INVESTIGACiÓN REVISTA MEXICANA DE FÍSICA 47 (1) 62-69 FEBRER0200¡

Development of a microwave dielectric spectroscopy system for materialscharacterization using the open-ended coaxial probe technique

I. García-RuizI and D. Avilés-Castro2

Centro Nacional de Metrología, División de Mediciones ElectromagnéticasCarretera a Los Cués Km 4.5, 76900 El Marqués, Qm., Mexico

e-mai!: ligarcia@cenam.mx.2caviles@cellam.mx

H. Jardón-AguilarSección de comunicacio~les, Centro de Investigación y de Estudios Avanzados de/Instituto Politecnico Nacional

Av. Instituto Poli/eeniro Nacional 2508,07360 Zaca/enea, México, D.F., Mexicoe-mail: hjardon@enigma.red.cinvestav.f1L'(

Recibido el I de junio de 2000; aceptado elide septiembre de 2000

Diclcctric spcctroscopy is a measurement tcchniquc lo charaClerize the intcraClion hctween electromagnctic cncrgy and macroscopic samplesas a function 01' frequency. h is based on the rneasurernent of cornplex permittivity plus conductivity and it has shown to be very useful toprovide inforrnation ahout internal structure of matter. It has sorne advantagcs over others like optical or chemical analysis: it is very fast.easy to implernent. rcquires little or no preparation of the sample, it can be nondestructive and/or minimally intrusive. In this paper thedeveloprnent 01'a dielectric spectroscopy system for the microwave frequency range (50 MHz-20 GHz). using an open-ended coaxial probeas sensor. is describcd. The complete systcm includcs a vector network analyzer, a microwave coaxial cable, the probe, a sample holder anda compuler to i1l1tomate measurcments and further data processing. This system has been used to mensure sorne Iiquid and salid materialssuch as alcohol. water and teflon. The real and imaginary parts of permittivity as function of frequcncy. for several sugarcane alcohol anddeionised water mixtures, tequilas and tenon samples are given. Measurement repeatability and accuracy considerations were taken and itwas identified that uncertainty of reference standards and systcm rcpeatability are the most important error sources. AIso. it was found thatopen-endcd coaxial probe techniquc is appropriate for measuring not only liquids but also solid materials. Sorne of the ohtained results werecompared 10 those reported in literature and good convergence was observed.

Keyw()rd.~: Complex permittivity; open-ended coaxial probe; microwaves

La espcctroscopía dieléctrica es una técnica moderna de medición para caracterizar la interacción entre la energía electromagnética y muestrasmacroscópicas como función de la frecuencia. Esta técnica se basa en la medición de la pcrmitividad compleja y conductividad de losmateriales y ha mostrado ser muy útil para proporcionar información sobre la estructura interna de éstos. Tiene algunas ventajas sobre otrascomo las técnicas óptica y el análisis químico: es muy rápida, fácil de implantar. requiere mínima o ninguna preparación de la muestra a medir,puede ser no destructiva y mínimamente intrusa. En este artículo se descrihe el desarrollo de un sistema de espectroscopía dieléctrica en elintcrvalo de frecucncias de microondas (50 MHz-20 GHz), usando una sonda coaxial abierta como sensor. El sistema completo está formadopor un analizador de redes vectorial, un cable coaxial de microondas. la sonda, un porta-muestras y una computadora para automatizaciónde mediciones y procesamiento, de datos. El sistema se ha utilizado para medir algunos materiales líquidos y sólidos tales como alcohol,agua y tcnón. Se presentan las partes real e imaginaria de la permitividad como función de la frecuencia medidas para mezclas de alcoholde caila yagua dcsionizada. tequilas y teflón. Haciendo consideraciones de exactitud y repetibilidad de las mediciones. se identificó que In.incertidumbre de los materiales de referencia y la repctibilidad del sistema son las fuentes más importantes de error. También, se encontróque la técnica de la sonda coaxial abierta resulta apropiada no sólo para medir líquidos, sino también sólidos. Algunos de los resultadosohtenidos fueron comparados con valores de la literatura observándose buena convergencia.

Dcscriptores: Permitividad compleja: sonda coaxial abierta; microondas

PACS: 77.22.Ch: 77.22.Gm

1. Introduction

Dicleclric spcctroscopy is a measurement technique to char-actcrizc the interaction bctween an elcctric f1eld and mat-(eL Thc rcslIlting phenomcna, polarization, can he cxpressedby mcans of the frequency dependent complex permittivityand conductivity quantities. which characterizc charge den-sily flllctllations within the matter. Those charge tlllctuationscome from the reorientation of dipoles. existing eithcr perma-nently or induced by the electric field. which can he formcd

hy the electron clouds around atom nuclcus, molecules. oreven larger rnicroscopic structurcs.

The cornplex permittivity has been defined in the formé* = él - jéll• where é' is comlnonly known as the dielectricconstant, and £11as the 105s factor. The rclationship é'l/él isalso known as the los s langent (tall Ó) and provides informa-tion ahout the energy ahsorption in lhe material.

Several tcchniques have heen developed to mcasure com-plex permittivity. hoth for low and high frequency ranges anda general overview can he found in Refs. I and 2. Regard-

DEVELOPMENT OF A MICROWAVE DIELECTRIC SPECTROSCOPY SYSTEM FOR MATERIALS ... 63

(2)

(1)

ing the range of frequencies that can be covered. they canhe grouped in wide-hand or narrow-band techniqucs Thoscwhich are hased on waveguide artifacts fall into Ihe narrow-hanJ class and the extent of the frequencies that can be cov-ered is limited lo ahout an octave. Conversely, those balied oncoaxial artifacts like the open-ended prohe arc broad-banded,which rcprcsents a significant advantage over others [3-6]. Inlhis mClhod, complcx permittivity is obtained fram the renec-lion cocfticient when the malerial under tcsl is put in conlaclwilh the prohe interfacc. This reflection coefficient can be ei-ther calculalcd lhrough full wave analysis mathemalical 50-

IUlion ofthe elcctramagnetic fields present at the pro he inler-face. and/or measured with sorne instrumentation Iike lhe re-ncctomeler, the Ilelwork analyzer, or admittance/impedancchridges. In Ihe past, reflectometry was implemcntcd as a limedomain analysis lechnique hut in the modern days nelworkanalyzers, which are frequency dornain instruments, are moreversalile ano accurate, though can be more expensive.

t\.1elhods proposing mathematical solulions [7-121 areinlended lo he ahsolule. that is, to eliminate lhe necessityof using reference materials for probe calibration; however.lhey dcmam.! cxhaustive computational cffort and are limc-consurning. How c10se equations represenl the fields presental the interface ami how long iteration roulines are allowed torun determine lhe precision of malhcmatical solutions [:3, GJ.BcsiJes Ihis. Illost nI' them [3,7,12] slill recognize depen-dence on lhe use of reference materials either lo calihrale lheprohe or lOadjust and correct the theorClical SOIUliolls.

Other approaches rely on equivalent circuit 1ll0l.!-els [13-16]. which. as identified by Rer. 3. hecome invalidas soon as we Illove into lhe microwave range of frequencieshecause pro he capacitances are complicated functions 01'rre-Ljuency and permittivily. Modeling the coaxial prohe Iike ananlenna [1il also has a high frequeney limit. amund 3 GHz;il can he shown thal this model can he reduced to a cir-cuil approximalion with their inherenl Iimitalions [31. Olherproposcd solutions are incipient like the frequency varyingIllelhod proposed in [18J hut they are nol accurate enough.

Several models giving a relationship betwecn lhe com-plex permiltivily ami complex reftection coefficicnt can hcfound in Refs. 1-28; the hilinear calihration model, firsl pro-poscd hy Cole 1191, will be used here. )( comhines a circuitmudel anu a hilinear lransforrnation, which provides errorcorrcction righl al lhe prohe interface, increasing accuracyami making lhis modcl a powerful tool. This approach re-lies on the use 01"reference material s with known permittivi-tieso which makes probe calibration a simple task [6. 19-22].Comparison 01"this technique with other more complicatedmodels can he found in Ref. 6.

This paper deals with the complex permittivity of suh-strales for microwave circuils and lhe change in permittivilyas a funclion of water content in sugarcane alcohol, and onlyolle indcpendent ref1ection is ncedcd (6]. The opcn-cndcdcoaxial prohe can he used lo measure the complex pcnnil.(ivity (JI' one or morc layers [8110,16], and it produces sur-facc wavcs, radiative waves and radial guided waves. ami its

analysis is given in Refs. 7-10. 14 and 23. lt also allows awidc frequency spectrum measurcment. To carry out the cal-ibralion ofthe measuring system, three well known referencemalerials [6. i. 9, 20-22] were used. To determine the best setof reference matcrials the following critcria were used: wellknown permiHivity values, high repealability, easy c1eansing,and high availabilily.

The main daims of Ihe present paper are: the open-endedcoaxial prohe can he an eftlcient mean s for assessing thequality 01"spirits like sugarcane alcohol. tequila. elC., in ad-dition to the applieations f()und in literature [1-28]. Modifiedlow-cost connectors like type-N or SMA can he used cm-cienlly as open-cnded coaxial prohes fmm few MHz up lOlenlhs of GHz; the hilinear model of calibration can hc ex-tended heyond 10 GHz wilh low loss of aeellraey. The teeh-nique can be used accurately not only for liquids. where goodconlact is easier to achieve, but also for solids by modifyingthe calibration rautine; and finally, lhe idenlification and eval-uation of main sources of lhe measuremenl uncertainly.

2. Oielectric relaxation

The interaction between an electric field and a dielectric ma-terial is possible because 01' the existence of free charge car-ricrs and electric dipoles existing either permanently or in-duced hy the action of lhe clectric lield. Thc arising of in-duced dipoles can occur in several ways: atomic, when elec-lron clouds are displaced fmm lheir equilibrium position;molecular. when atoms share their electrons in an asymmetri-cal way; or struclural. when an accumulation of charge carri-ers of some polarity at interfaces or structures in lhe materialexists 111.

UIll.!crthe aClion of an electric field. oipoles are displacedand tend to reorient following the electric tleld direction. giv-ing place to the phenomena 01"polarization; this interactioncan he expressed by

P1+-_.EoE

where [- is the material perrnillivity, P is lhe polarizationvector. E is lhe elcctric f1eld vector and Eo is the free-spacepennittivily. As the frequcncy of lhe clectric lield ¡ncreases,dipoles lose their abilily lo follow the ficld direction changeand vectors P and E are no longcr in-phase, and because ofthis, [- is a complex quantity, commonly expressed as

whcre. E' is known as the dielectric constant, [" as thc lossfactor, and j = J=T. Relationship tn.n6 = E" /EI is knownas lhe IOS5tangent.

Therc are certain frcqucncies where many dipolcs cxpcri-cncc a signiticant loss oftheir mohilily. giving rise to a notori-ous change in pennittivily valuc. Thc real pan of permittivitywill exhibit a sudden decrease and the imaginary part will in-crease. These changes are known as diclcclric relaxation [1].

Re\'. Ml'x. Fú. 47 (1) (200 1) 62-69

1, GARCíA-RUIZ. D. AVILÉS.CASTRO. AND H. JARDÓN-t\GLJILAR

3, Tite open-ended coaxial probe

(X)

M••e'~'=nundel tes' .

(! (.(,;"!

I',t'f - r.r''r,1'!' + f;¡, .

{' =

Tellon seal \

•

wilh

Fl(iUR[ 1,(a) Opcn-cmkJ cO;lxi~Jl prohc and lh) its lumpcd equiv-aknt circuir.

A more complele approach to calculale complex pcrmil-livily from rellection codliciellt Illeasurernents is tile hilinearcalibralion mude!. propoSL'd hy Colc f19], \I,/hich (:omhinesIht: prohe equivaleJ1l circllil mollel already descriheu plus alwo pon error correctioll model similar ro lhal lIsed in nel-work analyzcr lllt:asurclIlenl error correction.

In the hilinear calibratioll model, Ihree reference materi-<lIswith known penniltivily are needt:lI to calihrate the prohe,Using this approach. the cOlllplex permittivily 01"an unknownmaterial can he ealculaled by lIsing Ihe expression (IUI

4. Developmenl nI' lite measuremenl syslem

where E;er and C'pr are (he complex permitlivity ami the lllea-sured (omplex relkclion c(leflicienl 01' one of lhe referencematerials; A anu n me t\\'o comple.x ealihralion constantsohtaincd by solvillg cqualion (7) for the t\\'o aJditional rcfcr-ence materials. ami I'.r is Ihe llleasurcJ rcf1cclion coefficicnlfor the unkno\\'n material.

Equalion (7) Illaps a ¡mini frolllthc complex ref1cction (0-

efliciellt planc into a point in lhe complcx permittivity plane.That is lhe uscfulness of Ihe hilinear Iransformation, thal ital10ws to translate points l'L'prescntcd in a two-coordinale sys-tcm (Iike lhe complcx one) inlo points located in anotherI\\'o-l'oordinalc systelll, The hilincar calihralion mOllel is avery practical one amI can IL'•.l(1 lO highly accurale measurc-lIlenls ir appropriate rderellce malerials are selcclcd ano cali.hralion process and malerial measurernents are carcfully per-formed [21].

t/lnel conductOf

"Outer conductor and flange /'

(5)

(4)

(3)

_ Z,. - Zor (wJ = Z Z'

~f. + o

E'(W) = '00 + ( "El J ) + _(_"_EC_' J-) +.1+)- 1+)-

/rl fr2

whcre ~E í is the dielcetric inerclllellt between a relaxalionalld Ihe Ilcxt one. frí is the i-Ih relaxarion frequeney anu ECQ

is lhe oplical pcrmiltivily,

when: [- is the comr1ex permitlivity, ECQ is Ihe oplical per-millivilY (dielectric constant for I"requencies mucil higherIhan /1")' £.~is the static permittivity (very low-frcquellcy di-elcclric conslanl). J" is the rclaxation frequency, j = J=T.and / is lhe frequency. This model has shown lo be lIscful todescrihe single relaxalion rhcllomena. Iypical in highly po-lar malerials (1. 28], ror malcrials exhibiting more than onerelaxalioll. Eq, O) c<ln he extended in this \Vay:

Rclleclioll cocftleienl 01"a transmission line is a measurc ofimpcdance changcs along the line ami il is ;¡ eomplex qllan-lit y, FOl"ti coaxial probe. as shown in rig. 1, il is given as

whcre r- is the relleclion coeHicienl. Zo is the mcasuremcnlsyslclll char<lcteristic impcdance, Z,. is lhe coaxial probeimpedance. and w is Ihe angular frequeney. Exprcssing the re-I1CClioll coefllcienl in tenns of tile equivalent eircuit complexadmitlance. Fig. lb. \Ve llave lhe following cquation 11, :q:

Polar Ill<llcrials sueh as deionised water and organic alcoholexhihil a single relaxation in the 50 MHz-20 GHz frequencyrangc: scveral rclaxalion phcnolllcna can bc ohserved in or-ganic lissuc~ [28]. hccallse as freqllcncy ¡ncreases diffcrcntkind of structllrcs lose lheir <lhilily 10 move with lhe clcetriefield.

SOllle empirical 1Il0dels have heen proposed to descrihedielcclric relaxatioll phcnomena. Thc Debyc model(l, 281 isgivcn hy Ihc cxpression

r' = rN = 1- jwZIl[G(E') + G/], «(,)1 + jwZIl[G(E') + G/]

whcrc C([*) is the capacilancc formcd allhe probe open enddlh ..~ lo lhe presence 01' Ihe material unuer lest and ef is anilllrinsic capaeil<lnce due lo geollletry. Equation (6) can hl.:'sol ved \O extraet E-. ho\','cvcr it lIlles not take into accounlSOlllC additional cffecls like spurious rclleetions inside Iheprohe. mechanical imperfections 01"the prohe, energy radi-ation el"fects. cte. Moreover. the capacitance C(E*) is alsofrequellcy dependent.

Several prototypes of lile pro he wcre manufacturcd usingcOlllme:-cially availahle type-N ami SMA coaxial connectors.A high quality typc-N connector is norrn<llly specilied to per-fmm \\'e11 to frL'quendes as high as 20 GHz free fmm high-orde.- Illodcs. Howcyer, fm lhis \\'ork \\'e uscd In\V-cost con-ncclOrs. \••..ith performance specilied up to nnly a fe\\' GHz.Onc of the rcsults is Ihal Ihis frequency restriction was over-come hy lhe prohe calihralion proccss and good performancewas achieved lo freqllencies hcyond 10 GHz. This sho\Vs Iheexlenl and the po\Vcr nI' the hilinear ealihralion Illode!' Fc-male chassis type-N ami St\lA conneetors were modified hy

Rc\', Mex. 1-'1.\',47 (1) (lOO]) 62-69

I>EVELOI't-.1ENT or A MICROWAVE D1ELECTRIC SPECTROSCOPY SYSTEM FOR MATERIALS ... 65vector Network AnalYler

Coaxialp«""

I S.mpleunder test

/

TAnLE 1. Pcrmiltivity rO[ rcfcrencc malcrials al 22.5°C

l\lntcrial ~.~ ~= jr(GHz) Reference

Deioniset.J water 7R.J 4.9 19.41 [1,3.4.291

~1cthannl 33.1 5.7 2.83 11.3.4.29)Air (1.20)

1= ¡'¡!t¡- :. ". ~ ~~.i.,:o" .:.:...~.:..

••• 0

-::~\

FlCiURE 2. Complete complcx pcrmittivity measurement system.

clItling-olf Ihe protrllJing central conductor and then polish.ing Ihe surface ulllil achieving a llat interface. A compleleprohe consists 01' Ihis Illodilied conncctor and a microwavecoaxial cahle. Microwave rellection and impedancc measurc-I11cnts are normally scnsilive to cahle llexures so the prohe\.....as fhctl llsing a lahoratory nxture holder. To improve mea-surelllenl repealahility. matcrialllnucr test was !llovcd up UI1-til rcaching good (olllact \vith lhe prohc hy using a lahoraloryjack (instead 01" Illoving the prohe). Liquid materials underlIleasurelllcnl wcrc (olllained in glass heakers.

Rcl1e(tion eoeflicients are Illcasllrcd with an X51OC Net-\vork AnalYl.er SYSICIll. A software was developed in BA-SIC to conlrol Ihe nelwork analyzer Ihrough lhc IEEE-488inlerface. Pro he calihraljol1. Illeasuremenls and data proeess-ing \verc I"ully aUlomalcd by Ihis software and a user friendlygraphic inlerface is provided. The complele syslClll Jiagramis shol,\'l1 in Pig. 2.

5. SyslclII calihratinn

.,".,'"

1 "'"20

","

30

!20

l""

"

.¡

'"Frequ,"""",. GHz

(a)

~~.:......:.~.:\~

."'"• ~1133• 75/25

."'"• ~OOIO

• 61133

- 75125

."'"

. ''''''

"'"

6.1. l\lcaslIrt.'mcnt 01' liqllids

6. i\Icasllrcmclll lit" malcrials

FIGURE J. :-'fe;Isured permillivity valllcs in sllgarcanc alcohol anJdcioniscd water mixtures: a) real anJ h) imaginary parts.

""'"(h)

""

ker is useu for air. By doing Ihis, unJesircd wall rcllcctionsare ealihrated out and an)' auvcrse effccls minimizcd.

l'v1easurclllenls were performed wilh lhis system and sOlllematerial characterizatioll sllldies were carriet.J out with liq-uids like organic laboratory alcohol amI sugitrCanc alcohol.soft solids like fats, ami solid microwave suoslrales likc tcllonantl Rexol;te 4422

Samples 01' sllgarcane alcohol/deionised waler mixtures inproportions 01' 50/50. 67/33. 75/25. SO/20 ami 100/0 wereprepared. Complcx pcrmittivily was Illeasurcd for cal'h sam-pie al 22.;j°C; Fig. 3 shows real ami imaginary parts 01' pcr-mittivity plottcd against frequency. As can he secn in Fig. 3,

Calihration is pC'rformed al the llat interface plane 01' lheprobe by Illcasuring tlle rcfercncc malerials. By doing Ihis,lhe calihralion proccss corrects lhe cffects 01"the probe il11-perfccliolls. As was prcviously Illenlioncd, il is necessary lolIleasure lhree known reference malerials. SOl11e dcsirahlecharacteristics rOl' lhese malerials are: well-known pcrmiltiv-ily values. high purity. high rcpcalahilily, high availahility.ami casy clcansing wilh minimal rcsiduals. To increase ae-eurac)' and prohc scnsitivily il is desirahlc lhat stalic pcrmit-livily values be close to lhe expecled valucs. Aftcr an cxtcn-sive hihliographical research [1, :~, ,1. 20, 201. SOIllCmaterialsfulnlling those characteristics were selecteJ. thrce 01' thelllshoWIl in Tahle l. with pennitlivity values al 22.ij°C.

As ( •.1Ilbe seen in Tahle 1, lhe statie permittivity values areevenly distributed. Using ai!" as a refcrence standard is veryconvenienl since ils permitlivity is well known, it is casilyIlleasured (by silllply Icaving lhe prohe open). therc is 110ne-cessity 01"having a conlainer, therc is 110Ilecessity 01' c1eans-ing the pro he afler J1leasuring lhis material. ele. DcioniscJwater and lIlethanol are easily removed hy using cOlllpresscJ¡¡ir and, hccausc 01' its purity. no addilional cleanscrs areIIceded. AH of this spcet.Js IIp the calihralion process. LiLJuidshavc lo he COlllaincJ in glass hcakers. which can potelltiallyintroJlIce undesircd wall rel1eclions. To mainlain calihrationCOIH.JitioIlSequaJ for the three standards. an empty glass oea-

Rel'. Me.\". Fh. "'7 (1) (200 1) 62 .....út)

66 L GARCfA-RUIZ. D. AVILÉS-CASTRO. ANDII. lARDÓN-AGUILAR

r-'IGURE4. Rclationship belween alcohol concenlration in thealcohol-water mixtures and static permittivity.

-~8075

-r-0-

70StltIc permltUvlty

20: L1

10! _ __ ~~_

O £--+ .60 65

100 .

90 II

8O!

l 70 ~

'O 801~o

" 50~••e~ 40 :•~

30~••

IllcasurcJ PCTlllittivity values are scnsitivc lo sugarcanc al-cohol concentration and changes can be apprcciatcd. Staticpcrmittivity values wcrc calculatcd for c3ch set of mcasurcdpermittivily oy fitting dala lO loe Deoye model (Eq. 3) andfound lo oc oelween 64.1 I{" toe 10010 samplc and 71.2 forlhe 50/50 sample. In Fig. 4 lois relalionsoip oetween alco-hol conccntration amI static pcrmittivity is plottcd along witha linear rcgrcssion fit. From linear regression a calihratiollcquation can he obtained; Ihis, would allow obtaining the al-cohol concentration of any alcohol/dcioniscd water mixturelhrough the IlIcasurcmcnt of its pcrmittivity.

Other rncasurcmenls wcre carricd out on samplcs oC dif-ferenl orands 01'lequila oougol al a supermarkeL A sample 01'cach of six brand s was takcn and measurcd. Figure 5 shows(a) real and (o) imaginary pan 01'permittivily for loe six sam-pies. plottcd on the same graph. Diclcctric response for each

I

Frequeney, GHz

10 ¡-- U

100_010_0

_.,

,o

,.., 1--

otd--c.0.1

5

~~ 15 r--'.i

(a) (b)

r-'[(JURE 5. Complcx pcrmittivity for six samplcs oftequila, a) real part, h) imaginary part.

sample can he distinguished from eaeh olher. AH 01' Ihemshow a single strong relaxation (Iypical in highly polar rnale-rials) in the range 01"6 to 8 GHz; static permittivity for satll-pies falls in Ihe rangc of 55 lo 65. It can he see thal lelJuilahas a characlcristic "dieleetric footprinl". Difrerences atllongsamplcs can he caused mainly hy faclors like: proportionsof principal components (ethanol, water and rnelhanol), andpresence (or ahsence) of the so-eal1ed gcneric compounds,which appear as a resull of processes Iike aging.

6.2. i\1easllrernent of solids

Olher measurcments were pcrforrned on samplcs of lellonrrrFE and a soft variant 01' tellon known as gorc malerial,\\"hich are normally used as insulators ano dicleclric suh-slratcs in microwave devices. Toluene, air ami chloroformwere chosen as suitahle reference malerials for lesting theselow-Ioss. low permittivity samples, following Ihe same crite-ria as in the case 01'high.loss and high permittivity rnaterials.Their stalic pennittivily, optical permiltivity and relaxalionfrequeney pararnelers were investigated and ohlained from

IRefs. 2 and 22. Complex perrnittivity 01'these references wasgellerated for aH the test frequencies using the Debye relax-al ion lIlodel 01'(3) and shown in Fig. 6.

Preparalion of solid samples lo he tested is straighlfor-ward and reqllircs on1y a nat surface to make contael with theprohe interface. Figure 7 shows oOlh real and imaginary partsof pcrrnittivity ror tellon PTFE measured in the 100 MHz-20 GHz frclJuency range and plotted along with a linear fil.It can he ohscrvcd in Fig. 7 Ihal dielectric response is nearlyBat for real part and loss factor increases with frequency. Acloser look al Ihe graph shows that Ihe real part (diclectricconstarH) is aoout 2.0 inSlcad of the most well-acecptcd valucof 2.1 (rneasured wilh narrow hand techniques Iike the reso-nanl cavily) 01' le!lon PTFE. \Ve think thal this difference 01'ahout 5% can rcslIlt from a) incorrect permittivity values inone or more reference material s, and/or b) inadequalc contactal prohc interface. Sevcrallests were perfonned to investigalethe origin 01'Ihal differenee from correct values. It was iden-litied that Ihc calihration routine would have to oe modified

Ht'l'. Mex. Fís. 47 (1) (2(X)J) 62--69

DEVELOPMENT OF A MICROWAVE D1ELECTRIC SPECTROSCOPY SYSTEM FOR MATERIALS .. 67

0.03

005

0,27

o

-0,03

100010,0'o

2

"

FIGURE 6. Pcrmittivity values of reference materials used in low.los5 low permittivity malcrials measurcmenl.

2S

J~4 t-j+H-f 045I I H-H ::::1'.~ o.•

03'

--+ 03

" 025 ~

: -1- 02!•015J01

" 005

oo I I I I I

-005o , 10 " 20

F..-qlMncy, GHz

FIGURE 7. Measured permittivity for tellon M"fE.

and, al Icast, a so lid reference material includcd. This haslo do with lhe contact al rhe prohc interface; whilc almostperfcct contact is achicvcd with ¡¡quids, solid surfaccs canprcscnt impcrfcctiolls likc roughncss. wavincss. ctc., whichIlecd lo be takcn ¡nlo account. Studics nI' lhe cffccts nI' sur-faec impcrfcctions ovcr pcrmittivity can he found in Rcfs. 10amI 26 whcrc post-proccssing corrcctions are also proposcd.

One ofthe ohjeclivcs ofthis work is lo show Ihal calihra-lion routine (the hilinear one that we are Llsing)musl providecorrect pcrmittivity values and also calihrale oul mosl imper-feclions without needing any further post-proeessing correc-lion routine. Including a solid reference material allows thislo OCachicvcd. Rexolile 4422, a salid diclectric thal cxhihitsa nat response with a dielectric constant of2.55 from low fre-qucocy up lo around 3(X)GHz [1,301 was chosen lo replacetoluene as reference material.

Preparation of this reference material was perfonned lhesallle way as test samples. After pcrforming the new calihra-tion routine. samples of tellon were Illcasurcd again and lheresults ohtaincd prescnt a suhstantial improvemenl. rigure Sshows real and imaginary parts of pcrrnittivity of lellon JYfFEror hoth calihration mutines. It can he appreciated that dielce-

Fl'K~ncla, GHz

FIGURE 8. Comparison of mcasured permittivity values of leftonPTFE obtained after lWOdiffcrent calibralion roulines: (l) normal.using 21iquids anu air as refercnces. and (2) modificd routine, usinga liquid. a solid and air as references.

Irie response is cven smoother and the value for PTFE is nowc10ser to 2.1. It is necessary to emphasize that in this workthe whole response for each material is obtained in just onestep with a ealibration rouline of abollt five minutes and arneasurernent run taking about a minute. Olher aeeurate tech-niqucs likc rcsonant eavity [1.2], take longcr and only a nar-row hand can he covercd with a single cavity.

7. Measurement repeatabílity and accuracyconsiderations

Measuremenl unccrtainty assessment is a topie that has be-come of great relevance in the last years. It is now considercda must in lechnieallilcrature and it has been addressed in sev-eral papers where eomplex permittivity values are reported asohlaincd using different approaches, either using coaxial test-ing artifacts or olhcrs [3, 10,31]. However, in the case of thehilinear calibration model. only a few works, as far as wekIlOW,have rcported measured values with a measurcrncntuIlcertainly asscssment ineludcd [21]. Somctimcs. what is re-ported as "uncertainty" is the standard deviation of measureddata. Aecording to the aecepted guide for llncertainly cxprcs-sinn 132], both systcmatic ami random components have to heconsidcred in the calculation of uncerlainty. Following theseguidelines, wc have performed a detailed unccrtainty anal y-sis for lhe hilincar model lhal can be found in ReL 31 and,for Ihe sake 01' completeness. we extraet and present sorneconsiderations hcre.

From Eq. (7). il is seen lhat £' calculalion depends onknovm reference matcrials and mcasured renection eoef~ficienl ratios. Thcsc represent main systematie uncertainlysOllrces. The 1l10st important sources af random errors aredrifts of the vector nctwork analyzer. mechanieal movcments01' the prohc ami microwave cables. llndcsirable reneclions,tcrnperature dependence of reference materials permittivity.and contaminatinn nf lhe probe during handling.

Re" Mn. Fis. 47 (1) (2001) 62-<i9

óX 1.GARCíA-RUIZ. D. AVILÉS-CASTRO. AND 11.JARDÓN-AGUILAR

Ncglccting lhe possihlc corrclation. lhe systcmatic llllccrtainty cquation can he slatcd in this way:

(9)

whcrc E;..(, éj ami £:1 are reference material complcx pcrmiltivitics ami p lhe rctlcction cocflkicnts relationship as prescntcd inEq. (X)

Producls in hrackcts are complcx and produce fOUT lcrms cach lhal. ancr unfoldcd, can he grouped as contrioutors lo realand imaginary parls of ¡¡2(é*):

II'(E') =

1/2 (E") =

[np~E' ll(E;,,)], + [Im~<E' ll(E~,.r)]' + [BP'O":'u(E~)]' + [ImO~'ll(Eul]'U'-rt'f U'-ref ••.1 D:'1

+ [BP~~: 1I(E;f + [!I11~:: u(E~f + [RP~; lI(p'f + [hU ~; ll(Pul r[BeoO~E'll(E~.rl]' + [lmoO<E'I/(E;,.r)]' + [B" ~:. 11(E'n] , + [1mO:" ll(E')]'

'-rd '-rd (J .•. ¡ D ...¡

+ [BP~~>(E~f + [lm~~>(E;f + [np~>(pUf + [hll~;ll(p,f

( lOa)

(IOb)

TABLE 11. ObSCfvcd standard dcvialions ((1) in rcpcalahilily tests in alcohol mcasuremcnts. T = (22.5::i:: O.5tC.

Typc uf test Ohscrvcd C1 for E' (%) Observed a !"ur [" (%)

range typica! va1uc range lypical valuc

Kcpeatahilily alllong prohc calihrations

Repcalahilily among lTlcasurcmcnls aftcr a prohc ca1ihration

0.33 lo 0.53(J. 1') In ().4J

0.49

0.33

0.31 lo 1.900.14 lo 482

0.580.22

TABI.E 111. SUlllmary of lInccr!;]inly conlrihutions for Ihe rcal (E') amI imaginary (EII) par! 01' pcrllliltivity in a lypical measurement of alcohol

al scvenl! freqllencies.

real par! (e') imagi nary P;]rt (E")

Freqllcncy Unccrlainty l'OlllrihtHions (%) C(lInhincJ Tolal Uncer!ainty cOlllrihulions (%) Combined Total

(GHz) Systclllatic Typc A Uncerlainly ((J¡,) Systcl1latic Type /\ Unccrtainly (%)

01 0.79 0.11 0.80 11.75 024 0.79

05 D.')2 0.02 0<J2 0.98 0.14 0.99

1 1.27 006 1.27 1.37 0.03 1.37

2 2.61 0.04 2.61 2.64 0.07 2.64

3 3.53 o.m J53 3.53 0.11 3.53

011 Ihe olhcr hantl. in order lo cvaluale and incllH..k Ihe cf-fccts 01' rcpcatahility in the calculalion of tOlal lI11ccrtainty.we ran several Illeasurelllcnl cxpcriments. Firsl. wc cvalu-atetl repeatahility ilmong calihralions, which consistctl 01" aprohc calibralÍon ami sevcra! suhscqllcnl pel"mitLivily lllca-surclllcnls. Thc (llher one <.:onsistcd 01' laking llleasurctlwnlsc\'ery half-hour for several hours. artcr a prohc calihration.Standard dcvialiotls ohscrvcJ rol' cthanol range hClween lilll-ils .•.•110\\'11 UIl Tahk 11.

Using Eqs. (lOa) and (IOb) wilh partialllnccrtainty <.:on-lrihutions fmm rcfercnce materials. total uIH.:ertainty wasohtainetl ami SOIllC results are prcscnted in Tahle Ill. The

COlUlllllS lahcletl as '\ystematic" represenl contribulions fromsyslcmatic crrccts like reference material uncerlainlies antlvcctor network analyzer instrumentation errors in ¡he reflec-tioll codlicient mcasurements. The colurnn laheled "Typc A"shO\vs conlrihutions fmm random sourccs and were evaluatedwilh statistical methoJs.

S. COI\c1usiol\s

A fixture consisling 01' an open-enJcd probe and a vector net-\\'ork analyzer is found to he a good mean s to measure IhecOlllplex pcrmittivity 01" ¡iquid anJ solid malerials. The main

Rel'. Me.\". Fú. -t7 ( 1) (200 1) 62-69

DEVELOPMENT OF A MICROWAVE DIELECTRIC SPECTROSCOPY SYSTE1\.1FOR MATERIALS . 69

sourccs 01' error of the measurcment syslem are the uncer-tainlies 01' reference standmds and system repcalahility. Air,melhanol and deionised waler are exccllcnt material s whcnused as rcfcrcllces in prohc calihration for high loss, highpcnniltivity matcrials. The bilinear calihration technique canbe extended to frcquencies higher than 10 GHz wilhout in-troducing significant ermrs. This measurement system showsgood pOlenlial ror delermining and assessing the authenticityamI quality 01'spirits; its applicability is hound hy the Iimitsof lhe mcasurelllenl uncertainty. For measuring low-Ioss, lowpcrmiltivity materials like tellon, plastics, ele., the lechniqueis also elTeClive. Accurate traditional techniques like rcsonantcavity are narrow-hand, hard lo implant and limc-consuming;

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Acknowled!(ments

Authors wish to thank Consejo Nacional de Ciencia y Tec-nología (CoNaCyT) for supporting this work.

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RCI'. Mcx. F(s . .17 (1) (2001) ó2-ó9