Dielectric properties by rectangular waveguide.
For many years, evaluation of dielectric properties of materials has been known to be a fundamental aspect of microwave and millimeter-wave technology . Knowledge of complex permittivity, and permeability, of materials proves to be of great interest in scientific and industrial applications. The measurement of [[epsilon].sup.*] and [[mu].sup.*] in the microwave frequency range finds direct application in different areas . Generally, the integration of material in an application system requires the exact knowledge of its dielectric parameters (permittivity and permeability) , . Reliable and accurate determination technique of complex permittivity of practical materials is a challenging problem . In the literature, several techniques have been proposed for extracting permittivity and permeability of materials , . The rectangular waveguide technique is one of class of two ports measurement (Transmission/ Reflection). It has been extensively employed as an easy way for studying the dielectric proprieties of materials in the microwave frequency .In general, this technique makes use of the reflected and/or transmitted waves by and through a dielectric-filled transmission line in order to analytically or numerically determine the dielectric properties of the material . The present study aims to contribute for the establishment and validation of simulation of complex permittivity of low loss materials. The present paper branches out into two related topics. The first one extracts the relative complex permittivity of a homogeneous sample (from scattering coefficient measurements) using the classical Newton-Raphson method. This iterative method is applicable to the coaxial line and rectangular waveguide . The second topic is concerned about the implementation of a computational modeling to predict the dielectric behavior of the tested materials using the electromagnetic three-dimensional simulation software Ansoft HFSS. The experimental and simulated results show a good convergence that guarantees the application of the used methodologies for the characterization of different low loss materials in the microwave frequency range.
The problem of measuring relative complex permittivity of a solid sample which is inserted in the rectangular waveguide transmission line is depicted in figure1. In the analysis, it is assumed that the sample is isotropic, symmetric, homogenous, and flat. We also assume that only the dominant mode ([TE.sub.10]) is present inside the waveguide , , 
By the transmission/reflection line theory, the expressions for the total transmission and reflection through a series of dielectric inside a waveguide are given in (1) and (2), respectively. In the analysis, we also assume that the dominant mode [TE.sub.10] is present inside the waveguide , .
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
Ts, [GAMMA]s and are the transmission coefficient and the reflection coefficient respectively, and d is the sample length. Ts and [GAMMA]s can be expressed in terms of the propagation parameters of the transmission line as:
[T.sub.S] = exp(-[[gamma].sub.S] x d) (3)
[[GAMMA].sub.s] = [[gamma].sub.O] - [[gamma].sub.S]/[[gamma].sub.O] + [[gamma].sub.S] (4)
[[gamma].sub.O] = j.2[pi]/c [square root of ([f.sup.2]-[f.sup.2.sub.c])] (5)
[[gamma].sub.S] = j.2[pi]/c [square root of ([f.sup.2]([[epsilon]'.sub.R]-[[epsilon]".sub.R])-[f.sup.2.sub.c])] (6)
[[epsilon].sup.*.sub.R] = [[epsilon]'.sub.R] - j[[epsilon].sub.R]" is the relative complex permittivity. It is obvious that [S.sub.11] and [S.sub.21] are functions of complex permittivity of the sample under test. Therefore, once the measured reflection and transmission coefficients are obtained, the complex permittivity of the sample can be extracted by an optimization procedure such as the classical Newton-Raphson method , . The equation to solve can be written as follows :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
According to the equation (7), [beta] varies as function of the sample length, uncertainty in scattering parameters, and loss characteristics of material [6. The iterations continue until convergence which is reasonably quick. Initial estimates can be obtained using Nicholson-Ross technique  at the starting frequency, with subsequent iterations using the values determined at the previous frequency. A Matlab program was written to obtain relative complex permittivity of sample for 201 frequency points over Ku band. In the case of a low loss dielectric materials ([beta] = 0) and therefore the estimated value is optimal and the complex permittivity is only extracted from the [S.sub.21] parameter , . However, only complex permittivity of low-loss dielectric materials were estimated in this work.
3 METHODS OF COMPLEX PERMITTIVITY DETERMINATION
3.1 Numerical Simulations
A new approach is presented that relies upon 3D electromagnetic simulation results to characterize the complex permittivity of homogeneous low-loss dielectric solid materials. The procedure has been tested with WR62 waveguide operating in the frequency range Ku band. The scattering parameters of the tested structure were obtained by performing simulations using the 3-D electromagnetic software Ansoft HFSS, as this procedure provides flexibility to explore different materials without the need for fabrication , . In this approach, we simulated the frequency response of the rectangular waveguide structure by providing specific material characteristics and extracted these parameters from the full-wave EM scattering parameters. The design structure in HFSS is presented in figure 2.
The numerical simulations were carried with Ansoft HFSS. In this case, the relative complex permittivities of each solid sample were deduced from a scattering matrix defined between the sample planes. The experimental constitutive parameters using the procedure previously described in section 2, were used in simulation technique to predict the scattering parameters of sample which is completely filled in waveguide.
3.2 Experimental Measure
The measurement cell we have manufactured is a transmission line rectangular wave guide composed of two rectangular wave guides with the following dimensions: length L= 60 mm, cross-section, (15.79x7.89) [mm.sup.2], to operate in the Ku band. The sample holder with a length of 6.3 mm is equally produced with the same (RWG) cross-section. To measure the real and the imaginary parts of the [S.sub.ij] scattering parameters of each (MUT), an HP 8520 C (VNA) is used and connected to both ports of (RWG) using two coax-to-waveguide adapters as indicated in Figure 3.
The measurement system is calibrated using Thru-Reflect-Line (TRL) calibration. The TRL calibration technique is used to provide the ultimate accuracy , . To reduce the effect of air gap, between the conducting walls of sample holder and the (MUT), the samples have been machined carefully to completely fill the sample holder . To determine the complex permittivity, only via [S.sub.21], it was used the one-port transmission approach, with low loss material, smooth, flat faces, and completely filling the fixture cross section. The source of network analyzer generates the signal to the material under experiment. The [S.sub.21] parameters were detected at the receiver, and they also produced the real and imaginary parts which can be seen on the display. After the [S.sub.21] parameters measurements, the relative complex permittivity ([[epsilon].sup.*]) of each (MUT) was calculated according to the procedure previously described in section 2.
To verify the validation of the proposed procedure, the scattering parameters of the tested structure were extracted with Teflon sample using the procedure described earlier. The measured and simulated values of S21 scattering parameters together with relative complex permittivity of Teflon (which is known as low loss material) are evaluated and compared. The comparison between simulated and measured values of S21 shows the accuracy of the simulation procedure in this study, but it is also observed a slight difference. To understand this difference, it is important to mention that the simulation configuration takes place in an ideal environment, where temperature, misalignment, and air gap effects are not taken into account. According to the measured and simulated values of relative complex permittivity describe the same dielectric behavior. These results agree well to the published data , , . After the validation of the experimental and the simulation methods, the S21 parameter values of the dry cellular concrete, plaster, and wood samples are simulated and measured using the procedure previously described in Section 3. The values of the relative complex permittivity of each tested material are estimated.
According to the comparisons, the simulation results of [S.sub.21] parameters show a good agreement with the measured values. Additionally, it is seen that the simulated values of relative complex permittivity agree reasonably well with the published data , . In tables 1 and 2, we respectively show the real and imaginary parts of dielectric complex permittivity for selected frequency points across the frequency range from 12 through 18 GHz.
For error estimations, several factors which affect the accuracy of the complex permittivity determination are extensively treated in the literature , , . In simulation configuration, the sample length, the sample holder length, the reference planes, and uncertainty in magnitude and phase of [S.sub.iJ] parameters are accurately known. In this case, we are interested in the percentage errors between experimental values of relative complex permittivity and those obtained from simulations. The simulated and measured values are used to find the percentage errors on real and imaginary parts of relative complex permittivity from the following equations:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
Where [[epsilon]'.sub.s], [[epsilon]'.sub.m],[[epsilon]".sub.s], and [[epsilon]".sub.m] are the real and the imaginary parts of relative complex permittivity from simulations and measurements, respectively. The percentage errors are presented in the table 3, showing the percentage errors between the simulated and measured values of each tested sample at selected frequency over Ku band.
It's seen that the percentage errors on the real part of relative complex permittivity are between 0.22 % and 6.43 % on the selected frequency points over the Ku band. Concerning the imaginary part of relative complex permittivity, the percentage errors are between 2.58 % and 8.19 for the same selected frequency points across Ku band. In general way, the simulations and measurements practically describe the same dielectric behavior of the tested samples.
A simulation procedure of rectangular wave guide structure for the determination of complex permittivity of solid materials has been proposed. The method is based on simulating the Sij parameters of each sample using electromagnetic three-dimensional simulation Software Ansoft HFSS. The simulated parameters are then compared with the measured values of the complex permittivity by network analyzer. The simulation procedure, which employs the Software Ansoft HFSS, has been described and verified through experimental measurements over the frequency range [12-18] GHz. We have validated the proposed approach with the complex permittivity determination of building dielectric solids in the Ku band. Considering the simplicity and accuracy over a broad frequency band, this method proves to be useful for the prediction of complex permittivity of solid materials for a wide range of applications.
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M. D. Belrhiti (1,2), S. Bri (1) A. Nakheli (1) A. Mamouni (3)
(1)--Materials and Instrumentations group, High School of Technology, ESTM, Moulay Ismail University--Morocco
(2)--Spectrometry Laboratory of Materials and Archeomaterials (LASMAR) Faculty of Sciences Moulay Ismail University, Meknes--Morocco
(3)--CSAM Group, Institute of Electronics, Micro-electronics and Nanotechnology, UMR CNRS 8520 IEMN-DHS, Cite scientifique, Avenue Poincare-B.P 60069 59652 Villeneuve d'Ascq Cedex France
Table 1. Real part of the measured and simulated complex permittivity of each tested material for selected frequency points across the Ku band. Teflon Frequency Simulated Measured (GHz) value value [[epsilon]'.sub.s] [[epsilon]'sub.m] 12 2.034 2.005 14 1.986 1.99 16 1.97 2.006 18 2.01 1.997 Dry cellular concrete Frequency Simulated Measured (GHz) value value [[epsilon]'.sub.s] [[epsilon]'.sub.m] 12 1.852 1.832 14 1.786 1.841 16 1.772 1.768 18 1.796 1.77 Plaster Frequency Simulated Measured (GHz) value value [[epsilon]'.sub.s] [[epsilon]'.sub.m] 12 2.832 2.994 14 2.967 3.053 16 3.098 2.964 18 3.013 3.001 Wood Frequency Simulated Measured (GHz) value value [[epsilon]'.sub.s] [[epsilon]'.sub.m] 12 2.301 2.324 14 2.382 2.238 16 2.329 2.229 18 2.341 2.206 Table 2. Imaginary part of the measured and simulated complex permittivity of each tested material for selected frequency points across the Ku band. Teflon Frequency Simulate Measure (GHz) d Value d value [[epsilon]".sub.s] [[epsilon]".sub.m] 12 0.026 0.027 14 0.0478 0.05 16 0.0503 0.049 18 0.0507 0.049 Dry cellular concrete Frequency Simulate Measure (GHz) d value d value [[epsilon]".sub.s] [[epsilon]".sub.m] 12 0.049 0.052 14 0.028 0.0302 16 0.027 0.029 18 0.0295 0.031 Plaster Frequency Simulate Measure (GHz) d value d value [[epsilon]".sub.s] [[epsilon]".sub.m] 12 0.048 0.046 14 0.032 0.034 16 0.029 0.0276 18 0.039 0.042 Wood Frequency Simulate Measure (GHz) d value d value [[epsilon]".sub.s] [[epsilon]".sub.m] 12 0.28 0.305 14 0.287 0.31 16 0.293 0.311 18 0.301 0.291 Table. 3. Percentage errors between the simulated and measured values of each tested sample at selected frequency over Ku band Frequency Teflon (GHz) % Error on([epsilon]') on([epsilon]") 12 1,4258 3,8461 14 0,2014 4 ,6025 16 1,8274 2,5844 18 0,6467 3,3530 Frequency Dry cellular concrete (GHz) % Error on([epsilon]') on([epsilon]") 12 1,0799 5,7692 14 3,0795 6,9767 16 0,2257 6,8965 18 1,4477 4,8387 Frequency Plaster (GHz) % Error on([epsilon]') on([epsilon]") 12 5,4108 4,3478 14 2,8169 5,8823 16 4,5209 5,4545 18 0,3998 7,1428 Frequency Wood (GHz) % Error on([epsilon]') on([epsilon]") 12 0,9896 8,1967 14 6,4343 7,4193 16 4,4863 5,7877 18 6,1197 3,4364
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|Author:||Belrhiti, M.D.; Bri, S.; Nakheli, A.; Mamouni, A.|
|Publication:||International Journal of Emerging Sciences|
|Date:||Jun 1, 2013|
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