International Journal of Wirele Communication and Mobile Computing 0; (4): 9-95 Publihed online October 0, 0 (http://www.ciencepublihinggroup.com/j/wcmc) doi: 0.648/j.wcmc.0004. The RCS of a reitive rectangular patch antenna in a ubtrate-upertrate geometry Amel Boufrioua Electronic Department, Technological Science Faculty, Univerity Contantine, Ain El Bey Road, 5000, Contantine, Algeria Email addre: boufrioua_amel@yahoo.fr To cite thi article: Amel Boufrioua. The RCS of a Reitive Rectangular Patch Antenna in a Subtrate-Supertrate Geometry. International Journal of Wirele Communication and Mobile Computing. Vol., No. 4, 0, pp. 9-95. doi: 0.648/j.wcmc.0004. Abtract: The cattering radar cro ection (RCS) and the reonant frequency problem of a upertrate loaded reitive rectangular microtrip patch which i printed on iotropic or uniaxial aniotropic ubtrate are invetigated, where an accurate deign baed on the moment method technique i developed. The choice of two type of bai function (entire domain and roof top function) i illutrated to develop the unnown current on the patch. The accuracy of the computed technique i preented and compared with other computed reult. Keyword: Supertrate, Aniotropy, Reitive, Radiation, Patch, Antenna. Introduction Microtripantenna are now extenively ued in variou communication ytem due to their compactne, economical efficiency, light weight, low profile and conformability to any tructure. However, microtrip patch antenna i limited by it inherent narrow bandwidth. Therefore, thi problem ha been addreed by reearcher and many configuration have been propoed for bandwidth enhancement [-6]. The tudy of the upertrate layer i of interet, it can affect the performance of printed circuit and antenna and may prove beneficial or detrimental to the radiation characteritic, depending on the thicnee of the ubtrate and upertrate layer, a well a relative dielectric contant []. In thi paper we extend our tudy [, ] to the cae of a upertrate-loaded reitive rectangular microtrip tructure, where the upertrate layer loaded on the microtrip tructure i often ued to protect printed circuit antenna from environmental hazard, or may be naturally formed during flight or evere weather condition [, 4]. The full-wave moment method ha been applied extenively and i now a tandard approach for analyi of microtrip geometry [-4], [7]. In thi paper the integral equation include a upertrate reitive boundary condition on the urface of the patch and the effect of aniotropic ubtrate are developed. It i worth noting that the effect of non-zero urface reitance and the uniaxial aniotropy on the cattering propertie of a upertrate loaded rectangular microtrip tructure ha not yet been treated. A novel propoed tructure pertaining to thi cae will be preented in thi paper.. Theory The geometry for the upertrate-loaded reitive rectangular patch antenna i hown in Figure. The reitive patch with length a and width b printed on the grounded ubtrate, which ha a uniform thicne of h and having a relative permittivity ε r (region ). The upertrate of thicne d with relative permittivity ε r i obtained by depoiting a dielectric layer on the top of the ubtrate (region ). Figure. Reitive rectangular patch inaubtrate-upertrate geometry
9 Amel Boufrioua: The RCS of a Reitive Rectangular Patch Antenna in a Subtrate-Supertrate Geometry In the cae of a uniaxially aniotropic ubtrate ε r can be repreented by a tenor or dyadic of thi form []: [ ε, ε ε ] ε ε.diag 0, = r x x z () ε0 i the free-pace permittivity; all the dielectric material are aumed to be nonmagnetic with permeability µ 0. εz i the relative permittivity in the direction of the optical axi. εx i the relative permittivity in the direction perpendicular to the optical axi. The tudy i performed by uing a full wave analyi and Galerin moment method to examine the cattering propertie of a upertrate loaded rectangular patch antenna with a urface reitance, in which we extend our tudy [, ] to the cae of thi propoed geometry. The principal modification are done epecially at the Green function and at the reitance urface. We have included the effect of the upertrate in the Green function formulation a [4] which are efficiently determined by the (TM, TE) repreentation []. G( Where i T m T e G ) = 0 TM i = ωε0 = co d ε + iind ε = co d + iind i 0 0 TE G D T 0 m m 0 0D T [ ε co h i in h] ε coh + i [ co h i in h] co h + i e e inh inh inh () () (4) = cod + i in d (5) ε D m = co d + i in d (6) D e = ε, i =,,, ε =. 0 (7-a) + = x y, 0 =ω µ 0ε0 (7-b) ωthe angular frequency; The tranvere wave vector; = x x + y y and = ; j = x, y Unit vector in x and y direction, repectively; An integral equation can be formulated by uing thi Green function on a thic dielectric ubtrate to determine the electric field at any point. The detail of the olution of the tranformed integral equation are preented in [-]. Entire domain inuoid bai function and roof top ubdomain bai function are introduced to expand the unnown current on the metal patche of thi propoed antenna[, ]. Since that we have included the effect of uniaxial aniotropic ubtrate and the effect of upertrate in the Green function, alo the effect of the non-zero urface reitance at the reitance matrix and conequently at the impedance matrix the different antenna characteritic can be eaily obtained imilar to [-4], [7, 8].. Numerical Reult The moment method technique with entire domain and roof top bai function ha developed to examine the reonant frequency and the cattering propertie of a rectangular patch antenna. For all our computation the mode that we will be tudying i the TM0 mode with the dominant component of the current in the y direction. To implify the analyi, the antenna feed will not be conidered. To enure that the computer program are correct, comparion are hown in Figure for a perfectly conducting patche of different ize without dielectric ubtrate (air) and with no upertrate, the ubtrate ha a thicne h = 0.7 cm. It i important to note that the normalization i with repect to f 0 of the magnetic wall cavity. The calculated reult for the two et of bai function hown in Figure agree very well with experimental reult obtained by other author [7], we found an excellent agreement with a light hift in the reonant frequency when we ue entire domain bai function compared to the meaured reult given by [7], on the other hand computation how that the roof top ubdomain bai function provide a ignificant improvement in the computation time with le iteration in the evaluation of the reonant frequency of a microtrip patch compared to the entire domain inuoid bai function [, 8]. It hould be noted that the convergence of the olution wa invetigated by varying the number of ubection. A mentioned previouly, good convergent olution are reached by uing entire domain bai function, for thi reaon, the ue of thee bai function ha developed to examine the reonant frequency and the cattering propertie for the following reult.
International Journal of Wirele Communication and Mobile Computing 0; (4): 9-95 9 Figure. Meaured and calculated reonant frequencie veru the dimenion of the patch for a rectangular microtrip antenna with no upertrate. The ubtrate ha a relative permittivity of ε r=.5 with a uniform thicne of h=0.cm and the patch dimenion i 6.0cm x5.0cm. In Figure and 4, the reonant frequency (the real part of the complex reonant frequency) and the band width veru the upertrate thicne for different dielectric contant of the upertrate are hown. The obtained reult how that when the upertrate thicne a well a the upertrate permittivity i increaed, the reonant frequency decreae. Figure 4. Normalized band width of a upertrate-loaded rectangular patch veru the upertrate thicne d. The variation of the band width i very mall for d le than about 4h. A the upertrate thicne increae (4h<d) the variation become ignificant for high upertrate permittivitie. The obtained reult how that the reonant frequency and the band width vary more ignificantly when the upertrate permittivity i greater than that of the ubtrate. Thee behavior agree very well with thoe obtained by [4] with light hift in frequency and band width between our reult and thoe of [4] are noted. It i worth noting that for thee two figure the normalization i with repect to that of the perfectly patch (R=0 Ohm) with no upertrate (d=0). Figure. Normalized reonant frequency of a upertrate-loaded rectangular patch veru the upertrate thicne d. Figure 5. Normalized radar cro ection veru angle θ for different dielectric contant of the upertrate loaded rectangular patch antenna, d=0.cm at φ = 0.
94 Amel Boufrioua: The RCS of a Reitive Rectangular Patch Antenna in a Subtrate-Supertrate Geometry Figure 6. RCS veru angle θ for variou value of thicnee of the upertrate loaded rectangular patch antenna, ε r =4.0. Figure 5 and 6 how the normalized cattering radar cro ection RCS of a upertrate-loaded rectangular microtrip veru the angle θ for different dielectric contant and different thicnee of the upertarate loaded rectangular patch antenna. Reult howing RCS reduction are preented for high upertrate thicnee and low upertrate permettivitie. Figure 7 how the normalized cattering radar cro ection RCS of a upertrate-loaded rectangular microtrip veru the angle θ for different urface reitance R. We oberve that when the urface reitance i increaed, the level of the radar cro ection decreae. Conequently the addition of a reitance on the urface of a microtrip patch antenna ha been hown to decreae the cattered energy from the antenna. For Figure 5, 6 and 7 the normalization i with repect to that of the perfectly patch (R=0 Ohm) with no upertrate (d=0). Figure 8. The effect of the urface reitance on the electric field E θ, at φ =0. Figure 8 how the cattering propertie for the E θ component of the electric field at φ =0 plane diplayed a a function of the angle θ and a a function of urface reitance. It i clear that when the urface reitance on the patch i increaed, the level of the component E θ decreae conequently. However, it i important to note that our reult for the E φ component do not change with the urface reitance at φ =0. According to the imulation it i worth noting that the component E φ i dominant than the component E θ and the total field tae the hape of the component E φ. Table how the cattering radar cro ection RCS for an imperfectly conducting patch with the urface reitance R=0 Ω compared to a perfectly one and printed on a ubtrate of thicne h=0. cm, where iotropic, poitive and negative uniaxial aniotropic ubtrate are conidered. The patch dimenion are: a=.5cm, b=.0 cm. It can be een clearly that the permittivity ε z ha a tronger effect on the cattering radar cro ection than the permittivity ε x for both cae. Alo it i noted that the tudy in thi table i done with no upertrate. Table. Effect of the urface reitance on the radar cro ection for iotropic, negative and poitive uniaxial ubtrate, θ =60, φ =0, a=.5cm, b=.0cm, h =0.cm. εx ε z AR RCS(dBm) R(Ω)=0 R(Ω)=0.. -9.7-8.57 4.64. -9.9-8.8 Figure 7. Radar cro ection veru angle θ for different urface reitance R of a upertrate loaded rectangular microtrip patch; h=0.cm, d=0.59cm ε r= ε r =.5 at φ = 0...6-9. -8.05.6. 0.5-9.5-8.68. 4.64 0.5-9.64-9.50
International Journal of Wirele Communication and Mobile Computing 0; (4): 9-95 95 4. Concluion The moment method technique ha been developed to examine the complex reonant frequency, the half band width, the radar cro ection (RCS) and the radiation of a upertrate loaded reitive rectangular microtrip patch which i printed on iotropic or uniaxial aniotropic ubtrate with the optical axi normal to the patch. The formulation i carried out in the pectral domain. The choice of roof top ubdomain bai function and the entire domain were illutrated to develop the unnown current on the patch. The accuracy of the computed technique wa preented and compared with other computed reult. Reference [] N. G.Alexopoulo, D. R.Jacon, Fundamental upertrate (cover) effect on printed circuit antenna, IEEE Tran. Antenna Propagat,vol., 984,pp. 807 86. [] A.Boufrioua, A.Benghalia, Effect of the reitive patch and the uniaxial aniotropic ubtrate on the reonant frequency and the cattering radar cro ection of a rectangular microtrip antenna Elevier, AST, Aeropace Science and Technology, vol. 0, 006,pp. 7-. [] A.Boufrioua, Reitive rectangular patch antenna with uniaxial ubtrate, In: Antenna: Parameter, Model and Application, Editor. Albert I. Ferrero: Nova Publiher. New Yor. 009, pp. 6-90. [4] J-S.Row,andK. L.Wong, Reonance in a upertrate-loaded rectangular microtrip tructure, IEEE Microwave Theory and Technique,vol. 4, 99, pp. 49 55. [5] B-L. Ooi, S.Qin,andM-S.Leong, Novel deign of broadband taced patch antenna, IEEE Tran. Antenna Propagat, vol. 50, 00,pp. 9-95. [6] A. A.Dehmuh, G.Kumar, Formulation of reonant frequency for compact rectangular microtrip antenna, Microwave and Optical Technology Letter, vol. 49, 007,pp. 498-50. [7] W. C.Chew, Q.Liu, Reonance frequency of a rectangular microtrip patch, IEEE Tran. Antenna Propagat, vol. 6, 988,pp. 045 056. [8] A.Boufrioua, A.Benghalia, Radiation and reonant frequency of a reitive patch and uniaxial aniotropic ubtrate with entire domain and roof top function, Elevier, EABE Engineering Analyi with Boundary Element, vol., 008,pp. 59-596.