Upper Bounds on the Bandwidth of Electrically Small Single Resonant UHF-RFID Tags

Transcription

1 Upper Bounds on the Bandwidth of Eletrially Small Single Resonant UHF-RFID Tags Gerard Zamora, Member, IEEE, Simone Zuffanelli, Member, IEEE, Pau Aguilà, Student Member, IEEE, Ferran Paredes, Member, IEEE, Ferran Martín, Fellow, IEEE, and Jordi Bonahe, Member, IEEE Abstrat In this per, the upper limits on the bandwidth of single resonant UHF-RFID tags as a funtion of the tag size are investigated, with and without foring perfet mathing between the antenna and the pliation speifi integrated iruit (ASIC). By means of a iruit network analysis, it is found that bandwidth upper bounds of small tags are signifiantly higher in omparison with onsidering onjugate mathing. Partiularly, it is shown that the half-power bandwidth is times (proximately 4%) higher, requiring a proper relaxation of the mathing level at resonane. It is also shown that bandwidth of small real tags with perfet mathing, whih is typially far from its upper bound, an also be enhaned proximately the same fator at the expense of a small redution (.4%) in the peak read range. A pratial example is provided where two small SRR-based tags of same size (k a =.) are designed. It demonstrates that suh improvement on the tag bandwidth an be proximately obtained by simply hanging the hip position, without the need of an external mathing network. The improved tag was fabriated and measured, as a proof of onept. The results obtained from the proposed analysis allow RFID designers to determine how well a tag performs, ompared to theoretial bandwidth limits. Index Terms Antennas, bandwidth, quality fator, radio frequeny identifiation (RFID), RFID tags, split-ring resonator (SRR). I. INTRODUCTION Radio frequeny identifiation (RFID) is a ridly developing tehnology that provides objets tagging and traking ability by means of eletromagneti waves []. Typial pliations of this tehnology are asset identifiation, retail item management, aess ontrol, animal traking and vehile seurity, among others. Passive tags operating at the UHF-RFID frequeny band are espeially employed for this kind of pliations. A passive tag onsists of an antenna mathed to an pliation speifi integrated iruit (ASIC), whih ontains the information about the tagged item. Aording to the urrent regulations for passive UHF-RFID systems [], the frequeny range omprised between 864 MHz and 98 MHz is operated within all the ountries alloations authorized for RFID pliations. In the last years, the ost of tags has experiened a signifiant derease, mostly due to the development in semiondutor tehnology and mass prodution. This has involved an inrease of the number of pliations where RFID beomes a profitable solution. One of the most hallenging aspets regarding passive UHF-RFID tag design is size redution. Sine RFID hips are always muh smaller than tag antennas, tag dimensions are determined by the antenna size, or the antenna plus the mathing network when it is present. The most ommonly used tehnique for tag size redution onsists in antenna meandering [], [4]. However, as it is well known, size redution leads to a trade-off between effiieny and bandwidth, espeially when eletrially small antennas (ESAs) are This work was supported by MINECO-Spain (TEC-46-R, TEC R), Generalitat de Catalunya (4SGR-57), Instituió Catalana de Reera i Estudis Avançats (awarded F. Martín), and by ERDF. The authors are with GEMMA/CIMITEC (Departament d Enginyeria Eletrònia), Universitat Autònoma de Barelona. 89 BELLATERRA (Barelona). Spain. Gerard.Zamora@uab.at. treated [5], [6]. An antenna is onsidered to be small when k a <.5 aording to [5], [6], where k denotes the resonane wavenumber, and a is the radius of an imaginary sphere irumsribing the largest dimension of the antenna (heneforth alled antenna size for the sake of brevity). Bandwidth limitations of resonant antennas are losely related to the antenna quality fator (), whih is required to be minimized for bandwidth enhanement [6] [9]. The of a tuned (to have zero reatane at the resonane frequeny ω ) antenna is defined as the quotient between the power stored in the reated field and the aepted power (power loss within the antenna plus radiated power). This definition presumes that the antenna may be tuned by an external mathing iruit to provide a real input impedane at the operation frequeny [6], [8]. Yaghjian and Best [8] derived the relationship between bandwidth and of single resonant antennas under onjugate mathing ondition. However, unlike onventional antennas, RFID antennas must be mathed to an ASIC having a omplex input impedane, rather than a purely resistive port. This produes a diret effet upon tag bandwidth upper bounds. In [], the equivalent iruit network required to ahieve the upper limit of the area under the return loss urve (determined by the Bode riterion []) was obtained for single resonant tags with perfet mathing between the hip and the antenna. Meaning that maximum bandwidth at all mathing levels was obtained under onjugate mathing ondition. The present per shows, by means of a iruit network analysis, that suh bandwidth an only theoretially be ahieved by using antennas that are not eletrially small. Moreover, upper bounds on the bandwidth of single resonant UHF- RFID tags, with and without foring perfet mathing, are inferred as a funtion of the tag size. It is also shown that the bandwidth of small real tags with onjugate mathing an be onsiderably enhaned by means of a proper redution of the mathing level at resonane, without neessarily involving an inrease in the tag size. II. UPPER BOUNDS ON THE TAG BANDWIDTH The input impedane of an UHF-RFID ASIC an be modeled by a parallel ombination of a ondutane G and a aitane C []. Let us onsider an indutive antenna (or antenna plus mathing network) with an equivalent iruit model onsisting of a parallel ombination of a general antenna suseptane B a and a frequeny dependent ondutane G a, tuned at a frequeny ω by the hip aitane. The antenna ondutane G a = G r + G l is modeled as a parallel ombination of the radiation antenna ondutane G r and the loss ondutane G l (that aounts for the ondutive and dieletri losses of the antenna). To maintain generality, both G r and G l are assumed to be frequeny dependent. The effiieny of the antenna is related to the elements of the antenna equivalent iruit model by η = G r /G a []. The quality fator of a general one port lossy linear antenna tuned at ω (presenting a single suffiiently isolated resonane within its operating bandwidth) with >> ( greater than usually suffies) an be aurately proximated from the antenna input impedane by [8]

2 Z Z ( ), () R( ) where Z '(ω ) = R '(ω )+jx '(ω ) is the frequeny derivative of the input impedane of the tuned antenna (assuming C to be the tuning element) at ω, R '(ω ) and X '(ω ) being the frequeny derivative of the input resistane R and reatane X of the tuned antenna at ω, respetively. It is lear from () that minimum (required for bandwidth broadening) is obtained by reduing Z '(ω ), whih an be written in terms of the ondutane G and suseptane B of the tuned antenna using R '(ω ) = G '(ω )/G (ω ), X '(ω ) = B '(ω )/G (ω ). Beause the tuning aitor is onneted in parallel with the antenna, G = G a and B = B a +B (B = ω C being the hip suseptane at ω ). Thus, assuming a frequeny independent antenna ondutane makes R '(ω ) =. Whereas, X '(ω ) is minimized making B a '(ω ) as small as possible. As it was pointed out in [], the Foster s reatane theorem [4] holds for the antenna equivalent iruit network required to obtain a single tag resonane with proper impedane mathing between the hip and the antenna, i.e., B a '(ω ) >. The Foster network that provides a ertain negative suseptane (indutane behavior) at a given frequeny with the lowest frequeny derivative of suh suseptane is simply an indutor (L a ) [5]. This leads to B '(ω ) = C and Z = ω C /G a. There is a well-known lower bound on the for a general singlemode (fundamental TE or TM mode) tuned antenna, the Chu limit, whih is related to the value of k a, namely Chu = η[(k a) +(k a)] [6]. Chu onsidered eletrially small antennas, but later Sievenpiper et al. [7] showed that it serves as a good design guideline even for non-esas. To ahieve a lose to that limit, the antenna must fully oupy the spherial volume defined by k a [8]. However, most UHF-RFID antennas must fit in a planar she and, therefore, the antenna annot proah to the Chu bound as losely as in the ase of onsidering antennas with a spherial she. Reently, Gustafsson et al. [9], [] derived a new limit for antennas of arbitrary she using a sum rule. In [], Yaghjian and Stuart used a quasi-stati analysis to obtain a bound on in terms of antenna volume and stati polarizability. Lately, Mohammandpour Aghdam et al. [] plied the result given in [] to planar strutures (i.e., the volume tends to zero) with retangular she. From [], the theoretial lower bound on that an be ahieved by a linearly polarized planar tuned antenna an be written as, () ka where ζ, an be onsidered a strutural penalty whih depends on the antenna geometry. Gustafsson et al. found in [] that the minimum value for ζ (9π/8) an only be obtained by means of planar antennas presenting a irular disk she with radius a. However, in real life, most UHF-RFID tag antennas are enlosed by a retangular she and provide a single pure linear polarization (typially a single TM mode) in the diretion along the length. The minimum strutural penalty for this kind of antennas is around ζ = 5. (onsidering diretivity.5, aording to Gustafsson onditions []), whih ours for an optimum aspet ratio (i.e., length to width ratio) of.84 []. Notie that for a fixed effiieny, inrease ridly as k a dereases. In order to satisfy, B '(ω ) must be inreased (with respet to C ) for very low k a, by adding an additional shunt element in the tag iruit model. The simplest network able to raise B '(ω ) maintaining the tag resonane at ω is a single aitor, named here C a. Thus, an RLC parallel-iruit antenna model, asaded to the ASIC, is to be onsidered to obtain the upper bounds on the bandwidth of RFID tags (see Fig. ). Fig.. Equivalent iruit model of single resonant UHF-RFID tags based on an RLC parallel-iruit antenna model. A. Upper Bounds under Conjugate Mathing Condition By isolating B from the power refletion oeffiient s between the hip and the antenna in Fig. [] s G Ga B G Ga B it is found that there are two solutions for a ertain value of the power refletion oeffiient s = α: B G G G G a a,. Foring the left hand side of (4) to be the suseptane of a parallel ombination of a aitane C p = C a +C (i.e., parallel onnetion of C and C a, aording to Fig. ) and an indutane L a = /(ω C p ) (to ahieve tag resonane at f ), the resulting frational bandwidth evaluated at α an be written as G G FBW, Ga Ga where = ω C p /G a, see for example [4]. By foring G a = G in (5), it is lear that upper bounds under perfet mathing ondition are ahieved if =. Suh a ondition requires the antenna aitane to be C a = (G /ω ) C. Thus, upper bound on bandwidth inreases with the antenna size (as expeted from the literature) while C a dereases. However, it ahieves its maximum value when reahes (the hip quality fator evaluated at ω given by = ω C /G [4]) and onsequently C a vanishes. The resulting iruit model orresponds to the ideal iruit for bandwidth broadening obtained in []. This leads to FBW onj,ub, () (4) (5) (6a) (6b) It is worth mentioning that (6a) perfetly agrees with the relationship between bandwidth and derived in [8], and (6b) is in agreement with the db maximum bandwidth inferred in []. Notie that (k a) onj = (ηζ/ ) / (inferred by foring = ) orresponds to the minimum antenna size required to ahieve maximum bandwidth under perfet mathing ondition, given by (6b). Suh bandwidth an only be reahed by non-esas, sine (k a) onj >.5 for typial tags (ζ = 5., ~ ) with η >.. For lower sizes, bandwidth upper bounds are determined by the antenna, whereas for higher sizes by the ASIC. B. Upper Bounds Compared to the Conjugate Mathing Case Maximization of tag bandwidth an be thought as a onstrained optimization problem in whih the frational bandwidth (5) beomes a funtion of two variables (G a and C a ), subjet to the following three onstraints:, G a > and C a. Suh inequalities are referred to as the Karush-Kuhn-Tuker (KKT) onditions for the stated

3 HP-BW (MHz) HP-BW (MHz) TABLE I ELEMENTS OF THE IDEAL RLC PARALLEL-CIRCUIT ANTENNA MODEL Region G a C a L a I (ESA) II III G C G C C Ca C G C generalization of the method of the Lagrange multipliers), three different set of solutions for the variables G a and C a were found, as a funtion of or, equally, k a (see Appendix). The upper bounds for the tag frational bandwidth were found to be (7a) FBW ub (7b) (7) The onstituent elements of the RLC parallel-iruit antenna model, as well as the of the tuned antenna, required to ahieve the upper bounds on the tag bandwidth are summarized in Table I. It an be demonstrated that the three different regions in (7), as well as the orresponding boundaries, ollse to (6) when γ tends to (or, equivalently, α tends to ). For γ > (i.e., bandwidth upper bounds are onsidered at α > ), (k a) onj splits into (k a) = (ηζ/γ ) / and (k a) = (ηζγ/ ) /, and onsequently an intermediate region (alled here region II) pears. As γ inreases, this region beomes wider, and bandwidth upper bounds separates more and more towards higher values with respet to the onjugate mathing ase, exept at (k a) onj. A plot representation of (6) and (7) for α = / (half-power bandwidth) and ζ = 5., using the Alien Higgs (SOT- pakaging) ommerial hip, is showed in Fig. (a) for further omprehension. It was onsidered η =. in order to show the three different regions in a < k a < plot. It an be seen that both bandwidths are equal at (k a) onj, as dedued by omparing (6) and (7). Thus, it orresponds to the unique antenna size that requires perfet mathing at resonane to ahieve bandwidth upper bounds at all mathing levels. Within region I, = is ahieved by gradually reduing the antenna aitane C a as k a inreases, until it is aneled at (k a). Whereas, in region II the same ondition for is obtained by inreasing the antenna ondutane with k a from G /γ to γg, going through G at (k a) onj. Therefore, besides (k a) onj, bandwidth upper bounds at a ertain mathing level requires sarifiing perfet mathing at resonane. Lowering the effiieny of the antenna involves a displaement of the boundaries (k a), (k a), and (k a) onj towards lower values of k a, as well as an inrease of (6a), (7a) and (7b), while the maximum upper bounds (6b) and (7) remain onstant. Thus, bandwidth upper bounds of small tags (i.e., tags based on ESAs) inrease by dereasing η, as expeted from the well-known trade-off between effiieny and bandwidth [7]. However, small tags with relatively high values of the antenna effiieny are of speial interest in RFID, sine they provide higher read ranges and size redution. Assuming small tags based on effiient antennas and typial RFID hips ( ~ ), we find that bandwidth upper bounds evaluated at α / It is worth mentioning that the antenna ondutane in the ESA region agrees with equation (6) in [7], where the iruit of Fig. was onsidered for bandwidth maximization of single-tuned T-math-dipole tags. a) 4 a (m) 4 5 Upper bound Conj. math. I II k a (radians) k a (radians) Fig.. Upper bounds on the tag half-power bandwidth against antenna size with (blue) and without (blak) foring onjugate mathing, onsidering the Alien Higgs and ζ = 5. in the (a) three regions (light gray, gray and dark gray, respetively) with η =., and (b) ESA region for η =.6,.8 and. are given by (6a) and (7a). This result omes from the fat that region I extends beyond the limit for ESAs, i.e., (k a) >.5. Thus, it seems reasonable to identify (7a) as the ESA region. A omparison between (6) and (7) within the ESA region FBWub, (8) FBW onj,ub reveals that bandwidth upper bounds of small tags are signifiantly higher (for a relatively large value of γ) with respet to the ase of onsidering onjugate mathing. However, as mentioned previously, it requires a redution of the mathing level at resonane, namely s (ω ) = α (inferred by evaluating () at f where B = ). Speifially, the half-power bandwidth results in a fator of (proximately 4%) higher, at the expense of reduing the mathing level at resonane to /4. Fig. (b) shows a plot representation of the upper bounds on the half-power bandwidth of small tags based on effiient ESAs and the Alien Higgs hip. Notie that bandwidth upper bounds are governed by (6a) and (7a), when high effiienies are onsidered, and inrease by lowering η. From the previous analysis, we onlude that the antenna determines bandwidth upper bounds of small tags, whereas both the ASIC and the antenna determine bandwidth upper bounds for non- ESAs. Conversely, the maximum ahievable tag bandwidth is determined by the ASIC, and an only be reahed by using antennas that are not eletrially small. III. READ RANGE ANALYSIS AND DISCUSSION The read range is defined as the maximum distane at whih the RFID reader an detet the baksattered signal from the tag. It an be alulated as [4] EIRP G RR, (9) P 4 where λ is the wavelength and EIRP is the equivalent isotropially radiated power, determined by loal ountry regulations (e.g.,. W in Europe and 4 W in USA). P is the minimum threshold power neessary to ativate the RFID hip, G is the gain of the tag antenna, and τ is the power transmission oeffiient, whih is related to the power refletion oeffiient by = ( s ). It an be observed in (9) that the read range is proportional to the square root of. This indiates that a signifiant redution (to some extent) of the onjugate mathing level at the tag resonane might not involve an important degradation of the read range. The ratio between the peak read ranges (ahieved at the tag resonane [4]) inferred using = α (halfpower bandwidth upper bound) and = (onjugate mathing ase) in (9), namely RR, () RR peak ub peak onj III b) a (m) Upper bound, Conj. math., Upper bound, Conj. math., Upper bound, Conj. math.,

4 Read Range (m) Frequeny (GHz) Fig.. Simulated read range of small tags exhibiting upper bounds on the half-power bandwidth with (blak) and without (blue) onjugate mathing for k a =.,.,.5. The dashed line indiates the half-power read range level peak / ). The UHF-RFID band is highlighted in gray. (RR onj Upper bound Conj. math.. reveals that the aforementioned 4% inrease of the upper bounds on the half-power bandwidth of a small tag ompared to the onjugate mathing ase (see Setion II) involves a redution of.4% in the peak read range. Expression () was obtained assuming EIRP, P, and G to be equal in both ases. This an be preiated in Fig., where a read range plot of square-shed (i.e., assuming ζ = 5.) small UHF-RFID tags, onsidering both upper bounds on the halfpower bandwidth with and without onjugate mathing, is shown for different antenna sizes (k a =.,. and.5). It was obtained with the help of (9) onsidering EIRP = 4 W, G = ηd (assuming η = and D =.5, i.e., diretivity of an elementary eletri or magneti dipole []). The power refletion oeffiient was obtained from simulation (Keysight ADS) of the iruit of Fig. using the Alien Higgs hip (G = /5 Ω, C =.9 pf, and P = 7 dbm, aording to the manufaturer). As expeted, proximately (notie that RR also depends on λ) a 4% higher bandwidth evaluated at the half-power read range level (see Fig. ) and a.4% redution on the peak read range is obtained, in agreement with the value predited by (8) and (), respetively. Notie also that the read range of the upper bound tag beomes flatter within the UHF-RFID frequeny band, ompared to the onjugate-mathed tag. For a real tag, deviations from the ideal quality fator ( ) towards higher values are expeted. Also, deviations from the ideal equivalent iruit model for the tag antenna (an RLC parallel-iruit) are ommon. Consequently, the resulting bandwidth is typially far from its upper bound. Bandwidth of a small real tag presenting onjugate mathing at resonane an be proximated by (7a) when is replaed by the quality fator of the tuned antenna [8]. In virtue of the suseptane slope onept [4], bandwidth of small real tags designed to exhibit proper antenna ondutane (G /γ) for bandwidth optimization an be proximated by (6a), replaing by of the tuned antenna. Therefore, (8) and () are proximately valid for real tags of same size, provided and G are equal in both tags under omparison. UHF-RFID hips exhibit strongly aitive input impedane and small resistane (the real part being about an order of magnitude smaller than the imaginary part) []. This fores the tag antenna to exhibit an indutive reatane muh higher than the resistane at ω, i.e., X a (ω ) >> R a (ω ), in order to ahieve proper impedane mathing. Thus, the equivalent antenna ondutane and suseptane of a general tag antenna evaluated at ω an be proximated by G a (ω ) R a (ω )/X a (ω ) and B a (ω ) /X a (ω ), respetively. Of ourse, the reatane of the tuned antenna is equal to zero at the tuned frequeny (ω = ω ), and R a (ω ) = R (R being the real part of the hip impedane) for onjugate mathing. Equivalently, the suseptane B of the tuned antenna is equal to zero at the tag resonane, and the ondutane of the tuned antenna satisfies G (ω ) = G a (ω ) = G for perfet mathing. It diretly follows that G R /X a (ω ). Therefore, by foring the antenna resistane to be R a (ω ) = R /γ, one obtains that G a (ω ) G /γ and, onsequently,..5 bandwidth enhanement with respet to the onjugate mathing ase, proximately given by (8), is expeted. The input resistane of symmetrially fed small wire antennas (ommonly used for tag design) is in general muh lower than the hip resistane R, giving rise to a signifiant impedane mismath. However, it is possible to inrease the input resistane to obtain good impedane mathing by hanging the hip position, without the need of an external mathing network [], [8]. This proedure avoids lowering η for bandwidth enhanement (a ommonly used tehnique in pratie), allowing the design of effiient small tags with high read range. IV. PRACTICAL EXAMPLE Two small RFID tags (same size) based on a split-ring resonator (SRR) antenna and a ommerial integrated ASIC (the Alien Higgs with SOT- pakaging) were designed (by means of the Keysight Momentum ommerial software) for bandwidth omparison purposes. The input impedane of this hip provided by the manufaturer is Z = 5 j9 Ω at f = 9 MHz. The following points were onsidered as design guidelines: () bandwidth broadening was fored at the half-power level (α = /), () the tag antenna was fored to be eletrially small; meaning that k a <.5, () the available ASIC with the lowest sensitivity was seleted, sine it provides higher read range without affeting the upper bounds on bandwidth within the ESA region, (4) the effiieny of the antenna was fored to be high enough to ensure operating within the ESA region (i.e., k a k a). The Arlon CuClad 5LX with thikness h s =.49 mm, relative permittivity ε r =.4, and loss tangent δ loss =.8, was seleted as a substrate. We first design a onjugate-mathed tag following the design proedure presented in [8]. The dimensions of the tag antenna (see Fig. 4a) are a = 6.5 mm (λ /, k a =.), =. mm, d =.5 mm, and the slit width. mm. The hip position was found to be φ p = º. A seond tag was designed for half-power bandwidth enhanement by foring the antenna resistane to be R a (ω ) = R /γ = 5/ Ω. To this end, the hip position was hanged to φ p = 76º, and the distane between rings was adjusted to d =.8 mm in order to maintain resonane at f. The simulated results for the onjugate-mathed tag and the tag with improved bandwidth are summarized in Table II. The effiieny is similar in both ases and muh higher than the minimum value (.9 in this ase) to ensure operation within the first region. It an be also seen that the quality fator of the improved antenna is slightly higher, due to small differenes in the geometry (i.e., distane between rings hanges). The simulated power refletion oeffiient s of the designed tags is depited in Fig. 4(b). The improved tag reahes.9 MHz half-power bandwidth, i.e., a 7% bandwidth inrease with respet to the onjugate-mathed ase (9.4 MHz), whih is very lose to the expeted value (4%), inferred using (8). Suh small differene is mainly attributed to the fat that the quality fator of the antenna with improved bandwidth is somewhat higher. The simulated frational bandwidth is very lose to the predited value for the perfet-mathed (.7%, 9.6 MHz) and the improved (.4%,.8 MHz) tag, inferred respetively from (6a) and (7a), replaing by Z. Aording to (6a) and (7a), the upper bounds on the tag half-power frational bandwidth are FBW ub =.4% (.6 MHz) and FBW onj,ub =.4% (.7 MHz). It was onsidered η =.7 and ζ = 9π/8 (orresponding to planar antennas with a irular disk she) whih leads to = 8, that is signifiantly smaller than Z for both tags. This suggests that further inrease of the tag bandwidth an theoretially be obtained maintaining the same maximum antenna dimension and she, by simply restruturing the tag antenna to redue its interior fields and therefore its (whih is out of the sope of this per) [8]. Of ourse, as Fano shows [9] and Sievenpiper illustrates [7], designing an antenna with multiple resonanes and avoiding a perfet math an exeed the upper bounds on bandwidth given in (7), within the Bode limit [].

5 Read Range (m) s (db) 5 Fig. 4. (a) Topology of the SRR. The ut at the bottom of the external ring indiates the hip position. (b) Simulated power refletion oeffiient of the designed tags. a) a) Conj. Math. s (db) TABLE II SIMULATED RESULTS OF THE DESIGNED TAGS k a η Z HP-FBW RR peak (m) % (9.4 MHz). Improved % (.9 MHz) 9.8 b) 9 6 b) Conj. Math. Optimized Fig. 5. (a) Photogrh of the fabriated tag and (b) simulated and measured read range. A simulation of the onjugate-mathed tag is also shown for omparison purposes. The gray region indiates the UHF-RFID band. The designed tags behave as small urrent loops providing a dipole-like radiation pattern within the entire UHF-RFID band [8]. The simulated read ranges (see Fig. 5b) were obtained from (9) assuming a onstant gain over frequeny with D =.6 and η =.7 (obtained from eletromagneti simulation at f ). It an be seen that the read range of the optimized tag was signifiantly improved in most of the band presenting a peak value of 9.8 m, i.e., a.5% redution with respet to the perfet-mathed tag, whih is very lose to the expeted.4%. The tag designed to enhane the half-power bandwidth was fabriated (see Fig. 5a) and the experimental read range was obtained in a TEM ell environment as reported in [8]. Simulated and measured results (Fig. 5b) are in good agreement, showing a small frequeny shift of MHz between them. The experimental read range reahes a peak value of proximately m, whih is very lose to the value obtained from eletromagneti simulation (9.8 m). Moreover, the experimental read range halfpower bandwidth ( MHz), is lose to the simulated value (.9 MHz). The differene is mainly attributed to variations on the tag antenna gain over frequeny (not onsidered in the simulated read range) and frequeny variations of the hip sensitivity []. V. CONCLUSION Frequeny (GHz) Frequeny (GHz) Sim. Conj. Math. Sim. Optimized Meas. Optimized Frequeny (GHz) In this per, the upper bounds on the bandwidth of single resonant UHF-RFID tags related to the maximum tag dimension, with and without onsidering onjugate mathing, have been explored. We have found that the antenna determines bandwidth - - upper bounds of small tags (k a <.5), see (7a), whereas both the ASIC and the antenna determine bandwidth upper bounds for non- ESAs. Conversely, the maximum ahievable tag bandwidth, given by (7), is determined by the ASIC, and an only be reahed by using antennas that are not eletrially small. It has been shown that the upper bounds on the bandwidth of small tags are substantially higher with respet to the ase of onsidering perfet mathing at resonane. Speifially, the tag half-power bandwidth is 4% higher, requiring a relaxation of the onjugate mathing ondition at the tag resonane in an propriate manner. Moreover, two SRR-based tags of same size (k a =.) has been designed to show that bandwidth of small real tags with onjugate mathing (typially muh smaller than its upper bound) an also be improved proximately the same fator by simply hanging the hip position, at the expense of a small redution (.4%) of the peak read range. The enhaned tag has also been fabriated and measured, as a proof of onept. The analysis presented in this work provide RFID designers with the ability of determining how well a tag performs in terms of bandwidth, ompared to theoretial upper bounds. APPENDIX THE KARUSH-KHUN-TUCKER METHOD Let us onsider the frational bandwidth funtion (5) to be maximized for a given RFID ASIC, subjet to the following onstraints:, G > and C. This problem an be simplified by onsidering a new funtion f, resulting from squaring the produt between the right hand side of (5) and ω, to be maximized, i.e., GG G G Max. f ( G, C ), C C (A.) subjet to the aforementioned neessary onditions or, equivalently, g C C G (A.) g G g C. To solve this problem by means of the Karush-Kuhn-Tuker (KKT) method [5], [6], we first define the Lagrangian funtion as L f ( G, C ) g, (A.) i i i where λ i are the KKT (or Lagrange) multipliers. We then define the KKT onditions as L = G igi. These onditions give rise to the following equations G G C C C C G L C G G G G = C G C C C G G C. (A.4) (A.5)

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