Reflection measurement methods for characterization of dielectric properties

Transcription

1 Reflection measurement methods for characterization of dielectric properties M. Zimmermanns, B. Will, and I. Rolfes, Member, IEEE Index Terms Reflection measurements, dielectric materials, free space, material characterization. based on three reflection measurements similar to the wellknown reflectometer calibration [8]. Hence, three reflection measurements are performed with three different, completely known loads. This procedure requires a reciprocal device under test. In this case, the three measured reflection coefficients yield the scattering parameters of the measured object. Thus the method combines the advantages of two and one port measurements. Here solely the reflection properties of the sample are determined, which is very useful in particular for industrial applications. Additionally the method delivers all four scattering parameters, if the material under test is reciprocal. This requirement is fulfilled by a number of materials of interest like substrates or bulk materials. Therefor the developed double transmission method offers a powerful method for the characterization of dielectric materials based on scattering parameters. To compare the results obtained by the method full two port measurements are performed. For both measurements a vector network analyzer (VNA) is used. Dielectric materials are measured in rectangular waveguides and in a free space setup, as well. I. I NTRODUTION II. D OUBLE TRANSMISSION METHOD D IELETRI material characterizations are often based on the measurement of scattering parameters by use of transmission line setups, like waveguides or free space setups []. This approach can be used in two different ways, with regard to the respective application. The preferable way is to perform a full two port measurement in order to obtain as many information of the sample as possible. Based on the four measured scattering parameters several algorithms are suitable for the characterization of the dielectric properties of the measured sample [] - [4]. With regard to several applications transmission measurements are difficult to realize. In this case reflection measurements are suitable for the characterization of the material parameters. The measured reflection coefficient enables the determination of the permittivity and the permeability with different mathematical algorithms [5][6]. However, full two port measurements are advantageous since all scattering parameters are measured. The approach of this contribution deals with the determination of all scattering parameters based on reflection measurements. This so-called double transmission () method is The authors are with the Institute of Microwave Systems, Ruhr-University Bochum, Bochum, 448, Germany ( marc.zimmermanns@rub.de) The developed double transmission method is based on a well-known reflectometer calibration procedure [8]. In Fig. the block diagram for the calibration of a reflectometer is shown. error box RF-source Abstract A popular method for the characterization of dielectric materials is based on the calculation of the permittivity from the measured scattering parameters. ommonly full two port measurements are performed to obtain all four scattering parameters of the investigated material. With regard to a variety of applications, often no possibility exists to perform transmission measurements. In this case, reflection measurements are performed and the dielectric properties of the sample are calculated from the reflection coefficient. There are several algorithms to extract the dielectric properties based on transmission and reflection measurements, respectively. However an algorithm using all four scattering parameters is advantageous compared to material characterizations based only on the measured reflection coefficient of the investigated material. This contribution introduces the so-called double transmission () method. This technique offers the possibility to measure all scattering parameters of the sample from reflection measurements. Therefore, reflection measurements with different known loads are performed. Similar to reflectometer calibration methods, three reflection measurements yield the scattering parameters of a reciprocal two port. Thus the double transmission method combines the advantage of a two port measurement, which yields all four scattering parameters, with the more compact setup of a one port measurements. Z am [R] b a Γi Fig.. Block diagram of a reflection measurement setup including the error box R, the measuring points and and the reflecion Γi The objective is to find the scattering parameters for the error box R. This knowledge allows the calculation of the ideal reflection coefficient from the measured one. To obtain the error parameters R, R R and R it is necessary to measure three well known, but different loads. This procedure can be described by using the scattering

2 matrix of the error box: R = b R sample R am R a am calibrated VNA () b [S] a Γi a () b = Γi. () a This relation yields the following equation for the measured reflection coefficient µi : R R Γi = R + (4) R Γi Thus three measurements with three different loads lead to three equations, where R, R R and R are the unknown parameters. Related to the three unknown error terms this method is called -term method. Due to the fact no real transmission measurements are performed R and R can not be separated. Regarding the calibration procedure a separation of the forward transmission R and the backward transmission R is not necessary for the error correction. The solution for the error terms, and thus the complete description of the error box R is given by: µi = [µ Γ Γ (µ µ ) +µ Γ Γ (µ µ ) + µ Γ Γ (µ µ )] b Fig.. Block diagram of a double transmission () measurement setup scattering parameters of the sample it is again necessary to perform measurements with three different completely known reflections. The mathematical algorithm can be described by the same equations as the -term method. Hence, the scattering parameters of the sample depend on the measured reflection coefficients µi and on the completely known reflection coefficients Γi as follows: S = [µ Γ Γ (µ µ ) +µ Γ Γ (µ µ ) + µ Γ Γ (µ µ )] () [ Γ (µ µ ) Γ (µ µ ) Γ (µ µ )] S = R = (5) S S = S S S [ Γ (µ µ ) Γ (µ µ ) Γ (µ µ )] R = R R = R R R () () [ µ Γ (µ µ ) µ Γ (µ µ ) µ Γ (µ µ )] (4) = Γ Γ (µ µ ) + Γ Γ (µ µ ) + Γ Γ (µ µ ). (5) S = (6) (7) [ µ Γ (µ µ ) µ Γ (µ µ ) µ Γ (µ µ )] (8) = Γ Γ (µ µ ) + Γ Γ (µ µ ) + Γ Γ (µ µ ). () R = Hence, the error box is now completely known and a calibrated measurement of the reflection coefficient can be performed. The reflection coefficient ΓS of the sample depends on the measured reflection coefficient µs and the error terms as follows: µs R. () ΓS = R µs + R R R R The developed method is based on a similar procedure. In this case a calibrated VNA is used as shown in Fig.. Here the measuring object is a two port, which is terminated by different completely known loads Γi As shown in Fig. the measurement setup is quite similar to the -term method. Thus the sample can be interpreted as an additional error box and its scattering matrix can be determined by one further -term procedure. To obtain the As already mentioned, this procedure offers no real transmission measurement. Thus, it is not possible to separate S and S. Hence, the determination of all scattering parameters by using the method requires a reciprocal sample. In this case it holds: S = S, (6) and S = S S S. (7) In summary, the method offers the possibility to determine the complete scattering matrix of a reciprocal sample based on reflection measurement. The assumption of reciprocity is valid for a variety of material samples. Thus, the method is a suitable method for material characterizations, which combines the advantages of a full two-port measurement and a reflection measurement setup. III. M EASUREMENTS For the verification of the described method several measurements are performed by using a four channel VNA

3 with 8 frequency points in a frequency range from GHz to GHz. oncerning the reflection measurements the VNA is calibrated by a -term calibration. In this case, the three different reflection coefficients are realized by a sliding short []. For the double transmission measurements, which are performed after the -term calibration, the same sliding short is used. For comparison full two-port measurements are performed as well. Here, the VNA is calibrated by the well-known thrureflect-line (TRL) method [7]. In a first approach the method is verified by measurements in rectangular waveguides. The sample is a waveguide with a length of 4 mm, which is filled with dry sand. Here, three different loads are realized by a sliding short circuit in a waveguide. The magnitudes of the scattering parameters S, S and S of the sample obtained with the method and with a full two port measurement are shown in Fig.. tivity of the sample is determined with the help of the Baker-Jarvis algorithm []. The real parts of the resulting permittivities achieved with the method and the full twoport measurement, respectively, are shown in Fig ε r Fig. 4. Extracted εr of a waveguide with a length of 4 mm, which is filled with dry sand S Again the resulting permittivities show a good agreement. Hence, the scattering matrix determined by the method can be used to extract dielectric properties with an algorithm, which is originally developed for real transmission measurements. In a next step double transmission measurements are performed in a free space setup. This setup consists of two linear horn antennas and two double hyperbolic lenses as shown in Fig S antenna holding appliance lens lens antenna positioning units Fig. 5. Free space measurement setup with focusing horn-lens antennas S Fig.. Magnitude of the scattering parameters of a rectangular waveguide filled with dry sand This result shows a very good agreement of the method and a full two-port measurement. Based on the measured scattering parameters the permit- Again the three necessary loads are realized by a sliding short circuit in a waveguide. Here, the receiving antenna is terminated by the sliding short and thus serves as a reflector. As a reciprocal sample a 6 mm thin plate of polyvinyl chloride (PV) is used. Again a TRL calibrated full two port measurement is performed for verification. The magnitude of the scattering parameters S and S achieved with the method and the full two-port measurement, respectively, are shown in Fig. 6. While the resulting return loss S shows good agreement, the resulting insertion loss S differs with regard to the two different measurement concepts. This difference with an average of.5 is mainly caused by the free space setup itself. This free space setup does not include any absorbing materials. In addition, the holding

4 4 insertion loss S measured with the method. A higher loss results in a higher permittivity. Nevertheless, both results show the same frequency behavior. Hence, the method is suited for the determination of material parameters of a reciprocal sample based on its scattering parameters. S IV. ONLUSION S Fig. 6. Magnitude of the scattering parameters of a 6 mm plate of polyvinyl chloride (PV) appliances needed for antennas, lenses and the sample itself cause multiple reflections. The errors depend on delay times which vary with regard to the respective sample. Thus, these parts can cause errors even if the setup is calibrated in advance. Another reason for the variation of the insertion loss is given by the method. ompared with the full two-port measurements, the transmission path within the measurements is two times longer. This leads to higher losses and higher influences of disturbing parts within the measurements. Again, the permittivity of the sample is determined by using the Baker-Jarvis algorithm and the obtained scattering parameters. The resulting real part of the permittivity of the sample is shown in Fig εr Fig. 7. Extracted εr of a 6 mm plate of polyvinyl chloride The real part of the permittivity measured with the method is higher than the permittivity measured with a full two-port measurement. This is caused by the.5 higher The described double transmission method is a promising approach for the measurement of the complete scattering matrix of a given sample based on reflection measurements. The key benefit of the method is that no transmission measurements are necessary. Instead, three reflection measurements with different completely known loads are performed. These measurements yield the complete scattering matrix for a reciprocal sample. This measurement concept is verified by several measurements and the results are comparable with full twoport measurements. Thus, the developed double transmission method offers a compact measurement setup due to the fact, that no transmission measurements are necessary. In addition, the complete scattering matrix of a reciprocal sample is determined, which is advantageous compared with common reflection measurements. Hence, the method is suitable for scattering parameter measurements and material characterization respectively AKNOWLEDGEMENT The authors gratefully acknowledge the IEEE Microwave Theory and Techniques Society for making this work possible, due to the selection for the MTT-S Pregraduate scholarship /. R EFERENES [] L. F. hen,. K. Ong,. P. Neo, V. V.Varadan, and V. K. Varadan Microwave Electronics: Measurement and Materials haracterization, England: John Wiley & Sons, Ltd, 4. [] J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, Improved technique for determining complex permittivity with the transmission/reflection method IEEE Trans. Microwave Theory & Tech., vol. 8, pp. 6-, Aug.. [] A. M. Nicolson, and G. F. Ross, Measurement of intrinsic properties of materials by time domain techniques IEEE Trans. Instrum. Meas., vol. IM-, pp. 778, November 7. [4] W. B. Weir, Automatic measurement of complex dielectric constant and permeability at microwave frequencies Proc. IEEE, vol. 6, pp. 6, January 74. [5] J. Baker-Jarvis, M. D. Domich and R. G. Geyer, Transmission/reflection and short-circuit line methods for measuring permittivity and permeability NIST Technical Note 55 (revised) National Institute of Standards and Technology, U.S. Department of ommerce,. [6] G. Gajda, and S. S. Stuchly, An equivalent circuit of an open-ended coaxial line IEEE Trans. Microwave Theory & Tech., vol., pp. 5658, 8. [7] G. Engen and. Hoer, Thru-reflect-line: An improved technique for calibrating the dual six-port automatic network analyzer IEEE Trans. Microwave Theory & Tech., vol. 7, no., pp. 87-, 7. [8] H. J. Eul, and B. Schiek, Thru-Match-Reflect: One Result of a Rigorous Theory for De-Embedding and Network Analyzer alibration Microwave onference, 8th European, pp. -4, -5 Sept. 88. [] G. Engen, alibration Technique for Automated Network Analyzers with Application to Adapter Evaluation IEEE Trans. Microwave Theory & Tech., vol., no., pp. 55-6, 74

5 5 Marc Zimmermanns was born in Wuppertal, Germany, in 86. He received the B.Sc. degree in electrical engineering from Ruhr-University Bochum, Bochum, Germany, in. Since, he is with the Institute of Microwave Systems, Ruhr-University Bochum, as a Research Assistant. His current fields of research are concerned with material characterization, and calibration methods. Bianca Will was born in Marburg, Germany, in 8. She received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from Ruhr-University Bochum, Bochum, Germany, in 6 and, respectively. From 6 to, she was with the High Frequency Measurements Research Group, Ruhr-University Bochum, as a Research Assistant. Since, she has been a Research Assistant with the Institute of Microwave Systems, Ruhr-University Bochum. Her current fields of research are concerned with material characterization, moisture measurements, and calibration methods. Ilona Rolfes (M 6) was born in Hagen, Germany, in 7. She received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from the Ruhr- University Bochum, Bochum, Germany, in 7 and, respectively. From 7 to 5, she was with the High Frequency Measurements Research Group, Ruhr-University Bochum, as a Research Assistant. From 5 to, she was a Junior Professor with the Department of Electrical Engineering, Leibniz Universität Hannover, Hannover, Germany, where in 6, she became Head of the Institute of Radiofrequency and Microwave Engineering. Since, she has led the Institute of Microwave Systems, Ruhr-University Bochum. Her fields of research are concerned with high-frequency measurement methods for vector network analysis, material characterization, and noise characterization of microwave devices, as well as sensor principles for radar systems and wireless solutions for communication systems.