Junal Teknlgi DIELECTRIC MEAUREMENT FOR LOW-LO MATERIAL UING TRANMIION PHAE-HIFT METHOD K. Y. Yu a *, Y.. Lee b, L. Zahid b, M. F. A. Malek c, K. Y. Lee d, E. M. Cheng e, N. H. H. Khamis a a Cmmunicatin Engineeing Depatment, Faculty f Electical Engineeing, Univesiti Teknlgi Malaysia, 80 UTM Jh Bahu, Malaysia b chl f Cmpute and Cmmunicatin engineeing, Univesiti Pelis Malaysia, 0600 Pelis, Malaysia c chl f Electical ystems Engineeing, Univesiti Malaysia Pelis, 0600 Pelis, Malaysia d Depatment f Electical and Electnic Engineeing, Faculty f Engineeing and cience, Univesiti Tunku Abdul Rahman, 600 elang, Malaysia e chl f Mechatnic, Univesiti Malaysia Pelis, 0600 Pelis, Malaysia Full Pape Aticle histy Received July0 Received in evised fm 9 July 05 Accepted 5 Nvembe 0 *Cespnding auth kyyu@fke.utm.my Gaphical abstact Abstact This pape pesents a calculatin f the dielectic ppeties f lw-lss mateials using the tansmissin phase-shift methd. This methd can pvide calibatin-independent and psitin-insensitive featues, and it was veified expeimentally by measuing seveal well-knwn samples using X-band ectangula waveguides. Keywds: Rectangula waveguides, dielectic cnstant, lss fact, tansmissin phaseshift, sample thickness Abstak Ketas keja ini membentangkan pengiaan sifat dielektik untuk bahan lengai dengan menggunakan kaedah penghantaan caa anjakan-fasa. Kaedah ini bebas daipada penentukuan dan tidak besanda kepada kedudukan bahan yang diletakkan dalam pandu gelmbang. Kaedah ini telah disahkan secaa ekspeimen dengan menguku bebeapa sampel yang tekenal dengan menggunakan X-band pandu gelmbang yang bebentuk segi empat. Kata kunci: Pandu gelmbang bebentuk segi empat, pemala dielektik, fakt susutan, penghantaan caa anjakan-fasa, ketebalan sampel 05 Penebit UTM Pess. All ights eseved 77:0 (05) 69-77 www.junalteknlgi.utm.my ein 80 7
70 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77.0 INTRODUCTION Cnventinally, the elative pemittivity, ε, and elative pemeability, μ, f a sample filled in a waveguide ae btained by measuing and cnveting the cmplex eflectin cefficient,, and the cmplex tansmissin cefficient,, by using Nichlsn-Rss- Wei (NRW) - impved NRW utines. -5, 8-9 me methds f matching the ppagatin bundaies have been ppsed that equie the measuement f nly ne f these ppeties f nn-magnetic, thin samples. Hweve, the phase f the measued and depends n the psitin f the calibatin efeence plane and n cnsistent psitining f the sample in the waveguide. The uncetainty f phase shift in the measued and can esult in an incect pedictin f the pemittivity f the sample. Thus, nmally, the calibatin plane is efeed t the ai-mateial inteface, and the thickness f the sample is essentially cnstant. Anthe pblem that can ccu in the badband measuements f and is phase-shift ambiguity. Althugh, the thickness, d, f the mateial shuld be less than 5% f the peatinal wavelength, i.e., λ/, this cnditin des nt guaantee the eliminatin f phase ambiguity ve a ange f peatinal fequencies. In ealie wk, the ambiguity pblem was slved by using gup-delay analysis - and iteative/nn-iteative methds. - Recently, seveal new calibatin-independent and mateial psitin-invaiant techniques 0- have been used t educe the cmplexity f the de-embedding pcedues and t pvide techniques that ae applicable f diffeent thicknesses f samples when using this measuement methd. In thei calibatin pcedues, mst f these new techniques equie btaining the slutin f a matix the slutin f matix deteminants. 0, In additin, the pedictin f the tangential lss, tan δ, f lw-lss samples fm measued and lacks sufficient eslutin. 9 It is well knwn that esnance measuement techniques ae gd chices f detemining lw tan δ values, but such techniques cannt be used f the measuement f swept fequency. This pape pesents the simple calculatin f dielectic ppeties based n the diffeence in the phase shifts f the measued between the ai and the sample, which was capable f handling the abve issues. In this wk, fmulatins wee explicitly expessed f the dielectic cnstant, ε, and the lss fact, ε. This methd des nt invlve having t make an initial estimate f the anticipated value slving a matix. Hweve, t make these calculatins, the samples wee assumed t be hmgeneus, istpic, and nn-magnetic istpic, and nn-magnetic (μ =). Incident TE0 mde d d Figue Rectangula waveguide with a sample f d thickness..0 PRINCIPLE OF THE TRANMIION LINE ε The tansmissin () /eflectin () measuement using ectangula waveguide is shwn in Fig., in which a hmgeneus and istpic sample slab with thickness d is patly placed in the ectangula waveguide. TE0 mde A TE0 mde A ample A A d ample d (a) (b) ample c d j d d j M B e ample d ample d N b a c d j e B ample c d j d d j M B e N Waveguide, b ample ample c d d j e B b Figue (a) Mdel f a tansmissin line: ppagating TE0 wave, attenuatin and phase shifted inside waveguide. (b) A sample f d thickness filled in waveguide hlde with length f d.
7 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77 F the TE0 ppagatin mde, the elatinship between the tansmissin phase shift, (in adians), and the ppagatin cnstant, γ, in an ai-filled ectangula waveguide with the length f d, can be epesented by a mdel (css-sectinal view f ectangula waveguide) as shwn in Fig. (a). The shifted phase, (at efeence BB ), can be embedded t suface, MN, which has a length f d fm AA : The diffeence between the phase shift f () and the phase shift f () can be witten as: ample d j j d () Fm (), the dielectic cnstant, ε and the lss fact, ε f the sample can be expessed as: d j d d j d C jd a whee αc is the cnduct attenuatin cnstant (in nepes/mete). When the waveguide is filled with a sample that has a thickness f d (in mete), as shwn ample in Fig. (b), the phase shift, (in adians) fm efeence suface, AA t suface MN, will be changed based n its new ppagatin cnstant, γ, as shwn: ample d j d d j d C jd j a whee = πf/c is the ppagatin cnstant f fee space (c =.997958 ms - ); a (in mete) ae the width f the apetue f the waveguide, espectively (Xband: a = 0.086 m, b = 0.006 m); ε = ε - j ε and α (in nepes/mete) ae the elative pemittivity and the dielectic attenuatin cnstant f the sample, espectively. The α is calculated fm: ample ample lg0.595 lg0 whee and ae the measued linea ample ample magnitudes f the eflectin cefficient and the tansmissin cefficient f the sample, espectively. () () () ample k a d a k a d ample Hweve, (5) and (6) ae nly applicable f the ideal case. Nmally, the dielectic cnstant, ε f the mateial can be accuately pedicted using (5) and (6) at the cente peating fequency, fcente f the waveguide (X-band: fcente=0. GHz). F badband measuements, (5) and (6) shuld be mdified by multiplying (5) with A tem as: A k a d ample A k a d a whee ample f A f cente ymbl f is the peating fequencies. The β is a cnstant value depended n the mdel and the quality f the ectangula waveguide. In this study, the β is equal t 0.. In fact, the A cefficient is used t cect the impefectin f ppagatin wave (such as VWR effects) in the ectangula waveguide at lwe uppe limit f the peating fequencies. (5) (6) (7) (8)
7 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77.0 MEAUREMENT ETUP The linea magnitude,,, and the phase shift,, f ai and the sample wee measued with an Agilent E507C vect netwk analyze (VNA) using tw X-band ectangula waveguides (Flann 609-F0 Mdel waveguide adapts) fm 8. GHz t. GHz. F the cnventinal measuement techniques (such as NWR methd Keysight 8507E sftwae), the thu-eflect-line (TRL) calibatin shuld be dne n the suface f CC and DD which ae the exact suface between the samples and the waveguide as shwn in Fig. (a). Thus, the psitin f the sample in the waveguide is dependent n the calibatin plane. Hweve, in this study, eithe pensht-lad-thu (OLT) TRL calibatin is equied. The OLT calibatin is nmally applied t VNA-pts n AA and BB planes, espectively. If thee is existing waveguide calibatin tl kits, thus, the calibatin pcess can be pefmed n plane CC and DD, espectively. The sample with thickness d is pemitted t place in any psitin in the ectangula waveguide, which des nt affect the accuacy f the measuement. VNA pt VNA pt A A B B (c) Figue (a) Css-sectinal view f expeimental setup. (b) Actual measuement setup. (c) Custmized sample hldes. (d) Well knwn dielectic samples in plastic cve. The actual measuement setup is shwn in Fig. (b). The nyln 6 (d = 5 mm), (d = 5 mm), (d = 5 mm), and (d =.7 mm) samples, espectively, wee placed in the waveguides and measued f ample Table Abslute es due t ±0. adian deviatin in ( ) d (m) (d) ± Δ ε ± (Δε /Δε ) 0 GHz 5 GHz 0 GHZ 5 GHZ 0.0 0.07 0.05 0.05 0.00 0.005 0.5 0.0 0.05 0.00 0.00 0.80 0.56 0.0 0.009 C D Table Dielectic cnstant and lss tangents C D Mateial ε -0 GHZ. GHz 0. GHz This tudy VNA pt (a) d ample VNA pt..9 5. ± 0.05 6.07.5.5 5.99.6.5.88 ± 0.0 6.76..9 7.8 Mateial Lss tangent, tan δ -0 GHZ. GHz This tudy 0. GHz 0.000 0.000 5 0.000 0.0 0.05 5 0.0 0.006 0.000 0.0079 6 0.007 0.08 0.0 7 0.056 (b)
7 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77 validatin. The dimensins f the samples wee pecisely machined by using a cmpute numeical cntl (CNC) cutte in de t fit the sample int the waveguide hlde..0 REULT AND ANALYI The uncalibated measuements tk int accunt the ttal ppagatin wavelength (>λ/) within the length f the waveguide and the length f the sample, which caused phase-ambiguity egins due t the vaiatin f phase shift between ai and the sample ve a given fequency ange, as shwn in Fig. (a). Thus, the pedicted values f ε and ε wuld be incect. In this study, the phase ambiguity was slved by using MATLAB s unwap cmmand, as shwn in Fig. (b). (ad) 5 0 - - - - Ambiguity egins -5 8 9 0.5 (a) (ad) 0 -.5-5 -7.5-0 -.5 Phase-unwapping -5 8 9 0.5 (b) Figue (a) Phase ambiguity in uncalibated measuements between ai and nyln; (b) Phase ambiguity slved by using the phase-unwapping methd As knwn that the cnventinal NRW methd equies sample thickness must be less than λ/ in de t avid phase ambiguity in the dielectic measuements. Hweve, f this study methd, the minimum thickness f the sample was limited t λ/8. The uncetainty measuement is high f a thin sample due t the deceasing f the sensitivity f the tansmitted wave thugh the sample, especially f tansmitted waves that have lnge wavelengths. F instance, a deviatin f ±0. adian in the ample measuement f ( ) f nyln, may cause diffeent abslute es, i.e., Δ ε and Δ ε, in the pedictin f the dielectic ppeties depending n the thickness, d, f the nyln, as shwn in Table I. The ε esults at 0. GHz using this study methd wee in gd ageement with the measuements btained fm liteatues, 5-7 as tabulated in Table II. Fig. 5 (a) and (b) shw the measued dielectic cnstant, ε and lss tangent, tan δ (=ε /ε ), f fu types f lw lss samples using NWR methd (ee Appendix) fm 8. GHz t.75 GHz. The ambiguity phase exists when the peating fequency exceeds.75 GHz f the 0.5 mm thickness f the samples. The dielectic cnstant, ε f the same samples wee als calculated using Keysight 8507E sftwae f cmpaisn and validatin, as illustated in Fig 6. The pedicted values f ε and ε /ε vesus peating fequencies f the fu samples by using (7) and (8), espectively, ae shwn in Figs. 7 (a), (b) and 8. Clealy, the ε esults wee in gd ageement with the measuements btained using Agilent 8507E sftwae. It shuld be nted that the calibatin planes f Figs. 5, 6 and 7 cases ae efe t plane CC and DD, which the waveguide thu-eflect-line (TRL) calibatin was applied t the planes. On the the hand, f the case f Fig. 8, the calibatin is nly dne at plane AA and BB using caxial pen-sht-lad-thu (OLT) technique (Keysight 8505D calibatin kits). In this case, the mismatch at the suface f the sample, the waveguide and impefectins in the waveguide intduced nise in the calculatins f ε and ε /ε. In additin, es in the measuements can als be caused by the ai gap that existed between the sample and the metal walls f the waveguide. Meve, the flatness f the sample sufaces can als be ne f the facts t. It was vey challenging t get accuate esults f the badband lss tangent (ε /ε ) calculatins in the case f Fig. 8 because the values f ε /ε wee t small and they wee vey sensitive t measuement es. In fact, the fluctuatin f the andm nise is lage than the values f ε /ε. Despite that, the andm nise in the badband dielectic cnstant measuements can be smthed using filte techniques 8.
7 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77.5.5.5.5,.5,.5.5.5 0.5 8 9 0 (a) Dielectic cnstant, ε 0.5 8 9 0. Figue 6 Cmpaisn f measued ε (Keysight 8507E sftwae with waveguide fm Flann Inc.). 0..5 0.08,, /, 0.06 0.0 0.0 0-0.0 8 9 0 (b) Lss tangent (ε / ε ) Figue 5 Cmpaisn f (a) measued ε and (b) measued ε / ε. (NRW Methd with waveguide fm Flann Inc.).,.5.5.5 0.5 8 9 0. (a) Dielectic cnstant, ε
75 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77,, /, 0.07 0.06 0.0 0.0 5.0 CONCLUION In this wk, equatins (7) and (8) wee deived t pvide badband calibatin-independent and sample psitin-insensitive techniques f measuing the dielectic ppeties f lw-lss mateials. Acknwledgement This study was suppted by a Reseach Univesity Gant (GUP) fm Univesiti Teknlgi Malaysia unde pject numbe Q.J0000.5.0H77 and the Ministy f Highe Educatin f Malaysia (MOHE). 0-0.0 8 9 0. (c) Lss tangent (ε / ε ) Figue 7 Cmpaisn f (a) measued ε and (b) measued ε / ε. (with thu-eflect-line (TRL) calibatin at plane CC and DD ). The ed slid lines ae the smth filte lines.,.5.5.5.5 0.5 8 9 0. Figue 8 Cmpaisn f measued ε. (with pen-sht-ladthu (OLT) calibatin at plane AA and BB ). The ed slid lines ae the smth filte lines. Refeences [] A. M. Niclsn, G. F. Rss. 970. Measuement Of The Intinsic Ppeties Of Mateials By Time-Dmain Techniques. IEEE Tans. Instum. Meas. 9(): 77-8. [] W. B. Wei. 97. Autmatic Measuement Of Cmplex Dielectic Cnstant And Pemeability At Micwave Fequencies. Pc. IEEE. 6(): -6. [] J. Bake-Javis, E. J. Vanzua, W. A. Kissick. 990. Impved Technique F Detemining Cmplex Pemittivity With The Tansmissin/Reflectin Methd. IEEE Tans. Micwave They Tech. 8(8): 096-0. [] A. H. Bughiet, C. Legand, A. Chaptn. 997. Nniteative table Tansmissin/Reflectin Methd F Lw- Lss Mateial Cmplex Pemittivity Deteminatin. IEEE Tans. Micwave They Tech. 5(): 5-57. [5] O. Luuknen,. I. Maslvski,. A. Tetyav. 0. A tepwise Niclsn-Rss-Wei-Based Mateial Paamete Extactin Methd. IEEE Antennas and Wieless Ppagatin Lettes. 0: 95-98. [6] K. aabandi, F. T. Ulaby. 988. Technique F Measuing The Dielectic Cnstant Of Thin Mateials. IEEE Tans. Instum. Meas. 7(): 6-66. [7] B. K. Chung. 007. Dielectic Cnstant Measuement F Thin Mateial At Micwave Fequencies. Pgess in Electmagnetics Reseach. 75: 9-5. [8] L. F. Chen, C. K. Ong, C. P. Ne, V. V. Vaadan, V. K. Vaadan. 00. Micwave Electnics (Measuement and Mateials Chaacteizatin). U. K: Jhn Wiley & ns, Ltd : 75-0. [9] J. heen. 009. Cmpaisns Of Micwave Dielectic Ppety Measuements By Tansmissin/Reflectin Techniques And Resnance Techniques (Tpical Review). Meas. ci. Technl. 0: -. [0] U. C. Hasa. 008. A New Calibatin-Independent Methd F Cmplex Pemittivity Extactin Of lid Dielectic Mateial. IEEE Micw. Wieless Cmpn. Lett. 8(): 788-790. [] K. Chalapat, K. avala, J. Li, G.. Paaanu. 009. Wideband Refeence-Plane Invaiant Methd F Measuing Electmagnetic Paametes Of Mateials. IEEE Tans. Micwave They Tech. 57(9): 57-67. [] Z. Caijun, J. Quanxing, J. henhui. 0. Calibatin- Independent And Psitin-Insensitive Tansmissin/Reflectin Methd F Pemittivity Measuement With One ample In Caxial Line. IEEE Tans. Electmagn. Cmpat. 5(): 68-689. [] MathWks. 0. Dcumentatin Cente [Dcumentatin each].available:http://www.mathwks.cm/help/matlab /ef/unwap.html. [] Agilent 8507 Mateials Measuement ftwae Technical Oveview. 0. UK: Agilent Technlgies Inc. [5] ECCOTOCK. (R) Lw Lss Dielectics & Othe Cmmn Mateials. Dielectic Mateials Chat. Available:
76 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77 http://www.eccsb.eu/sites/default/files/files/dielecticchat.pdf. [6] D. K. Ghdganka, V. V. Vaadan, V. K. Vaadana. 989. Fee-pace Methd F Measuement Of Dielectic Cnstants And Lss Tangents At Micwave Fequencies. IEEE Tans. Instum. Meas. 7(): 789-79. [7] Hitachi Chemical C. Ltd. Lw Tansmissin Lss Multi-Laye Mateial f High-peed & High-Fequency Applicatins. Available:http://www.ieee80.g//bj/public/nv/ikeda _0_.pdf. [8] K. Y. Yu, Z. Abbas, M. F. A. Malek and E. M. Cheng. 0. Nn-Destuctive Dielectic Measuements And Calibatin F Thin Mateials Using Waveguide-Caxial Adapts. Measuement cience Review. (): 6-. Appendix A. Niclsn-Rss-Wei (NRW) Methd The -paametes ( and ) at calibated plane CC and DD ae measued by vect netwk analyze. The is the cmplex eflectin cefficient f the ds thickness f the sample at plane CC. On the the hand, the is the cmplex tansmissin cefficient f the ds thickness f the sample at plane DD. The actual eflectin cefficient, Г and tansmissin cefficient, T f the infinite sample can be calculated using measued -paametes -5 : K K (A) and (A) whee K T (A) set t ze. On the the hand, fm fist esnance t secnd esnance fequency, n is set t. B. Altenative Methd F nnmagnetic sample (μ =), the actual eflectin cefficient, Г at plane CC f an infinite dielectic sample (ε = ε - j ε ) filled in the waveguide can be simplified as: (B) On the the hand, the tansmissin cefficient, T at plane DD can be educed as: T exp d (B) whee γ is the ppagatin cnstant f the waveguide filled with d thickness f sample and given as: The Г < cnditin is equied in de t find the cect t value using (A). Fm Г and T, the elative cmplex pemeability, μ f the sample can be pedicted as: j j a (B) j ln d T c (A) And the elative cmplex pemittivity, ε f the sample is given as: (A5) ln c d T The phase ambiguity may lead t ambiguities in etieving the values f ε and μ. Thus, the ln(/t) tem in (A) and (A5) is mdified as: ln ln j n T T (A6) whee n is the intege value (n = 0,,, ). Fm the cutff fequency t the fist esnance fequency, n is The measued cmplex value f at plane DD is witten as -5 : T (B) T Instead (B), (B) and (B) int (B), yields exp j d a 0 exp j d a (B5) Find the value f ε in (B5) using MATLAB s fslve cmmand. The value f ε is ptimized in de t find a t ( ze) f (B5). F Fig. B case, (B5) is equied t be mdified as (B6).
77 K.Y.Yu et al. / Junal Teknlgi (ciences & Engineeing) 77:0 (05) 69-77 exp j d a R 0 exp j d a (B6) whee R is efeence plane (at plane DD ) tansfmatin as: A A B B d C C d ample Figue B Thickness f sample, d less than length f sample hlde, d (Distance fm plane CC t plane DD ). D D R j k d d a exp (B7)