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Procedia Engineering 100 ( 2015 ) 100 – 104
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of DAAAM International Vienna doi: 10.1016/j.proeng.2015.01.
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25th DAAAM International Symposium on Intelligent Manufacturing and Automation, DAAAM
Measurement of Complex Permittivity in Free Space
Petr Skocik*, Petr Neumann
Tomas Bata University in Zlín, Nam. T.G.M. 5555, Zlín 76001, Czech Republic
Abstract
The paper describes the measurement of complex permittivity in free space. It is an advanced non-contact method which is used to find the electromagnetic properties of materials. In this case it involves the materials which are used in aviation technology, especially for hardening the avionics against electromagnetic interference. A specialized laboratory workplace equipped with the vector network analyzer ZVA 67 from Rohde and Schwarz was built for the measurement. Initial measurements were performed at high frequencies from 220 to 325 GHz on a Teflon sample because of the ease of verifying the results. The high frequency range was achieved by using ZVA-Z325 converters from the same company and the respective antenna systems. This measuring system was used for determining the transmission coefficients. The complex permittivity which characterizes the electromagnetic properties of the material for the above frequency range was found by iterative method programmed in Matlab environment. © 2015 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of DAAAM International Vienna.
Keywords: Complex permittivity; circular horn antenna; free space method; vector network analyzer; S-parameters
1. Introduction
Measurement of the complex permittivity in free space is based on placing a sample of unknown material in space between the transmitting and receiving antennas and let a plane electromagnetic wave pass through it [6]. The measurement principle depends on the fact that phase and attenuation of the passing or reflecting wave vary according to the material properties which are defined by the relative complex permittivity ɂ (^) ୰ which can be expressed as [1]
© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of DAAAM International Vienna
0 0
ZH
V
H
H
H
H r r i (1)
where ɂ (^) ୰ is the relative permittivity or the relative dielectric constant, σ is the conductivity of the sample, ɂ (^) ൌ ͺǡͺͷǤͳͲି ଵଶ^ Ȁ is the dielectric constant of free space, ω = 2πf is the angular frequency of the electromagnetic wave.
A loss tangent tan G is often introduced and is defined as a ratio of the imaginary to the real component of the complex permittivity [1]
Re(~ )
Im(~) tan r
r
H
H
G (2)
In this case equation 1 can be expressed in the form [1]:
H~ (^) r H r ( 1 i tan G) (3)
The phase and attenuation of the plane electromagnetic wave which passed through or is reflected from the sample depends on the complex permittivity of the dielectric. For the calculation it is assumed that the sample is a plane-parallel plate because the microwave method in free space uses plate-shaped samples for determining the electromagnetic properties of the materials.
2. Calculation of relative permittivity from measured data
Transversal electromagnetic wave, the sample of unknown material with permittivity ε = ε 0 .εr and permeability μ = μ 0 .μr can be described as [2]:
jkd
T e
(4)
Only one pass of the wave through the material is considered. The parameter k is the propagation constant and d is the thickness of the material. The complex relative permittivity is expected in the form ߝ ߝ ൌ ǡ ߝ െ ǡǡ [4] and the complex relative permeability ߤ (^) ߤ ൌ (^) ǡ^ ߤ െ (^) ǡǡ^ [2]. Because the nonmagnetic material with ߤ (^) ൌ ͳ is measured the propagation constant can be simplified in the form [3]:
, , ,
k 2 S f H 0 .H r H r j H r (5)
and for small losses
,, ,
,, ,
,,
r
r r
r r
j r^ j pro
H
H
H
H
H
H
Transmission coefficient can be written as multiplication of two exponential functions representing the module and phase [3]:
, 0
,, , 0
2
c
fd r
r c r j fd
T e e
S H
H S^ H (7)
For the imaginary part of the permittivity the following equation apply [3]:
This laboratory is equipped with the Rohde and Schwarz’s vector network analyser ZVA 67. The frequency range is from 10 MHz to 67 GHz. These limits were expanded by four sets of frequency converters to the final 325 GHz. These converters are ZVA-Z90E (60 to 90 GHz), ZVA-Z140 (90 to 140 GHz), ZVA-Z220 (140 to 220 GHz) a ZVA-Z325 (220 to 325 GHz). Every frequency range must have its own antenna system which are custom made. The circular horn antennas are chosen for better achievement of the Gauss shape of the beam. The movement of the converters with attached antennas is supported by motion drivers through the motion controller from the Newport company. The whole measuring equipment can be seen in Fig. 1.
4. Example of the measurement
As an example of the measurement of the complex relative permittivity in free space a sample of Teflon plate is chosen because of its known parameters. The thickness of the sample is 2 mm and is placed between the transmitting and receiving antenna. The main goal of the measurement is to verify the accuracy of the measurement and following calculation of the permittivity value. The measurement is performed in the range from 220 to 325 GHz. Collected data from the analyser were processed in the Matlab environment. Neither the lens system nor mirrors were used to transform the beam to the plane electromagnetic wave.
Fig. 2. Calculated real part of the permittivity.
As can be seen in Fig. 2 the real part of the Teflon sample permittivity in measured frequency range is approximately 2.07 which corresponds to the 2.1, which is the theoretical value.
Conclusion
In this contribution a free space method was used for determine the complex permittivity of the material. A sample of nonmagnetic Teflon was used for the measurement due to its known parameters. This material also serves as a reference to prove correctness of the chosen method and calculation of the permittivity from the measured data. An iterative program in Matlab environment was used for determine the permittivity. According to the data the method seemed to be suitable for dielectric parameter estimation of materials. These materials can be used for example in avionics. In the future an extension of the measuring equipment is planned. A set of lenses will be added to transform the beam to a plane electromagnetic wave. Also the iterative method should be improved or replaced by a more precise one. The effect of vertical rotation of the material sample towards the emitting antenna will be studied in future research.
220 230 240 250 260 270 280 290 300 310 320
Frequency [GHz]
permittivity - real part [-]
References
[1] J. Musil, F. Žáček, Microwave Measurements of Complex Permittivity by Free Space Methods and Their Applications, Academia, Prague, Czechoslovakia, 1986. [2] Ch. Orlob, T. Reinecke, E. Denicke, B. Geck, I. Rolfes, Compact Unfocused Antenna Setup for X-Band Free-Space Dielectric Measurements based on Line-Network-Network Calibration Method, IEEE Transactions on Instrumentation and Measurement, VOL. 62, NO. 7 (2013) 1982-1989. [3] M. Hudlička, A. Kazemipour, Určování materiálových parametrů ve volném prostoru (in Czech), 39. Pravidelné setkání zájemců o mikrovlnou techniku, Praha (2013), ISBN 978-80-02-02488-0. [4] S. Biju Kumar, U. Raveendranath, P. Mohanan, K.T. Mathew, M. Hajian, L.P. Ligthart, A simple free-space method for measuring the complex permittivity of single and compound dielectric materials, Microwave and optical technology letters, VOL. 26, NO. 2 (2000) 117-
[5] Rohde And Schwarz. Measurement of Dielectric Material Properties [online]. 2012 [cit. 2014-11-03]. Available from: http://www.rohde- schwarz.com/en/applications/measurement-of-dielectric-material-properties-application-note_56280-15697.html [6] Z. Awang, F. A. M. Zaki, N. H. Baba, A. S. Zoolfakar and R. A. Bakar, A Free-Space Method for Complex Permittivity Measurement of Bulk and Thin Film Dielectrics at Microwave Frequencies, Progress in Electromagnetics Research B, Vol. 51 (2013) 307 – 328, ISSN 1937-
