International journal of advanced scientific and ... - RS Publication

International journal of advanced scientific and technical research Available online on http://www.rspublication.com/ ijst/index.ht ml

Issue 2 volu me 5,October 2012 ISSN 2249-9954

Experimental Complex Permittivity Determination of Low-loss Dielectric Materials at Microwave Frequency Band N. Jebbor #1 , S. Bri #2 , A. M. Sánchez #3 , M. Chaibi#4 #1 Spectrometry Laboratory of Materials and Archeomaterials (LASMAR) Faculty of Sciences, Moulay Ismail University, Meknès – Morocco #2 Electrical Engineering Department, Technology High School (ESTM) Moulay Ismail University, Meknes- Morocco #3 Department of Communication Engineering, University of Cantabria Avd. Los Castros, Plaza de la Ciencia, s/n 39005 Santander, Spain #4 Telecommunications and Information Technologies (TTI) PCTCAN, Calle Albert Einstein 14, 39011 Santander, Spain ABSTRACT The work of this article is a contribution to the characterization of new materials at microwave frequencies and enrichment of the existing database. The transmission/reflection technique for complex permittivity determination is employed to characterize a set of low- loss dielectric materials. The algorithm for permittivity extraction eliminates mathematically the systematic errors of the experimental setup. This technique needs two uncalibrated scattering parameter measurements by the Vector Network Analyzer; the first is done with a partially filled rectangular waveguide by a standard dielectric Teflon sample (PTFE), and the second is performed with the sample under test. The relative complex permittivity of Delrin, Peek, Spanish Peek, Nylatron, Vulkollan, Arnite and Celotex materials are measured over the X-band frequencies (8.2 - 12.4 GHz), and the average relative errors between the calibrated and uncalibrated results are calculated. As other non-resonant methods, rough results are indicated of the imaginary part of the permittivity for very low- loss samples. Key words: Dielectric Materials, Complex Permittivity, Uncalibrated Measurements, Xband. Corresponding Author: Nawfal Jebbor INTRODUCTION Application of materials in the microwave, aerospace, and communications de mands an accurate knowledge of material properties such as complex permittivity and complex permeability. The active research fields like materials science and electrical and electronic engineering [1] need necessarily information about permittivity and permeability for developing novel microwave materials. In the radar absorbing material design, the complex permittivity and/or permeability are the fundamental elements that have to be taken primarily into count. In addition, the material characterization is an important issue in many industrial areas, and numerous microwave methods are proposed in literature. Each technique has its own benefits and limitations. Several Page 1



factors influence the choice of technique to obtain the desired information on material under test MUT. For example, the frequency band, the sample size, contacting or non-contacting, material state (solid, liquid and powder), etc. are the major factors to take into consideration when selecting the characterization technique. In general, microwave methods can be categorized into three groups: 1) free-space techniques; 2) resonant or cavity perturbation techniques; 3) non resonant techniques based on coaxial or rectangular waveguide. The free-space methods are employed when material is available in a large sheet and when we want to characterize composite materials that their intrinsic heterogeneity does not permit to have small representative samples of the entire material. The free-space techniques are nondestructive and contactless. They are ideally suited at variable incidence of the electromagnetic wave and for high temperature measurements. But unwanted reflections surrounding objects and diffractions from the edges of the sample make the free-space measurements less accurate. The resonant methods [2] are more accurate, but they require elaborate sample preparation, and can be applied to medium- and low- loss materials at narrow frequency band. Microwave non resonant methods [36] are widely used over a wide range of frequencies, even though these techniques are less accurate than the resonant methods. In one- and/or two-port measurement techniques, the reflection and/or transmission coefficients of a sample material filled in the coaxial line or rectangular waveguide are measured using the Vecto r Network Analyzer VNA. Using the inverse procedure, the constituent parameters of the MUT are extracted. In these measurements, the cross section of the MUT is the same of the transmission line and only the dominant mode is assumed. The work presented in this paper is a continuation of that published in [7], emphasizing the validity of the Transmission/Reflection T/R method in [7] for a variety of solid low- loss dielectric materials. Based on our knowledge, the permittivity information of these materials (Delrin, Peek, Spanish Peek, Nylatron, Vulkollan, Arnite, and Celotex) is unknown at X-band. This T/R technique is applied to uncalibrated scattering parameters (S-parameters). However, the standard calibration manipulations are not needed; these manipulation procedures produce inevitable errors affecting the final results. The calibrated and uncalibrated measurement results are compared between them and the relative errors are calculated over the X-band frequencies. THEORY The complex permittivity of dielectric material is determined with the transmission / reflection (T/R) method [7] based on the S-parameter measurements. The MUT is machined to the same section dimensions of the rectangular waveguide. The MUT is assumed non- magnetic and only the dominant mode TE10 propagates through the structure. The figure 1 presents the measurement cell partially filled by the MUT sample. We calculate the transmission matrices Mi according to: 1 S12iS21i S11iS22i S11i Mi i 1 or 2 (1) S22i 1 S21i M1 : corresponds to measurement that the waveguide is filled by the reference dielectric PTFE (Polytetrafluoroethylene) sample. M2 : corresponds to measurement that the waveguide is filled by the MUT sample. These two transmission matrices can also be written as a product of five matrices: Page 2



1 x.T ref1.T1 .Tref1 .y

M1

(2) 1 ref2

M2

x.T ref2.T2 .T

.y

The impedance jumps Air / sample / Air cause reflections of the electromagnetic wave that whose transmission matrix is Tref i

Tref i

1 1 Γi Γi 1 Γi

Γi 1 Γi 1 1 Γi γid

e

Ti

0

and Γ i

γ0 γ0

γi (μ *r 1) γi

(3)

0 i= 1 or 2 eγ i d

(4)

d

Port 1

Air

Air

MUT

Port 2

Measurement Cell Fig 1: Measurement cell waveguide partially filled by the MUT sample. The errors matrices x and y are assumed unchanged during the measurements. They represent the systematic errors of the experimental setup like source and load match errors, tracking (frequency) errors, effects of wires carrying interconnections, hardware imperfections of VNA, etc. [3][7][8]. Ti is the transmission matrix of an ideal line with length d and propagation constant γ i . γ0

2π j 1 λ0

λ0 λc

2

;

γi

λ0 λc

2π * * j ε riμ r λ0

2

γ 0 and γ i : The propagation constantsin vacuumandthe dielectric ε *ri respectively. c

*

and

0

: wavelength cutoff of the waveguide and wavelengthin free spacerespectively.

and *r2 are the complex permittivity of the PTFE and MUT samples respectively. To remove the influence of the two error-ports on the device parameters, asimpleprocedure basedon the product andthe inversematrixis used. Matrix product of M1 and M2 -1 is written in theform of equation(5). r1

M1.M2

1

1 1 x.Tref1.T1.Tref1 .Tref2.T2 1.Tref2 .x

1

(5) Page 3



It is obvious thatthe matrix y iseliminated. The equation (5) shows that the matrices M 1.M 2 1 and 1 1 are similar, thisimplies that theyhave the sametrace [7], defined bythe Tref1.T1.Tref1 .Tref2.T2 1.Tref2 sum ofthe diagonal elements of the square matrix M1 M2 -1 . 1 1 1 (6) Tr(M1.M2 ) Tr(Tref1.T1.Tref1 .Tref2.T2 1.Tref2 ) Tr is the trace of the square matrix. 1 1 Let’s f (ε *r 2 ) Tr(T ref1.T1 .Tref1 .Tref2.T2 1 .Tref2 ) , f is a function of ε *r 1 , λ 0 , λ c and d where ε*r 2 is the single unknown. Many complex values of ε *r 2 can satisfy the function f. If a good initial guess of ε *r 2 is available, solving function f iteratively leads directly to the true value of ε *r 2 . In this section, we have proposed a rigorous mathematical approach based on the wave cascading matrix without any approximation. This approachtakes into account allreflectionsof the electromagnetic wave on bothsidesof thesample through the waveguide. The method is more flexible; and it can be applied to the calibrated or uncalibrated S-parameter measurements. The technique eliminates mathematically the out-port errors of the measurement cell. Two measurements in T/R are sufficient to evaluate the complex permittivity of the dielectric sample; the first is that the sample holder filled with the reference dielectric PTFE ( * r1 =2.1-j0.0016), and the second with the MUT. A precise location of the sample in the waveguide is not needed. The nonlinear function is solved using any two-dimensional root finding algorithms [9]. NUMERICAL VALIDATION The finite element method (FEM) is well established as a versatile numerical tool for solving eigenvalues and scattering parameters of a great variety of electromagnetic structures. A wellknown drawback of the method is the relatively large amount of memory space and required CPU time, in particular case, for the 3D full-wave analysis. Several structures can be reduced to 2D electromagnetic analysis. This yields a further reduction in the computational requirements. In this paper, we simulate the measurement cell presented in figure 1by HFSS and COMSOL MultiPhysics software based on the FEM. HFSS and COMCOL are employed to solve the field problem of the studied structure for 3D and 2D full-wave analysis respectively. The dielectric characterization technique of section 2 is applied to the calculated S-parameters in order tovalidate numerically the proposed technique at X-band frequencies.The figures 2a and2b are the simulated structures in COMSOL and HFSS respectively. They represent a rectangular waveguide WR90 of length equal to 80 mm. The MUT of length d=10 mm is filled into the waveguide. The S-parameters are calculated at ports 1and 2 and the microwave source is implemented only in port 1. Because it is a key parameter for the electromagnetic problem, the electric field distribution in the case of 2D simulation is presented in figures 3a and 3b at 8.2 GHz and 12.4 GHz. The MUT is the Silicon ( r=12.1, bulk conductivity =10-12 S/m). The S-parameters of the tested structures were obtained by performing 2D and 3D simulations. The simulated results of relative complex permittivity of Silicon and Mica ( r=6, =2.01.1015 S/m) are presented in figures 4 and 5. With the help of the proposed technique, we track down the real and the imaginary parts of the relative permittivity implemented in the material properties of the software. In order to verify the accuracy, the simulation results are compared between them and a very small relative error nearly equals to zero can be noticed. This may be due to the influence of evanescent higher modes. A general viewpoint, we can conclude that analyzing the structure can be based on the fundamental mode TE10 only with a significant reduction in memory space and computational time in the 2D case. Page 4


PEC

Air

MUT

d=10 mm

Port 2

Port 1

80 mm

Air


PEC

(a)

Air Air

PEC

(b) Fig 2 : Simulation of partially filled waveguide WR90 in COMSOL (a) and HFSS (b). d is the length of the dielectric sample. The top and bottom in (a) and all external surfaces except ports in (b) are perfect electrically conducting (PEC).

(a)

(b)

Fig 3: Schematic of the FEM -calculated electric field distribution in the 2D case at 8.2 GHz (a) and 12.4 GHz (b). The MUT is the Silicon ( r=12.1). The microwave source is implemented in port 1. On the PEC boundary, the tangential components of the electric field and the normal component of the magnetic field must vanish.

Page 5

International journal of advanced scientific and technical research Available online on http://www.rspublication.com/ ijst/index.ht ml 0.05 HFSS 3D COMSOL 2D 6.05

6

5.95

5.9

8.5

9

9.5

10 10.5 11 Frequency (GHz)

11.5

Imaginay part of complex permittivity

Real part of complex permittivity

6.1


0.03 0.02 0.01 0 -0.01 -0.02 -0.03

12

HFSS 3D COMSOL 2D

0.04

8.5

9

9.5


11.5

12

(a) (b) Fig 4 : Real and imaginary parts of relative complex permittivity of a Mica sample over the X-band obtained using the proposed method. 2D and 3D simulations are performed with COMSOL and HFSS software. 0.05 HFSS 3D COMSOL 2D

12.16

12.12

12.08

12.04

12

8.5

9

9.5


11.5

12

Imaginary part of complex permittivity


12.2

HFSS 3D COMSOL 2D

0.03

0.01

-0.01

-0.03

-0.05

8.5

9

9.5


11.5

12

(a) (b) Fig5 : Real and imaginary parts of relative complex permittivity of a Silicon sample over the X-band obtained using the proposed method. 2D and 3D simulations are performed with COMSOL and HFSS software.

EXPERIMENTAL SETUP We consider the measurement setup shown in figure 6. The MUT with thickness d=10mm is imprecisely located in the WR90 rectangular waveguide of sections (22.86×10.16) mm². The E8634A VNA is connected to two coaxial-to-waveguide adapters. We suppose that only the dominant mode TE10 propagates in the structure. The dielectric samples are machined to the same waveguide sections.The uncalibrated S-parameters of PTFE and MUT are measured. Then, the computer program can determine the complex permittivity of the MUT. In the following section, the uncalibrated and calibrated results were compared for validation of the employed method proposed in second section. The Thru-Reflect-Line TRL calibration technique [10] is utilized for calibrating the experimental setup. All measurements are performed at [8.2-12.4] GHz band with 201 frequency points.

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To E8634A Vector Network Analyzer Ports

Calibration planes

30 mm Air

d=10 mm

40 mm Air

MUT

80 mm

Coaxial-to-Waveguide Adapter

WR90 Waveguide

Fig 6 :The rectangular waveguide measurement setup. EXPERIMENTAL RESULTS AND DISCUSSION The proposed method was used to determine the relative complex permittivity of seven low- loss dielectric materials cited above. According to our knowledge, these materials are not cited in literature and especially their permittivity information over X-band frequencies. Given its stability, the relative complex permittivity of PTFE ( * r1 =2.1-j0.0016) is taken as a reference dielectric and the S-parameters of PTFE sample are measured only once. A single specimen of each material is necessary to extract its dielectric constant. The table 1 presents the average values of the relative complex permittivity of the MUT < * calib> and < * uncalib>, and the average relative error percentage on the real and imaginary parts defined as: %Error ' %Error "

' uncalib

' calib ' calib

" uncalib

" calib " calib

100 100

and * uncalib= ’uncalib-j ”uncalib are the complex relative permittivity of the MUT determined from calibrated and uncalibrated S-parameter measurements respectively. The average values are evaluated using the standard average such as the number of measurements points is equal to 201. *

’ ” calib= calib-j calib

201 * calib, uncalib * calib, uncalib

i 1

201 Table 1. Average relative complex permittivity < calib> and < * uncalib> determined from the calibrated and uncalibrated scattering parameter measurements, respectively. and are, respectively, the average relative error percentage on the real and imaginary parts of the complex permittivity at X-band frequencies. *

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Materials


2.9380-j0.0805 3.2032-j0.0130 3.0662-j0.0431 3.2284-j0.0804 2.9894-j0.2105 3.0949-j0.0232 4.0222-j0.3488

0.027 0.00 0.00 0.018 0.006 0.019 0.019

2.484 6.154 3.944 5.099 1.187 7.327 1.089

Calculations based on measured information have indicated that the error in the real part is very small (close to zero), but that in the imaginary part can be large (within 7.5%) for the used lowloss materials. Like any other S-parameter based methods, this is a common phenomenon. We note according to the error values that the relative error in the imaginary part decreases considerably toward 1% for Vulkollan and Celotex samples. The latter two materials have significantly high dielectric losses compared to the other studied materials; it appears that the method is well adapted for medium- loss materials. The figures 7 and 8 represent the variation of the real and imaginary parts of the complex permittivity over the X-band. It is seen that the permittivity values are very stable over the frequency range and near to the average values cited in the table 1; except the Celotex sample, that the real part decreases from 4.1 to 3.95. An overall view in both figures, the imaginary parts of all samples are not stable like the real parts, which explain the high average error values in the imaginary parts. Assuming that the experimental conditions are considered the same for all samples, the errors produced between calibrated and uncalibrated results can be explained to the uncertainty in sample lengths and the difference between the eliminating methods of the systematic errors: mathematically or experimentally.


4 Celotex 3.8 Nylatron Peek

3.6

Arnite Spanish Peek Delrin

3.4

Vulkollan

3.2 3 8

8.5

9

9.5

10 10.5 Frequency (GHz)

11

11.5

12

12.5

Fig 7 :Measured real part of the relative complex permittivity over the X-band using uncalibrated S-parameter measurements.

Page 8


Imaginary part of complex permittivity

0.4


Celotex

0.35 0.3 Vulkollan 0.25 0.2 0.15

Nylatron

Spanish Peek

Delrin

Peek

0.1 Arnite

0.05 0

8

8.5

9

9.5

10 10.5 Frequency (GHz)

11

11.5

12

12.5

Fig 8 : Measured imaginary part of the relative complex permittivity over the X-band using uncalibrated S-parameter measurements. CONCLUSION We proposed a dielectric characterization for a set of dielectric materials not cited in the literature. We utilized the Transmission/Reflection technique. This method needs two scattering parameter measurements; the first is performed with a filled rectangular waveguide by a standard dielectric that its complex permittivity is stable and well known over the X-band, and the second is done, in the same experimental conditions, with the material under test. This technique is well suited for the calibrated or uncalibrated measurements. The relative errors between these two types of measures are calculated for each sample. Errors in the real parts are close to zero, but in the imaginary parts they are within 7% for very low-loss and within 1% for medium- loss materials.

REFERENCES [1] L. F. Chen, C. K. Ong,, C. P. Neo, V. V. Varadan, and V. K. Varadan, Microwave electronics: measurement and materials characterization,John Wiley & Sons, West Sussex, England, 2004. [2] E. Li, Z.P. Nie, G. Guo, Q. Zhang, Z. Li, and F. He, Broadband measurements of dielectric properties of low- loss materials at high temperatures using circular cavity method, Progress In Electromagnetics Research PIER,Vol.92, pp.103-,2009. [3] J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick,Improved technique for determining complex permittivity with the transmission/reflection method,IEEE Trans. Microwave Theory Tech.,Vol.38(8), pp.1096-1103,1990. [4] A. Boughrit, C. Legrand, A. Chapoton,Noniterative stable transmission/reflection method for low- loss material complex permittivity determination, IEEE Trans. Microwave Theory Tech.,Vol.45(1), pp.52-57, 1997. [5] M. D. Belrhiti, S. Bri, et al.,Complex permittivity measurement for dielectric materials at microwave frequencies using rectangular waveguide,European Journal of Scientific Research., Vol.49(2), pp.234-248, 2011. Page 9



[6] U. C. Hasar, M. T. Yurtcan,A microwave method based on amplitude-only reflection measurements for permittivity determination of low-loss materials,Measurement.,Vol.43, pp.1255-1265, 2010. [7] N. Jebbor, S. Bri et al.,Complex permittivity determination with the transmission / reflection method,International Journal of Emerging Sciences.,Vol.1(4), pp.682-695, 2011. [8] U. C. Hasar,A new calibration- independent method for complex permittivity extraction of solid dielectric materials,IEEE Microwave and Wireless Components Letters, Vol.18(12), pp.788-790, 2008. [9] W. H. Press, S. A. Teukolsky, W. T. Vtterling, and B. P. Flannery,Numerical Recipes in C: The art of scientific computing,Cambridge Univ. Press, New York, 1992. [10] G. F. Engen, and C. A. Hoer,Thru-Reflect-Line: an improved technique for calibrating the dual six port automatic network analyzer,IEEE Microw. Theory Tech.,Vol.27(2), pp.987993, 1979.

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