INTERNATIONAL JOURNAL OF ELECTRONICS AND     International Journal of Electronics and Communication Engineering & Technolo...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 097...
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Dominant mode resonant frequency of circular microstrip antennas with and without air gap

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Dominant mode resonant frequency of circular microstrip antennas with and without air gap

  1. 1. INTERNATIONAL JOURNAL OF ELECTRONICS AND International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), pp. 111-122 IJECET © IAEME: www.iaeme.com/ijecet.html Journal Impact Factor (2011): 0.8500 (Calculated by GISI) ©IAEME www.jifactor.com DOMINANT MODE RESONANT FREQUENCY OF CIRCULAR MICROSTRIP ANTENNAS WITH AND WITHOUT AIR GAP B.Ramarao1 M.Aswini2 D.Yugandhar1 Dr.P.V.Sridevi3 1. Associate professor Dept of E.C.E. Aditya Institute of Technology and Management, TEKKALI AP.-532201 2. M.Tech(student), Dept of E.C.E., Aditya Institute of Technology and Management, TEKKALI AP.-532201 e-mail: maswini407@gmail.com 3. Associate professor, Dept of E.C.E.,AU College off Engg. VISAKHAPATNAM-533001ABSTRACT Circular microstip antennas offer performance similar to that of rectangulargeometries. In some applications such as arrays, circular geometries offer certainadvantages over other configurations .Recent experimental results have shown that circulardisk microstrip elements may be easily modified to produce a range of impedance,radiation pattern and frequency of operation. In this paper an improved analytical model is presented for calculating the resonantfrequency of circular microstrip antennas with and without air gaps. Unlike the previousmodels, the present one is widely applicable to all patch diameters—from very large tovery small compared to the height of the dielectric medium below the patch and also to thesubstrates covering the entire range of dielectric constants. The computed results fordifferent antenna dimensions and modes of resonance are compared with the experimentalvaluesKey word: Microstrip antenna.I INTRODUCTION The concept of microstrip radiators was first proposed by Deschamps as early as1953. The first practical antennas were developed in the early 1970’s by Howell andMunson. Since then, extensive research and development of microstrip antennas andarrays, exploiting the numerous advantages such as light weight, low volume, low cost, 111
  2. 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEMEplanar configuration, compatibility with integrated circuits, etc., have led to diversifiedapplications and to the establishment of the topic as a separate entity within the broad fieldof microwave antennas. Various types of flat profile printed antennas have been developed-- the microstripantenna, the stripline slot antenna, the cavity backed printed antenna and the printed dipoleantenna.I.I Definition of a microstrip antenna As in figure, a Microstrip antenna in its simplest configuration consists of aradiating patch on one side of a dielectric substrate (εr≤ 10), which has a ground plane onthe other side. The patch conductors, normally of copper and gold, can assume virtuallyany shape, but conventional shapes are generally used to simplify analysis and performanceprediction. Ideally, the dielectric constant, εr of the substrate should be low (εr ~ 2.5), so asto enhance the fringe fields which account for the radiation. However, other performancerequirements may dictate the use of substrate materials whose dielectric constants may begreater than 5. Various types of substrates having a large range of dielectric constants andloss tangents have been developed. Flexible substrates are also available which make itpossible to fabricate simple conformal wraparound antennas. Figure 1.1 Microstrip Antenna configurationII. DESIGN OF SINGLE PATCH MICROSTRIP ANTENNA Circular microstrip antennas offer performance similar to that of rectangulargeometries. In some applications such as arrays, circular geometrics offer certainadvantages over other configurations. Recent experimental results have shown that circulardisk microstrip elements may be easily modified to produce a range of impedances,radiation patterns, and frequencies of operation. 112
  3. 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME Figure 2.1II.I Analysis of a microstrip disk antennaThe different methods used for the calculation of radiation fields and input impedanceare • Simple cavity model • Cavity model with source • Modal expansion model • Wire grid model • Green’s function method The cavity model is the simplest method used for predicting adequately theradiation characteristics of circular shaped microstrip antennas. The methods of analyzingmicrostrip disk antennas appear in ascending order of complexity. Thus the cavity model isthe simplest, while Green’s function method is the most involved. In all cases, thesubstrates thickness h is assumed to be much less than λ0. Parameters of circular disk antennas: A circular disk operating in the dominant mode is the most prevalent circular microstripantenna configuration. The following is a design procedure for this configuration. Element radius:The first design step is to select a suitable substrate of appropriate thickness. Bandwidthand radiation efficiency increase with substrate thickness, but excess thickness isundesirable if the antenna is to have a low profile and be conformal. The three mostcommonly used substrate materials are duroid (εr = 2.32) , rexolite (εr = 2.6) and alumina(εr = 9.8) . Since the relative dielectric constants of rexolite and duroid are close to eachother, the design curves below will be limited to duroid and alumina.For a known dielectric substrate at a specified operating frequency fr, the radius of themicrostrip disk element is: 113
  4. 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME k a= 1/ 2  2h   πk   1+ ln  +1.7726  π ε r k   2h   8.794 × 109 where k = and f r is in GHz. f ε r rDisk radius as a function of frequency for various values of εr and h is determined. It maybe noted that the effects of substrate thickness are insignificant for frequencies less than 2GHz.Input impedanceA reasonably accurate evaluation of the input impedance of a microstrip antenna isnecessary to provide a good match between the radiating element and the feed point. TheLO approach provides good agreement between the experimental results for microstrip feddisk radiators and the theoretical values. Equation ω Ζin = jΧL − C J12 (Re(κ11ρ0 )) ω2 − ω111+ j Q  2    Tprovides a reasonably simple basis for calculating the input impedance of a disk antennafor any coaxial feed location. For a microstrip fed element, this relation may be used with Χ L = 0.Radiation patternAs previously various mathematical models have been suggested for predicting theradiation characteristics of a circular disk microstrip radiator, the far-field expressionsobtained for the cavity model are simple and adequate for practical purposes. As such theradiation patterns may be plotted either by using equations Vak 0 e − jk0r Εθ = j n cos nφ 2 r [ Jn+1 ( k0 a sin θ ) – Jn-1 ( k0 a sin θ ) ] and[Jn+1( k0 a sin θ ) + Jn-1 ( k0 a sin θ ) ]Where V=h E0 Jn (ka) and is known as the edge voltage at φ = 0 . 114
  5. 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEMEOr Equations Vak e− jk0r sin( 0hcosθ ) k Εθ = jn 0 cosnφ 2 r k0hcosθ [ Jn+1 ( k0 a sin θ ) – Jn-1 ( k0 a sin θ ) ] Vak0 e− jk0r sin(k0h cosθ ) And Εφ = jn cosθ sin nφ 2 r k0h cosθ [ Jn+1 ( k0 a sin θ ) + Jn-1 ( k0 a sin θ ) ]The E-plane and H-plane radiation patters for disk elements at 2 GHz and εr = 2.32, εr =9.8 are plotted in figures. The E-pattern of a microstrip disk antenna using a high dielectricconstant material such as alumina, is almost constant with scan angle.Radiation resistance, q factor and losses:The radiation resistance may be evaluated from equation 2 960 Rr = V = 2 Pr (ak0 )2 I1for n=1 or Figure can be used to determine this, using appropriate thickness of thesubstrate. These curves have been computed assuming that tanδ =0.0005 and the diskmetallization is of copper.The frequency selectivity of a radiating element is determined by the quality factor QT. Thetotal Q-factor of a disk radiator is given by equation −1  1 hµf (k0a)2 I1  Q = + tanδ +  Εφ = jn Vak0 e− jk0r cos nφ sin nφ T h(πfσµ) 1/ 2 { } 240(ka) − n2  2 2 rAnd is plotted in figure for a typical set of parameters. For εr = 2.32 and f ≥ 500 MHz, thequality factor decreases with increase in resonant frequency and substrate thickness.Similarly for εr = 9.8 and h =0.1275 cm, QT decreases with increasing resonant frequencyfor f ≥ 500MHz.III. RESONANT FREQUENCY OF CIRCULAR MICROSTRIP ANTENNAS WITHAND WITHOUT AIR GAPS An analytical model for calculating the resonant frequency and the input impedanceof circular microstrip antennas with and without air gaps ( Figure3.1) has recently beendeveloped and is also employed in designing some integrated antenna modules. The 115
  6. 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEMEformulation, though incorporating the improved results of some earlier works, is valid forthe antenna parameters a/h > 2 and ε r < 10. Thus the model is not applicable to smallvalues of a, particularly when an air gap increases the value of h ( = h 1 + h 2 infigure). Moreover, the calculation of the resonant frequency involves an erroneousequation, as discussed in the following sections. All these limitations and shortcomings areaddressed in this paper to satisfy the current interests of designing active and passiveantennas employing circular microstrip patches. An improved formulation is proposed tocalculate an accurate, or very closely approximate, theoretical value of the resonantfrequency for any a/h value of the antenna printed on the substrate covering the entire rangeof dielectric constants. The theory has been verified with the experimental results available in the literaturefor the antennas having various patch diameters (a/h > 2) and heights of the air gap belowthe substrate. A set of prototype coax-fed antennas with a/h ~ 2 and a/h < 2 has beenfabricated and experimentally investigated. The theory shows very close agreement withthe experiment in all cases. Figure 3.1BackgroundThe simple resonator model of a circular disk cavity given by Watkins was modified byWolff and Knoppik incorporating the effect of the fringing fields in a disk capacitor and byintroducing dynamic dielectric constant ε r , dyn defined. The latter one, along with the resultsobtained by Chew and Kong for the fringing fields of a circular disk capacitor, has beenapplied to calculate the resonant frequency of TM modes in circular microstrip antennaswith and without air gaps. The effect of the air gap below the substrate, shown in Fig. 1,was accounted for by an equivalent dielectric constant of the medium below the patchgiven by 116
  7. 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME ε re = ( ) ε r 1 + h2 h1 (1 + ε h2 h1) rWhere ε r is the dielectric constant of the substrate. For the microstrip without an airgap, h 2 /h 1 = 0 and, hence, ε re = ε rPresent formulationFollowing the analytical model by Wolff and Knoppik, an improved formulation ispresented by introducing a new effective dielectric constant εr,eff in place of the dynamicdielectric constant εr,dyn of the medium below the patch to calculate the resonant frequencyof a circular microstrip antenna as α nm c f r ,nm = 2πaeff ε r ,effWhere αnm is the mth zero of the derivative of the Bessel function of order n, the value ofwhich (α01=3.832, α11=1.841, α21=3.054, α31=4.201) determines the lowest and higher ordermodes as TM110, TM210, TM010, and TM310 modes. c is the velocity of light in free space,αeff is the effective radius of the circular patch defined through, and εr,eff is defined as 4ε reε r , dyn ε r , eff = ( ε re + ε r , dyn ) 2The term εr,eff is introduced to take into account the effect of εre , the equivalent dielectricconstant of the medium below the patch in combination with the dynamic dielectric 4ε reε r , dynconstant εr,dyn to improve the model. εr,eff is deduced as ε r , eff = to yield the ( ε re + ε r , dyn 2 )resonant frequency as an average of the frequencies resulting from f r ,nm = α nm c by 2πaeff ε r ,effsubstituting εre and εr,dyn separately in place of εr,eff. The evaluation of εre is straightforward, as given by , and that of εr,dyn is a functionof the static main and static fringing capacitances and the mode of resonance as given byε re = ( ) and that of εr,dyn ε r 1 + h2 h1 is a function of the static and static fringing capacitances (1 + ε h2 h1) rand the mode of resonance as given by cdyn (ε = ε 0ε re ) ε r , dyn = cdyn (ε = ε 0 )Where cdyn is the total dynamic capacitance defined as cdyn = c0, dyn + ce, dyn 117
  8. 8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEMEco,dyn and ce,dyn are the dynamic main and dynamic fringing capacitances of the differentmodes determined from the static main and static fringing capacitances co,stat and ce,statrespectively, asWhere c0, dyn = γ n c0, stat Where γ n = 1.0, for n = 0 = 0.3525 =1 = 0.2865 =2 = 0.2450 =3 And 1 ce, dyn = ce, stat δ Where δ = 1, for n = 0 =2 n≠0 A comparatively recent formulation for the static capacitance of a circularmicrostrip disk obtained by Wheeler is applied to calculate co,stat and ce,stat since the result ismuch improved over the earlier ones and is widely applicable to the entire range ofdielectric constants and to all a/h values of the antenna. The expression of the capacitancegiven by Wheeler can be more explicitly written as ε 0ε reπa 2 c= (1 + q ) hWhere a is the physical radius of the patch and q = u + v + uv 1 + ε re 4 u= ε re πa / h 2 ln( p ) 1 v= +  − 1 / g t = 0.37 + 0.63ε re 3t 8 + πa / h  t  118
  9. 9. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME 1 + 0.8(a / h ) + (0.31a / h ) 2 4p= 1 + 0.9 a / h g = 4 + 2 .6 a / h + 2 .9 h / a In equation ε 0ε reπa 2 c= (1 + q ) hthe first term is equal to the static main capacitance co,stat and the term q arises due to thefringing fields at the edge of the disk capacitor. The static fringing capacitance ce,stat thus isdefined as ce , stat (ε ) =c 0, stat (ε )qWhere c0, stat (ε ) = ε 0ε reπa 2 / hIt can be noted that the ce,stat evaluated in equation 1 + ε re 4 u = ε re πa / h Erroneously equates the total capacitance of a microstrip disk instead of thefringing capacitance only, which is thoroughly investigated in equation aeff = a (1 + q ) . 2Equation c = ε 0ε reπa (1 + q ) also defines the effective radius of the microstrip disk as h aeff = a (1 + q )RESULTSThe computed results are presented and compared with the previously computed valuesavailable in the literature for certain dimensions of the antenna having small a/h values.The dependence of the factor q arising due to the fringing fields at the edge of the diskcapacitor on the disk parameter a/h for two єre values is verified. The fringing field is thesignificant function of the dielectric constant of the substrate and the dimensionalparameter a/h , particularly when a/h < 3. The theoretical values of εr,eff and εr,dyn as a function of antenna dimension a/h, withεre as a parameter, are verified. The quantity εr,eff, though, becomes closer to εr,dyn at verylarge values of a/h , and differs significantly as a/h decreases. The parameter εr,effintroduced in the present theory thus becomes significant for all large and small values ofa/h. The computed resonant frequencies of some circular patch antennas without an airgap are presented in Table 1 and compared with some theoretical results reported earlier. 119
  10. 10. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEMEMore recent results are included in Table 1, where the ce,stat has been correctly evaluatedfollowing of the previous section. Wolff’s model employing Wheeler’s result for the staticcapacitance of circular microstrip disk is highly relevant for comparison with the presenttheory and is also included in Table 1. Of all the theoretical values f the resonantfrequency, the present values show the closest approximation with the experimental valueswith 0.04%-0.64% errors. Table 2 compares the theoretical and Abbound calculated resonant frequencies ofthe dominant two higher order modes of a circular patch antenna with an air gap for threedifferent air gap heights. The present theory shows the closest agreement with theexperiment for all the three modes.Table 1: Theoretical and Experimental Values of Resonant Frequency For DominantMode of Circular Microstrip Antennas Without AirgapAntenna Parametersh1=1.5875mm;h2=0mm;€=2.65 Abbound Wolf Shen Present A (mm) (GH) (GHz) (GHz) (GHz) 11.5 4.609 4.576 4.4 5.17 10.7 4.938 4.903 47. 5.37 9.6 5.473 5.436 5.2 5.69 8.2 6.346 6.307 6.1 6.18 7.4 6.981 6.941 6.8 6.51Table 2: Theoretical And Experimental Values Of Resonant Frequency For DominantMode Of Circular Microstrip Antennas With AirgapAntenna Parametersa=50mm, h1=1.5875mm, €=2.65 Present Air Gap height Abbound Mode (MHz) h 2(mm) (MHz) TM11 1153.9 1118.8 0 TM21 1927.0 1855.9 TM31 2665.3 2552.9 TM11 1298.9 1276.1 0.5 TM21 2167.0 2115.8 TM31 2994.9 2922.8 TM11 1368.0 1342.1 1 TM21 2280.8 2235.5 TM31 3150.2 3055.6 120
  11. 11. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEMECONCLUSION A single patch circular microstrip antenna at a given resonant frequency iscalculated. An improved analytical formulation based on a resonator model is presented forcalculating the resonant frequency of circular microstrip antennas with and without airgaps. The formulation overcomes the limitations of the earlier models in predicting theresonant frequencies for small patch diameters (a/h<2) and higher dielectric constants ofthe substrate (εr>10) and is thus applicable to a wide range of patch dimensions- from verylarge to very small values of a/h printed on the substrate covering the entire range ofdielectric constants. The theory is verified with the previously calculated results reportedearlier for different dimensions of patch with a/h>2, heights of air gap, and modes ofresonance. The theoretical resonant frequency for small patch dimensions with a/h=1.875and 2.31 also shows close agreement with the previously calculated values.REFERENCES[1] K. F. Lee and J. S. Dahele, “Mode characteristics of annular-ring and circular-discmicrostrip antenna with and without air gaps,” in IEEE AntennasPropagation Soc. Int. Symp. Dig., 1983, pp. 55–58.[2] K. F. Lee, K. Y. Ho, and J. S. Dahele, “Circular disc microstrip antenna with an airgap,” IEEE Trans. Antennas Propagat., vol. AP-32, pp. 880–884, Aug. 1984.[3] S. Dahele, S. Mem, and K. F. Lee, “Theory and experiment on microstrip antennaswith air gaps,” Proc. Inst. Elect. Eng., pt. H, vol. 132, no. 7, pp. 455–460, Dec. 1985.[4] J. A. Navarro, L. Fun, and K. Chang, “Active integrated stripline circular patchantennas for spatial power combining,” IEEE Trans. Microwave Theory Tech., vol. 41, pp.1856–1863, Oct. 1993.[5] “Novel FET integrated inverted stripline patch,” Electron. Lett., vol. 30, no. 8, pp.655–657, 1994.[6] R. A. Flynt, L. Fun, J. A. Navarro, and K. Chang, “Low cost and compact activeintegrated antenna transceiver for system applications,” IEEE Trans. Microwave TheoryTech., vol. 44, pp. 1642–1649, Oct. 1996.[7] C. M. Montiel, L. Fun, and K. Chang, “A novel active antenna with selfmixing andwideband varactor-tuning capabilities for communication and vehicle identificationapplications,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 2421–2430, Dec. 1996.[8] K. L.Wong and Y. F. Lin, “Circularly polarized microstrip antenna with a tuning stub,”Electron. Lett., vol. 34, no. 9, pp. 831–832, 1998. [9] K. L. Wong and J. Y. Jan,“Broadband circular microstrip antenna with embedded reactive loading,” Electron. Lett.,vol. 34, no. 19, pp. 1804–1805, 1998.[10] F. Abboud, J. P. Damiano, and A. Papiernik, “A new model for calculating theimpedance of coax-fed circular microstrip antennas with and without air gaps,” IEEETrans. Antennas Propagat., vol. 38, pp. 1882–1885, Nov. 1990.[11] I. Wolff and N. Knoppik, “Rectangular and circular microstrip disk capacitors andresonators,” IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 857–864, Oct. 1974.[12] W. C. Chew and J. A. Kong, “Effects of friging field on the cacapacitance of circularmicrostrip disk,” IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp. 98–104, Feb.1980. 121
  12. 12. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME[13] J. Watkins, “Circular resonant structures in microstrip,” Electron. Lett., vol. 5, pp.524–525, Oct. 1969.[14] H. A. Wheeler, “A simple formula for the capacitance of a disc on dielectric on aplane,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 2050–2054, Nov. 1982.[15] L. C. Shen, S. A. Long, M. R. Allerding, and M. D. Walton, “Resonant frequency of acircular disc, printed-circuit antenna,” IEEE Trans. Antennas Propagat., vol. AP-25, pp.595–596, July 1977.[16] M. S. Leong et al., “Determination of circular microstrip disc by Noble’s variationalmethod,” Proc. Inst. Elec. Eng., vol. 128 H (M.O.A.), pp. 306–310, Dec. 1981.[17] D. Guha, “Comment on ‘A new model for calculating the impedance ofcoax-fed circular microstrip antennas with and without air gaps’,” IEEETrans. AntennasPropagat., vol. 48, pp. 1010–1011, June 2000.[18] T. Itoh and R. Mittra, “Analysis of microstrip disk resonator,” Arch. Eleck.Übertragung, vol. 27, no. 11, pp. 456–458, 1973. 122

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