Reduced rcs uhf rfid gosper and hilbert tag antennas
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Reduced rcs uhf rfid gosper and hilbert tag antennas Reduced rcs uhf rfid gosper and hilbert tag antennas Document Transcript

  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME ENGINEERING AND TECHNOLOGY (IJARET)ISSN 0976 - 6480 (Print)ISSN 0976 - 6499 (Online) IJARETVolume 3, Issue 1, January- June (2012), pp. 35-47© IAEME: www.iaeme.com/ijaret.html ©IAEMEJournal Impact Factor (2011): 0.7315 (Calculated by GISI)www.jifactor.com REDUCED RCS UHF RFID GOSPER AND HILBERT TAG ANTENNAS T. G. Abo-Elnaga 1, *, E. A. F. Abdallah 1, and H. El-Hennawy2 1 Microstrip Dept., Electronics Research Institute El-Tahrir Street, Dokki 12622 Giza, Egypt, +21006751840, tgaber010@yahoo.com 2 Faculty of Engineering, Ain Shams University, Cairo, EgyptABSTRACTIn this paper printed flexible conventional, Gosper and Hilbert loop shape antennaswith reduced structure mode radar cross section RCS are proposed for small objectidentification. Conventional wire loop antenna input admittance using Fourier seriesanalysis for the equivalent half-loop antenna excited with a transverse electromagnetic(TEM) mode is rearranged to obtain the wire loop input impedance versus loop radiusat 900 MHz. T-matched charts as a method of matching the antenna input impedancewith the chip input impedance is also introduced. The proposed Gosper and Hilbertshapes have size reduction of 76.26% and 83.75 % compared to conventionalstructure. RCS reduction of 99.67 % and 99.12 % are obtained for Gosper and Hilbertloop antennas respectively, compared to conventional one at 900 MHz. Both Gosperand Hilbert loop antennas are fabricated, measured and the results are discussed.1. INTRODUCTIONRadio-frequency identification (RFID) is one of the fastest growing wirelesstechnologies in recent decades. Recent interest for RFID technologies increasesstudies and applications of these devices. Many different purposes of RFID are foundsuch as warehouse management, access control system, electronic toll collection, etc.UHF RFID requires three components, a transponder, an antenna and a transceiver.The transponder, or tag, contains data and is attached to the item. The antennatransmits the UHF radio signal to the transponder, powering and activating it. Theactivated transponder then transmits the data stored on the tag back to the transceiver.There are many standards for UHF RFID systems and they differ according to thecountry [1]. The paper idea is to introduce a flexible RFID tag antennas with reducedradar cross section to identify object location precisely such as weapons, bullets andall military stuff. Also, it can be used commercially to identify object location in huge 35
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEMEwarehouses. Methods aiming to decrease object RCS is of great practical interest andmany solutions have been proposed. Some approaches modify the target shape ororientation to deflect the scattered energy away from the detecting radar while otherconverts the radio frequency energy into heat [2]. Passive and active cancellationtechnology could be also used [3]. The radar cross section RCS of an antenna isdetermined by an antenna component and by a structural term [3-4]. Our investigationwill focus on the reduction of structural scattering of an antenna. Liquid crystalpolymer LCP substrate with dielectric constant , thickness of 0.05 mm andloss tangent is used as antenna substrate where flexible, reliable andlow cost features are provided, so the proposed structure gains these features. In thispaper conventional, Gosper and Hilbert loop shape antennas are proposed. Gosperand Hilbert shapes have size reduction of 76.26% and 83.75 % compared toconventional structure. RCS reduction of 99.67 % and 99.12 % are also obtained forGosper and Hilbert shapes respectively, compared to conventional one at 900 MHz.The paper is organized as; section 2 introduces conventional loop analyses usingFourier series analysis, T-matched chart and conventional loop with T-matchedsection design. Sections 3 and 4 introduce the design of Gosper and Hilbert loopantenna. Comparison among the aforementioned proposed antennas is introduced insection 5. Experimental results are introduced and discussed in section 6. Conclusionsare given in section 7.2. CONVENTIONAL LOOP ANTENNAIn this section Fourier series analysis is used and rearranged to obtain the wire loopinput impedance versus loop radius at 900 MHz and a suitable radius is chosen. T-matched chart as a method of matching the antenna input impedance with the chipinput impedance is also introduced. Conventional printed T-matched loop is designed.2.1 Conventional loop antenna analysesFourier series analysis for the equivalent half-loop antenna excited with a transverseelectromagnetic (TEM) mode assumed in the aperture of the coaxial line was used toobtain the input admittance of the wire loop antenna [5]. The antenna has radius R,resonant wavelength λo , constructed from a perfectly conducting wire of radius ai , and β o = 2π λo . The wire circular loop input admittance Yin isfound as:Yin = G + jB = I (0) Vo ) =  I o + 2∑ I n  Vo ∞   (1)  n =1  − jVo bnIn = n = 0,1,2,... (2) ξ oπ a n βoR n2 (3)an = (K n +1 + K n −1 ) − Kn 2 βo R 1 a 2 a 2 1  2( 2 2 ) 0.5 Kn = B0  i n 2 − (βo R )  H 0  i n 2 − (β o R )  + γ + ln 4 n − β o R  π R  R  π   2β R 2 n −1 1 1 o (4) − ∑ − ∫ [Ω2 n ( x) + jJ 2 n ( x)]dx π m = 0 2m + 1 2 0 36
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME abn = 1 ( B0 i (n + 1)2 − (βo R )2  ⋅ {H 0  ai (n + 1)2 − (βo R )2  ln(ao ai )  R    R   a − H0  o (n + 1)2 − (βo R )2 } + B0  ai (n − 1)2 − (β o R )2     (5) R  R  a ⋅ {H 0  i (n − 1)2 − (βo R )2  − H 0  ao (n − 1)2 − (βo R )2 })    R  R In Eqs. (1) to (5), G and B are the input conductance and susceptancerespectively, B0 and H 0 are the modified Bessel functions of the first and secondkinds and order zero, Ω 2 n is the Lommel-Weber function of order 2n, J 2 n is theBessel function of the first kind and order 2n, Eulers constant γ = 0.57722 andξ o = µo ε o with µ o and ε o are free space permeability and permittivity,respectively. This method is rearranged and programmed for the wire circular loopantenna radii prediction in free space at the 900 MHz resonant frequency, Fig.1.2.2 T-matched chartThe T-matched chart is a method to match the chip input impedance with dipole inputimpedance . Referring to Fig. 2, a dipole of length is connected to a second dipoleof length , placed at a close distance b from the first and larger one. It can beproved, that the impedance at the source point is given by [6]: (10)Where b 3500 Real Imag 3000 2500 2000 ad (1+α) :1 1500 Impedance (Ω) 2 l Za 2Z 1000 t 500 0 2w -500 -1000 -1500 10 20 30 40 50 60 70 80 90 2w R (mm)Fig. 1 Circular loop antenna input impedance Fig. 2 T-matched configuration forversus different radii with = 0.5 mm planar dipoles and equivalent circuit.(fabrication purpose), coaxial outer raduis =1.15 mm at 900 MHz. 37
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME2.3 Conventional T-matched loop antenna designAs a prototype design, wire circular loop antenna with external radius of 57 mmwhich has an input impedance of (63.16 + j8.14) would be suitable for conjugatematching with chip input impedance of 13.9 - j143.6 at 900 MHz. This is mainlyreferred to the fact that the loop antenna input impedance does not change very muchwhen R is within the range from 50 mm to 64 mm, Fig. 1. It should be mentioned thatthe operating frequency for the chip will cover the band from 860MHz to 960 MHz,and its input impedance varies from 15.69 - j152.6 Ohm at 860 MHz to 12.61 - j137 at960 MHz [7]. Chip input impedance of 13.9 - j143.6 at 900 MHz is chosen as thevalue to be matched with the designed antenna. By choosing this value the designedantenna input impedance will be remain in an acceptable level of variation relative tothe variance of the chip input impedance with frequency. Transform the structure toplanar one [8] and using the IE3D simulator, the input impedance of the loop antennais calculated using an LCP substrate with 50 substrate thickness and of 2.9. It isfound to be (130.5 - j44.3) at 900 MHz (difference between input impedancepredicted by IE3D and that obtained from Fig. 1 may be attributed to the approximatewire to planar transformation formulae and the presence of LCP material). This valueis used as input impedance for the T-matched circuit. The T-matched chart is shownin Fig. 3 which indicates that the matching condition with the chip could be met with and ranges from 0.11 to 0.18. IE3D simulator was used and finaloptimized dimensions are shown in Fig. 4 which indicates that on averageand . The power reflection coefficient, shown in Fig. 5, indicates that afrequency band from 780 MHz to 1122.2 MHz is covered which is suitable for UHFuniversal tag application. As shown in Fig. 6, RCS of 0.182 at 900 MHz isobtained indicating that the tag antenna is detectable. CMF of 0.837 is obtained at 900MHz, as shown in Fig. 7, indicating that conjugate matching is at a good level. Fig. 8shows the radiation pattern which is almost figure of 8 at the E-plane and H-plane.Other antenna parameters such as conjugate match gain and radiation efficiency aregiven in table 1. 5 Imag Real 41.29 143.2 182 1.922 24.73597 44.49266 4.5 6 .789 1 56 761 30.9 64.24935 5 202 123.5 82.5 823 10.3558 .54 4 84.00 51 .6.03 16 3 486 194 62 088 8 103.7 604 20.6 627 72 2 .23 691 3.5 53 b/2w 18 61 41 14 3 2.7 .92 .29 1 24.73597 3.2 44.4926 89 21 56 76 5 30 64.2 .98 12 3.5 51 3 16 23 2.5 6 493 10. 84 .6.03 19 0 82 .00 355 4 5 88 10 20 .76 604 8 3 .66 27 2 91 30 1.5 12 .98 3.5 23 44 19 .4 64 4 92 .24 10 84 .0 2 10 3 0 .6 .35 66 93 5 58 0 604 .7 6 6 91 27 1 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 ad / l Fig. 3 Conventional printed circular loop antenna T-matched chart ( ) 38
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME m 55 m m m 57 R= = R us dius di ra r ra t er u O Inne Fig. 4 Conventional printed circular loop antenna T-matched circuit section. 3 0 -3 -6 PRC (dB) -9 -12 -15 -18 -21 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Frequency (GHz)Fig. 5 PRC versus frequency for Fig. 6 RCS versus frequency forconventional printed loop antenna with T- conventional printed loop antenna withmatched circuit (R=55mm). T-matched circuit (R=55mm).Fig. 7 CMF versus frequency for Fig. 8 Conventional printed loopconventional printed loop antenna with T- antenna with T-matched circuitmatched circuit (R=55mm). radiation pattern at 900 MHz (R=55mm). 39
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME 2. GOSPER LOOP ANTENNAThe Gosper curve is a space filling curve discovered by William Gosper, an Americancomputer scientist, in 1973, and was introduced by Martin Gardner in 1976. TheGosper curve is a recursive curve constructed by recursively replacing a dotted arrow,called the initiator, by seven arrows, called generator, Fig. 9 [9].Fig. 9(a) Gosper curve Fig. 9(b) Gosper curve Fig. 9 Gosper curveinitiator, generator initiator, generator initiator, generatorreplacement for n=1. replacement for n=2. replacement for n=3. Matlab code for Gosper curve generation of any order is built and Gosper curve oforder 2 is shown in Fig. 10. The resonance frequency of the aforementionedconventional circular loop was found to be 1.25 GHz. Gosper loop antenna wasdesigned at the same resonance frequency using IE3D simulator. Its radius was foundto be 26.8 mm. Gosper loop antenna achieves size reduction of 76.26% compared toconventional loop antenna. It was chosen as a prototype to complete the T-matchedcircuit design at 900 MHz. At 900 MHz, the input impedance is (8.15 + j103.95) .We considered the structure as asymmetric dipole loaded by Gosper loop antenna. 50 45 40 35 Gosper width (mm) 30 25 20 15 10 5 0 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 Gosper length (mm) Fig. 10 Gosper loop antenna (n = 2)The T-matched diagram shown in Fig. 11 was used as an indicator for the total inputimpedance performance. It should be noted that conjugate matching condition withthe chip input impedance is difficult to obtain. As a starting point waschosen and varying through changing the length till matching condition wasreached. IE3D simulator was used to get the optimum design dimensions, Fig. 12. Thepower reflection coefficient is shown in Fig. 13 and clearly covers the frequency bandfrom 884 MHz to 936 MHz which is suitable for the bands of 920.5 - 924.5 MHz inChina, 920 - 925MHz in Singapore and 902 - 928 MHz in USA, Canada, Mexico, 40
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEMEPuerto Rico, Costa Rica, Latin America. As shown in Fig. 14, RCS of 0.0006 at900 MHz is obtained indicating that the tag antenna is detectable. We should mentionthat this small RCS is useful in small targets in package identification. As shown inFig. 15, CMF is 0.62 at 900 MHz, indicating that conjugate matching is at acceptablelevel. Fig. 16 shows the radiation pattern which is almost omnidirectional at the H-plane and figure of 8 at the E-plane. Other antenna parameters such as conjugatematch gain and radiation efficiency are given in table 1. Fig. 11 Gosper loop antenna T-matched chart ( 8.15 + j103.95 ) Fig. 12 Optimum dimensions of Gosper loop antenna with T-matched circuit. 41
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME 3 0 PRC (dB) -3 -6 -9 -12 -15 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Frequency (GHz)Fig. 13 PRC versus frequency for Gosper Fig. 14 RCS versus frequency for Gosper looploop antenna. antenna.Fig. 15 CMF versus frequency for Gosper Fig. 16 Radiation pattern at 900 MHz forloop antenna. Gosper loop.4. HILBERT LOOP ANTENNAIn 1891 Hilbert defined a space filling curve [10]. The general idea is to divide, at stepn, the unit square in 4n equal subsquares each of them containing an equal length partof the curve (except the first and the last ones which contain a part of length 1/2). AMatlab program is built to draw Hilbert curve of any order n. Hilbert curve of order 4,Fig. 17 is simulated using IE3D and input impedance of (10.78 + j53.17) isobtained at 900 MHz. T-matched chart for that input impedance is shown in Fig. 18.Choosing and varying from 0.35 to 0.55 till matched conditionwas obtained. The optimum structure is shown in Fig. 19. The PRC is shown in Fig.20 which covers the frequency band from 901 MHz to 928 MHz which is suitable forthe UHF RFID application at China (920.5 - 924.5 MHz), Singapore (920 - 925MHz),USA, Canada, Mexico, Puerto Rica, Costa Rica and Latin America (902 - 928 MHz).RCS, Fig. 21 of 0.0016 at 900 MHz is obtained indicating that the tag antenna isdetectable and is useful at small target identification. As shown in Fig. 22, CMF of0.49 is obtained at 900 MHz. Fig. 23 shows the radiation pattern which is almost 42
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEMEomnidirectional at the H plane and figure of 8 at the E plane. Other antennaparameters such as conjugate match gain and radiation efficiency are given in table 1. Fig. 17 Hilbert mean curve (n = 4). 5 Imag Real 2.671 21 26 .51 7 67.11865 20.42183 35.98744 51.55 305 82 .68 426 5.320 82 4.5 21 .21 8 98 .24987 7. 97043 11 3.8 155 7 14 4.9 12 9.3 8 13 .26 97 10 .62 15 .9111 18 .56 5 4 467 16 0.5.86 8 93 89 23 123 1 3.5 b/2w 2.671 21 5 3 35.98744 67 .11 865 20.42183 51 .55 30 82 .68 4 5.320 82 21 . 98 .24 7.970 21 8 11 3 14 4 12 9 13 .2 26 10 .6 5 15..3 81 18 . 987 .8 15 43 2.5 .9 4 91 91 6 97 56 8 2 16 23 67 5 3 9 0.5.8 16 81 23 2 21 1.5 .21 7. 98 . 14 85 2.6 11 82 0 82 12 1 18 4.9 5. 97 24 10 3. 13 9.5 .9 .6 .56 46 32 .62 8 15 .26 9 71 0 4 98 38 1 84 3 7 11 3 9 89 7 21 5 7 26 1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ad / l Fig. 18 Hilbert loop antenna T-matched chart ( 10.78 + j53.17 ). 43
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME Fig. 19 Optimum structure of Hilbert loop antenna with T-matched circuit structure. 1 0 -1 -2 -3 PRC (dB) -4 -5 -6 -7 -8 -9 0.80 0.85 0.90 0.95 1.00 Frequency (GHz)Fig. 20 PRC of Hilbert loop antenna versus Fig. 21 RCS of Hilbert loop antenna versusfrequency. frequency.Fig. 22 CMF versus frequency for Hilbert loop Fig. 23 Hilbert loop antenna radiationantenna. pattern at 900 MHz. 44
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME5. COMPARISON AMONG CONVENTIONAL, GOSPER AND HILBERTLOOP TAG ANTENNASThis section introduces a comparison among various proposed loop antenna structuresnamely Conventional, Gosper and Hilbert tag antennas. The comparison includesradiator and T-matched section areas, conjugate match gain, radiation efficiency,bandwidth, minimum values of PRC, structure RCS and conjugate match factor CMF,table 1. As indicated by table 1, Gosper antenna introduces the most reduced RCScompared to the other two antennas’ RCS and area. Also Gosper antenna radiationefficiency is 99.8 % which is better than the conventional and Hilbert antennas.Table 1 Comparison among performance of Conventional, Gosper and Hilbert loopantennas. Loop Shape Conventional Gosper HilbertParameterRadiator area ( ) 9503.33 2256.4 1600T-matched section area ( ) 48 709.8 243.375Conjugate match gain (dB) -0.29 -1.2 -2.1Radiation efficiency (%) 80.28 99.8 58Bandwidth (MHz) 780-1122.2 884-936 901-928Minimum value of PRC (dB) -20.5 -13.5 -8.1RCS ( ) at 900 MHz 0.182 0.0006 0.0016CMF at 900 MHz 0.837 0.62 0.496. GOSPER AND HILBERT LOOP ANTENNA EXPERIMENTAL RESULTGosper printed loop antenna was fabricated using LCP substrate as shown in Fig.24(a). The input impedance was measured by measuring half of the structure overground plane and multiply the resultant input impedance by two then, powerreflection coefficients are calculated. Since Gosper antenna is asymmetrical at theexcitation, so both halves are considered and the average is used in power reflectioncoefficient calculation and denoted as PRCM. As shown in Fig. 24(b), there is adifference between computed and simulated PRC which may be attributed mainly tothe presence of the air gap between the half Gosper structure and the ground planewhich was difficult to be eliminated due to the flexible nature of the LCP substrate.So, computed PRC was considered twice once with an air gap with 1 mm inserted atthe excitation symmetrical plane through all the structure, (0.5 mm between halfstructure and the ground plane), and the resultant power reflection coefficient isdenoted as PRCs1 and PRCs is the resultant power reflection coefficient in theabsence of that air gap. The obtained PRCs1 agree with the measured PRCM. Wemay also refer the difference between PRCM and PRCS1 to the average process in themeasured results. Hilbert loop antenna was also fabricated using LCP substrate, Fig.24(c) and the input impedance was measured as aforementioned method used inmeasuring Gosper antenna input impedance. Also, the difference between simulatedpower reflection coefficient denoted by PRCs and the measured power reflectioncoefficient denoted by PRCm may be attributed to the presence of the air gap betweenthe half Hilbert structure and the ground. So, an air gap of 1 mm was inserted at thesymmetrical plane of the proposed structure (0.5 mm between half structure and the 45
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEMEground plane), simulated PRCs1 was obtained which agree very well with themeasured one, Fig. 24(d). PRCM PRCs 3 PRCSs1 0 -3 -6 PRC (dB) -9 -12 -15 -18 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Frequency (GHz)Fig. 24(a) Fabricated Gosper Fig. 24(b) Computed and measured PRC ofloop antenna. Gosper loop antenna. PRCs 3 PRCs1 PRCm 0 -3 -6 -9 PRC (dB) -12 -15 -18 -21 -24 -27 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Frequency (GHz)Fig. 24(c) Fabricated Hilbert Fig. 24(d) Computed and measured Hilbert looploop Antenna. Antenna.7. CONCLUSIONSIn this paper a loop type tag antenna, Conventional, Gosper and Hilbert loop tagantennas were presented. Both Gosper and Hilbert loop tag antennas were fabricatedusing LCP substrate and the measured results agreed with computed ones.Comparison among Gosper, Hilbert and Conventional loop tag antenna was done andsize reduction relative to conventional one was obtained. Both Gosper and Hilbertloop antennas had a reduced RCS compared to their physical areas and conventionalloop one. The proposed antennas may be used in tagging a small object whereidentifying its location is a must. 46
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEMEREFERENCES[1] Barthel H., “Regulatory status for RFID in the UHF spectrum,” EPC Global, Brussels, Belgium, March 2009.[2] Zhang H., Fu Y., and Yuan N., “RCS Reduction of ridged waveguide slot antenna array using EBG radar absorbing material,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp.473-476, 2008.[3] Knott E. F., Shaeffer J. F., and Tuley M. T., Radar cross section, 2nd ed. Raleigh, NC: SciTech Pub., 2004.[4] Hansen R. C., “Relationship between antennas as scatterers and as radiators”, Proc. of the IEEE, vol. 77, no. 5, pp. 659-662, May 1989.[5] Guangping Z., Glenn S. S., “An accurate theoretical model for the thin-wire circular half-loop antenna,” Antenna and Propagation Symp. (APS), vol. 39, no. 8, pp. 1167-1177, 1991.[6] Chu Q. X., Wang L., Zhou J. K., "A novel folded T-matched dipole in base station,” Int. Conf. Microwave and Millimeter Wave Technology ICMMT, pp. 1–3, 2007.[7] Higgs-2 integrated single chip UHF RFID tag IC data sheet, EPC global Class 1 Gen 2, Alien Technology Corporation, July 2008.[8] Butler C. H., " The equivalent radius of a narrow conducting strip" IEEE Trans. Antennas and Propagation, vol. AP-30, no. 4, pp. 755 - 758, July 1982.[9] Fukuda H., Shimizu M. and Nakamura G., "New Gosper space filling curves," in Proc. Int. Conf. on Computer Graphics and Imaging, pp. 34–38, 2001.[10] Azad M., Ali M., "A compact Hilbert planar inverted-F antenna (PIFA) for dual-band mobile phone applications", IEEE Antennas and Propagation Society International Symposium, vol. 3, pp. 3127 - 3130, 2004. 47