Available online at www.sciencediect.com ScienceDiect Pocedia Engineeing 1 (215 ) 1 14 25th DAAAM Intenational Symposium on Intelligent Manufactuing and Automation DAAAM 214 Measuement of Complex Pemittivity in Fee Space Pet Skocik* Pet Neumann Tomas Bata Univesity in Zlín Nam. T.G.M. 5555 Zlín 761 Czech Republic Abstact The pape descibes the measuement of complex pemittivity in fee space. It is an advanced non-contact method which is used to find the electomagnetic popeties of mateials. In this case it involves the mateials which ae used in aviation technology especially fo hadening the avionics against electomagnetic intefeence. A specialized laboatoy wokplace equipped with the vecto netwok analyze ZVA 67 fom Rohde and Schwaz was built fo the measuement. Initial measuements wee pefomed at high fequencies fom 22 to 325 GHz on a Teflon sample because of the ease of veifying the esults. The high fequency ange was achieved by using ZVA-Z325 convetes fom the same company and the espective antenna systems. This measuing system was used fo detemining the tansmission coefficients. The complex pemittivity which chaacteizes the electomagnetic popeties of the mateial fo the above fequency ange was found by iteative method pogammed in Matlab envionment. 215 The The Authos. Published by Elsevie by Elsevie Ltd. This Ltd. is an open access aticle unde the CC BY-NC-ND license (http://ceativecommons.og/licenses/by-nc-nd/4./). Pee-eview unde esponsibility of DAAAM Intenational Vienna. Pee-eview unde esponsibility of DAAAM Intenational Vienna Keywods: Complex pemittivity; cicula hon antenna; fee space method; vecto netwok analyze; S-paametes 1. Intoduction Measuement of the complex pemittivity in fee space is based on placing a sample of unknown mateial in space between the tansmitting and eceiving antennas and let a plane electomagnetic wave pass though it [6]. The measuement pinciple depends on the fact that phase and attenuation of the passing o eflecting wave vay accoding to the mateial popeties which ae defined by the elative complex pemittivity which can be expessed as [1] * Coesponding autho. Tel.: +42 57635285 E-mail addess: skocik@fai.utb.cz 1877-758 215 The Authos. Published by Elsevie Ltd. This is an open access aticle unde the CC BY-NC-ND license (http://ceativecommons.og/licenses/by-nc-nd/4./). Pee-eview unde esponsibility of DAAAM Intenational Vienna doi:1.116/j.poeng.215.1.347
Pet Skocik and Pet Neumann / Pocedia Engineeing 1 ( 215 ) 1 14 11 ~ ~ i (1) whee is the elative pemittivity o the elative dielectic constant σ is the conductivity of the sample is the dielectic constant of fee space ω = 2πf is the angula fequency of the electomagnetic wave. A loss tangent tan is often intoduced and is defined as a atio of the imaginay to the eal component of the complex pemittivity [1] Im( ~ ) tan (2) Re( ~ ) In this case equation 1 can be expessed in the fom [1]: ~ (1 i tan ) (3) The phase and attenuation of the plane electomagnetic wave which passed though o is eflected fom the sample depends on the complex pemittivity of the dielectic. Fo the calculation it is assumed that the sample is a plane-paallel plate because the micowave method in fee space uses plate-shaped samples fo detemining the electomagnetic popeties of the mateials. 2. Calculation of elative pemittivity fom measued data Tansvesal electomagnetic wave the sample of unknown mateial with pemittivity ε = ε.ε and pemeability μ = μ.μ can be descibed as [2]: T e jkd (4) Only one pass of the wave though the mateial is consideed. The paamete k is the popagation constant and d is the thickness of the mateial. The complex elative pemittivity is expected in the fom [4] and the complex elative pemeability [2]. Because the nonmagnetic mateial with is measued the popagation constant can be simplified in the fom [3]: 2 f. j k (5) and fo small losses 1 j 2 1 j po 1 (6) Tansmission coefficient can be witten as multiplication of two exponential functions epesenting the module and phase [3]: 2fd j c fd c T e. e (7) Fo the imaginay pat of the pemittivity the following equation apply [3]:
12 Pet Skocik and Pet Neumann / Pocedia Engineeing 1 ( 215 ) 1 14 c lnt fd (8) whee c is speed of light. Without consideing multiple eflections inside the mateial the measued tansmission coefficient S 12 and the ideal one is bound with the elation [3]: whee 2 2 2 1 T 1 T T S12 S 2 12 (9) 2 2 1 1 T 1 1 (1) and the initial estimation of the paamete is deived fom the phase of S 12. 3. The measuing equipment Numbe of diffeent methods exist fo the measuement of the complex elative pemittivity e.g. in dielectic waveguide [5]. Unfotunately this method is inappopiate fo measuing of small examples of the mateial because of the difficulty in ensuing the contact conditions because unwanted signal wapping may occu. Futhe this measuement must be conducted fo high fequencies in the ode of tens o hundeds of gigahetz. Because of this dawback a new laboatoy fo measuing the complex pemittivity in fee space was assembled. Fig. 1. Equipment fo measuing in laboatoy envionment.
Pet Skocik and Pet Neumann / Pocedia Engineeing 1 ( 215 ) 1 14 13 This laboatoy is equipped with the Rohde and Schwaz s vecto netwok analyse ZVA 67. The fequency ange is fom 1 MHz to 67 GHz. These limits wee expanded by fou sets of fequency convetes to the final 325 GHz. These convetes ae ZVA-Z9E (6 to 9 GHz) ZVA-Z14 (9 to 14 GHz) ZVA-Z22 (14 to 22 GHz) a ZVA-Z325 (22 to 325 GHz). Evey fequency ange must have its own antenna system which ae custom made. The cicula hon antennas ae chosen fo bette achievement of the Gauss shape of the beam. The movement of the convetes with attached antennas is suppoted by motion dives though the motion contolle fom the Newpot company. The whole measuing equipment can be seen in Fig. 1. 4. Example of the measuement As an example of the measuement of the complex elative pemittivity in fee space a sample of Teflon plate is chosen because of its known paametes. The thickness of the sample is 2 mm and is placed between the tansmitting and eceiving antenna. The main goal of the measuement is to veify the accuacy of the measuement and following calculation of the pemittivity value. The measuement is pefomed in the ange fom 22 to 325 GHz. Collected data fom the analyse wee pocessed in the Matlab envionment. Neithe the lens system no mios wee used to tansfom the beam to the plane electomagnetic wave. 2.9 2.85 2.8 pemittivity - eal pat [-] 2.75 2.7 2.65 2.6 2.55 Fig. 2. Calculated eal pat of the pemittivity. As can be seen in Fig. 2 the eal pat of the Teflon sample pemittivity in measued fequency ange is appoximately 2.7 which coesponds to the 2.1 which is the theoetical value. Conclusion 2.5 22 23 24 25 26 27 28 29 3 31 32 Fequency [GHz] In this contibution a fee space method was used fo detemine the complex pemittivity of the mateial. A sample of nonmagnetic Teflon was used fo the measuement due to its known paametes. This mateial also seves as a efeence to pove coectness of the chosen method and calculation of the pemittivity fom the measued data. An iteative pogam in Matlab envionment was used fo detemine the pemittivity. Accoding to the data the method seemed to be suitable fo dielectic paamete estimation of mateials. These mateials can be used fo example in avionics. In the futue an extension of the measuing equipment is planned. A set of lenses will be added to tansfom the beam to a plane electomagnetic wave. Also the iteative method should be impoved o eplaced by a moe pecise one. The effect of vetical otation of the mateial sample towads the emitting antenna will be studied in futue eseach.
14 Pet Skocik and Pet Neumann / Pocedia Engineeing 1 ( 215 ) 1 14 Refeences [1] J. Musil F. Žáček Micowave Measuements of Complex Pemittivity by Fee Space Methods and Thei Applications Academia Pague Czechoslovakia 1986. [2] Ch. Olob T. Reinecke E. Denicke B. Geck I. Rolfes Compact Unfocused Antenna Setup fo X-Band Fee-Space Dielectic Measuements based on Line-Netwok-Netwok Calibation Method IEEE Tansactions on Instumentation and Measuement VOL. 62 NO. 7 (213) 1982-1989. [3] M. Hudlička A. Kazemipou Učování mateiálových paametů ve volném postou (in Czech) 39. Pavidelné setkání zájemců o mikovlnou techniku Paha (213) ISBN 978-8-2-2488-. [4] S. Biju Kuma U. Raveendanath P. Mohanan K.T. Mathew M. Hajian L.P. Ligthat A simple fee-space method fo measuing the complex pemittivity of single and compound dielectic mateials Micowave and optical technology lettes VOL. 26 NO. 2 (2) 117-119. [5] Rohde And Schwaz. Measuement of Dielectic Mateial Popeties [online]. 212 [cit. 214-11-3]. Available fom: http://www.ohdeschwaz.com/en/applications/measuement-of-dielectic-mateial-popeties-application-note_5628-15697.html [6] Z. Awang F. A. M. Zaki N. H. Baba A. S. Zoolfaka and R. A. Baka A Fee-Space Method fo Complex Pemittivity Measuement of Bulk and Thin Film Dielectics at Micowave Fequencies Pogess in Electomagnetics Reseach B Vol. 51 (213) 37 328 ISSN 1937-6472.