A new technique is presented to determine the complex permittivity of each layer for a bi-layer dielectric material. The bilayer material sample is loaded in a Ku-band rectangular waveguide WR62 and its two port S-parameters are measured as a function of frequency using the E8634A Network Analyzer. Also, by applying transmission (ABCD) matrix, expressions for the S-parameters of the bi-layer dielectric material as a function of complex permittivity of each layer are developed. To estimate the complex permittivity of each layer’s dielectric material, the square sums of errors between the measured and calculated S-parameters are minimised using a nonlinear optimization algorithm. The complex permittivity of each layer for a bi-layer dielectric material such as FR4-Teflon, FR4-Delrin and Delrin-Teflon are determined at the Ku-band frequencies, and the average relative errors between the individual dielectric materials and those of each individual layer of the bi-layer dielectric materials are calculated

Ammor, Hassan

Chaibi, Mohamed

Elmajid, Hassan

Mediavilla Sánchez, Ángel

Terhzaz, Jaouad

Journal of Engineering Science and Technology Review

English

UCrea

	Journal of Engineering Science and Technology Review 9 (1) (2016) 61-65		Research Article   Determination of the Complex Permittivity of Each Layer for a Bi-layer Dielectric Material Using Transmission (ABCD) Matrix in Ku-Band Frequency  H. Elmajid1,*, J. Terhzaz1,2, H. Ammor1, M. Chaïbi3 and A. M. Sánchez3  1Electronic and Communication Laboratory EMI, Mohammed V University-Agdal, Rabat, Morocco 2Centre régional des métiers de l'éducation et de la formation(CRMEF), Casablanca, Morocco 3Communications Engineering Depart.,U. of Cantabria, Los Castros  Av.s/n 39005,Santander, Spain  Received 1 February 2016; Accepted 10 April 2016 ___________________________________________________________________________________________  Abstract  A new technique is presented to determine the complex permittivity of each layer for a bi-layer dielectric material. The bi-layer material sample is loaded in a Ku-band rectangular waveguide WR62 and its two port S-parameters are measured as a function of frequency using the E8634A Network Analyzer. Also, by applying transmission (ABCD) matrix, expressions for the S-parameters of the bi-layer dielectric material as a function of complex permittivity of each layer are developed. To estimate the complex permittivity of each layer’s dielectric material, the square sums of errors between the measured and calculated S-parameters are minimised using a nonlinear optimization algorithm. The complex permittivity of each layer for a bi-layer dielectric material such as FR4-Teflon, FR4-Delrin and Delrin-Teflon are determined at the Ku-band frequencies, and the average relative errors between the individual dielectric materials and those of each individual layer of the bi-layer dielectric materials are calculated.    Keywords: Complex permittivity, Microwave, transmission ABCD matrix, Dielectric material, Optimizations methods. ___________________________________________________________________________________________  1. Introduction  The bi-layer dielectric materials are currently used in many practical applications such as microwave integrated circuits and monolithic microwave integrated circuits. By choosing the electromagnetic properties and appropriate thickness for each layer, it is possible to synthesize composite bi-layer materials with novel electromagnetic properties otherwise not found in a single material [1].  The choice of a technique of characterization is initially determined by the exploited frequency band, then by the physical properties of material. A number of techniques have been developed and used to determine the complex permittivity of single layer dielectric materials [2-3]. These include free space methods, cavity resonators techniques, and transmission line or waveguide techniques. Each technique has its distinct advantages and drawbacks. The free space methods are used when the material is available in a big sheet form [4] [5]. These measurements are less accurate because of unwanted reflections from surrounding objects. The resonant cavity measurement technique is more accurate [6]. The disadvantage of this technique is that it is narrowband. For measurements of complex permittivity of material over a wideband of frequencies, transmission line, or waveguide techniques are widely used [7-8].   In this paper, a waveguide measurement method is presented to estimate the complex permittivity εr* of each layer of a composite bi-layer material. This method requires associating an optimization program with dynamic electromagnetic analysis. The electromagnetic analysis is based on the use of transmission ABCD matrix. The complex permittivity computed from a data-processing program, using a numerical optimization procedure to match calculated and measured values of the S-parameters. Lately, the same procedure has been used for the measurement of the complex permittivity of each layer’s substrate, and good results were obtained in the Ku-band.   2. Theory   2.1 Direct Problem This section presents computation of the ABCD parameters of rectangular waveguide loaded with bi-layer dielectric sample presented in figure1. The S-parameters is found from an analysis of the electric field at the sample interfaces.   Fig.1 Rectangular waveguide loaded with bi-layer dielectric material.   Assuming that only the dominant TE10 mode propagates in the loaded waveguide (see Fig. 1), the formulation of the Sij-parameters can be expressed in terms of bi-layer dielectric material sample thickness (L1,L2) and unknown permittivity  (εr1, εr2), using ABCD-parameters as follows [9-10]: Jestr  JOURNAL OF Engineering Science and Technology Review   www.jestr.org  ______________      *  E-mail address: hassinfo_10@yahoo.fr ISSN: 1791-2377 © 2016 Eastern Macedonia and Thrace Institute of Technology.  All rights reserved.  	H. Elmajid, J. Terhzaz, H. Ammor, M. Chaïbi and A. M. Sánchez/ Journal of Engineering Science and Technology Review 9 (1) (2016) 61-65 		62  					 A# B#C# D#	= 	cosh γ#L# Zsinh γ#L#1234 567686cosh γ#L#            (1)\  													 A BC D 	= 		A# B#C# D##9:;																																						(2)		   Where γ#,	Z# and  Z?	 are the propagation constant, wave impedance of the  material sample and  empty waveguide impedance respectively, and given as:  γ =πaB− ωBµF∗εF∗																																																																(3)  Z# =jωµγ#																																																																																			(4)  Z? =jωµ?γ?																																																																																				(5)   Where (a) is the appropriate (maximum) cross-sectional dimension of the waveguide, (εr1, εr2) are the complex permittivity relative of bi-layer dielectric material and ω is the angular frequency.  The ABCD-parameters can be directly converted to S-parameters using the following equations:   S;; =A + B/Z? − CZ? − D	)X																																														(6)  S;B =2(AD − CB)X																																																																(7)  SB; = 	2X																																																																																			(8)  SBB = 	−A + B/Z? − CZ? + D	X																																										(9)  		X = 	 A + B/Z? + CZ? + D	 																																														(10)  2.2 Inverse Problem This section presents computation of the complex dielectric constant in a given sample with a specific prior knowledge of the thickness of each layer. For this an optimization method on MATLAB [11], by using fminsearch function which is based on the Nelder-Mead sequential simplex algorithm[12].   which finds the minimum of a scalar function of several variables from an initial guess of the complex permittivity was   εr'= 1.0, εr''=0.001 and optimization settings by using maximum number of function evaluations= 1000, and termination tolerance on the function value = 10-08 to find the complex permittivity of each layer of bi-layer dielectric sample to match the measured S29#-parameters and calculated Sij-parameters. The error function (objective function) we want to minimize is written as follows:  F = ((	Real(S29(εF[ , εF[[) −2,9:;,BS29#))B				  + Imag S29 εF[ , εF[[ − S29# )B 																																													(11)   With                F=	F εF;[ , εF;[[ , εFB[ , εFB[[    3. Experimental Setup and Results   We consider the measurement setup shown in figure 2. The Sij-parameters at references plane of a Ku-band rectangular waveguide WR62 (with dimensions: a=15.8mm and b=7.9mm) loaded by a   bi-layer dielectric material was measured using Network Analyzer. Before the measurements, a calibration using a standard waveguide calibration kit is done to measure the Sij-parameters at references plane. The material sample is sufficiently machined, in order to minimize the effect of the gap between conductive walls and the sample material to be characterized. However, the sample occupies a part of the cutting plane of the waveguide. All measurements are performed at Ku- band with 401 frequency points.   (a)  (b) Fig. 2 Rectangular waveguide measurement setup loaded by a bi-layer dielectric material H. Elmajid, J. Terhzaz, H. Ammor, M. Chaïbi and A. M. Sánchez/ Journal of Engineering Science and Technology Review 9 (1) (2016) 61-65 		63  To validate  the  direct  problem, the Sij-parameters of rectangular waveguide loaded by the bi-layer dielectric material FR4 (εr′=4.4,εr″=0.08 and thickness D1=1.5mm)  with  Teflon  (εr′= 2.08, εr″= 0.002 and thickness D2=1.9mm) are calculated using the procedure described in section (2.1) and measured with  E8634A Network Analyzer as shown in figure 3. It is seen, from these results, an excellent agreement between measured and calculated Sij-parameters.  (a) (b) Fig.3 Measured and calculated Sij-parameters of rectangular waveguide loaded by the bi-layer dielectric sample FR4 (εr′=4.4, εr″=0.08) with Teflon (εr′= 2.08, εr″= 0.002).    For the inverse problem, using the procedure described in sections (2.1) and (2.2), the complex permittivity (εr', εr'') of each layer for bi-layer dielectric material was determined in the Ku-band frequencies. In the first estimate for the starting frequency, the initial guess of the complex permittivity was εr'= 1.0 and εr''=0.001. To validate our method we characterize a single layer dielectric material using iterative Nicholson Ross method [13]. This method allows to determine the complex permittivity of single layer dielectric material, but it does not allow to determine the complex permittivity of each layer for bi-layer material. The values of complex permittivity of FR4 with thickness D1=1.5mm and Teflon with thickness D2=1.9mm for bi-layer material FR4-Teflon are determined and plotted in fig.4.   The results obtained for the complex permittivity of each layer for bi-layer FR4-Teflon by using the procedure described in this work are in good agreement with the results obtained of the same single layer of Teflon and FR4 using iterative Nicholson Ross method [13].  Fig.4 Complex relative permittivity of each layer for bi-layer material FR4-Teflon by Transmission ABCD parameters and Iterative Nicholson Ross   To validate this technique, the complex permittivity (εr', εr'') of Delrin with thickness D1=2mm and Teflon with thickness D2=1.9mm for bi-layer Delrin-Teflon were determined in the Ku-band frequencies and presented in figure 5. From this figure, it is seen that the results obtained agree quite well with the results obtained with iterative Nicholson Ross method [13]. Using the same procedure as described above, the complex permittivity (εr', εr'') of FR4 with thickness D1=1.5mm and Delrin with thickness D2=2mm for bi-layer FR4-Delrin were determined in the Ku-band frequencies and shown in fig.6. The results in this figure are compared very well with the results obtained with iterative Nicholson Ross method [13], which agree well with the published data imply that this technique is able to provide acceptable accuracy in real applications.  The table 1 shows that the error in the real part of complex permittivity is small (within 1.96%), but in the imaginary part can be large (≤ 3.7%) for the studies materials. The results show a good agreement between the average values of the relative complex permittivity of individual dielectric materials and those for each layer of the bi-layer dielectric materials. H. Elmajid, J. Terhzaz, H. Ammor, M. Chaïbi and A. M. Sánchez/ Journal of Engineering Science and Technology Review 9 (1) (2016) 61-65 		64  Fig. 5 Complex relative permittivity of each layer for bi- layer material Delrin-Teflon by Transmission ABCD parameters and Iterative Nicholson Ross   Fig 6 Complex relative permittivity of each layer for bi-layer material FR4-Delrin by Transmission ABCD parameters and Iterative Nicholson Ross   Table 1 Average relative complex permittivity and the average relative error percentage on the real and imaginary parts of the complex permittivity at Ku-band frequencies Bi-layer materials individual layer <  𝐫	∗ > <%Error	 𝐫	[ >  <%Error  𝐫	[[ > Bi-layer measurement (Transmission ABCD parameters) Iterative Nicholson Ross FR4-Teflon FR4 4.4670 - j0.0918 4.4089 - j0.0889 ≤1.96% ≤3.7% Teflon 2.0331 - j0.0073 2.0802 - j0.0037 FR4-Delrin FR4 4.4988 - j0.0971 4.4089 - j0.0889 Delrin 2.8553 - j0.0756 2.9023 - j0.0643 Delrin-Teflon Delrin 2.8423 - j0.0704 2.9023 - j0.0643 Teflon 2.0203 - j0.0104 2.0802 - j0.0037   The complex permittivity values estimated for FR4, Teflon and Delrin by this technique described in this work with those obtained by another method of single layer material are similar. These results show that the technique developed in this work allows determining the complex permittivity of each layer for a bi-layer dielectric material.   Fig.7 presents the complex relative permittivity of each individual layer for bi-layer dielectric material FR4-Teflon with and without air-gap, by different air-gap measurement, we can say that the average relative error percentage on the real and imaginary parts of the complex permittivity of Teflon and FR4 without and with air gap within 1.7%, 3%, 7% for 0.1mm, 0.15mm, 0.20mm respectively at Ku-band frequencies. Therefore it can be concluded that the air gaps around samples has a negligible effect on the measured value of permittivity of low loss materials provided that the air-gap length is less or equal 0.1mm.  4. Conclusion  In this paper, the transmission (ABCD) matrix method combined with the fminsearch MatLab optimization search function has been presented to determine the complex permittivity of each layer for bi-layer dielectric material at the Ku-band using rectangular waveguide measurements WR62. The S-parameters are measured using the E8634A Network Analyzer and calculated using transmission (ABCD) matrix. The technique developed in this work makes it possible to determine the complex permittivity of each layer for bi-layer dielectric material. By matching the calculated value with the measured value of Sij-parameters of a Ku-band rectangular waveguide, loaded by bi-layer dielectric material. The results obtained using this method are in good agreement with values of complex permittivity obtained with iterative Nicholson Ross method. H. Elmajid, J. Terhzaz, H. Ammor, M. Chaïbi and A. M. Sánchez/ Journal of Engineering Science and Technology Review 9 (1) (2016) 61-65 		65  (a)  (b) Fig. 7 Complex relative permittivity of each layer for bi-layer material a)FR4-b)Teflon with and without air-gap.______________________________ References  1.  M. D. Deshpande and K. Dudley, “Estimation of complex permittivity of composite multilayer material at microwave frequency using waveguide measurements”, NASA Langley Res. Center, Hampton, VA, USA, NASA Tech. Memo. 212 398, 2003. 2. B.J. Wolfson, S.M. Wentworth, “Complex permittivity and permeability measurement using a rectangular waveguide”, Microwave and Optical Technology Letters., 27, pp.180-182, (2000). 3.  J.Baker-Jarvis, “Transmission/reflection and short-circuit line permittivity measurements”, National Institute of Standards and Technology, Boulder, Colorado, 80303–3328, (1990). 4.  Hasar, U. C., O. 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Determination of the complex permittivity of each layer for a bi-layer dielectric material using transmission (ABCD) matrix in Ku-Band frequency

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