverse section of the line by the sample(Figure 2) This involves strong machining constraints of thesample ring because of the presence of an air gap between itand the conductive walls of the line

Although mechanical tolerances met by the end of themachining process are low the manual insertion of thesample inside the line inevitably implies the presence of anair gap It will influence the accuracy of measurement resultsTo illustrate this problem we have studied the effect of theseerrors on the determination of the dielectric permittivity120576119903

Errors of measurement due to the presence of air spacebetween the sample and the line conductors are graduallylarger as the frequency increases For this we have establisheda correction (sample of 5mm long and with no air gap)

45 Correction of the Air Gap In these simulations and toreduce the number of parameters we have assumed that theair gap between the material and the outer conductor is zero


1 2 3001

01

1

Die

lect

ric lo

sses

Frequency (GHz)

Figure 4 Delrin dielectric losses

No air gapInner air gapOuter air gap

001 0101

1 10

1

10

100Re

al re

lativ

e per

mitt

ivity

erro

r (

)

Frequency (GHz)

Figure 5 Error of relative permittivity of Delrin

Figure 5 shows that the error increases very rapidly with thethickness of air space and the value of the permittivity ofthe material This has the effect of lowering the value of themeasured permittivity

To correct the errors related to the imperfections of thetest device (such as the connecting cable of the analyser thecoaxial conicalcoaxial transition associated with the discon-tinuity lineguide and metal losses due to finite conductivityof the conductors used to make the alignment of the variouselements) we added formula (9) in the MathCAD programA formula has been derived to estimate the effective complex


1 2 31

2

3

4

Rela

tive p

erm

ittiv

ity aft

er co

rrec

tion


Frequency (GHz)

Figure 6 Relative permittivity after correction of the Delrin

001

01

1

Die

lect

ric lo

sses

after

corr

ectio

n


1 2 3Frequency (GHz)

Figure 7 Dielectric losses after correction of Delrin

permittivity 120576lowast119903eff from the total capacitance consisting of a

mixture of three coaxial layers air a bulk material and air

120576lowast

119903eff = ln(119887119886)[ln( 119887119886

1199030

119903119894

) +ln(1199030

119903119894

)

120576lowast119903nom

]

minus1

(9)

where 120576lowast119903nom is the nominal complex permittivity 119886 and 119887 are

the inner and outer radii of the sample holder and 119903119894

and1199030

are the inner and outer radii of the sample To obtain agap correction formula this equation can be rearranged by

001 01 1 1001

1

10

100

Frequency (GHz)


1 times 10minus3

Relat

ive e

rror

after

corr

ectio

n (

)Figure 8 Relative permittivity error after correction of Delrin

Figure 9 Constituents of the small and large coaxial line inreflexion

renaming 120576lowast119903eff rarr 120576

lowast

119903119898

and 120576lowast119903nom rarr 120576

lowast

119903119888

(corrected complexpermittivity) and solving for 120576lowast

119903119888

(11)Wall thickness was calculated by subtracting the inner

diameter of the sample from its outer diameter and dividingthe difference by 2

To extract the initial dielectric loss we simulate a casewith (120590AP) losses and (120590SP) lossless dielectrics The differencebetween the two extracted electrical conductivities gives theelectrical conductivity of the dielectric 120590

119889

after correction isgiven by the following

120590119889

= 120590AP minus 120590SP (10)

The correction of the electrical conductivity has allowed us tofind its actual value This allows to conclude that the chosenmodel and the applied extraction procedure are good

In practice we do not have material without losses andcannot perform dielectric measurements without losses

From (9) we obtain

120576119903eff119888=

120576119903eff119898

sdot ln (1199030

119903119894

)

ln (119887119886) minus 120576119903eff119898

sdot ln [1198871198861199030

119903119894

] (11)


Figure 10 Photo of small coaxial line in reflection (15mm)

Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 1016

18

2

22

24

2035

Frequency (GHz)

Re(120576reff1)

Figure 11 Teflon real relative permittivity (sample of 15mm)

To correct error of eccentricity we add the following formula

120576119903eff=

120576119903eff119888

radic1 + ((119878 sdot Δ sdot 120576119903eff119888) 120572)

2

(12)

where 120572 = log(119887119886) Δ = 2(119889 minus 119886)(119889 + 119886) Δ is a deviationfraction on inner diameter 119889 is the air gap between centralconductor and sample and 119904 = Δ119888(119889minus119886) is the parameter ofeccentricity

Without eccentricity (119904 = 0) andwith complete eccentric-ity (119904 = 1)

5 Simulation Results

Thesimulation results of the set of Figures 1 to 8were obtainedafter extraction of the permittivity from the 11987811 parameters InFigures 3 and 4 we can see that the real part of the relativepermittivity (of Delrin) and the dielectric losses decreasewhen the frequency and the value of the gaps increasedwhereas Figure 5 shows that the error of relative permittivityof Delrin increases with the value of the gaps and weak fora line without gap After correction the results of Figures

001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

01

001

1

1 times 10minus5

1 times 10minus4

1 times 10minus3

310minus4

Tan 1205751

Figure 12 Teflon dielectric losses (sample of 15mm)

001 01 1 10

Frequency (GHz)

01

1

10

100

Rela

tive p

erm

ittiv

ity er

ror (

)

Err Re120576r

Figure 13 Teflon relative permittivity error (sample of 15mm)

Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 10

Frequency (GHz)

1

2

3

4

365

Figure 14 Delrin real part of effective relative permittivity (sampleof 15mm)


001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

01

001

1

Tan 1205751

Figure 15 Delrin dielectric losses (sample of 15mm)

001 01 1 10

Frequency (GHz)

Real

par

t of r

elat

ive p

erm

ittiv

ity

1

2

3

4

365

Re(120576reff1)

Figure 16 Delrin relative permittivity (sample of 5mm long andwith no air gap)

001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

1 times 10minus3

01

001

1

Tan 1205751

Figure 17 Delrin dielectric losses (sample of 5mm long and withno air gap)

Frequency (MHz)10

10

100 1 times 103 1 times 1041 times 10minus4

1 times 10minus3

001

01

1

Relat

ive p

erm

ittiv

ity an

d di

elec

tric

loss

es

Tan 120575m

Re(120576reff m)

Figure 18 Teflon relative permittivity and dielectric losses (sampleof 5mm long and with no air gap)

Frequency (MHz)101 100 1 times 103 1 times 104

1 times 10minus3

001

01

10

1

Relat

ive p

erm

eabi

lity

and

mag

netic

loss

es

Tan MmRe(Ureffm)

Figure 19 Teflon relative permeability and magnetic losses (sampleof 5mm long and with no air gap)

6 7 and 8 show clearly the improvement of the results andthe cancellation of the effect of the air gap We see thatthe three curves merge into one especially for the dielectriclosses

6 Experimental Validation

Before beginning measurements we must define the refer-ence plans that will support the practical implementationof the cell and then we perform the calibration proce-dure to eliminate systematic errors of the measurement of


the reflection coefficient Finally we validate the imple-mentation method from the measurement of the com-plex permittivity of dielectric materials with well-knownproperties

61 Realization of the Measuring Cell To ensure the repre-sentativeness of the measurements performed on the dis-continuity lineguide with respect to the electromagneticproperties of the samples the measuring cell must have anoutside diameter equal to 115mm Under these conditionsthe connection of the measuring cell to the vector networkanalyser requires the use of a coaxialcoax transition Thistransition consist in an SMA connector suitable for theconnecting cable of the network analyser (diameter 35mm)and a coaxial conical portion which ensures the progressivevariation of the diameter of the line between the coaxial lineand the discontinuity which has a line diameter of 5mm(Figure 9)

To limit the effets of propagation discontinuity in theconical section the ratio between the internal diameter of theouter conductor and the diameter of the central conductor ison the whole length of the section 23mm (conditions of 50ohms impedance matching)

62 Experimental Results To exploit reflectance measureswe used a network analyser type VNAE5062A This impliespositioning the reference plan of the measurement of thereflection coefficient at the end of the coaxial access lineon the front face of the cylindrical sample characterization(Figure 10)

The experimental results of Figures 11 12 and 13 presentrespectively the relative permittivity the dielectric losses andthe relative permittivity error for Teflon (sample of 15mm) InFigures 14 15 16 17 and 18 we plot the parameters of DelrinThese results were considered very good since the obtainedvalues of all these parameters were very near to the typicalvalues in this considered frequency range Figures 17 and 18are obtained for Derlin without air gap (sample of 5mm)Wecan notice fromFigure 18 that the losses are less than 01 after50MHz For the same sample and in the same conditions thesimulation and experimental results are very closeThis goodagreement proves for the corrected measurements by usingthe kit short-circuitopen-circuitstandard material that theused technique and the calibration procedure were successfulover the entire frequency band

In Figures 18 and 19 we plot respectively the relativepermittivity and the relative permeability andmagnetic lossesof Teflon (sample of 5mm long and with no air gap) Thesefigures show that the losses are constant over the entirefrequency range Figure 20 illustrates the relative permittivityfor Delrin (sample of 5mm long and with air gap of 05mmin inner diameter) The red traces are the corrected valuesobtained by using (11) and (12) to take into account the airgap effects

We present respectively in Figure 21 the initial andcorrected values of relative permittivity for Teflon (sample of5mm long and with air gap of 05mm in inner diameter) We

0 1 times 103 2 times 103 3 times 103

Frequency (MHz)

1

2

3

4

5

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m2)3

Re(120576reff m)

Figure 20 Delrin relative permittivity (sample of 5mm long andwith air gap of 05mm in inner diameter)


1

15

2

25

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m)

Re(120576reff m2)

Figure 21 Teflon relative permittivity (sample of 5mm long andwith air gap of 05mm in inner diameter)

notice here that after correction the relative permittivity isimproved

7 Application of the Method forMultilayer Materials

We will show that the proposed method can also be appliedsuccessfully to multilayer materials We rely primarily onthe principles of the coaxial probe in reflection Let us put


a bilayer dielectric in the metallic cavity (Figure 22(a)) InFigure 2 we invert the position of the layers In literaturestudies have shown that the coaxial probe is sensitive to thesurface of the sample which is in contact with the centralconductor [6] This sensitivity is due to the distribution ofelectromagnetic fields in the vicinity of the central conductor[7 8] This implies that the overall capacitance created is notthe same as the orientation of the sample (120576

1199031

= 1205761199032

)

71 Extraction of Each Layerrsquos Complex Permittivity Weconsider that the bilayer dielectric in contact with thegreatest metal surface (point C) entails that overall losses aredepending on the orientation of the sample Moreover at theinterface of the two dielectrics (point B) the capacitance isthe same regardless of the orientation of the sample

We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)

When we put (13) in (14) we obtain the effective permittivityof the first layer as a function of that of the reference

120576119903-Delrin = (2 sdot radic120576119903-tot minus radic120576119903-Teflon)

2

(16)

This extraction method has the privilege of not necessarilybeing based on prior knowledge of the thickness of each layerOnly the thickness of the aggregate layer must be known inorder to meet the dimensions of the test frame

72 Experimental Results We have plotted in Figures 23 and24 respectively the relative permittivity and the magneticlosses of Delrin (sample 5mm without air gap) In Figure 23we show that the read plot which represents the relative per-mittivity of the Delrin obtained using the bilayers methodsis praticallly the same blue plot obtained with single samplein the same frequency range between 10MHz and 1GHz butthe accepted value is until 100MHz as shown in Figure 24in this range of frequecy the dielectric losses are between2 at 10MHz and 5 at 100MHz We have obtained a goodprecision

Theuse of coaxial fixture in reflection so as to characterizemultilayers materials has led to satisfactory results Theapplication of dielectric Delrin permits us to prove themethodrsquos feasibility

Meanwhile the method is based on the principle thatelectrical parameters of one layer are well known and that theglobal thickness of the layers is precisely known

8 Conclusion

We presented the technique of coaxial probe having acavity end to characterize single and bilayer materials Itsfeasibilitywas validated by electromagnetic simulation resultsand experimental results after completing the experimentalaluminum test frame which is lighter than copper

D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)

Figure 22 (a) Bilayer coaxial probe in the presence of a sample ofthe same thickness (configuration 1) (b) Bilayer coaxial probe in thepresence of a sample of the same thickness (configuration 2)

120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10

Two couchesReference



Tan(120575)

001

01

1

Frequency (GHz)001 01 1 10

1 times 10minus3

ReferenceTwo couches


This technique is applicable to dielectrics and semi-conductors It is solely based on the reflection parametersusing a capacitive model and helps to increase frequencyband of model Although efforts are yet to be made forits improvements especially in the extraction losses formultilayer materials this method is easy to implement andrapid in extracting electrical parameters and precise in termsof repeatability whose relative error is about 5This methodoffers the possibility to extract low loss tangent (2 sdot 10minus4) up to1 GHz using an SMA connector

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C C Courtney ldquoTime-domain measurement of the elec-tromagnetic properties of materialsrdquo IEEE Transactions onMicrowave Theory and Techniques vol 46 no 5 pp 517ndash5221998

[2] T W Athey M A Stuchly and S S Stuchly ldquoMeasurement ofradio frequency permittivity of biological tissues with an open-ended coaxial line part Irdquo IEEE Transactions on MicrowaveTheory and Techniques vol 30 no 1 pp 82ndash86 1982

[3] K J Bois L F Handjojo A D Benally K Mubarak andR Zoughi ldquoDielectric plug-loaded two-port transmission linemeasurement technique for dielectric property characterizationof granular and liquid materialsrdquo IEEE Transactions on Instru-mentation amp Measurement vol 48 no 6 pp 1141ndash1148 1999

[4] S-G Pan ldquoCharacteristic impedances of coaxial system consist-ing of circular and noncircular conductorsrdquo IEEE TransactionsonMicrowaveTheory and Techniques vol 36 no 5 pp 917ndash9211988

[5] J Baker-Jarvis TransmissionReflection and Short-Circuit LinePermittivity Measurements National Institute of Standards andTechnology 1990

[6] M Moukanda F Ndagijimana J Chilo and P Saguet ldquoCar-acterisation desMateriauxMulticouches enUtilisant une SondeCoaxiale en Presence dun Plan De Masserdquo in 15eme JourneesNationales Micro-Ondes (JNM) Toulouse France Mai 2007

[7] N Belhadj-Tahar O Meyer and A Fourrier-Lamer ldquoBroad-band microwave characterization of bilayered materials usinga coaxial discontinuity with applications for thin conductivefilms for microelectronics and material in air-tight cellrdquo IEEETransactions on Microwave Theory and Techniques vol 45 no2 pp 260ndash267 1997

[8] N Belhadj-Tahar O Dubrunfaut and A Fourrier-LamerldquoBroad-bandmicrowave characterization of a tri-layer structureusing a coaxial discontinuity with applications for magneticliquids and filmsrdquo IEEE Transactions on Microwave Theory andTechniques vol 46 no 12 pp 2109ndash2116 1998

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P1 P2P0

Short circuit

SMA connector

Air

Sam

ple

Figure 1 Presentation of the coaxial reflective frame with sample

To move from plan P1 to plan P2 as shown in Figure 1we apply the following formula [1] with l being the lengthbetween P0 and P1

1198781015840

119894119895

= 119878119894119895

sdot 1198902sdot119895sdot120574119897

(1)

3 Presentation of the CoaxialFrame in Reflection

A coaxial frame is a coaxial line comprising a centralconductor and a cylindrical outer aluminum conductor Thisline is connected to the tester bymeans of an SMA connectorwhich is placed on one of its ends so as to measure the 11987811parameters in which the electrical parameters of the materialare extracted [2] On the termination of the coaxial line weconnect a short circuit or open circuit so that the materialunder test is in direct contact with the short circuit (Figure 1)

For the modeling of this frame we have calculated all theparameters of the transmission line as well as the dimensionsof the samples to be characterized before proceeding to thesimulation step

4 Electromagnetic Simulations and Validation

We simulated the structure of the frame with and withoutsample in the case of loss and lossless dielectric using CSTand HFSS111 simulators The simulation is made with thefollowing steps

41 Impedance Matching Bandwidth The test structure com-prises a radiating coaxial transmission line in a semi-infiniteenvironment with a given thickness and ended by a metalplate for short circuit The ratio of the inner diameter (2119886)and of the outer conductor (2119887) is set so that the characteristicimpedance of the transmission line is equal to 50Ω inwithoutsample

42 Extraction of the Electrical Parameters of the DielectricThe 11987811 parameters obtained by simulation allow easy accessto propagation phase 120574119897 in the presence and in the absence ofmaterial Consider

119885 (119878) = 119885119899 sdot1 + 119878

1 minus 119878 (2)

where 119885(119878) is the impedance characteristic function of 119878parameters 120574 is the propagation constant and 119897 is the lengthof the line

In the absence of the dielectric material we have

119885119888air = radic119885119888air119888119888 sdot 119885119888air119888119900

120574119897air = 119886 tanhradic119885119888air119888119888

119885119888air119888119900

(3)

In the presence of the dielectric material

119885119888mat = radic119885119888mat119888119888 sdot 119885119888mat119888119900

120574119897mat = 119886 tanhradic119885119888mat119888119888

119885119888mat119888119900

(4)

where 119885119888 is the characteristic impedance of the lineThese two measures of parameter 120574119897 [3 4] allow easy

access theoretically to parameters 120576119903

and tan 120575119889

of thedielectric material

From the line impedance in short circuit and open circuitto extract the propagation parameters of a transmission linewe can measure the 11987811 reflection parameters in two differentconfigurations namely the line in short circuit and the linein open circuit [5] Any transmission line can be representedby its propagation constant (119885119888 120574119897)

The input impedance119885in of a transmission line loaded byimpedance 119885

119877

is determined by the following expression

119885in = 119885119888119885119877

+ 119885119888 tanh (120574119897)119885119888 + 119885

119877

tanh (120574119897) (5)

In the case of a short-circuit line (119885119877

= 0) the impedanceseen at the input line is written as

119885in119888119888

= 119885119888 sdot tanh (120574119897) = 119885119899

1 + Γcc1 minus Γcc

= 119885cc (6)

where 119885119899

is the standard resistance that is equal to 50Ohmand Γ is a coefficient of reflexion

In the case of an open-circuit line (119885119877

= infin) theimpedance seen at the input of the line is

119885in119888119900

=119885119888

tanh (120574119897)= 119885119899

1 + Γ119888119900

1 minus Γ119888119900

= 119885119888119900

(7)

43 Extraction of the Complex Relative Permittivity Thecomplex relative permittivity and the loss angle are obtainedfrom

120576eff =120574119897mat + 119885119888air120574119897air + 119885119888mat

tan 120575 =120574119897mat sdot 119885119888mat120574119897air sdot 119885119888air

(8)

where 120576eff is the effective relative permittivity and tan 120575 is thedielectric losses



1 2 31

2

3

4


Real

par

t of r

elat

ive p

erm

ittiv

ity

Frequency (GHz)







1 2 3001

01

1

Die

lect

ric lo

sses

Frequency (GHz)



001 0101

1 10

1

10

100Re

al re

lativ

e per

mitt

ivity

erro

r (

)

Frequency (GHz)





1 2 31

2

3

4

Rela

tive p

erm

ittiv

ity aft

er co

rrec

tion


Frequency (GHz)


001

01

1

Die

lect

ric lo

sses

after

corr

ectio

n






120576lowast

119903eff = ln(119887119886)[ln( 119887119886

1199030

119903119894

) +ln(1199030

119903119894

)


]

minus1

(9)



and1199030


001 01 1 1001

1

10

100

Frequency (GHz)


1 times 10minus3

Relat

ive e

rror

after

corr

ectio

n (




lowast

119903119898


lowast

119903119888


119903119888




119889


120590119889

= 120590AP minus 120590SP (10)



From (9) we obtain

120576119903eff119888=

120576119903eff119898

sdot ln (1199030

119903119894

)

ln (119887119886) minus 120576119903eff119898

sdot ln [1198871198861199030

119903119894

] (11)



Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 1016

18

2

22

24

2035

Frequency (GHz)

Re(120576reff1)



120576119903eff=

120576119903eff119888


2

(12)





001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

01

001

1

1 times 10minus5

1 times 10minus4

1 times 10minus3

310minus4

Tan 1205751


001 01 1 10

Frequency (GHz)

01

1

10

100

Rela

tive p

erm

ittiv

ity er

ror (

)

Err Re120576r


Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 10

Frequency (GHz)

1

2

3

4

365



001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

01

001

1

Tan 1205751


001 01 1 10

Frequency (GHz)

Real

par

t of r

elat

ive p

erm

ittiv

ity

1

2

3

4

365

Re(120576reff1)


001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

1 times 10minus3

01

001

1

Tan 1205751


Frequency (MHz)10

10


1 times 10minus3

001

01

1

Relat

ive p

erm

ittiv

ity an

d di

elec

tric

loss

es

Tan 120575m

Re(120576reff m)



1 times 10minus3

001

01

10

1

Relat

ive p

erm

eabi

lity

and

mag

netic

loss

es

Tan MmRe(Ureffm)














Frequency (MHz)

1

2

3

4

5

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m2)3

Re(120576reff m)



1

15

2

25

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m)

Re(120576reff m2)







1199031

= 1205761199032

)


We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)



2

(16)





8 Conclusion


D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)


120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10




Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1 2 31

2

3

4


Real

par

t of r

elat

ive p

erm

ittiv

ity

Frequency (GHz)







1 2 3001

01

1

Die

lect

ric lo

sses

Frequency (GHz)



001 0101

1 10

1

10

100Re

al re

lativ

e per

mitt

ivity

erro

r (

)

Frequency (GHz)





1 2 31

2

3

4

Rela

tive p

erm

ittiv

ity aft

er co

rrec

tion


Frequency (GHz)


001

01

1

Die

lect

ric lo

sses

after

corr

ectio

n






120576lowast

119903eff = ln(119887119886)[ln( 119887119886

1199030

119903119894

) +ln(1199030

119903119894

)


]

minus1

(9)



and1199030


001 01 1 1001

1

10

100

Frequency (GHz)


1 times 10minus3

Relat

ive e

rror

after

corr

ectio

n (




lowast

119903119898


lowast

119903119888


119903119888




119889


120590119889

= 120590AP minus 120590SP (10)



From (9) we obtain

120576119903eff119888=

120576119903eff119898

sdot ln (1199030

119903119894

)

ln (119887119886) minus 120576119903eff119898

sdot ln [1198871198861199030

119903119894

] (11)



Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 1016

18

2

22

24

2035

Frequency (GHz)

Re(120576reff1)



120576119903eff=

120576119903eff119888


2

(12)





001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

01

001

1

1 times 10minus5

1 times 10minus4

1 times 10minus3

310minus4

Tan 1205751


001 01 1 10

Frequency (GHz)

01

1

10

100

Rela

tive p

erm

ittiv

ity er

ror (

)

Err Re120576r


Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 10

Frequency (GHz)

1

2

3

4

365



001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

01

001

1

Tan 1205751


001 01 1 10

Frequency (GHz)

Real

par

t of r

elat

ive p

erm

ittiv

ity

1

2

3

4

365

Re(120576reff1)


001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

1 times 10minus3

01

001

1

Tan 1205751


Frequency (MHz)10

10


1 times 10minus3

001

01

1

Relat

ive p

erm

ittiv

ity an

d di

elec

tric

loss

es

Tan 120575m

Re(120576reff m)



1 times 10minus3

001

01

10

1

Relat

ive p

erm

eabi

lity

and

mag

netic

loss

es

Tan MmRe(Ureffm)














Frequency (MHz)

1

2

3

4

5

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m2)3

Re(120576reff m)



1

15

2

25

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m)

Re(120576reff m2)







1199031

= 1205761199032

)


We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)



2

(16)





8 Conclusion


D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)


120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10




Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 2 31

2

3

4

Rela

tive p

erm

ittiv

ity aft

er co

rrec

tion


Frequency (GHz)


001

01

1

Die

lect

ric lo

sses

after

corr

ectio

n






120576lowast

119903eff = ln(119887119886)[ln( 119887119886

1199030

119903119894

) +ln(1199030

119903119894

)


]

minus1

(9)



and1199030


001 01 1 1001

1

10

100

Frequency (GHz)


1 times 10minus3

Relat

ive e

rror

after

corr

ectio

n (




lowast

119903119898


lowast

119903119888


119903119888




119889


120590119889

= 120590AP minus 120590SP (10)



From (9) we obtain

120576119903eff119888=

120576119903eff119898

sdot ln (1199030

119903119894

)

ln (119887119886) minus 120576119903eff119898

sdot ln [1198871198861199030

119903119894

] (11)



Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 1016

18

2

22

24

2035

Frequency (GHz)

Re(120576reff1)



120576119903eff=

120576119903eff119888


2

(12)





001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

01

001

1

1 times 10minus5

1 times 10minus4

1 times 10minus3

310minus4

Tan 1205751


001 01 1 10

Frequency (GHz)

01

1

10

100

Rela

tive p

erm

ittiv

ity er

ror (

)

Err Re120576r


Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 10

Frequency (GHz)

1

2

3

4

365



001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

01

001

1

Tan 1205751


001 01 1 10

Frequency (GHz)

Real

par

t of r

elat

ive p

erm

ittiv

ity

1

2

3

4

365

Re(120576reff1)


001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

1 times 10minus3

01

001

1

Tan 1205751


Frequency (MHz)10

10


1 times 10minus3

001

01

1

Relat

ive p

erm

ittiv

ity an

d di

elec

tric

loss

es

Tan 120575m

Re(120576reff m)



1 times 10minus3

001

01

10

1

Relat

ive p

erm

eabi

lity

and

mag

netic

loss

es

Tan MmRe(Ureffm)














Frequency (MHz)

1

2

3

4

5

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m2)3

Re(120576reff m)



1

15

2

25

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m)

Re(120576reff m2)







1199031

= 1205761199032

)


We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)



2

(16)





8 Conclusion


D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)


120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10




Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 1016

18

2

22

24

2035

Frequency (GHz)

Re(120576reff1)



120576119903eff=

120576119903eff119888


2

(12)





001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

01

001

1

1 times 10minus5

1 times 10minus4

1 times 10minus3

310minus4

Tan 1205751


001 01 1 10

Frequency (GHz)

01

1

10

100

Rela

tive p

erm

ittiv

ity er

ror (

)

Err Re120576r


Real

par

t of r

elat

ive p

erm

ittiv

ity

001 01 1 10

Frequency (GHz)

1

2

3

4

365



001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

01

001

1

Tan 1205751


001 01 1 10

Frequency (GHz)

Real

par

t of r

elat

ive p

erm

ittiv

ity

1

2

3

4

365

Re(120576reff1)


001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

1 times 10minus3

01

001

1

Tan 1205751


Frequency (MHz)10

10


1 times 10minus3

001

01

1

Relat

ive p

erm

ittiv

ity an

d di

elec

tric

loss

es

Tan 120575m

Re(120576reff m)



1 times 10minus3

001

01

10

1

Relat

ive p

erm

eabi

lity

and

mag

netic

loss

es

Tan MmRe(Ureffm)














Frequency (MHz)

1

2

3

4

5

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m2)3

Re(120576reff m)



1

15

2

25

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m)

Re(120576reff m2)







1199031

= 1205761199032

)


We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)



2

(16)





8 Conclusion


D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)


120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10




Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

01

001

1

Tan 1205751


001 01 1 10

Frequency (GHz)

Real

par

t of r

elat

ive p

erm

ittiv

ity

1

2

3

4

365

Re(120576reff1)


001 01 1 10

Frequency (GHz)

Die

lect

ric lo

sses

1 times 10minus3

1 times 10minus3

01

001

1

Tan 1205751


Frequency (MHz)10

10


1 times 10minus3

001

01

1

Relat

ive p

erm

ittiv

ity an

d di

elec

tric

loss

es

Tan 120575m

Re(120576reff m)



1 times 10minus3

001

01

10

1

Relat

ive p

erm

eabi

lity

and

mag

netic

loss

es

Tan MmRe(Ureffm)














Frequency (MHz)

1

2

3

4

5

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m2)3

Re(120576reff m)



1

15

2

25

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m)

Re(120576reff m2)







1199031

= 1205761199032

)


We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)



2

(16)





8 Conclusion


D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)


120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10




Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Frequency (MHz)

1

2

3

4

5

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m2)3

Re(120576reff m)



1

15

2

25

Rela

tive p

erm

ittiv

ity w

ith an

d w

ith n

o ai

r gap

Re(120576reff m)

Re(120576reff m2)







1199031

= 1205761199032

)


We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)



2

(16)





8 Conclusion


D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)


120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10




Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1199031

= 1205761199032

)


We know that

120574119897 =119895119908119897radic120576

119903

119888 (13)

120574tot119897tot = 12057411198971 + 12057421198972 (14)

119897tot = 1198971 + 1198972 (15)



2

(16)





8 Conclusion


D d

Sonde coaxialA B C

120576r1 120576r2

1205731 1205732

l1 l2

Ze1 Ze2

(a)

D d

Sonde coaxialA B C

120576r1

1205731

120576r2

1205732

l1l2

Ze1Ze2

(b)


120576998400r

Frequency (GHz)

1

2

3

4

001 01 1 10




Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Tan(120575)

001

01

1


1 times 10minus3






References











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Technique of Coaxial Frame in...

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