Microsoft Word - ETASR_V13_N3_pp10664-10669 Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10664-10669 10664 www.etasr.com Ho & Le: Accurate Estimation without Calibration of the Complex Relative Permittivity of Multilayer … Accurate Estimation without Calibration of the Complex Relative Permittivity of Multilayer Dielectric Material based on the Finite Integration Technique Manh-Cuong Ho Faculty of Electronics and Telecommunications, Electric Power University, Vietnam cuonghm@epu.edu.vn Trong-Hieu Le Faculty of Electronics and Telecommunications, Electric Power University, Vietnam hieult@epu.edu.vn (corresponding author) Received: 7 February 2023 | Revised: 18 March 2023 | Accepted: 20 March 2023 Licensed under a CC-BY 4.0 license | Copyright (c) by the authors | DOI: https://doi.org/10.48084/etasr.5665 ABSTRACT In this paper, a simple and effective solution is proposed to accurately estimate the complex relative permittivity of individual layers and multilayers of dielectric material samples from the S-parameters measured by two waveguide cells having equal or different lengths filled with the same vacuum/empty material without having to calibrate before performing experiments. The measurement system is set up by modeling using the Computer Simulation Technology (CST) software. In the modeling, a single layer/multilayer material sample is placed in the X-band rectangular waveguide and it has two ports used for the electromagnetic wave supply and measurement of S-parameters. From the S-parameters measured, the complex relative permittivity of individual layers and the multilayers of the material samples are estimated by the proposed method. The known single-layer and multilayer materials such as Garlock, Bakelite, and Teflon have different dielectric constants and thicknesses. The results show that the complex relative permittivity of the samples matches the measured and calculated values of S-parameters in the frequency range of 8.2GHz to 12.4GHz. Keywords-complex relative permittivity; multilayer dielectric material; finite integration technique I. INTRODUCTION Multilayer dielectric material substrates are used in many practical applications, especially in high-speed circuits, such as the Microwave Integrated Circuits (MICs) [1, 2], Monolithic Microwave Integrated Circuits (MMIC) [3-6], and wireless systems applications [7, 8]. The exact knowledge of the individual layers in the multilayer substrate permittivity characterization is of great importance for MIC and MMIC design. The multilayer material is formed by composite materials and has new properties that could not be found in the individual layers. For the measurement of the electric properties over a wide frequency range, the waveguide method is one of the most popular methods to determine the permittivity of multilayer dielectric substrates [9-14]. In the waveguide measurement method, a sample of the composite multilayer substrate is placed in a waveguide and two port S- parameters are measured using a Vector Network Analyzer. This nondestructive method is based on the reflection coefficient and transmission coefficient measurement from which the complex permittivity (εr) or the permeability (μr) of the materials can be determined. In addition, the sample preparation requirements are minimal, and the electric properties can be measured over a wide frequency range. However, the waveguide method is the same as the free space or transmission line method, which are less accurate due to the unavoidable measurement errors. Although there are calibration standards, such as the Short-Open-Load-Through (SOLT) [15-20], the Through-Reflect-Line (TRL) [21-24], and the multiline TRL [25-28], that should be performed before the experiments, these methods experience their own respective defects, such as the requirement of multi-measurement cells, or the presence of the air gap effect. This paper proposes a new approach to estimate the complex relative dielectric based on only one measurement of the S-parameters of the sample to eliminate the defects mentioned above by assuming the waveguide cell with the length l is determined to be filled with empty air inside (εr ≈ 1.0-j0.0) as a layer of dielectric material. The proposed method can eliminate the air gap between the waveguide and the surface of the material sample because the air layer in the Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10664-10669 10665 www.etasr.com Ho & Le: Accurate Estimation without Calibration of the Complex Relative Permittivity of Multilayer … waveguide reaching the surface of the sample is considered to be an air dielectric layer. II. PROPOSED MODEL ANALYSIS The proposed non-calibrated model to accurately estimate the complex relative permittivity of a multilayer dielectric material based on the finite integration technique is illustrated in Figure 1. In the proposed model, between the two waveguide cells, the dielectric material layers have thickness d with an empty air region with length l. The analytical electromagnetic method [11] is used to determine the S11 and S21 parameters of the multilayer dielectric material sample placed in the two ports of the rectangular waveguide as shown in Figure 1. In Figure 1, the two waveguide cells are filled with the same vacuum/empty material and are defined as layer#1 and layer#N with parameters (εr0, μr0), and the multilayer substrate consists of layer#2 to layer#N-1, where the m th layer has parameters (εrm, μrm), with N >=3. They are located between the transverse planes at z = zn-1 and z = zn. Fig. 1. Geometry of the multilayer dielectric material sample placed in the two ports of the rectangular waveguide for the estimation of S11 and S21. A. Calculating Procedure of the S11 and S21 Parameters To determine the S11 and S21 components of 2-port parameters, it is assumed that the TE10 mode of unit amplitude is incident on the interface at z = 0 from the region z ≤ 0. If Et0, Et1, Et2, ..., Etn are the transverse electric fields on the interfaces at z = z0 = 0, z1, z2, ..., zn, respectively, then the transverse electric fields in the various regions of the waveguide are obtained as: 1) For z ≤ 0: 0 0 0 0 0 0 0 0 sin( ) * i j z t i i i z E = -2je z E e ds e e              � � � � � (1) 0 0 0 0 0 0 0 0 0 0 0 cos( ) * i j z t i i i i z H = 2y h z E e ds y h e              � �� � � (2) 2) For zn-1 ≤ z ≤ zn:   1 2 0 1 sin n n n in i i E E E = e z            � � � � (1) where:    1 1 ( 1) sin * n n n i n t n i z z E = z z E e ds      � � �   2 1sin * n n n i n tn i z z E = z z E e ds     � � �   1 2 0 sin nn n n i in i i H - H H = y h j            � � �� (4) where:    1 1 ( 1) cos * n n n i n t n i z z H = z z E e ds      � � �   2 1cos * n n n i n tn i z z H = z z E e ds     � � � 3) For z ≥ zn: 1 ( ) 1 0 * n i n n j z z n tn i i i z z E = E e ds e e                  � � � � (5)  11 1 0 * n i n n j z zn n tn i i i i z z H = E e ds y h e                  �� � � (6) 4) For z = 0,       1 1 10 0 1 0 0 01 0 1 1 11 0 1 cos 2 * sin * sin n n i i i t i i i z zi i t i i i z zi y h = y y E e ds h j y E e ds h j                                 � �� � �� � (7) 5) For z = zn:         1 1 ( 1) 0 1 1 1 1 0 1 1 ( 1)1 0 1 0 * sin cos( ) cos( ) + sin sin * + * sin n n n n i i t n in i z zi n n n n ni n i n i i in n i i n i n n i i tn i t n in iz z z zi n y h = E e ds j h y y j j y h E e ds E e ds j                                         � � � � � � � � � (8) 6) For the interface located at z = zN:     1 ( 1) 0 1 0 0 * sin cos( ) + sin * n n N i i t N iN i z zi N N N Ni N i i iN i i N tN i z z y h = E e ds j h y y j E e ds                          � � � � � � (9) The obtained transverse electric fields over the interfaces are: X Y Z Port #2 Port #1 Transmitted Wave Incident Wave Reflected Wave Layer#2 Layer#3 Layer#4 Layer#1 Layer#N-1 Layer#N Z0 Z1Z2Z3 Z4 ZN-2 ZN-1 ZN Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10664-10669 10666 www.etasr.com Ho & Le: Accurate Estimation without Calibration of the Complex Relative Permittivity of Multilayer … 0 1 0 0 1 1 0 0 0 0 , , ,.... n N j J t j j t J J j J J J tn nJ J tN NJ J J J E T e E T e E T e E T e             � � � � � � � � (10) where T0J, T1J, ..., TNJ are the complex unknown coefficients. Using the Galerkin’s procedure, the complex amplitudes T0J, J = 1, 2, 3, …, J0, T1J, J = 1, 2, 3, …, J1, TNJ, J = 1, 2, 3, …, JN are all zero due to the orthogonal nature of vector modal functions. The solution of (N + 1) gives an estimate of the complex amplitudes T00, T10, T20, TN0 from which S11 and S12 are determined as: 0 0 11 00 21 0 1 and N j z NS T S T e    (11) B. Calculation Procedure of S22 and S12 Parameters The S22 and S12 parameters can be determined by following the procedure used for the estimation of S11 and S21, and reverse the locations of the layers as illustrated in Figure 2. Fig. 2. Geometry of the multilayer dielectric material sample placed in the two ports of the rectangular waveguide for the estimation of S22 and S12. III. COMPLEX PERMITTIVITY ESTIMATION RESULTS A. Estimation of S-Parameters In this section, the properties of the individual layers of the dielectric material and of the empty layers are assumed to be known, the S-parameters for various material layers are computed from the theory as a functions frequency and are compared with the simulated S-parameters. The S-parameter simulations of both proposed models in Figures 1 and 2 were performed using the commercial 3-D full electromagnetic simulation software CST Microwave Studio. Figure 3 is based on the finite integration technique. Fig. 3. Material layers with thickness d between two identical waveguide cells with an empty air region between them. In Figure 3, the thickness d of the dielectric samples is assumed to be known, whereas the sample is placed between two identical waveguide cells with length l = 15mm and the empty air region with electric properties εr = 1.0. B. Empty - Garlock - Empty In this case, a single Garlock layer with thickness d = 1.7mm and εr = 7.5 - j0.001 is shown in Figure 4(a). The simulation results and the calculation of the S-parameters of the sample are shown in Figure 4(b)-(c). The results show that the simulated and calculated values of the S-parameters are almost similar in the frequency range from 8.2GHz to 12.4GHz. (a) (b) (c) Fig. 4. (a) Garlock layer with d = 1.7mm between two identical waveguide cells with an empty air region between them with length l = 15mm, (b) real and (c) imaginary part of the simulated and calculated S- parameters of the Empty - Garlock - Empty layers. C. Empty - Bakelite - Teflon - Empty The considered composite sample consists of Bakelite and Teflon layers. The composite slab is formed by placing the Bakelite layer with d1 = 3.3mm, εr = 3.76 - j0.001 and the Teflon layer with d2 = 6.35mm, εr = 2.03 - j0.001 shown in Figure 5(a). The simulation and calculation results of the S- parameters of the sample are shown in Figure 5(b)-(c). The results show that the S-parameters simulated and calculated values agree well in the frequency range of 8.2GHz to 12.4GHz. X Y Z Port #2 Port #1 Transmitted Wave Incident Wave Reflected Wave Layer#N-1 Layer#N-2 Layer#N-3 Layer#N Layer#2 Layer#1 Z0 Z1 Z2Z3 Z4 ZN-2 ZN-1 ZN Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10664-10669 10667 www.etasr.com Ho & Le: Accurate Estimation without Calibration of the Complex Relative Permittivity of Multilayer … (a) (b) (c) Fig. 5. (a) Bakelite and Teflon layers with thickness d1 = 3.3mm and d2 = 6.35mm between two identical waveguide cells with an empty air region of length l = 15mm, (b) real and (c) imaginary parts of the simulated and calculated S-parameters of Empty - Bakelite - Teflon - Empty dielectric layers. D. Empty - Garlock - Bakelite - Teflon - Empty: The composite sample considered consists of Garlock, Bakelite, and Teflon layers. The composite slab is formed by placing the Garlock layer with d1 = 1.7mm, εr = 7.5 - j0.001, the Bakelite layer with d2 = 3.3mm, εr = 3.76 - j0.001, and the Teflon layer with d3 = 6.35mm, εr = 2.03 - j0.001 shown in Figure 6(a). The simulation and calculation results of the S- parameters of the sample are shown in Figure 6(b)-(c). The results show that the simulated and calculated values are in excellent agreement in the frequency range of 8.2GHz to 12.4GHz. E. Estimation of Complex Permittivity In this section, the simulated and calculated S-parameters of dielectric material samples, consisting of single or multilayer samples are used to estimate the complex permittivity based on the objective function and the MATLAB code from [11]. The results of the complex relative permittivity estimation of single- layer dielectric (Garlock), two-layer composite dielectric (Bakelite - Teflon), and three-layer composite dielectric (Garlock - Bakelite - Teflon) are shown in Figure 7, 8, and 9, respectively. (a) (b) (c) Fig. 6. (a) Garlock, Bakelite and Teflon layers with thickness d1 = 1.7mm, d2 = 3.3mmn and d3 = 6.35mm between two identical waveguide cells with an empty air region with length l = 15mm, (b) real and parts of the simulated and calculated S-parameters of Empty - Garlock - Bakelite - Teflon - Empty dielectric layers. Fig. 7. Relative permittivity (real and imaginary) of Garlock material estimated using simulated and calculated S-parameters. Fig. 8. Relative permittivity (real and imaginary) of Bakelite - Teflon material estimated using simulated and calculated S-parameters. Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10664-10669 10668 www.etasr.com Ho & Le: Accurate Estimation without Calibration of the Complex Relative Permittivity of Multilayer … Fig. 9. Relative permittivity (real and imaginary) of Garlock - Bakelite - Teflon material estimated using simulated and calculated S-parameters. Fig. 10. The root mean square error of the complex relative permittivity between calculation and simulation. The estimated results in Figures 7-10 show that that the error in the complex relative dielectric estimation from S- parameters simulated by the proposed waveguide calibration technique is extremely small or negligible in the frequency range of 8.2GHz to 12.4GHz. IV. DISCUSSION In this paper, a solution to eliminate the free space of the waveguide based on an improved measurement model and estimation algorithm is proposed. The novelty of the proposed model in comparison with the model in [11] is that there is no need to calibrate the waveguide when making the actual measurements because, in this study, the free space inside the waveguide is considered a layer of the dielectric material. However, the simulation test results show that the correctness of this solution is very satisfactory. In the future, we will continue to test this proposal by experimental measurements. V. CONCLUSION A simple and effective solution to estimate the complex relative permittivity of single and multi-layered dielectric material samples using waveguide measurements is proposed in this paper. The proposed system consists of modeling the S- parameters measurement using CST software combined with MATLAB. This estimation method is verified based on the complex relative permittivity estimation in the 8.2-12.4GHz frequency range of the reference composite samples Garlock, Bakelite, and Teflon, with known thicknesses. 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