Design of Boad-Beam Micostip Reflectaay PIYAPORN KRACHODNOK AND RANGSAN WONGSAN School of Telecommunication Engineeing, Institute of Engineeing Suanaee Univesity of Technology 111 Univesity Avenue, Muang Distict, Nakhon Ratchasima, 3 THAILAND Email: piam@sut.ac.th Abstact: - The eflectaay s elements aangement fo geneating an abitay phase distibution in the antenna apetue and thus a wide beamwidth of the fa field patten is pesented. The desied phase delay of eflectaay elements, which duplicated the same adiating apetue as backscattes, is detemined on the constuction of the cuvatue of a shaped backscatte suface with the help of Snell's law fo beam foming to cove a boad aea. The Method of Moments (MoM) and the infinite-aay ae applied to calculate eflection phase chaacteistics. The phase and adiation patten synthesis method fo micostip eflectaay that has to illuminate a pedefined cicula aea ae pesented by using a vaiety of discetization of elementay geometical functions such as, tiangula, quadatic, cicula, gaussian, cosine, squaed cosine, and paabolic distibutions. These backscatte functions ae discussed in tems of meits and demeits to find appopiate adiation chaacteistics such as adiation patten, -3 db beamwidth, and maximum gain fo utilization in Wieless Local Aea Netwok (WLAN) application. The optimized feed distance is calculated fom the apetue efficiency by consideing feed blockage efficiency and the influence of the feed position on the -3 db beamwidth and gain pefomance has been investigated. Having confimed the validity of this appoach, the X-band antenna pototype is designed and developed. This eflectaay is tested expeimentally and shows good pefomance. Key-Wods: - eflectaay, phase aay, boad-beam antenna 1 Intoduction The chaacteistics of antennas (pefomance, technology, and cost) ae an impotant issue in wieless communication systems. The shaped-beam antenna fo satellite communication was fist developed to give appoximately unifom coveage of the eath [1]-[]. Recently, the simila equiement but diffeent application; that is, the indoo high speed data tansmission: Wieless Local Aea Netwoks (WLAN) opeating in the millimete wave, again has attacted consideable attentions [3]-[7]. Especially, the lage-scale indoo base station of such system equies the wide-beam antenna fo coveing an effectively boad aea. Theefoe, the widely cicula beam antenna is an altenative fo WLAN applications as shown in Fig.1. The equied impotant featue is the tansmitted powe that has to be efficiently distibuted ove the coveage wheeas, outside the coveage, the field stength has to fall off apidly. In [5], Smuldes et al. pesented the design of a 6 GHz shaped eflecto antenna fo WLAN access points by using backscatte eflecto, which was fabicated fom the modified paabolic suface. Fom this design, the backscattes have been fabicated fom the cicula metal sheet that thei sufaces ae shaped to be geometic cuvatue. In case of WLAN systems, such antennas ae impope because thei stuctues suffe fom mechanical dawbacks such as bulkiness and the need fo an expansive custom mold fo each coveage specification. Fig. 1 Reflectaay fo WLAN lage-scale indoo base station. ISSN: 119-74 18 Issue 3, Volume 7, Mach 8
A micostip eflectaay that combines some of the best featue of micostip aays and paabolic eflecto was pesented in [8]-[14]. The eflectaay antenna consists of a flat eflecting suface and an illuminating feed as shown in Fig.. On the eflecting suface, thee ae many isolated elements (e.g. pinted patches, dipoles, o ings), which aay on flat pinted cicuit boad (PCB) without any powe division tansmission lines. A eflectaay configuation is attactive because it allows a single mechanical design to be used epeatedly fo a wide vaiety of diffeent coveage specifications without the need fo expensive fabication of a new mold. The only changes equie that the pinted eflecting element dimensions can be changed fo each design in ode to geneate the diffeent beams. Thus, many of the high ecuing costs associated with shaped eflecto antennas can be eliminated with flat pinted eflectaay [11]. The flat geomety of a eflectaay also lends itself to easie placement and deployment on the WLAN lage-scale indoo base station and also in tems of manufactue. In addition, a flat pinted eflectaay fulfils the antenna equiements fo low pofile and light weight. In this pape, we popose the design techniques of a wide-beam micostip eflectaay antenna using discetization of elementay geometical functions to synthesize the appopiated cuvatue fo foming a wide-beam patten of eflectaay. An effective technique fo optimum eflectaay design depend on the apetue efficiency by consideing feed blockage efficiency and the influence of the feed position on the -3 db beamwidth and gain pefomance has been investigated. To achieve such boad-beamwidth, phase of each aay element in the eflectaay antenna is designed specifically to emulate the cuvatue of the backscatte function by using patches of diffeent sizes [11]. In the fist section, we will pesent the geneal design appoach as fa as it involves the eflection phase chaacteistic (Section ) that descibes the desied phase delay of eflectaay elements and the phase calibation technique by using a full-wave method of moment and the infinite-aay. In Section 3, we apply this appoach to calculate the adiation patten of the poposed antenna. Design consideations of boad-beam micostip eflectaay and expeimental esults ae descibed in Section 4. Finally, the conclusions ae given in Section 5. Reflection Phase Chaacteistic.1 Geometical functions of backscatte The geomety of a eflectaay antenna, which duplicated the same adiating apetue as cuved backscatte eflecto, fed with a feed antenna is illustated on Fig.. The distibutions of backscatte cuvatue using the geometical function ae shown in Table 1. Whee D is assumed to be the diamete and A is the depth of the backscatte eflecto, espectively. The esults of these functions will be taken to find equied phase delay and adiation patten. Fig. Synthesis model of boad-beam micostip eflectaay. Table 1 Fomulations of elementay geometical functions. Backscatte Shapes Fomulations Cicula Gaussian Quadatic f ( z ) = A 1 z D f( z ) = Ae ( z ) D f( z ) = A 1 z D Paabolic = f ( z ) z /4f π Cosine f ( z ) = Acos( z ) D Squaed cosine Tiangula π = D f ( z ) Acos z f ( z') = A 1 z D With a given standad X-band hon as shown in Fig. 3, the appopiate distance between the hon and the cente of eflectaay can be estimated by consideing the spillove and tape efficiencies ISSN: 119-74 181 Issue 3, Volume 7, Mach 8
elations given in [14]. At optimum value of apetue efficiency, a feed distance to diamete atio (f/d) povides spillove and tape efficiencies of 76% and 84%, espectively. Thus, feed distance is chosen to be of 1.5 cm at 1λ eflecto diamete. This stuctue adiates the beam that illuminates a pedefined cicula aea without substantial spatial vaiation. 6 1 3 15 Feed pattens 18-3 -45 9 9 3 15 6 1 E-plane H-plane Fig. 3 Radiation patten of standad X-band hon. Efficiency (%) 1 9 8 7 6 5 4 3 Apetue efficiency 1 Tape efficiency Spillove efficiency..4.6.8 1 1. f/d Fig. 4 Reflectaay efficiency.. Requied Phase Delay Fig. illustates the incidence of wave on the suface of an analysis model of pinted micostip eflectaay, which paametes used in this figue ae descibed below:, i, ρi the vecto fom the feed to the -th eflectaay element, which can be obtained by using flat geomety; the eflected vecto fom the eflectaay suface to fa-field; the vecto fom the feed to the shaped eflecto suface, which can be obtained by using cuvatue geomety; ρ θ i θ D f the eflected vecto fom the shaped eflecto suface to fa-field; incidence angle; eflection angle; dimension of the eflecto; distance between the feed and the cente of the eflectaay. In geneal, the feed may be positioned at distance fom the eflectaay. The path lengths fom the feed to all eflectaay elements ae all diffeent, which lead to diffeent phase delays. In this pape, the desied phase delay is detemined on the constuction of the cuvatue of a shaped backscatte suface with the help of Snell's law. The elations of the micostip eflectaay suface to the shape of backscatte ae two coodinate systems in this figue: one descibes the coodinates ( x, y, z ) of the eflectaay and the othe descibes the coodinate ( xb, yb, zb) of the backscatte. The selected shaped eflecto is detemined by using functions of elementay geometic ( f ( z )) that apetue coss sections of all backscattes ae confined to be cicula, same diamete, and vey small adius of point souce. Since the eflectaay is designed, the following coodinate is used to find the point on the backscatte suface at a given patch element position on the eflectaay as given by (1). xb = x + f( z ) z tanθi cos i, y = y + f( z ) z tanθ sin, b i i (1) whee the phase cente of the feed is located at (,,) and the incidence angle can be descibed in tems of geometical dimensions 1 x + y θi = tan, f y i = 1 tan. x () (3) The total path length fom the feed to the eflectaay apetue is the sum of the distance fom the feed to a point on the backscatte suface and the distance fom that point to the coesponding point on the eflectaay with the ays satisfying Snell's law on the backscatte suface. In the analysis of backscatte, it is desiable to find a unit vecto that is nomal to the local tangent at the suface eflection point [ z f( z )] [ z f( z )] nˆ =. (4) ISSN: 119-74 18 Issue 3, Volume 7, Mach 8
With the help of Snell's law of eflection, the eflected angle fo the backscatte can be expessed in (5). ρ θ ˆ = 1 i cos n θi. ρi (5) The diffeential path length ( Δ L ) and the phase delay ( ΔΦ ) fo the -th eflectaay element ae given by z f Δ L = + (6) b ρi, i, sinθ 36 ( N) k L ΔΦ in degee = 1 Δ, (7) π whee N is intege. The above indicates that the compensating phase can be epeated evey 36 deg, and the potion that is an intege multiple of 36 deg can be deleted. The equied apetue phase delays of all elements ae calculated and will be used to design the dimension of the eflectaay elements as shown in Fig.5. These phase delays ae duplicated the same adiating apetue as shape of backscatte. To compensate these phase delays, the elements must have coesponding phase advancements designed. Requied phase delay (degee) 7 6 5 4 3 1 Cicula Gaussian Quadatic Paabolic Cosine Squaed cosine Tiangula -.15 -.1 -.5.5.1.15 Patch position (m) Fig. 5 Desied phase delay synthesis fo eflectaay elements using geometical functions..3 Element Chaacteization The most impotant and citical segment of the eflectaay design is its element chaacteization. To compensate fo above phase delays, the elements must have coesponding phase advancements designed. Its phase change vesus element change (patch size, etc.) must be calibated coectly. If the element design is not optimized, it will not scatte the signal fom the feed effectively to fom an efficiently fa-field beam. Also in this pape, the phase calibation technique uses a full-wave method of moment and the infinite-aay appoach to model the effect of the finite gounded dielectic substate undelying the single adiato [1],[14]. In ode to detemine the solution used to design and analyze a micostip eflectaay, we assume an incident plane wave with an electic field of the fom inc jk ( xui yvi zwi E = Ee + ), (8) whee the complex vecto E defines the amplitude and diection of the incident field and ui = sinθicos i, vi = sinθisin i, wi = cos θi. (9) The phase efeence fo this and the following fields ae at the bottom of substate. In the absence of aay elements, the eflected field fom the dielectic substate and gound plane can be expessed as E R E E = R E e ef θ θθ θ jk cosθi) = e ef R E jk cos θi), (1) whee Rθθ and R ae the plane wave eflection coefficients as given in [14]. The pesence of the elements gives ise to an additional scatteed field component given by E S S E E = S E e scat θ θθ θ θ jk cos θi) = e scat Sθ S E jk cos θi). (11) Evaluation of the total scatteed field fom the micostip eflectaay is based on the assumption that each element of the finite eflectaay scattes as a Huygens souce with eflection coefficient equivalent to the total eflection coefficient of an infinite aay of simila elements. E tot R = + S S E θθ θθ θ θ jk cos i e θ ) Sθ R + S E. (1) Fom (1), the eflection phase equied fo the design to compensate above phase delays can be found fom the esult of this esult. The scatteing coefficients ( S ), defined in (11), ae found by using a full-wave solution. The method of moment impedance matix fo infinite aay of unifom elements can be computed as ISSN: 119-74 183 Issue 3, Volume 7, Mach 8
m= n= 1 Z = J ( k, k ) G( k, k ) J ( k, k ), (13) ij i x y x y j x y s m= n= whee s is cente-to-cente elements spacing in both x and y diections, J is the Fouie tansfom of the ith expansion mode cuent, and G is the dyadic Geen's function fo the dielectic substate. The voltage vecto elements can be expessed in (14) V = J G( k u, k v ) J ( k u, k v ), (14) whee i s i i i i i J s xe ˆ( θ cosi E cosθisin i ) =. (15) η + ye ˆ( θ sini E cosθicos i ) Fig. 6 shows simulated esults of eflection phase of infinite aay. The obtained esults indicated that, if the element size L is excessively small, eithe the eflection phase cannot be made to cove the full equied to 36 phase ange, o it changes excessively fast aound the element esonance. This available phase shift ang is limited by the eflectaay antenna bandwidth (aound 4%). Reflection phase (Degee) 35 3 5 15 L = 6 mm L = 7 mm 1 L = 8 mm L = 9 mm 5 L = 1 mm L = 11 mm 8 8.5 9 9.5 1 1.5 11 11.5 1 Fequency (GHz) Fig. 6 Reflection phase of total eflected field fom an infinite aay of micostip patches. 3 Radiation Patten Synthesis With the compensating phases of all elements known, the fa-field adiation pattens can be calculated by the conventional aay theoy [13], whee the adiations of all elements ae summed togethe below. Consideing a plana aay consisting of M N elements that ae nonunifomly illuminated by a low-gain feed, the eadiated field fom the patches in an abitay diection, û, will have the fom M N Eu ( ˆ) = F ( ˆ ) ( ˆ az Ai u ) Auu ( ˆ ˆ ), (16) m= 1 n= 1 exp jk ( ˆ + i u) jδφ, whee F is the feed patten function, A is the eflectaay element patten function, is the vecto i fom the cente of eflectaay to -th element, uˆ is the unit vecto of eflected field, and ΔΦ is the equied compensating phase of the -th element calculated by (7). The calculated esults that indicate the diffeent adiation pattens fo vaious geometical functions ae shown in Fig.7. The steepness of the patten edges and the angula positions of these edges confim that the antenna efficiently illuminates the taget aea to be coveed (±65 ). Radiation pattens ae diffeent due to phase of eflectaay elements which ae duplicated the same adiating apetue as backscatte. Because of phase change vesus element change, each eflectaay type (as backscatte shapes) povides diffeent chaacteistics such as -3 db beamwidth (HPBW) and elative powe, epoted in Table. Fom Table, it is obseved that the HPBW of seven backscatte eflectaay types ae diffeent. Fo aveage consideation, it is appaent that the squaed cosine has the widest beamwidth and is followed, in ode, by gaussian, cosine, quadatic, paabolic, and cicula, which ae 166, 164, 156, 15, 14, and 133, espectively, while HPBW of tiangula is about 7 on each main beam. Since the elative powe is stongly coincided with the HPBW i.e., the naowe the beamwidth the highe the elative powe and vice vesa. Howeve, eflection suface fo eflectaay elements, which ae synthesized in this pape, ae placed position nea cente of shaped backscatte. Thus, the ciculaly geometical function yields the highest elative powe and followed, in ode, by paabolic, gaussian, tiangle, quadatic, cosine, and squaed cosine, espectively. Fom all the afoementioned adiation chaacteistics, it can be summaized that these eflectaays can be chosen accoding to the chaacteistic equiements in pacticable applications. Fo example, if the widest HPBW fo lage coveage aea is equied, then, the geometic function of squaed cosine should be the best choice. But its advantage, which should be concened, is the highest ipple level. Howeve, if we need a vey high gain eflectaay antenna, the ciculaly geometical function should be applied. Fom view gaphs of adiation pattens in Fig.7, it is ISSN: 119-74 184 Issue 3, Volume 7, Mach 8
easy to find the pope geometical function at which meets the equiement of the chaacteistic specifications. To get moe advantages in one chaacteistic while sacificing the meit of anothe chaacteistic in the same backscatte function is difficult to avoid. Relative powe (db) 35 3 5 15 1 5 Cicula -5 Gaussian -1 Quadatic Paabolic -8-6 -4-4 6 8 Elevation angle (Degee) (a) 4 Design Consideations of Boad- Beam Micostip Reflectaay and Expeimental Results As an example, authos clinch to choose compensating phase of eflectaay elements with the paabolic backscatte function because it has appopiate chaacteistics, i.e. low ipple level, high elative powe (high gain), and wide HPBW (wide coveage aea). To veify the theoetical calculation, the eflectaay pototype is fabicated at the opeating fequency of 1 GHz. This fequency is chosen coesponding to the available equipment. The eflectaay of 3 cm dimension is designed and measued with a standad X-band hon feed, which is placed in font of eflectaay suface. The cell elements of eflectaay ae pinted on a TACONIC substate with thickness.76 mm and pemittivity ε =.33. The cente-to-cente elements spacing is fixed at a distance s =.6λ in both x and y diections. Relative powe (db) 35 3 5 15 1 5-5 -1 Cosine Squaed cosine Tiangula -8-6 -4-4 6 8 Elevation angle (Degee) Efficiency (%) 1 9 8 7 6 5 4 3 Apetue efficiency Tape efficiency 1 Spillove efficiency Feed blockage efficiency..4.6.8 1 1. f/d (b) Fig. 7 H-plane adiation patten synthesis fo micostip eflectaay. Table. Chaacteistics of eflectaay with vaious geometical types. Backscatte Shapes HPBW (degee) Maximum elative powe (db) Cicula 133 3.9 Gaussian 164 8.49 Quadatic 15 5.58 Paabolic 14 8.87 Cosine 156 4.7 Squaed cosine 166.1 Tiangula 7 8.6 Fig. 8 Reflectaay efficiency by consideing the feed blockage efficiency. It is easy to calculate efficiency fo a feed hon patten and eflectaay due to illumination tape and spillove as given in [13],[14]. Howeve, thee ae seveal othe factos that can significantly educe efficiency. Because the feed hon and its suppoting stuctues ae in the beam diection of the eflectaay, theefoe, some pat of the adiation is blocked. Also, consideing the apetue, tape, spillove, and feed blockage efficiencies elations vesus distance between the feed and the eflectaay to a dimension (f/d) atio ae calculated and plotted in Fig. 8. As in the case of font feed eflecto, thee is an optimum value of f/d that maximizes apetue efficiency fo a given feed patten. This maximum value is slightly lowe than the optimum apetue efficiency fo the paabolic case because of a slightly lowe tape efficiency. ISSN: 119-74 185 Issue 3, Volume 7, Mach 8
When the feed blockage efficiency is consideed, maximum apetue efficiency is educed and feed distance is changed while a eflectaay dimension is fixed. In this pape, we have investigated the influence of the feed position on the -3 db beamwidth (HPBW) and gain pefomance befoe the eflectaay is fabicated. Whee the fist feed distance f is located at the point that maximizes apetue efficiency (61%). In ode to optimize the feed position of boadbeam eflectaay, the calculated esults as shown in Fig. 9 indicate the diffeent adiation pattens fo the vaious feed positions. The total eadiation field is computed as the summation of all the contibutions fom each aay element. The pescibed field equiements have been satisfied by an appopiate choice of the adiating patches selected fom the complex design cuves obtained in the analysis stage. Table 3 Chaacteistics of eflectaay. Feed distance HPBW (degee) Gain (dbi) @ θ = Maximum gain (dbi) f - 1% f 158 1.43 8.81 f - 5% f 151-6.13 9.35 f 144.3 1.75 f + 5% f 144 1.99 11.1 f + 1% f 145 1.5 1.16 Gain (db) 15 1 5-5 -1 Paabolic function f-1% f-5% f f+5% f+1% -8-6 -4-4 6 8 Elevation angle (Degee) distance is educed, then the ipple is inceased. Away fom the main beam, the phase cente may move aound and appea as multiple points, as stay eflections and suface cuents affect the adiation patten. Because of the phase change vesus element change, each feed distance povides diffeent chaacteistics such as HPBW and gain, which ae epoted in Table 3. Fom Table 3, it is found that the HPBW of eflectaays is diffeent when the feed distance is vaied. Fo aveage consideation, it is appaent that the feed position not fa away in distance fom eflectaay povides the widest beamwidth. Since the maximum gain is stongly coincided with the HPBW, i.e., the naowe the beamwidth the highe the maximum gain and vice vesa. Howeve, the position of eflection suface fo eflectaay elements is placed nea the cente of backscatte. Thus, the enlagement of the feed distance yields the lowest feed blockage efficiency and the highest gain at θ =. Howeve, it is geneally obseved that when the antenna beam is enlaged, the antenna gain is educed. With the optimum design equiement, the feed distance is chosen at 5 cm, which caused the maximum apetue efficiency to be educed by appoximately % but its gain is inceased. In Fig. 1, the pototype of eflectaay antenna is ealized following this appoach and measued. Fom the measuement as shown in Fig. 11, the antenna has the HPBW of 145 and maximum gain of 13 db at the fequency of 1 GHz. The measued gain pattens have been coected by db fo loss in the waveguide feed tansition. An additional cause of asymmety obseved in the pattens is fabication toleance. The computed pefomances of this eflectaay ae in accodance with those of the measued pototype. Howeve, the measued and computed adiation pattens taken along the stut show a elatively much lage ipple of almost 3 db in amplitude. Fig. 9 Radiation patten in H-plane of boad-beam eflectaay fo the vaious feed positions. The steepness of the patten edges and thei angula positions confimed that the antenna efficiently illuminates the taget aea to be coveed (±65 ). The obtained adiation pattens ae diffeent due to phase of eflectaay elements, which duplicated the same adiating apetue as paabolic backscatte. Moeove, the ipple appeaed on the top of each patten can indicate that if the feed Fig. 1 Reflectaay pototype. ISSN: 119-74 186 Issue 3, Volume 7, Mach 8
Gain (db) 15 1 5-5 -1 Calculated Measued -8-6 -4-4 6 8 Elevation angle (Degee) Fig. 11 Calculated and measued adiation pattens of designed eflectaay at 1 GHz. 5 Conclusion In this pape, we have investigated a theoetical appoach to design a eflectaay antenna usable of WLAN applications. The eflectaay can be chosen accoding to the chaacteistic equiements in pacticable applications by using the synthesis of phase and adiation patten of vaious eflectaay types. The optimized feed distance is calculated fom the apetue efficiency by consideing feed blockage efficiency and the influence of the feed position on the -3 db beamwidth and gain pefomance has been investigated. The simulation of this eflectaay demonstates that inceasing feed distance can enhance maximum gain but its HPBW is educed. Fom all the afoementioned adiation chaacteistics, it can be summaized that if we need to impove gain pefomance fo boad-beam eflectaay antenna, an optimum feed distance would povide a feed adiation patten which completely illuminates the eflectaay with minimal spillove. A test antenna built accoding to ou model is in ageement with ou expectations both in egads to coveage and maximum gain. The data show that flat eflectaays can also give a defined footpint as a conventional antenna but without the complicated tooling and othe dawbacks inheent in the latte. Refeences: [1] S.G. Hay, D.G. Bateman, T.S. Bid, and F.R. Cooay, Simple Ka-band Eath coveage antennas fo LEO satellites, IEEE Antennas Popag. Soc. Int. Symp., Vol.1, 1999, pp.11-16. [] A.D. Olve, P.J.B. Claicoats, A.A. Kishk, and L. Shafai, ed., Micowave Hons and Feeds, IEEE, New Yok, 1994. [3] T.S. Bid, J.S. Kot, N. Nikolic, G.L. James, and S.J. Bake, Millimete-wave antenna and popagation studies fo indoo wieless LANs, Antennas Popag. Soc. Int. Symp., Vol.1, 1994, pp.336-339. [4] C.A. Fenandes and J.G. Fenandes, Pefomance of lens antennas in wieless indoo millimetewave applications, IEEE Tans. Micowave Theoy Tech., Vol.47, No.6, 1999, pp.73-737. [5] P.F.M. Smuldes, S. Khusial, and M.H.A.J. Heben, A shaped eflecto antenna fo 6-GHz indoo wieless LAN access points, IEEE Tans. Veh. Technol., Vol.5, 1, pp.584-591. [6] R. Sauleau, P. Coquet, K. Shinohaa, J. P. Daniel, N. Hiose, and T. Matsui, Millimete wave antennas with gaussian adiation pattens, IEICE Tans Commun., Vol.E84-B, No.9, 1, pp.395-46. [7] A. Kuma, Antennas fo wieless indoo millimete-waves applications, Poc. IEEE CCECE, Vol.3, 3, pp.1877-188. [8] R.E. Munson, H.A. Haddad, and J.W. Hanlen, Micostip eflectaay fo satellite communications and RCS enhancement o eduction, U.S. patent 4 684 95, 1987. [9] D.C. Chang and M.C. Huang, Multiplepolaization micostip eflectaay antenna with high efficiency and low coss-polaization, IEEE Tans. on Antenna and Popag., Vol.43, No.8, 1995, pp. 89-834. [1] J.A. Encina, Design of two-laye pinted eflectaays using patches of vaiable size, IEEE Tans. Antennas and Popag., Vol.49, 1, pp.143-141. [11] D.M. Poza, S.D. Tagonski, and R. Pokuls, A shaped-beam micostip patch eflectaay, IEEE Tans. Antenna and Popag., Vol.47, Issue 7, 1999, pp. 1167-1173. [1] P. Kachodnok and R. Wongsan, Design of micostip eflectaay antenna using backscatteing technique, Poc. of ITC-CSCC 6, Vol. 3, 6, pp. 513-516. [13] J. Huang, Analysis of a micostip eflectaay antenna fo micospacecaft applications, The Telecommunications and Data Acquisition Pogess Repot 4-1, 1995, pp. 153-173. [14] D.M. Poza, S.D. Tagonski, and H.D. Syigos, Design of millimete wave micostip eflectaay, IEEE Tans. Antenna and Popag., Vol.45, No., 1997, pp. 87-96. [15] P. Kachodnok and R. Wongsann, Optimum design of boad-beam micostip eflectaay, Poc. the 11th WSEAS Intenational Confeence on COMMUNICATIONS, 7, pp. 11-16. ISSN: 119-74 187 Issue 3, Volume 7, Mach 8