2017-01 Design of a Wideband System for Measuring Dielectric Properties

Design of a Wideband System for MeasuringDielectric PropertiesXiangzhen Wang and Wen GeyiAbstract—A dielectric object placed in the near-field region of an antenna produces a scatteredfield,which alters the input impedance of the antenna.This property can be used to measure the electric parameters of dielectric materials.A wideband system for measuring the dielectric properties in the frequency range from1.1to3.5GHz is designed and prototyped.The system consists of a wideband directional antenna,a wideband radio frequency circuit,and a data processing unit and has been tested by using different dielectric samples across the frequency band, and good measurement results have been obtained.Index Terms—Dielectric materials,dielectric measurements, input impedance,loss tangent,permittivity.I.I NTRODUCTIONW ITH the rapid development of microwave circuit technology,the study of dielectric materials by the computer optimization design has attracted more and more attention[1].The accuracy of predicting dielectric mater-ial properties depends on the measurement accuracy of the electromagnetic parameters of the dielectric materials.Many methods for measuring the electromagnetic parameters of dielectric materials have been proposed[2]–[6],and they can roughly be classified as the nonresonance methods[7]–[14] and the resonance methods[15]–[20].The nonresonance methods primarily include the transmission/reflection method[7]–[9],the free-space method[10]–[12],and the time-domain method[13],[14]. For the transmission/reflection method,the dielectric sample is placed in a coaxial line or a rectangular wave guide, and the permittivity of the dielectric sample can then be computed by solving a scattering equation.It can accurately measure high-loss to medium-loss dielectric materials.But, the measurement accuracy is relatively low for low-loss materials.For the free-space method,two antennas are used to receive the electromagnetic energy reflected and refracted from the dielectric sample,so that the relative permittivity of the sample can be determined.It is suitable for the broadband measurement.Especially for high-loss to medium-loss dielectric samples,it has a higher measured accuracy.But,the measured accuracy becomes worse for Manuscript received November22,2015;revised August8,2016;accepted August11,2016.Date of publication November1,2016;date of current version December7,2016.This work was supported in part by the Jiangsu Innovation&Entrepreneurship Group Talents Plan and in part by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The Associate Editor coordinating the review process was Dr.Sasan Bakhtiari. The authors are with the Research Center of Applied Electromagnetics, Nanjing University of Information Science and Technology,Nanjing210044, China(e-mail:1002291879@;wgy@).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TIM.2016.2619019the low frequency and the drawback of the method is that it requires a largeflat parallel-faced sample of homogeneous materials.All the methods discussed earlier are conducted in the frequency domain,and they can also be applied in the time-domain measurement.But,they are restricted by rapid sampling technology,and the frequency cannot be too high. The resonance methods primarily contain resonator meth-ods[15]–[17]and resonant perturbation methods[18]–[20]. In the resonator methods,the sample under measurement is excited as a resonator in the measurement circuit,and its permittivity can be obtained from its resonant properties. The resonant perturbation methods are based on the fact that a dielectric sample placed in a resonant cavity will affect its resonance frequency and quality factor Q.The permittivity of dielectric sample can be deduced from the change of the resonance frequency and the quality factor Q of the cavity.The resonance methods have higher measure-ment accuracy,especially for the low-loss dielectric mate-rials.But,they are not suitable for wideband measurement and for high-loss materials the measurement accuracy is relatively low.Another method for measuring dielectric properties is based on the perturbation of antenna input impedance.A dielectric sample placed in the neighborhood of an antenna will alter the input impedance of the antenna,from which the permittivity and the loss of the dielectric sample can be derived[21]. The feasibility of this method has been demonstrated by using the network analyzer as the receiver[22]and by a prototype system working at a single frequency of 2.45GHz[23]. In this paper,we report a new design of a wideband system for measuring the properties of dielectric materials in the frequency range from1.1to3.5GHz based on the method of perturbation of antenna input pared with the previous publications[22],[23],a more accurate calibra-tion process,including how to eliminate the leaked waves, and a new design for a wideband directional antenna have been included in this paper.The new wideband measurement system consists of three parts:a wideband monopole antenna, a radio frequency(RF)transceiver,and a data processing unit. We have discussed the design procedure of each part,the elimination of the leaked wave,and the calibration process in detail.The measurement system has been tested by using different dielectric samples,and good measurement results have been obtained.II.T HEORY OF THE M EASUREMENT M ETHOD Fig.1shows a homogeneous region V p located in front of a transmitting antenna.Two scenarios will be considered[21].0018-9456©2016IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.See /publications_standards/publications/rights/index.html for more information.Fig.1.Dielectric sample in front of antenna.1)Scenario 1:The region V p is free space (without the dielectric sample),and the antenna input impedance can be expressed asZ =−1I 2V 0E ·J dV +Z internal .(1)2)Scenario 2:The region V p is occupied by the dielec-tric sample,and the antenna input impedance can be expressed asZ=−1I 2V 0E’·J dV +Z internal .(2)Here,V 0is the source region bounded by ∂V 0,Z internal stands for the internal impedance of the antenna,I is the terminal current at the reference plane,and E (E )is the electric field generated by the antenna without (with)the dielectric sample.Both the impressed source current J (this is not the induced current on the antenna surface)and the internal impedance Z internal are assumed to be constant.Subtracting (1)from (2),and using the compensation theorem and the frequency-domain reciprocity theorem,we obtainZ−Z =1I 2V p {−[σ −σ+j ω(ε −ε)]E ·E’}dV .(3)where V p is the region occupied by the dielectric sample.The field E in (3)is assumed to be known,and the field E’in (3)can be determined from E by quasi-static methods [24].From (3),we can obtain the relative permittivity and the loss tangent of the dielectric sample as follows [22],[23]:εr =ImI 2(Z −Z )ωε0 V p E ·E’dV +1(4)tan δ=ReI 2(Z −Z )ωε0εr V p E ·E’dV(5)for a homogeneous dielectric sample.These are the basic formulas that we use to measure the electric properties of the dielectric samples.The input impedance Z and the electric field E can be obtained before measuring and are presaved in the data processing unit.An RF circuit will be designed to measure the input impedance Z when the dielectric sample is placed in front of the antenna.III.D ESIGN OF THE S YSTEMFigs.2and 3are the block diagram of the wideband measurement system and the photograph of the prototype system,respectively.The wideband measurement system is divided into three main parts:the wideband antennaunit,Fig.2.Block diagram of the measurementsystem.Fig.3.Photograph of the measurement system.the wideband RF transceiver unit,and the data processing unit.The antenna input impedance will change if a dielectric sample is introduced in front of the antenna.The RF circuit is designed to measure the antenna input impedance in the frequency range from 1.1to 3.5GHz.The magnitude and phase of the antenna input impedance are converted to direct-current (dc)voltage as the output of the RF circuit unit,and they can be readily measured by the data processing unit.The relative permittivity and the loss tangent can be determined from (4)and (5),and displayed on the light-emitting diode screen.A.Design of Wideband Directional AntennaPlanar printed monopole antenna has been investigated extensively in recent years for ultra wide band (UWB)sys-tems due to its attractive features,such as low cost,simple structure,and wide bandwidth [25],[26].The geometry of the wideband planar monopole antenna used in the paper is shown in Fig.4,and the detail dimensions are listed in Table I.The fabricated antenna is shown in Fig.5,which is built on an FR4substrate of the size 100mm ×100mm ×1mm with relative permittivity εr =4.4and loss tangent tan δ=0.02.The design uses a trapezoidlike patch with curved bottom as the main radiating element,which is fed by a tapered strip line.In order to obtain a directional radiation pattern,a rectangu-lar conducting reflector with the same size of the substrate is placed behind the planar antenna,as shown in Fig. 6.The spacing h 2between the antenna and the reflector is aWANG AND GEYI:DESIGN OF A WIDEBAND SYSTEM FOR MEASURING DIELECTRIC PROPERTIES71Fig.4.Antenna geometry.(a)Top view.(b)Side view.TABLE IA NTENNA PARAMETERSFig.5.Fabricated antenna.(a)Top view.(b)Bottom view.variable to be optimized with Ansys HFSS with the goal of maximizing the product of gain and bandwidth,and the optimized value is h 2=40mm.An inverted trapezoidlike ground is introduced to ensure that the antenna is long enough in electrical length to cover the lower frequency.Fig.7shows the measured reflection coefficient for the antenna with the reflector.Fig.8shows the radiation patterns for the antenna with the reflector at typical frequencies across the band.All the radiation patterns are directional along the positive z-direction where the dielectric sample is placed.It is noted that the high directivity of the antenna would enhance the impact of the dielectric sample on the antenna input impedance andreduceFig.6.Rectangular reflector is placed behind theantenna.Fig.7.Measured reflection coefficient (a)amplitude and (b)phase.the disturbances caused by the surrounding environments,and thus increase the accuracy of the measurement system.Fig.9shows the transverse field distributions of the antenna at r =20mm for different frequencies with r being the vertical distance to the antenna.It can be seen that the field energy is well centralized across the frequency band.This provides a guide as to where the dielectric samples should be placed.Fig.10shows the measured antenna gain in the positive z -direction across the frequency band.B.RF Circuit DesignThe RF circuit consists of two paths.Path 1detects the phase of antenna reflection coefficient and path 2delivers the magnitude of antenna reflection coefficient.The directional coupler is used to separate the incident wave and the reflected wave at the antenna port.It makes the two paths contain only72IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT,VOL.66,NO.1,JANUARY2017 Fig.8.Measured radiation patterns at different frequencies.(a)1.5GHz.(b)3GHz.Fig.9.Simulated electricfield distribution at XOY plane at r=20mm.(a)1.5GHz.(b)3GHz.Fig.10.Measured antenna gain against frequency on the z-axis.the reflected wave from the antenna.The low passfilters areused tofilter all high-frequency components from the mixer.In path2,two low noise amplifiers are used in the mixerlocal oscillator(LO)input branch in order to satisfy therequirements that LO input power should be greater than theRF input power,as well as the maximum and minimum LOinput power ratings.In order to simplify the system design,theantenna input and LO input of the mixer share the same source,which makes IF output(dc voltage)easier to be measured bydata processingunit.Fig.11.RF circuit with ideal directional coupler.The measurement system must be calibrated before it canbe used to measure the dielectric properties.All the calibrationresults are saved in the data processing unit,which is a one-time effort.This process is essentially the determination of thepath losses and phase delays of the two paths shown in Fig.11.In antenna input reference plane1(the orange dashed-dottedline in Fig.11),the input voltage V in and reflected voltage V refmay be expressed as V in=ae jαand V ref=be jβ,wherea andb are the magnitudes;αandβare the phases.Thereflection coefficient at the antenna input can be written asS11=V refV in=bae j(β−α).(6)Note that the antenna input impedance is given by Z=Z0(1+S11)/(1−S11),where Z0is the characteristic impedanceof the feeding line.If the frequencies of the two inputs ofthe frequency mixer are the same,the downconversion outputbecomes the dc voltage.The output of the mixer will changealong with the phase difference θof the two inputs as shownin the following:V=A cos( θ).(7)Here,A is the magnitude of the output of the mixer.In practice,the directional coupler is not an ideal compo-nent.The coupled port of the directional coupler(see Figs.2and11)not only contains the reflected wave from the antennabut also contains the leaked wave from the source.The powerof leaked wave may be greater than that of the reflected wavefrom the antenna and this would degrade the accuracy of themeasurement results.For this reason,wefirst need to eliminatethe leaked wave in the calibration process.First,we discuss the calibration process for path1when thedielectric sample is absent.Fig.12(a)and(b)shows theflowof the reflected wave and leaked wave in path1,respectively.At the mixer IF output,we haveV1=A cos( θ)+A1cos( θ1).(8)Here,A and A1are,respectively,the magnitudes at the outputof the mixer corresponding to the reflected wave and the leakedwave; θand θ1are the phase difference of the two inputsWANG AND GEYI:DESIGN OF A WIDEBAND SYSTEM FOR MEASURING DIELECTRIC PROPERTIES73Fig.12.Path 1in the layout of the RF circuit.(a)Flow of antenna reflected wave.(b)Flow of leaked wave of directional coupler.of the mixer corresponding to Fig.12(a)and (b),respectively.V 1is a known quantity during the calibration process.Once the antenna is replaced by a 50- matching load,the first term on the right-hand side of (8)vanishes and only the second term remains.We denote this term as V match .ThusV match =A 1cos ( θ1).(9)When the RF circuit is finalized,the leaked signal is then fixed.Thus,V match is also fixed and can be measured.Then,the first term of the right-hand side of (8)can be expressed asV ph =A cos ( θ)=V 1−V match .(10)Thus,the measuring error caused by leaked wave has been eliminated.Let the loss of path 1in Fig.11be denoted by L 1(dB ),the power of the source be P (dBm ),and the path loss between the source and the antenna input be L (dB ).Then,we haveP (dBm )+L (dB )+|S 11|(dB )+L 1(dB )=A (dBm ).(11)In Fig.12(a),θ0represents the phase difference between antenna input and RF input of the mixer,α1stands for the phase difference between antenna input and the source output,and α2is the phase difference between the LO input of the mixer and the output of the source.Thus,the phase difference θmay be determined as follows:θ=β+θ0−(α−α1+α2)=β−α+θ0+α1−α2.(12)Fig.13.Path 2in the layout of the RF circuit.Here,(β−α)is the phase of the antenna reflection coefficient,which can be measured with the dielectric sample being absent;(θ0+α1−α2)is the phase delay,which can be esti-mated by the S-parameters of the components and the length of microstrip line.Finally,from (10)–(12),the loss L 1(dB )in path 1can be derived as follows:L 1(dB )=V 1−V matchcos (β−α+θ0+α1−α2)(dBm )−P (dBm )−|S 11|(dB )−L (dB ).Next,we discuss the calibration process for path 2.Simi-larly,we should rule out the inaccuracy caused by the direc-tional coupler leaked wave first.Fig.13shows that both the LO input and the RF input of mixer contain reflected wave and leaked wave in path 2,which is different from path 1where only the RF input involves antenna reflected wave and leaked wave.Thus,the calibration process for path 2is different from that of path 1.At the output of the mixer,we haveV 2=A 3cos ( θ3)=A 3(13)where θ3=0by design of path 2(see Fig.13).A 3is the magnitude at the output of the mixer corresponding to the sum of the reflected wave and the leaked wave.Note that V 2is a known quantity in the process of calibration.As shown in Fig.13,the path loss of path 2can be broken down into two parts:L 2(dB )=L 21(dB )+L 22(dB ),where L 21(dB )is the path loss between antenna input and reference plane 2and L 22(dB )is the path loss between reference plane 2and IF output of the mixer.The wave V t at reference plane 2,as shown in Fig.14,is the superposition of the reflected waveV 4=A 4cos (ωt +β+θ1)and the leaked waveV 5=A 5cos (ωt +α−α1+α4).Thus,we haveV t =V 4+V 5=A t cos (ωt + θ4)(14)74IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT,VOL.66,NO.1,JANUARY2017Fig.14.Superposition of reflected wave and leaked wave at reference plane2.Fig.15.Dielectric samples illuminated by antenna.(a)Dielectric slab illuminated by antenna.(b)Dielectric column illuminated by antenna.whereA t =A 24+A 25+2A 4A 5cos (α−β−α1+α4−θ1)tan ( θ4)=A 5sin (α−α1+α4)+A 4sin (β+θ1)A 5cos (α−α1+α4)+A 4cos (β+θ1).Note that (β−α)is a known quantity;and also note that (−α1+α4−θ1)and A 5do not change when the dielectric sample is placed in front of the antenna.Then,we haveA 4(dBm )=P (dBm )+L (dB )+|S 11|(dB )+L 21(dB )(15)A 3(dBm )=A t (dBm )+L 22(dB ).(16)Finally from (13)–(16),the total loss L 2(dB )in path 2can be determined as follows:L 2(dB )=L 21(dB )+V 2(dBm )−A 24+A 25+2A 4A 5cos (α−β−α1+α4−θ1)(dBm ).Now,we have obtained several calibration curves,whichshow how the calibration parameters change within the frequency range from 1.1to 3.5GHz.These calibration parameters include the path loss L 1(dB ),the phase delay (θ0+α1−α2),the output voltage V match when a 50- matching load is selected to replace the antenna at the antenna input port,the magnitude of leaked wave A 5at reference plane 2,the path loss L 2(dB ),and the phase difference (−α1+α4−θ1).TABLE IIM EASURED R ESULTS FOR D IELECTRIC S LAB FR4When a dielectric sample is placed in front of the antenna,the reflection coefficient and the related quantities will change,and they will be denoted by primed ing (11)and (16),we obtainP (dBm )+L (dB )+|S11|(dB )+L 1(dB )=V 1−V matchcos [(β−α) +θ0+α1−α2](dBm )(17)V 2(dBm )=sqrt {A 24+A 25+2A4A 5·cos [(α−β) −α1+α4−θ1]}(dBm )+L 22(dB )(18)whereA 4(dBm )=P (dBm )+L (dB )+|S11|(dB )+L 21(dB )where V 1and V 2are dc voltages readily measured by the data processing unit.Other quantities can be retrieved from thecalibration curves.Finally,reflection coefficient |S 11|and the phase (β−α) can be obtained from (17)and (18).IV.R ESULTS OF THE M EASUREMENT S YSTEMThe prototype system has been tested by using different dielectric samples.The center of the antenna is selected as the origin of the rectangular system (x ,y ,z ),and the center of the dielectric sample is assumed to be on the positive z -axis.As shown in Fig.15,a dielectric FR4slab of dimensions 50mm ×50mm ×3mm with εr =4.4and tan δ=0.02at 2.45GHz,a dielectric column TP-2of dimensions 55mm ×5mm ×5mm with εr =16and tan δ=0.001at 2.45GHz,and a dielectric cylinder K21of length 55mm and a radius 2.5mm with εr =21and tan δ=1.5×10−5at 10GHz are selected as the testing samples.All the values mentioned earlier are relatively stable across the frequency band investigated.Tables II–IV list the measurement results from (4)and (5)for the three dielectric samples at different separation dis-tances r across the frequency range from 1.1to 3.5GHz.It isWANG AND GEYI:DESIGN OF A WIDEBAND SYSTEM FOR MEASURING DIELECTRIC PROPERTIES75TABLE IIIM EASURED R ESULTS FOR D IELECTRIC C OLUMN TP-2TABLE IVM EASURED R ESULTS FOR D IELECTRIC C YLINDER K21seen that the measured results for relative permittivity are in good agreement with the known values across the frequency band when the loss tangent is not extremely low.Note that the accuracy depends on a number of factors,such as the frequency,the sample,the separation between the antenna and the sample,and the calibration process.It also depends on the method used to predict the perturbedfield E’.In the present design,the quasi-static method is used tofind the electricfield E’,which places a limitation on the measuring accuracy when the permittivity(loss tangent)of the dielectric sample becomes very high(low).Experiments indicate that the effects of the size of the dielectric sample are not critical when it is fully illuminated by the radiatedfield from the antenna.There is an optimal range for the separation between antenna and the sample,in which the measuring results are relatively stable.For the frequency band from1.1to3.5GHz, the optimal range is found to be from20to25mm,as shown in Fig.16.When the distance from the antenna to the dielectric sample is very small,the interaction between the radiatedfields from the antenna and the dielectric material will be strong and the prediction of thefields close to the antennabecomes Fig.16.Relative permittivity against distance r at2GHz.a challenge.When the distance is very large,on the other hand,the dielectric material will have negligible impact on the antenna input impedance.In both cases,the measurement results become worse.In order to improve the measuring accuracy for samples with extraordinarily high permittivity or low loss tangent,we need a better solution to determine the perturbedfield E .V.C ONCLUSIONA wideband system for measuring the electrical parame-ters of dielectric materials in the frequency range from1.1 to3.5GHz is designed,prototyped,and tested.The system consists of a newly designed wideband directional antenna,a wideband RF circuit,and a data processing unit.Its working principle is based on the fact that the introduction of a dielec-tric sample into the near-field region will alter the antenna input impedance,from which the properties of the dielectric sample can be determined.Measurement results from the prototype system indicate that the system works very well and the measuring method is very pared with other measuring systems,our system is cost-effective and easy to use.In addition,the sample preparation is relatively simple.R EFERENCES[1]S.Cui and D.S.Weile,“Robust design of absorbers usinggenetic algorithms and thefinite element-boundary integral method,”IEEE Trans.Antennas Propag.,vol.51,no.12,pp.3249–3258, Dec.2003.[2]L.F.Chen,C.K.Ong,C.P.Neo,V.V.Varadan,and V.K.Vardan,Microwave Electronics:Measurement and Materials Characterization.New York,NY,USA:Wiley,2004.[3]M.S.Venkatesh,and G.S.V.Raghavan,“An overview of dielectricproperties measuring techniques,”Can.Biosyst.Eng.,vol.47,pp.7.15–7.30,2005.[4]T.Yilmaz,T.Karacolak,and E.Topsakal,“Characterization and testingof a skin mimicking material for implantable antennas operating at ISM band(2.4GHz–2.48GHz),”IEEE Antennas Wireless Propag.Lett., vol.7,pp.418–420,2008.[5] D. 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