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Dielectric properties by rectangular waveguide.

1 INTRODUCTION

For many years, evaluation of dielectric properties of materials has been known to be a fundamental aspect of microwave and millimeter-wave technology [1]. 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 [2]. Generally, the integration of material in an application system requires the exact knowledge of its dielectric parameters (permittivity and permeability) [3], [4]. Reliable and accurate determination technique of complex permittivity of practical materials is a challenging problem [1]. In the literature, several techniques have been proposed for extracting permittivity and permeability of materials [5], [6]. 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 [7].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 [8]. 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 [9]. 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.

2 THEORY

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 [5], [6], [7]

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 [9], [10].

[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)

Where

[[gamma].sub.O] = j.2[pi]/c [square root of ([f.sup.2]-[f.sup.2.sub.c])] (5)

and

[[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 [3], [2]. The equation to solve can be written as follows [6]:

[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 [11] 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 [9], [12]. 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 [13], [14]. 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 [15], [16]. 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 [6]. 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.

4 RESULTS

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 [3], [5], [9]. 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 [3], [17]. 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 [6], [9], [18]. 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.

5 CONCLUSION

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.

REFERENCES

[1.] Eves. E. E, Kopyt P, and Yakoviev. V. V, "Determination of Complex Permittivity with Neural Networks and FDTD Modeling", Microwave and Optical Technology Letters 40 (2004), 183-188,

[2.] Deshpande M. D, Reddy. J. C, Tiemsinu. C. P. I, and Cravey. R, "A new approach to estimate complex permittivity of dielectric materials at microwave frequencies using waveguide measurements", IEEE Transactions on Microwave Theory and Techniques, 45, 3 (1997), 359-366,

[3.] Belrhti. M. D, Bri. S, Nakheli. A, Haddad. M, and Mamouni. A, "Complex Permittivity Measurement for Dielectric Materials at Microwave Frequencies Using Rectangular Waveguide", European Journal of Scientific Research 49, 2 (2011), 234-248,

[4.] Costa. F, Amabile. C, A. Monorchio, and E. Prati, Waveguide Dielectric Permittivity Measurement Technique Based on Resonant FSS Filters, IEEE Microwave and Wireless Components Letters 21 (2011) pp 273-275,

[5.] Jarvis. J. B, Vanzura. E. J, and Kissick. W. A, "Improved technique for determining complex permittivity with the transmission/reflection method", IEEE Trans. Microwave Theory Tech, 38, 8(1990),1096-1103,

[6.] Jarvis J. B, Janezic. J, Grosvenor. M, and Geyer. R, "Transmission/ reflection and short-circuit line methods for measuring permittivity and permeability", Natl. Inst. Stand Techno, Tech. Note 1355-R (1993),

[7.] Cravey. R, Tiemsin. L. P, Bussell. I. K, and Dudley. K. L, "Dielectric Property Measurements in the Electromagnetic Properties Measurement Laboratory", Technical Memorandum 110147, NASA (1995),

[8.] Bois. K. J, HandJoJo. L. F, Benally. A. D, Mubarak. K, and Zoughi. R, "Dielectric Plug-Loaded Two-Port Transmission Line Measurement Technique for Dielectric Property Characterization of Granular and Liquid Materials", IEEE Transactions on Instrumentation and Measurement, 48, 6(1999), 1141-1148,

[9.] Boughriet. A. H, "Contribution a la caracterisation electromagnetique de materiaux en structures dipoles et quadripoles-application aux tissus biologiques et aux polymeres thermoplastiques", These de doctorat, Universite des Sciences et Technologie de Lille, France (1997),

[10.] Ogunlade. O, Pollard. R. D, and. Hunter. I. C, "A New Method of Obtaining the Permittivity of Liquids Using In-Waveguide Technique", IEEE Microwave and Wireless Components Letters, 16, (2006), 263-265

[11.] Nicholson. A. M, and Ross. G. F, "Measurement of the intrinsic properties of materials by time domain techniques", IEEE Trans. Instrum.Meas IM-19 (1970), 377-382,

[12.] Wang. Y, and Afsar. M. N, "Measurement of complex permittivity of liquid dielectrics", Microwave and Optical Technology Letters, 34, (2002), 240-243,

[13.] Hu. J, Sligar. A, Chang. C, Lu. S, and Settaluri. R. K, "A Grounded Coplanar Waveguide Technique for Microwave Measurement of Complex Permittivity and Permeability", IEEE Transactions on Magnetics, 42, (2006), 1929-1931,

[14.] Belrhti. M. D, Bri. S, Nakheli. A, Haddad. M, and Mamouni, "Dielectric constant determination of liquid using rectangular waveguide structure combined with EM simulation", J. Mater. Environ. Sci 3 (2012), 575-584,

[15.] Agilent Network Analysis Applying the 8510 TRL Calibration for Non-Coaxial Measurements, Product Note 8510-8A (2001),

[16.] Engen. G. F, and Hoer. C. A, "Thru-Reflect-Line : An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer", IEEE Transactions Microwave 'Theory and Techniques, 27 (1979), 987-993,

[17.] Rhim. H.C, and Buyukozturk. O, "Electromagnetic properties at microwave frequency range", Technical Paper, ACI materials Journal, 95, (1998), 262-271

[18.] Hasar U. C, "Permittivity measurement of thin dielectric materials from reflection-only measurements using one-port vector network analyzers", Progress In Electromagnetics Research PIER, 95, (2009), 365-380.

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

E.mail: briseddik@gmail.com

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
Article Type:Report
Geographic Code:4EUFR
Date:Jun 1, 2013
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