Analysis and Synthesis of UHF RFID Antennas using the Embedded T-match

Transcription

1 Analysis an Synthesis of UHF RFID Antennas using the Ebee Tatch Naaser A. Mohae, Kenneth R. Dearest, an Daniel D. Deavours The Departent of EECS University of Kansas Lawrence, Kansas Abstract The Tatch structure is coonly use to atch an RFID chip s reactive ipeance to a ipole. Moels that escribe Tatch are known, but they are neither sufficiently accurate to oel antennas nor to synthesize the antenna geoetry. Here, we present the ebee Tatch circuit oel, which is aenable to accurate analysis an synthesis. Keywors UHF RFID antennas; Dipole antennas; Ua analysis; Ebee Tatch antenna; synthesis. I. INTRODUCTION UHF RFID antennas have extensively been researche, an a brief suary of the relate work can be foun in [1]. In orer to achieve axiu power transfer between the antenna an the attache chip, an ipeance atching technique nees to be eploye. Generally, the attache chip ipeance is capacitive, thereby requiring the antenna ipeance to be inuctive to obtain a proper ipeance atch. Several ipeance atching ethos can be eploye in orer to achieve the atch. A coonly use atching technique is the Tatch structure. Tatch antennas have been analyze an verifie at length using the Ua oel [1 7]. Thiele et al. [4] showe that the transission line oe in the Ua analysis accurately preicts the input ipeance of the fole wire ipole when the two ars of the ipole are electrically close together. In [5], isser applie the Ua analysis to a strip fole ipole but neee to a correcting factors to achieve goo agreeent between the analysis an fullwave siulation results. The Ua analysis for the Tatch, though rigorous, is foun to lack analytical expressions for the various paraeters that escribe the circuit with sufficient accuracy. Although the Ua analysis provies excellent unerstaning of the Tatch antenna, we are not aware of any work which tests the accuracy of the Ua analysis on the Tatch antenna. In this paper we propose an augente Ua oel that will ai in better unerstaning the working of the Tatch antennas an help in synthesizing practical RFID antenna geoetries. In aition, we ientify the socalle Ebee Tatch antenna as particularly well suite to this augente Ua oel. A brief suary of rest of the paper is as follows: Section II of the paper iscusses the Ua oel an soe backgroun work. The avantages of the Ebee Tatch antenna structure, the accuracy of the Ua oel an troubleshooting of the oel constitute Section III. Section I introuces iproveent to the Ua oel an Section valiates the new oel. In Section I we evelop ethos to accurately synthesize the RFID antenna geoetry in orer to atch the antenna to specifie input ipeance. II. CLASSIC UDA MODEL A Tatch antenna is a cobination of two ipoles connecte together as shown in Fig. 1. Ua S. [3], analyze a Tatch antenna by consiering the raiating an non raiating coponents of the antenna. Figure 1. Wire Tatch antenna. In the Ua analysis, a faux voltage source is place in the a ar of the antenna. This allows the ecoposition of the antenna response into the su of coon an the ifferential oes as shown in Fig. an Fig. 3, respectively. The figures are agnifie to inicate the ivie voltage sources. In the coon oe, the voltage sources in the ars of the antenna have equal aplitue an are in phase. The currents in the two ars are relate to each other as I C = α I C1, where α is the splitting factor []. The coon oe ipeance is given by Z C = in I in L 1 L C I C 1 I C. a

2 In the ifferential oe, the port voltages are split such that the current in the ars have equal aplitue but are 180 out of phase. This is achieve by setting the voltages in ratio of the splitting factor α [], that is D1 = α D. The ifferential oe ipeance is given by Z D = D 1 D. α = cosh 1 v u 1 v cosh 1 v u 1 u v ln v ln v ln u, () u = a, an v =, where an a are the raii of the first an secon conuctors an is the spacing between the conuctors. a I C I C C/ C/ a The input ipeance of the antenna can be foun by realizing that in = C D1 an I in = I C, an by setting C = D ; then the expression for Z in is given by [] Z in = 1α Z C Z D 1α Z C Z D. (3) C/ C/ I C1 I C1 The equivalent circuit oel representing the Tatch antenna is shown in Fig. 5. The coputation of Z in using (1), (), an (3) constitutes the wire Ua oel. Figure. Coon oe. Z in (1α) : 1 D/ D / a Z D Z C D1/ D1/ Figure 5. Equivalent circuit oel Figure 3. Differential oe. Z D, the transission line oe ipeance, is oele analytically by assuing that the parallel ipoles constitute a shorte transission line with length L 1 /. The circuit epicting the oe is shown in Fig. 4. The expression for Z D is given by [3] Z D = j Z O tan k L 1, (1) where k is the free space wave nuber an Z O is the characteristic ipeance of the transission line. D1 D Z D / L 1 / Z O Figure 4. Transission line oe. The splitting factor for Fig. 1 is given by [] By applying the two port analysis to Fig. an 3 we can fin the expressions for the oel paraeters, in ters of the Z atrix paraeters as [6] Z c = Z 11 Z Z 1 Z 11 Z Z 1, (4) Z D = Z 11 Z Z 1, (5) α = Z 11 Z 1 Z Z 1. (6) The wire Ua oel provies insight to the working of the Tatch antenna but oes not provie analytical expressions to copute the necessary oel paraeters Z C, Z D an α. Due to these shortcoings, various evolutions of the oel have been propose [5, 79]. Marrocco [1] an Choo et al. [7], apply the Ua oel to a strip Tatch structure. The approxiation for conversion of rectangular slab to an electrical equivalent raius (W 1 = 4 ) [3] is use to apply (1) an () on a strip Tatch structure. However, the authors o not valiate the accuracy of the wire Ua oel on the strip Tatch antenna. Lape [8], erives the oel paraeters of the wire Ua oel for a coplanar strip fole ipole as shown in Fig. 6. Z C

3 was copute by fining the ipeance of an equivalent circular ipole with an effective raius. Z D was copute by using (1). The splitting factor, α was copute by realizing that the slot present in the antenna is an asyetric coplanar strip an that the charge istributions along the ars can be approxiate to have the sae for as a single strip charge istribution [89]. This results in expression of α to be t n = eλ n 1 e λ n 1, λ 1 = π W 1 h λ = π h,, α = I C I C 1 = Q = ln (4c c W 1 1 ) ln(w 1 ) Q 1 ln (4c c W 1 ) ln(w ), (7) λ 3 = π W h, where c = W 1 W 4. S Figure 6. Strip fole ipole W isser [5], as epirical correcting factors to copute the effective raius an the effective length in coputing Z C of a strip ipole. The equation for Z D (1) is also upate to take into account the effective ielectric constant of the ielectric slab. The correcting factors copute in [5] an [8] yiel accurate results when applie fole ipoles an but have not been shown to be applicable to a Tatch antenna. The effective ielectric constant ε eff can be copute an can be incorporate in calculation of Z O, the characteristic ipeance of a parallel strip transission line. The expression for Z O is [11] W 1 Z o = 60 π ε eff K(k 1 ) K(k 1 ), (8) where h is the height of the substrate. Nuerous approxiations have been perfore to copute Z C for a wire fole ipole an have been suarize in [10]. These approxiations for Z C were evelope fro analytical forulas for constant raius cylinrical ipoles using an equivalent raius. The RFID antennas are generally esigne as strip antennas an for strip Tatch structures approxiations for Z C are har to fin. Therefore, to copute Z C for the Tatch antenna we rely on nuerical ethos such as Metho of Moents (MoM) or Finite Eleent (FEM) solutions. III. EMBEDDED TMATCH ANTENNA In this section we propose to test the accuracy of the Ua analysis on Tatch structures using the strip ipole Ua oel. The strip ipole Ua oel coputes Z in using (1), (7), an (8). Furtherore, we also propose to a necessary enhanceent to iprove the accuracy of the strip ipole Ua oel. Fig. 7 shows soe coercially available Tatch RFID antennas. Many of these antennas have coplex geoetries, large nuber of antenna paraeters an are constructe with eaners. These coplexities ake it practically ipossible to fin close for expressions for the Ua circuit oel paraeters. For both unerstaning an synthesizing the antenna, the structure shoul to be siple an have relatively few antenna paraeters. where ε eff = 1 ε r 1 K(k 1 ) K(k 1 ) K(k ) K(k ). K(k) is the coplete elliptical integral of the first kin, where k = 1 k, k 1 = b 1 b, b = W, = W 1, Figure 7. Coercial RFID Antennas. where is the slot with. k = t 1 t (t 3 t ) t 1 t (t 3 t ), An Ebee Tatch antenna, which is a special case of the Tatch antenna, is coparatively a siple structure with a nuber of avantages. A siple Ebee Tatch antenna is shown in Fig. 8 an is constructe by ebeing the T

4 atch structure into the antenna itself. The avantages of this structure are: W it has only four inepenent antenna paraeters (L, W, W 1, S), the structure is siple, the Ua antenna oel can be applie to the structure, an the close for solutions foun in (1), (7) an (8) can potentially be applie to the structure. Figure 8. Ebee Tatch Antenna. The antenna paraeters for Ebee Tatch antenna are: the length of the antenna L, the with W, slot length S an withs W 1 an W. Fro Fig. 8, we observe that W = W 1 W. In this paper we will assue to be 1. To a first orer approxiation we foun that, the slot has negligible effect on Z C. That is, Z C epens ostly on L an W; this will be further verifie in the following sections. Observing (7) we can conclue that α epens only on W 1 an W. Z O also epens only on W 1 an W, fro (8). Therefore, Z D epens on the W 1, W an S, fro (1). A. Accuracy of the strip ipole Ua oel The accuracy of the strip ipole Ua oel when applie to an ebee Tatch antenna can be teste using (1), (7), (8), an coparing the resulting input ipeance with that obtaine fro a MoM solver. The antenna is place on 76 µ PET substrate (ε r = 3.), with 18 µ copper use for the antenna an operate at 915 MHz. The antenna paraeters are: L = 100, W = 10, W 1 = 3, W = 6 an S = 0. The analytic results obtaine for the oel paraeters are: Z C = j 15.5 Ohs, α =1.6, Z O = an Z D = j 101. Ohs. Using (3), we can now copute the analytic input ipeance as Z in = 1.85 j Ohs. To verify this result, the antenna was siulate using a MoM solver an the input ipeance is copute. Using a elta gap source, we foun siulate Z in = 1.4 j 83.1 Ohs. This results in an error of % between the analytic an siulate input ipeance. The oel was applie to siilar antennas an the error was foun to be consistently larger than 5%. B. Troubleshooting Using (3), the error in Z in can be accounte to errors in coputing the values of Z C, Z D, Z O, an α, or the expression (3) itself. To fin the error, we will next copare the calculate oel paraeter values to the values copute fro two port analysis. By placing a secon elta gap source on W ar in Fig. 8, we can apply the two port analyses for an ebee Tatch L S W W 1 Delta Gap Source antenna an obtain the Z atrix paraeters. We can then use (4), (5), an (6) to generate the siulate oel paraeters. The characteristic ipeance of the transission line can be obtaine by applying a HFSS (FEM solution) wave port solver to the transission line with withs W 1 an W. Fro the two port analysis using (4), Z C is copute as 15.5 j 15.9 Ohs. This is coparable to the siulate Z C, which proves the inepenence of S an W 1 on Z C. The coparisons of the results are tabulate in Table I. Moel Paraeters TABLE I. Coparison of analytic vs siulate oel paraeters Analytic Siulate % Error Z C j 15.5 α Z D j 101. j Z O Fro Table I, we realize that the error is foun in the coputation of α an Z D. In the following sections of the paper, we fin that the relatively sall error in α has negligible effect on Z in calculations. Therefore, the large error in Z in can be attribute ainly to the error in the transission line oe of the Ua analysis. To fin the source of the error, we will look into the assuptions that are use while analyzing of the antenna: the first assuption is that the ifferential oe solely rives a TEM wave, an the secon assuption is that the transission line is terinate with a short circuit. The etaile analysis of these assuptions is perfore in the following section. I. AUGMENTED UDA MODEL In the transission line oe, recall fro Fig. 3, that there are elta gap sources present in both ars of the antenna. These gaps cause fringing fiels to occur, thereby giving rise to higher orer oes. The effect of the fringing fiels can be oele by the presence of capacitance in the gap as shown in Fig. 9. D / D / W W W 1 W 1 D1 / D1 / Figure 9. Gap capacitance in Transission line oe Due to leftright syetry of the geoetry, there is a zeropotential plane fore. The fringing capacitance foun in Fig.

5 9 can be split into two series capacitances an be place on either sie of the zeropotential line as shown in Fig. 10. Z D = Z P Z t Z P Z t, (9) Figure 10. Capacitive coupling in transission line. In aition to the capacitive coupling, the transission line is terinate by a conuctor of finite length rather than an infinite conuctor as assue in transission lines. Due to this iperfect terination we nee to account for the presence of the finite conuctor by representing the conuctor by a shunt inuctance. The capacitances foun in Fig. 10 can be further split into parallel cobination of capacitances: that fore within the elta source gap an that outsie the gap. Let the capacitance between the two ars be W k C i (k = 1, ); where W k is the with of the ars an C i is the capacitance per unit length, an the capacitance fore outsie the ars C O. Also let the shunt inuctance be enote by X S. Figure 11 shows the transission line circuit for the augente Ua oel. D1 D Z D / C o C o D/ D/ W W W 1 W 1 D1/ D1/ W 1 C i W C i Z t zeropotential line S/ Z o jx s Coputing Z in using (9), (7), an (8) constitutes the augente Ua oel. Using the augente Ua oel, Z in is recalculate for the antenna exaple given previously. Equation (9) yiels the new analytic Z D as j74.86 Ohs with Z P = j 453. Ohs. The new analytic Z D yiels an error of only 1. % between the calculate an siulate Z D (Table I). Using (3) we can then recopute Z in (3) as 1.95 j Ohs. This results in error of.8 % between the siulate (Z in = 1.4 j 83.1 Ohs) an the calculate input ipeance as copare to an error of % for the strip ipole Ua oel. Therefore with the use of the augente Ua oel, the error is reuce consierably, which is a substantial iproveent over the previous oel. This proves that the augente Ua oel works well with the exaple, but to test the robustness of the oel we nee to valiate the oel.. ALIDATION An effective way to valiate the augente Ua oel is by coparing the calculate Z in (3) with values copute using nuerical solutions fro MoM an FEM coes. For a fixe L an W of antenna, we vary W 1 an S over a wie range an plot the corresponing input ipeance for the three ifferent ethos. The frequency for which Z in is copute is 915 MHz an the antenna is place on 76 µ PET substrate (E r = 3.) with 18 µ copper use for the antenna. In the nuerical tools, the antenna is siulate with the elta gap source with of 0.. For L = 100 an W = 15, using MoM solver we foun siulate Z C value to be 14.5 j Ohs. As S is varie fro 6 to 30, an W 1 fro 3 to 13 the coparison for the resistive an reactive coponent of the input ipeance is shown in Fig. 1 an Fig. 13 respectively. Here, the graphs are croppe to restrict the upper liit on the ipeance an results for only certain W 1 s are plotte. This is one to increase the clarity of the graph an to ake the curves istinguishable fro each other. Figure 11. Augente Ua Transission line oel. After conucting extensive experients we foun that X s, W k C i an C o epen on W 1 an W of the antenna an are relatively inepenent of W an L. For 76 µ PET substrate (E r = 3.), 18 µ copper at 915 MHz an W of 15, 0 an 5, using curve fitting technique we were able to estiate the values of variables as X s = j4 Ohs, C i = pf/ an C o = pf. Let C p1 = C i W 1 C o an C p = C i W C o. Then the total shunt ipeance is Z P = Z P1 Z P, where Z P1 = (jωc p1 ) 1 an Z P = (jωc p ) 1. For X s << Z o an S << λ/4, we can approxiate Z t, the input ipeance to the transission line as Z t = jz o tan(k S ) jx s. We can then fin the expression for the transission oe ipeance as the parallel cobination of Z P an Z t, Figure 1. Coparison of analytic vs siulate input resistance.

6 Equating the real an iaginary parts an solving for α an X D, we get α = R C ( R IC XIC ) R IC ( R C XC ) 1, (11) Z D = j X D = j R C R IC XIC R C X IC R IC X C. (1) Recall that fro (6) that α epens only on W 1, W an W; hence using (6) an the fact that α is onotonic, we can use bisection etho to copute the values of W 1 an W. Once we have these paraeters we can copute Z O using (7). Now using Z O (7), the require Z D (11) an augente Ua oel expression of Z D (8) we can solve for S. The expression for S is given by Figure 13. Coparison of analytic vs siulate input reactance. Fro the results shown in Fig. 11 an 1, we can conclue that the augente Ua oel is fairly robust an can be use to accurately analyze the Ebee Tatch antenna. Though the oel works effectively for wie range of W 1 an S, we foun that for extree cases the oel loses accuracy. For values of S < 5, we foun that the relative error increases. That is likely ue to the presence of higher orer oes that propagate at short istances. We also foun that for values of S > 30, the transission line acts as a short slot antenna. That introuces a sall resistive coponent in Z D. The error in that case can be reuce by consiering the resistive coponent of Z D in calculation of Z in. The last known source of error is in the expression of α (7). The expression was to becoe a significant source of error for α>4. I. SYNTHESIS RFID antennas are typically esigne to operate with a specific chip. Let the ipeance of this chip be Z IC. To synthesis the antenna geoetry, let L an W of the antenna an Z IC be known. The antenna paraeters S an W 1 nee to be copute to synthesis the antenna, such that the requireent Z in = Z IC is et. Few notations taken into account are as follows: Z IC = R IC j X IC, Z C = R C j X C, Z in = R in j X in, Z D = j X D. (10) Fro the given L an W, we can copute Z C using MoM solver. Using the given Z IC, copute Z C, (3), an the conjugate ipeance requireent, we can copute the values of require Z D an α by solving the following expression Z in = 1 α R C j X C jx D 1 α R C j X c jx D = R IC j X IC S = k tan 1 Z p Z D Z p Z D j X S 1 j Z o. (13) To test the synthesis process, let us esign an ebee T atch antenna. The given antenna paraeters are L = 100, W = 15, an Z IC = 11 j 133 Ohs. We are esigning the tag to be place on 76 µ PET substrate (ε r = 3.) with 18 µ copper use for the antenna an the frequency of operation is 915 MHz. For the given L an W, the siulate Z C is foun to be 14.5 j Ohs, using the MoM solver. Using (11) an (1) we foun the require α = an require Z D = j 84.9 Ohs. Using bisection etho an the require α value we get W 1 an W to be an 3.93 respectively, analytic Z O using (8) is foun to be Ohs, Z P for the antenna is foun to be j Ohs an X S = 4 Ohs. Fro (13) we copute S value to be 3.6. Using the antenna paraeter values obtaine above we can siulate the ebee Tatch antenna to copute Z in using MoM solver. The antenna paraeters use are L = 100, W = 15, W 1 = an S = 3.6, the antenna was siulate with elta gap source an we foun siulate Z in = 10.8 j 17.8 Ohs, which yiels an error of 3.9 % fro Z IC *. II. CONCLUSION The Ua oel when applie to the Ebee Tatch antenna results in large error. The sources of this error were the gap capacitance an the iperfect terination of the transission line. The oel was augente to inclue the ientifie errors an the new oel was calle the augente Ua oel. With this augente Ua oel, we were able to achieve excellent accuracy. The new oel was able to preict the input ipeance of the antenna over a wie range of antenna paraeter values with results coparable to those foun by nuerical ethos. The oel also helps in forulating a siple straightforwar etho to synthesis the antenna geoetry to present the require input ipeance. The oel also helps in better unerstaning the working of the Ebee Tatch antenna.

7 REFERENCES [1] G. Marrocco, The art of UHF RFID antenna esign: ipeanceatching an sizereuction techniques, IEEE Antennas an Propagation Magazine, 008, ol.50, No. 1, pp [] S. Ua an Y. Mushaike, YagiUa Antenna, Tokyo, Sasaki Printing an Publishing Co., 1954, pp [3] C. A. Balanis, Antenna Theory, Analysis an Design, 3r e., New York, John Wiley & Sons Inc., 005. [4] G. A. Thiele, E. P. Ekelan, an L. W. Henerson, On the accuracy of the transission line oel of the fole ipole, IEEE Trans. Antennas Propagation, 1980, ol. AP8, pp [5] H. J. isser, Iprove esign equation for asyetric coplanar strip fole ipoles on a ielectric slab, Antennas an Propagation International Syposiu, City, ST/Country, 007. [6] C. T. Tai, Theory of terinate onopole, IEEE Trans. Antennas Propagation, 1984, ol. 3, pp [7] J. Choo, J. Ryoo, J. Hong, H. Jeon, C. Choi an M. M. Tentzeris, Tatching networks for the efficient atching of practical RFID tags, European Microwave Conference, City, ST/Country 009, pp. 58. [8] R. W. Lape, Design forulas for an asyetric coplanar strip fole ipole, IEEE Trans. Antennas Propagation, 1985, ol. AP33, No. 9, pp [9] R. W. Lape, corrections to [7], IEEE Trans. Antennas Propagation, 1986, ol. AP34, No. 4, pp [10] R. S. Elliot, Antenna Theory an Design, Revise Eition, John Wiley & Sons, New York, 003. [11] R. Hoffan, Hanbook of Microwave Integrate Circuits, Artech House, Norwoo, MA, 1987.