Measurement of Complex Permittivity by Rectangular ... - IEEE Xplore

The 2014 International Conference on Advanced Technologies for Communications (ATC'14)

Measurement of Complex Permittivity by Rectangular Waveguide Method with Simple Specimen Preparation V. H. Nguyen2,3, M. H. Hoang1,2,3, H. P. Phan1 1

T. Q. V. Hoang2,3, T. P. Vuong2,3 2

Faculty of Electrical & Electronics Engineering Ho Chi Minh City University of Technology Ho Chi Minh, Vietnam [email protected], [email protected], [email protected]

University Grenoble Alpes, IMEP – LAHC 3 CNRS, IMEP – LAHC F-38000, Grenoble, France {thi-quynh-van.hoang, tan-phu.vuong}@minatec.inpg.fr

there would be no air gap that will affect the accuracy of measurement. In addition, the frequency band is imposed by the waveguide’s dimensions. Various techniques have been developed to make the method easier and more flexible to implement in order to respond to scientific and industrial applications. A full automated measurement system for realtime and dynamic determination of dielectric properties of materials was described in [9]. The direct and de-embed methods were presented in [10] for accommodating multilayered-material-characterization measurements. For the broadband characterization, a multimode technique based on simultaneous excitation of four orthogonal TE eigenmodes in a flattened rectangular waveguide was detailed [11].

Abstract—The characterization of materials by rectangular waveguide method usually requires a sample holder and a complicated procedure of preparing specimen in order to limit the air gaps between the specimen and the boundaries of the waveguide that will affect the accuracy of measurement. In this paper, we present a technique of complex permittivity measurement with a simple MUT (Material Under Test) preparation technique. The waveguides are first calibrated at the reference planes by the TRL calibration. Then, the scattering parameters in the presence of MUT specimen are measured at two SMA ports of the waveguides by an Agilent VNA. These coefficients are de-embedded to the reference planes by the TRL calibration. Finally, the Nicolson-Ross-Weir (NRW) algorithm is used to extract the dielectric constant and the loss tangent of the MUT. The simulation and measurement are performed at the 1.7-2.7 GHz band. The results demonstrate the validity of the proposed technique.

In this paper, we are interested in simplifying the overall measurement procedure. Indeed, no sample holder is required and no special preparation has to be performed for the specimen as in the conventional method. The measured specimen will be placed between two waveguides and we only need that the cross section of the specimen is larger than the waveguide’s one. The scattering parameters in the presence of MUT specimen are measured at two SMA ports of the waveguides and then de-embedded to the reference planes by the TRL calibration. After that, the Nicolson-Ross-Weir algorithm is used to convert the S-parameters to dielectric properties. The paper is further organized as follows. In section II, the general procedure of determining the material properties by rectangular waveguide method is detailed with explanations about the TRL calibration and NRW algorithm. In section III, three material specimens have been tested and some results simulated by the CST Microwave Studio 2013 and measured by the Agilent 8510C VNA are illustrated. Finally, the conclusions are given in section IV.

Keywords—dielectric constant; loss tangent; TRL calibration; material characterization; Nicolson-Ross-Weir method.

I. INTRODUCTION Knowledge of characteristics of materials at microwave frequency proves to be of great interest in antenna design, microwave circuit design, and other applications. Accurate measurement of these properties can provide engineers and scientists with valuable information which affects significantly the operation and characteristics of their designs [1]. Therefore, various methods have been developed over the years for characterizing the electromagnetic properties of materials [2][5]. These methods can be divided in two categories: resonant [6]-[7] and non-resonant [8]-[9]. Resonant methods give more accurate knowledge of electromagnetic properties over a very narrow frequency range or a single frequency, while the nonresonant methods give knowledge of electromagnetic properties over a rather wide frequency range.

II. TRANSMISSION/REFLECTION LINE METHOD BY RECTANGULAR WAVEGUIDE

This paper is dedicated to transmission/reflection method by rectangular waveguide, one kind of non-resonant methods. In this kind of method, a sample holder (e.g. a piece of the waveguide) is required and the measured specimen must be machined out to fit perfectly the cross section of this holder so

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Fig. 1 presents the general procedure to determine the dielectric properties of material using transmission/reflection method with rectangular waveguide. The frequency range for the characterization depends on the dimensions of the waveguide used. The waveguides are first calibrated at the

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reference planes by the TRL calibration. Then, the MUT specimen is placed between the waveguides and fixed to the waveguides boundaries by the screws (Fig. 2). The scattering parameters in the presence of MUT specimen are simulated/ measured at two SMA ports of the waveguides and then deembedded to the reference planes thanks to the TRL calibration. Finally, the electromagnetic properties of the MUT, its permittivity and permeability, can be derived from the scattering parameters by using NRW algorithm. This procedure is repeated at each frequency in order to obtain the results over the operating frequency band.

For the measurement, the Agilent 8510C VNA with attached cables is first calibrated by a full two-port SOLT calibration with the WILTRON 3652K calibration kit. Then, the waveguides are calibrated by the TRL method described above. B. Nicolson-Ross-Weir (NRW) algorithm In order to determine the electromagnetic properties of an unknown single-layered material from forward simulated/ measured scattering parameters, the well-known Nicolson– Ross–Weir algorithm [13][14] is predominantly used since it is relatively easy to implement and can accommodate materials with both dielectric and magnetic properties. The process for NRW algorithm is detailed in Fig. 3. We developed a loop frequency script in Matlab to realize this process from Sparameters input data over the operating frequency band.

Fig. 1. General procedure for material characterization using transmission/ reflection method with rectangular waveguide.

(b) Fig. 2. (a) Configuration of the MUT sample between the waveguides (b) Cross section of the waveguide with its boundaries.

A. TRL calibration The simulation and measurement are performed at the SMA connectors of the waveguides. However, the specimen is considered as a two-port network whose S-parameters used later in NRW algorithm are the parameters at two faces of the specimen. Therefore, TRL calibration (Thru-Reflect-Line) needs to be proceeded to set the plane of incident and reflected waves at the end of the waveguides (i.e. calibration planes in Fig. 2a) instead of at the SMA connectors. Three configurations are performed: first, two waveguides are connected directly by the screws and we obtain two values of S11 and S21; second, a reflector plane is placed at the end of one waveguide (consider that two waveguides are identical) and one value of S11 is achieved; third, a line (i.e. a piece of waveguide) is placed between two waveguides (Fig. 4a) and four values of S-parameters are obtained. With these seven values, the S-parameters at the calibration planes can be determined from those at the SMA connectors’ planes [12].

Fig. 3. Flowchart of Nicolson-Ross-Weir (NRW) algorithm [3].

III. SIMULATION AND MEASUREMENT RESULTS A. Rectangular waveguide description The rectangular waveguides have the dimensions of 109.22 mm × 54.61 mm and 100 mm length. Some dimensions concerning the SMA probes (Fig. 2b) are not provided in the manufacture datasheet, these dimensions were experimentally measured to build the simulation model of the waveguides. The frequency range recommended is from 1.7 GHz to 2.6 GHz in order to ensure that only one mode TE10 is transmitted over the waveguide.

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frequency band and except the resonant frequencies, a relative error less than 18% is observed.

B. Specimen description In order to validate the simulation and measurement methods, three known specimens were chosen to characterize. The details of dielectric properties and the thickness of these specimens are available in the Table I. PARAMETERS OF MUT SAMPLES

Material

Dielectric constant

Loss tangent

FR4

4.3

0.0250

Thickness L (mm) 0.800

Rogers 3010

10.2

0.0023

0.635

Rogers 4003

3.55

0.0027

0.203

Simulation Measurement Data of constructor

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Dielectric constant

TABLE I.

16 12 10 8 6 4 2 0 1.7

C. Measurement setup The frequency band was set at 1.7-2.7 GHz. An available 40 cm piece of waveguide was used as Line part for the TRL calibration as shown in Fig. 4a. The MUT specimen was fixed between the waveguides by screws as presented in Fig. 4b. These screws were placed only on the boundaries of the cross section of the waveguides, so there is no effect introduced in the thickness of the MUT layer to be measured.

1.9

2.1 2.3 Frequency (GHz)

2.5

2.7

(a) Dielectric constant of a 0.8 mm-thickness FR4 specimen 100

Simulation Measurement

Relative error (%)

80 60 40 20 0 1.7

1.9


2.5

2.7

(b) Relative error compared to data of constructor. Fig. 5. Simulated and measured results of a 0.8 mm-thickness FR4 specimen as a function of frequency.

MUT specimen (a) Waveguides with LINE of 40 cm

40

(b) Waveguides with MUT specimen


35

Dielectric constant

Fig. 4. Measurement setup.

D. Results The dielectric constant is defined as the real part of the complex permittivity while the loss tangent is the ratio between the imaginary and the real part.

30 25 20 15 10 5 0

Fig. 5a illustrates the dielectric constant of a 0.8 mmthickness FR4 specimen over the 1.7-2.7 GHz frequency band for three cases: simulation with CST, measurement, and data of constructor. It can be observed in Fig. 5b that in comparison to the value given by the constructor (εr = 4.3), the relative error for both simulation and measurement is less than 15% over the considered frequency band except at the resonant frequencies. Regarding the loss tangent, the values obtained is in range of 0.0014-0.05 for the simulation and in range of 0.0038-0.19 for the measurement, compared to 0.025 given by the constructor. The difference between these results of loss tangent can be explained partially by the tolerance of measurement and by the fact that the imaginary part of the complex permittivity is much smaller than the real one then just a small error in the overall measurement could give an important error in the value of imaginary part which decides the loss tangent value.

1.7

1.9


2.5

2.7

Fig. 6. Simulated and measured dielectric constant of a 0.635 mm-thickness Rogers 3010 specimen as a function of frequency.

A very thin specimen of 0.203 mm thickness was tested; the simulated and measured results of its dielectric constant are presented in Fig. 7. A little ripple is observed over the considered frequency band for the measured value. Nevertheless, the simulated and measured results are still coherent to the given value (εr = 3.55). Hence, the proposed method is also valid for a very thin specimen of about 0.2 mm thickness. Fig. 8 illustrates a parametric study of Line’s length used in the TRL calibration in the case of 0.8 mm-thickness-FR4 specimen characterization. It can be observed that when the Line is short (i.e. 5 cm), there is no resonant frequency and the calculated dielectric constant value is stable over the 1.72.7 GHz frequency band. We noted that the longer the Line is,

Fig. 6 presents the simulated and measured results of a thinner specimen: 0.635 mm-thickness Rogers 3010 with given dielectric constant of 10.2. A good agreement is remarked between these results and the given value. Over the measured

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the more resonant frequencies appear in the considered frequency band. Indeed, there is one resonant frequency for the 10 cm-length-Line, two resonant frequencies for the 30 cmlength-Line, and four resonant frequencies for 40 cm-lengthLine. It can be explained by the fact that the NRW method is divergent at the frequencies corresponding to integer multiples of one-half wavelength in the Line part. Actually, at these frequencies the S11 value is very small; therefore the uncertainty in the measurement of S11 phase is very important and causes the divergence of the NRW method [5]. Hence, if a shorter Line had been used in the proposed technique, the simulated and measured results would be better for the dielectric constant and the loss tangent. 16

ACKNOWLEDGMENT The authors would like to thank Mr. Antoine Gachon, Assistant Engineer of IMEP-LAHC, for his technical assistance and the region Rhone Alpes for its sponsorship in the CMIRA2013 project.


14

Dielectric constant

methods. In future work, much more material specimens will be characterized and the comparison with the other methods such as resonant method or free space method will be performed. A shorter Line should be used for the TRL calibration. Moreover, the improvement in the tolerance of measurement would be considered to obtain the better loss tangent value.

12

REFERENCES [1]

10 8

[2]

6

[3]

4 2 0 1.7

1.9


2.5

[4]

2.7

[5]

Fig. 7. Simulated and measured dielectric constant of a 0.203 mm-thickness Rogers 4003 specimen as a function of frequency. 16

Line 5 cm Line 10 cm Line 30 cm Line 40 cm

14 Dielectric constant

[6]

12

[7]

10 8

[8]

6 4 2

[9]

0 1.7

1.9


2.5

2.7

[10]

Fig. 8. Simulated dielectric constant of a 0.8 mm-thickness FR4 specimen as a function of frequency for different values of Line used in the TRL calibration. [11]

IV. CONCLUSION We proposed in this paper a modified rectangular waveguide method to characterize materials. The important advantage of this method lies in its simplicity of implementation and specimen preparation. Indeed, no sample holder is necessary and no special preparation has to be realized for the specimen as in the conventional method. The simulation and measurement were performed at the 1.7-2.7 GHz band. The results demonstrated the validity of the proposed technique in determination of dielectric constant for the materials having thickness of about 0.2 mm to 0.8 mm. The characterization of loss tangent is still a challenge for almost all

[12] [13]

[14]

[15]

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