Circuital characteristics and radiation properties of an UWB electric-magnetic planar antenna for Ku-band applications

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1 RADIO SCIENCE, VOL. 48, 13 22, doi:1.12/rds.215, 213 Circuital characteristics ad radiatio properties of a UWB electric-magetic plaar atea for Ku-bad applicatios N. Haider, 1 D. Caratelli, 1 ad A. G. Yarovoy 1 Received 31 August 212; revised 29 November 212; accepted 14 Jauary 213; published 27 February 213. [1] A plaar, directive atea with large fractioal badwidth is itroduced i this paper. A detailed discussio o the proposed atea topology ad its architecture is reported. The proposed elemet is a combiatio of a patch ad a loop radiator. A proper combiatio of the electric field radiator (patch) with a magetic field radiator (loop aroud the patch) is exploited for expadig the operatioal badwidth. A parametric study is preseted to ivestigate the effect of the atea geometrical parameters o its performace. A geeral ad computatioally efficiet procedure for extractig the atea equivalet circuit is described ad used to achieve a meaigful circuit theory-based isight ito the characteristics of the radiatig structure. The theoretical ad experimetal results are compared, ad it is demostrated that the elemet features over 1% fractioal badwidth, good impedace matchig, ad uidirectioal ad stable radiatio patters. Citatio: Haider, N., D. Caratelli, ad A. G. Yarovoy (213), Circuital characteristics ad radiatio properties of a UWB electric-magetic plaar atea for Ku-bad applicatios, Radio Sci., 48, 13 22, doi:1.12/rds Itroductio [2] For a wide scope of applicatios icludig surveillace, security, through-wall or rubble imagig, ad medical diagosis, ultrawidebad (UWB) radar is eeded. A wide badwidth provides a very fie rage resolutio for this type of radars. The wide operatioal badwidths of the ateas are crucial for the total system performace; however, there are oly a few radiators which are able to provide a fractioal badwidth close to 1%. [3] I the last 1 years, may atea elemets have bee desiged which are suitable for UWB or widebad applicatios [Schatz, 25; Qig ad Che, 29; Yarovoy ad Pugliese, 26]. However, i the majority of the cases, the ateas are ot suitable for radar applicatios due to their bidirectioal radiatio patter. Furthermore, for dese arrays, the elemets should be small eough to fit withi the allowable elemet spacig to avoid gratig lobes. A odispersive behavior of the atea is also required for optimal wave receptio ad trasmissio. The most widely used radiators i UWB arrays are Vivaldi-like ateas [Schaubert et al., 23; Qig et al., 26]. However, Vivaldi-based arrays are characterized by a large volume (3D array). For systems implemeted o a mobile platform, such as through-wall imagig radar ad radar systems for a umaed aerial vehicle, plaar atea arrays are preferred to miimize the total weight. The study preseted i this paper is aimed at 1 Microwave Sesig, Sigals ad Systems, Delft Uiversity of Techology, Delft, Netherlads. Correspodig author: N. Haider, Microwave Sesig, Sigals ad Systems, Delft Uiversity of Techology, Mekelweg 4, 2628 CD Delft, Netherlads. (S.N.Haider@tudelft.l) 213. America Geophysical Uio. All Rights Reserved /13/1.12/rds.215 developig a ovel class of UWB electric-magetic plaar ateas which satisfies the above metioed requiremets. It is experimetally demostrated that the cosidered radiatig elemets feature a good impedace matchig from 8 to 24 GHz ad, hece, are attractive cadidates for short-rage UWB imagig, satellite commuicatios, ad radar applicatios i X/Ku bad. The origial atea cocept has bee itroduced i Tra et al. [29, 211], ad its applicability as a polarimetric array elemet has bee addressed i Haider et al. [21]. I this paper, emphasis is put o the ehacemet of the impedace badwidth ad size reductio of the elemet, as well as the relevat experimetal verificatio. Furthermore, a detailed aalysis of the atea performace as a fuctio of the mai geometrical parameters is preseted i combiatio with a suitable equivalet circuit model. [4] The paper is arraged i the followig way. Sectio 2 describes the topology ad the geometry of the proposed atea. The parametric aalyses are preseted i sectio 3. I sectio 4, the atea equivalet circuit is discussed. The umerical ad experimetal aalysis of the atea performace i time ad frequecy domais is detailed i sectio 5. Fially, sectio 6 cotais the cocludig remarks. 2. Atea Structure [5] For ultrawidebad radiatio, it is importat to combie proper excitatio of both electric ad magetic fields [Schatz, 25, p. 247; Kwo et al., 28; Farr et al., 1999]. The goal of this research is to develop a ovel atea based o a combiatio of a patch ad a loop. The primary requiremets for a array elemet are uidirectioal radiatio patter ad compact elemet size to avoid gratig lobes. To desig a UWB atea with uidirectioal patter, we propose a topology where a patch atea is ecircled by a loop as show i Figure 1. The atea is etched o a commercially available Tacoic high-frequecy 13

2 1 2 P4 = 5.5 mm 3 P4 = 5.9 mm P4 = 6.25 mm P4 = 7 mm Figure 2. The effect of the patch width (P4) o the iput reflectio coefficiet of the atea. Figure 1. The atea architecture ad relevat geometrical parameters. material (TLY-5) with a relative permittivity e r = 2.2. The atea is modeled umerically by usig the commercially available simulatio tool CST Microwave Studio, based o the fiite itegratio techique (FIT). [6] The ier patch cotributes more to the radiatio i the higher part of the operatig bad where the patch legth becomes quarter to half of the guided wavelegth. O the other had, the perimeter of the loop is roughly oe wavelegth aroud the ceter frequecy. Due to the presece of the stubs, the actual loop perimeter will icrease, ad hece, the frequecy bad will expad toward the lower frequecies. [7] To cocurretly feed the radiatig patch ad the loop, a grouded coplaar waveguide (CPWG) is the most appropriate choice. Furthermore, it is well kow that the CPW structure has may advatages for widebad applicatios, such as costat effective permittivity, low radiatio ad coductace losses, less dispersio, simple structure, ad very wide operatioal badwidth. [8] To further expad the impedace badwidth, both the patch ad the loop geometry have bee optimized. First, two side otches are added to the radiatio patch to exted the electrical legth which implies that the curret will be forced to follow a loger path. Four stubs are attached to the upper side of the rig. The legth of the outer stubs is importat for the ceter frequecy. By itroducig these outer stubs, we are reducig the loop area. The ier stubs are importat for the lower resoace. These stubs are producig additioal path legth for the curret, ad the operatioal bad shifts toward the lower frequecies. 3. Parametric Aalyses [9] A parametric aalysis has bee carried out by evaluatig the effect of the variatio of geometrical parameters o the elemet performace. I this sectio, the impact of the key geometrical parameters of the atea is aalyzed ad discussed thoroughly. I doig so, oly oe parameter value has bee chaged at a time while keepig the others ualtered. [1] I Figure 2, the effect of the patch width (P4) o the impedace badwidth is illustrated. The patch width has a clear balacig effect betwee the lower ad higher frequecy bads. Whe P4 is reduced to less tha 6 mm, a strog resoace aroud 18 GHz is observed. O the other had, a patch width larger tha 6.6 mm results i a strog resoace aroud 11 GHz. This parametric aalysis shows prospective of the proposed structure as a frequecy-recofigurable atea elemet. For a wide operatioal bad, it is essetial to maitai balace betwee the resoaces, ad hece, P4 = 6.25 mm has bee chose. The patch legth (P3) has bee varied from 3 to 4 mm, ad the effect is show i Figure 3. Whe P3 is larger tha 4 mm, it has bee foud out that the retur loss level i the lower frequecy bad icreases. O the other had, whe the legth is decreased, the atea shows two clear separate resoaces aroud 1 GHz ad18ghz. [11] I Figure 4, the effect of the outer stub legth (P15) is illustrated. This study shows that P15 has a egligible impact o the total badwidth. O the other had, it plays a importat role for the atea matchig coditio i the ceter P3 = 3 mm P3 = 3.2 mm P3 = 3.5 mm P3 = 4 mm Figure 3. The effect of the patch legth (P3) o the iput reflectio coefficiet of the atea. 1 2 P15 =.3 mm P15 =.6 mm P15 = 1.2 mm P15 = 1.5 mm Figure 4. The effect of the outer stub legth (P15) o the iput reflectio coefficiet of the atea. 14

3 1 P13 =.2 mm P13 =.4 mm P13 =.6 mm P13 =.8 mm Figure 5. The effect of the trasitio curve radius (P13) o the iput reflectio coefficiet of the atea. 1 2 P9 = 1.94 mm P9 = 1.7 mm 25 P9 = 1.6 mm P9 = 1.4 mm Figure 6. The effect of the trasformer width (P9) o the iput reflectio coefficiet of the atea. Aalyze the ifluece of each parameter Determie for which frequecy rage the selected parameter has the foremost ifluece Determie a suitable value for each parameter i order to meet the fial objective Fial desig Figure 7. Select aother parameter Parametric aalyses flowchart. frequecy bad. The impact of the curve radius P13 is aalyzed i Figure 5. The obtaied umerical results clearly show that a smooth trasitio from the iput CPWG to the radiatig patch, amely, a larger value of P13, results i a ehaced retur loss respose i the frequecy spectrum of iterest. [12] The purpose of the impedace trasformer is to provide a good matchig betwee the 5 Ω coax cable ad the atea iput impedace over a large frequecy bad. Figure 6 shows that the trasformer width (P9) has the most effect o the ceter frequecy. This study shows that maximizig the trasformer width will provide good balace i the retur loss. Table 1. Geometrical Dimesio of the X-Bad Atea Elemet Symbol Dimesio (mm) Descriptio P1 1 Atea legth P2 1 Atea width P3 3.5 Patch legth P Patch width P Sigal width of CPWG P6.12 Gap width of CPWG P7 N/A Impedace trasformer legth P8 3 Legth of the feedig sectio P Trasformer width P1.99 Notch legth P11.17 Notch width P Slot curve radius P13.8 CPWG curve radius P14.72 Patch curve radius P Outer stub legth P Ier stub legth P Ier stub separatio P Ier stub width P19 1 Rig width H 5.52 Height of the substrate Figure 8. The proposed Foster-like etwork topology for the atea equivalet circuit. [13] The ifluece of other parameters, e.g., patch ier stub legth ad otch legth, has bee studied ad fie tued to achieve a wide badwidth (VSWR lower tha 2 betwee 8 GHz ad 24 GHz) ad liear phase respose. I Figure 7, a flowchart of the parametric aalyses procedure has bee outlied, ad the selected values of differet geometrical parameters are listed i Table 1. The performace of this radiator is further discussed i sectio Atea Equivalet Circuit [14] Typically, electromagetic field solvers ad measuremet systems, such as etwork aalyzers, geerate scatterig parameter represetatios of microwave compoets ad ateas. However, electroic circuit simulators, such as SPICE [Nagel ad Pederso, 1973], ca atively hadle covetioal circuits cosistig of lumped frequecy-idepedet elemets, whose behavior ca be coveietly modeled by differetial algebraic equatios which are solved usig suitable implicit itegratio methods i combiatio with sparse matrix techiques. I this cotext, a geeral ad computatioally efficiet procedure for extractig a equivalet circuit from a give S-parameter represetatio is highly desirable [Timmis ad Wu, 2]. [15] The procedure used to extract the equivalet circuit is based o a heuristic modificatio of Foster s etwork sythesis techique [Guillemi, 1965], useful to accout for ohmic ad radiatio losses occurrig i the atea structure. To this ed, suitable resistive elemets are itroduced i the equivalet etwork (see Figure 8) used to model the iput 15

4 HAIDER ET AL.: CIRCUITAL CHARACTERISTICS OF AN UWB ANT impedace ZiFIT ðf Þ of the device as computed by the adopted FIT-based electromagetic field solver. As a cosequece, the atea frequecy behavior is described by the followig series expasio [Caratelli et al., 26]: Zi ¼ j 2pf L þ N X R R ; þ 1 þ j 2pf t ¼1 1 þ j Q f f (1) where t = R C, R ad C beig the quasi-static iput resistace ad capacitace, respectively. I (1), L is the iductace accoutig for the effect of the higher-order modes ad the feedig structure, whereas N deotes the umber of resoat modes eeded to properly sythesize the iput impedace of the atea. I particular, each mode is assumed to be characterized by atural frequecy, quality factor Q, ad dampig resistace R. [16] A simple aalysis of the equivalet etwork topology show i Figure 8 readily allows evaluatio of the quasi-static resistace R ad capacitace C as follows: R ¼ limþ Re ZiFIT ðf Þ ; (2) f! Im YiFIT ðf YiFIT ðf Þ 1 lim ¼ C ¼ limþ 2p f!þ f! (3) Im YiFIT ðδf Þ ; 2pΔf where YiFIT ðf Þ ¼ 1=ZiFIT ðf Þ deotes the iput admittace, ad Δf is the frequecy step adopted to perform the discrete Fourier s trasform of the computed time domai atea respose. Furthermore, the resoat frequecies of the RLC subetworks ca be calculated, at a first approximatio, by determiig the values ðþ for which the real part of ZiFIT ðf Þ exhibits local maxima. Thereby, the iitial estimates of R ad Q are foud to be as follows: o RðÞ ¼ Re ZiFIT ðþ ; QðÞ ¼ ZiFIT ðþ 2R ðþ (4) Figure 9. Frequecy domai behavior of the iput reflectio coefficiet relevat to the cosidered ultrawidebad radiator as a fuctio of the width P4 of the metal patch: atea respose computed by the fiite itegratio techique ad sythesized by a Foster-like equivalet etwork of order N = 9. (5) Im ZiFIT ðþ Δf Im ZiFIT ðþ þ Δf ðþ 4R Δf ; Figure 1. Quasi-static resistace, iductace, ad capacitace relevat to the Foster-like equivalet circuit of order N = 9 used to sythesize the computed iput impedace of the atea as a fuctio of the patch width P4. 16

5 Figure 11. Natural frequecies of the RLC bipoles relevat to the Foster-like equivalet circuit of order N = 9 used to sythesize the computed iput impedace of the atea as a fuctio of the patch width P4. Figure 12. Quality factors of the RLC bipoles relevat to the Foster-like equivalet circuit of order N =9 used to sythesize the computed iput impedace of the atea as a fuctio of the patch width P4. 17

6 Figure 13. Dampig resistaces of the RLC bipoles relevat to the Foster-like equivalet circuit of order N = 9 used to sythesize the computed iput impedace of the atea as a fuctio of the patch width P4. respectively, with the values of L ðþ ad C their mutual relatioships, that is, L ðþ ðþ ¼ R Q ðþ! 2 C ðþ ¼ ðþ R ðþ ðþ Q ðþ 2p followig from : (6) [17] Upo doig so, it is straightforward to show that the quasi-static iductace ca be estimated as follows: L ðþ Im Zi FIT ðþ f ¼ lim XN L ðþ f! þ 2pf ¼1 Im ZFIT i ðδf Þ XN L ðþ 2pΔf : (7) [18] The parameter values so derived ca be used as iitial guess withi a iterative oliear fittig procedure, based o the gradiet method [Fletcher, 198], ad aimed to miimize, i the frequecy bad B of iterest, the relative mea square error: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e ðþ i R ðþ i ; L ðþ i ; C ðþ i B Γ FIT i ðþ Γ f i f ; R ðþ i ; L ðþ i ; C ðþ i u 2 df ¼ t B Γ FIT i ðþ f 2 ; df (8) with Γ i =(Z i Z )/(Z i + Z ) deotig the iput reflectio coefficiet, with respect to the referece impedace Z =5 Ω, relevat to the equivalet etwork show i Figure 8, expressed as a fuctio of the circuit parameters R R ¼1 R ðþ i, LðÞ i, C ðþ i ( =,1,..., N) attheith iteratio. I this way, the sythesis of the Foster-like circuit model that mimics the computed structure respose ca be umerically accomplished i a simple ad straightforward maer, thus providig a useful tool for the desig ad optimizatio of the atea frot-ed. [19] As it ca be oticed i Figure 9, oly a few resoat modes (N = 9) are eeded to accurately model the characteristics of the proposed atea elemet over a very wide bad. I particular, the depedece of the equivalet etwork parameters o the width P4 of the radiatig patch (see Figure 1) is show i Figures I this way, oe ca easily gai a meaigful circuit theory-based isight ito the properties of the atural resoat modes which Figure 14. Experimetal prototype of the Ku-bad elemet with the SMA coector. 18

7 occur i the device resultig i a ultrawidebad ( ) or rather multi-bad (P4 > 6.5 mm) behavior of the atea withi the cosidered frequecy rage up to f max = 3 GHz. 5. Performace Aalysis ad Experimetal Verificatio [2] I order to verify the theoretical results preseted i the previous sectios, a experimetal prototype has bee desiged ad fabricated (see Figure 14). The atea is prited simulatio measuremet Figure 15. Simulated ad measured iput reflectio coefficiet of the atea elemet show i Figure 14. o a Tacoic (TLY-5) substrate with relative permittivity e r =2.2ad17mm thick copper claddig. The thickess of the substrate has bee set to 5.52 mm, by bodig two 1.58 mm thick layers o both sides of a 2.36 mm thick substrate Impedace Badwidth [21] The impedace badwidth of the proposed atea structures has bee experimetally aalyzed. The Agilet E8364B etwork aalyzer has bee used for measuremets. The frequecy domai behavior of the iput reflectio coefficiet i X/Ku bad is show i Figure 15, ad a good agreemet betwee the experimetal ad theoretical results ca be oticed. I both cases, a good impedace matchig (with respect to 1 db retur loss level) is predicted i the frequecy rage from 8 to 24 GHz (Figure 15), Radiatio patter [db] simulated co pol simulated cross pol measured cross pol Radatio patter [db] simulated co pol simulated cross pol measured cross pol Radiatio patter [db] simulated co pol simulated cross pol measured cross pol (c) Figure 16. Realized gai of the atea at 15 GHz: copolarized ad cross-polarized compoet. Figure 17. Normalized copolarized ad cross-polarized patters for the H plae (XOZ plae) at 1 GHz, 15 GHz, ad (c) 25 GHz. The SMA coector has bee icluded i the umerical model. 19

8 correspodig to a fractioal badwidth of 1%. The slight differeces i the results are possibly caused by the additioal parasitic elemet of the SMA (SubMiiature versio A) coector, which is ot explicitly icluded i the umerical model of the radiatig structure Radiatio Patter [22] A thorough ivestigatio of the radiatio properties of the atea has bee, also, carried out. I Figure 16, the three-dimesioal view of the realized gai patter at the ceter frequecy f = 15 GHz is show. The atea elemet possesses a uidirectioal radiatio patter with about 1 db frot-to-back ratio (FBR). The FBR ca be further improved by extedig the groud plae size. The half power beam width at 15 GHz is about 65 i the E plae ad about 9 i the H plae. Furthermore, as expected from theory, Figure 16 reveals that cross-polarizatio level is miimum i the E plae ( =9 ) ad maximum i the H plae ( = ). Radiatio patter [db] 1 simulated co pol without SMA coector simulated co pol with SMA coector Radiatio patter [db] 1 simulated co pol without SMA coector simulated co pol with SMA coector Radiatio patter [db] 1 simulated co pol without SMA coector simulated co pol with SMA coector Figure 18. Normalized copolarized patters for the E plae (YOZ plae) at 1 GHz, 15 GHz, ad (c) 25 GHz. (c) (c) Figure 19. Simulated z compoet of Poytig s vector flow at 8 GHz, 16 GHz, ad (c) 25 GHz. 2

9 [23] The ormalized radiatio patters alog the H plae (xz plae) ad E plae (yz plae) of the atea at three differet frequecies are show i Figures 17 ad 18, respectively. A excellet agreemet betwee the experimetal ad umerical results ca be oticed. I particular, the measuremets have bee take i DUCAT (Delft Uiversity Chamber for Atea Test) by usig a referece TEM hor (GZ126ATP) as the trasmit atea. The radiatio patter of the atea is moderately stable over the frequecy rage of iterest with 2 6 dbi maximum realized gai level. At lower frequecies, the radiatio patter is slightly tilted i the E plae due to the presece of the SMA coector as predicted by the umerical aalysis (see Figure 18). Alog the E plae, the cross-polarizatio level is very small over the etire bad (i practice, values aroud the umerical errors of simulatios are observed) due to the atea symmetry ad therefore has ot bee plotted i Figure Poytig s Vector Flow [24] I order to ivestigate the ear-field behavior of a atea, usually surface curret distributio, electromagetic field stregth, or Poytig s vector flow is aalyzed. Poytig s vector idicates how the eergy of the radiated wave propagates aroud the atea. I Figure 19, the distributio of the z compoet of Poytig s vector is depicted. It is clear from this figure that Poytig s vectorflow is domiated by the loop-like radiatio cotributio at the lower frequecies while the ier patch cotributes more i the upper part of the operatioal bad of the atea. Norm. iput voltage [V] Time [s] Figure 2. Normalized PSD [db] Time domai behavior of the geerated pulse Figure 21. The power spectrum desity (PSD) of the geerated pulse Time Domai Behavior [25] The performace of a UWB system is heavily depedet o the time domai behavior of the radiated ad received pulse [Motoya ad Smith, 1996; Caratelli ad Yarovoy, 21]. I this sectio, the time domai characteristics of the elemet are ivestigated. To this ed, the moo-pulse fired by the pulse geerator (GZ1117DN-25), show i Figure 2, has bee used i all the measuremets. For umerical simulatios, the same trasmit pulse has bee used as excitatio sigal. The duratio of the pulse is.1 s for a level of 1% of the peak amplitude. The power spectrum desity (PSD) of the pulse is show i Figure 21. At 25 GHz, the PSD is about 3 db with respect to the maximum. [26] I order to estimate the radiated electric field distributio, two idetical elemets have bee used i the measuremet setup. I this way, the receivig trasfer fuctio of the idividual atea, h R (jo), for a fixed positio ca be extracted from the measured couplig coefficiet S 21 (jo) Norm. e field [V/m] Norm. e field [V/m] Norm. e field [V/m] Measured Simulated Time[s] Measured Simulated Time[s] Measured Simulated Time[s] Figure 22. Time domai behavior of the radiated electric field alog the H plae for R = 1 m ad # =, # =45, ad (c) # =9. (c) 21

10 betwee the radiatig elemets by applyig the followig relatio [McLea et al., 27; Licul ad Davis, 25; Farr ad Baum, 1992]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h R ðjoþ ¼ 2pc RS 21 ðjoþ jo e jbr ; (9) where R is the distace betwee the ateas, b is the propagatio costat, ad c deotes, as usual, the speed of light i free space. Afterwards, the ormalized icidet electric field stregth, e ic (jo), ca be expressed i terms of the ormalized received voltage, V r (jo), as follows: e ic ðjoþ ¼ V pffiffiffiffi rðjoþ ; (1) h R ðjoþ beig the wave impedace of the medium. By doig so, the magitude of the copolarized compoet of the electric field has bee evaluated for differet sca agles. As it ca be oticed i Figure 22, a good agreemet betwee the experimetal measuremets ad the umerical results has bee achieved. A margial disagreemet i the amplitudes of the peaks has bee oticed due to toleraces i the atea maufacturig ad oidealities of the measuremet setup. [27] It is worth otig that the proposed atea features a reasoably good fidelity factor [Lamesdorf ad Susma, 1994] varyig betwee.6 ad.8 for differet sca agles. Such performace is particularly importat i UWB imagig applicatios where a reduced sigal distortio i the scaig field of view is eeded i order to icrease the radar detectability of the target. 6. Coclusio [28] A ovel UWB atea topology has bee proposed ad utilized i the developmet of a atea elemet with 3:1 impedace badwidth. This ivestigatio cofirms that proper combiatio of electric ad magetic topologies ca icrease the impedace badwidth of a plaar radiator to 1% which is a substatial improvemet compared to 1 to 2% fractioal badwidth of a microstrip atea. Besides the eormous operatioal bad, this elemet ca provide uidirectioal patter with stable radiatio properties i time ad frequecy domais. I additio, the proposed atea is plaar ad compact i size (half of the free-space wavelegth at the ceter frequecy). Therefore, the proposed radiator is a attractive cadidate for radar-based imagig sesors. I this cotext, i order to ease the codesig of the atea with the relevat RF frot-ed i a SPICE-like simulator, a suitable frequecy-idepedet equivalet circuit has bee derived. This circuit model provides a isight ito the atural resoat processes which occur i the device ad evetually affect the frequecy respose of the atea. [29] Ackowledgmets. This research is coducted as part of the Sesor Techology Applied i Recofigurable systems for sustaiable Security (STARS) project. For further iformatio, please see the web site The authors gratefully ackowledge this support. The authors also wish to thak D.P. Tra, J.H. Zijderveld, ad P. 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