MICROSTRIP ANTENNA FOR WIRELESS LAN APPLICATIONS BY APPLYING MODIFIED SMITH-CHART REPRESENTATION

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1 MIOSTIP ANTENNA FO WIEESS AN APPIATIONS BY APPYING MODIFIED SMITH-HAT EPESENTATION Settapong Malisuwan, Ph.D. Depatment of Electical Engineeing hulachomklao oyal Militay Academy Nakhon-Nayok, Thailand Monton haoenwattanapon & Ut Goenchanat, Ph.D. Depatment of Electical Engineeing MET Pogam, angsit Univesity Pathumtani, Thailand Vichate Ungvichian, Ph.D. Depatment of Electical Engineeing Floida Atlantic Univesity Boca aton, F 3343, USA. Abstact The poposed algoithm depicting the amic pemittivity of the micostip stuctue diectly leads to a convenient and modified Smith-chat epesentation that includes the fequency-dependent influence of finging field and the lossy chaacteistics cohesively. The icacy of the model is illustated with an example concening a micostip patch antenna fo wieless AN applications. elevant simulations show that the input impedances calculated fom the model ae moe accuate than those fom the pevious model in the liteatue by compaing to the measue esults, as illustated with an example of a patch antenna. This model is compatible fo AD ots with MATAB facilitating fast and use-fiendly implementations. Key wod: AD, Smith chat, esonant fequency, ectangula micostip antenna and Wieless AN. 1 INTODUTION The micostip antenna is one of the most popula types of antennas fo wieless AN applications, because it is easily integated with othe passive and active micowave devices. elevant design equations in closed-fom using semi- 34

2 Micostip Antenna fo Wieless AN Applications empiical stategies specifying the fequency-dependent ective pemittivity concept and dispesion chaacteistics of a micostip line have been deived in the existing liteatue [1]-[7]. Although many compute-aided design (AD) systems have been developed using such algoithms with built-in micostip design capabilities, simple calculation methods fo micostip line paametes by hand-calculato and/o by pesonal compute ae needed fo peliminay design puposes, and/o fo quick cicuit evaluation puposes. Moeove, designes may need to obseve the physical consideations of micostip cicuits on stepby-step basis. Theefoe, many eseaches ae in seach of simple methods, which ae at the same time sufficient to explain the physical aspects of micostip cicuits, pecisely. The Smith-chat is a poweful visualization tool used in high-fequency engineeing fo designing impedancematching cicuits, filtes, amplifies, and evaluating the tansmission line chaacteistics. Although thee ae othe impedance and eflection coicient chats that can be used fo such poblem, the Smithchat is pobably the best known and most widely used. It was developed in 1939 by P. Smith at the Bell Telephone aboatoies. Today, it is has become an integal pat of much of the cuent compute-aided design (AD) softwae fo high-fequency designs. applications. The poposed model is set up fo use in compute-aided micostip design and is fully compatible with the needs and tends of moden compute-aided micostip antenna design. FEUENY-DEPENDENT SMITH- HAT (MODIFIED SMITH-HAT) The Smith-chat is an impedance epesentation in a complex plane depicting a set of cicles of constant esistance and patial cicles of constant eactance. The standad Smith-chat is based on the static chaacteistic impedance ( ) and does not include the fequency-dependent aspects of. Theefoe, a fequency-dependent facto is necessay fo inclusion in the calculations so as to impove the accuacy of the models. In this section, the fequency-dependent ective pemittivity concept is applied to constuct a fequency-dependent (lossy) Smith-chat to analyze micostip line chaacteistics. Befoe deiving the fequency-dependent Smith-chat elations, the capacitance paamete in micostip-line system can be consideed. The classical paallel-plate capacito is shown in Fig. 1. Fom the geomety shown in Fig. 1, the capacitance pe unit length of the stuctue can be expessed as [8]: In this eseach, the poposed algoithm depicting the amic pemittivity of the micostip stuctue diectly leads to a convenient and modified Smith-chat epesentation that includes the fequencydependent influence of finging field and the lossy chaacteistics cohesively. esults based on the poposed model ae compaed with the available data in the liteatue in espect to a micostip patch antenna in the fequency ange of wieless AN h l V w Fig. 1: A paallel-plate capacito Intenational Jounal of The ompute, The Intenet and Management, Vol. 11, No.3, 3, pp

3 w = (1) h A simple fequency-dependent capacitance of the paallel-plate capacito can be modeled in tems of any fequencydependent attibutes of. That is, w ( ω ) = o ( ω ) () h ( ω ) Whee is a complex pemittivity equal to (3) 1 + ( ϖ ) ( ) ( ω ) is the fequency-dependent tem given by [18]: [ 3 4 f n ( ϖ ) = P1 P ( P P ) ] (4).55 P1 = u exp ( f n ) P.336[ 1 exp 3 (.344 ) ( u) (5) = ] (6) P =.363exp ( 4.6u) f 1 exp n 38.7 (7) P4 = exp (8) Whee f n GHz.mm is the fequency nomalized with espect to the substate height, Theefoe, ( ω) fh f n = (9) 6 1 ( ) ( ω) ( ω ) = = = (14) ω b ( ) b ( ) w ( ω) h w 1 = = h ( ω ) ( ) ( ) ω (1) 1 = 1 (11) 1+ whee = o (w/h). Fo simplicity, the coicients of Eqn. (11) ae defined as follows: ( ) ( ) ω 1 b = 1 (1) 1+ If G (conductance pe unit length) and (esisto pe unit length) ae neglected, the chaacteistic impedance can be witten as: = (13) To obtain the fequency-dependent chaacteistic impedance ( (ω)), the fequency-dependent capacitance ((ω)) of Eqn. (11) is substituted into the capacitance () in Eqn. (13). The esulting fequency-dependent chaacteistic impedance is then given by: Now, the fequency-dependent (lossy) Smith-chat can be constucted by applying (ω) in Eqn.(14) into the nomalized teminal impedance expession following the pocedue as 36

4 Micostip Antenna fo Wieless AN Applications that fo a standad Smith-chat [9]. Hence, the esulting nomalized teminal impedance z is given by z = = b + ( ω ) jbx (Dimensionless) (15) whee and x ae the nomalized esistance and nomalized eactance, espectively. oesponding, the voltage eflection coicient of pesent Smith chat can be expessed as: z 1 Γ = Γ+ jγ= i (16) z + 1 o ( 1+ Γ ) + jγ i z = = b + jbx = (17) ( ω ) ( 1 Γ ) jγ i j1. Now, the desied set of equations depicting the modified Smith-chat ae: ' b ' 1 Γ + Γi = 1+ b ( 1+ b) (18) and ( ) j.5 j. ' ' 1 1 Γ 1 + Γi = (19) bx bx An example of Modified Smith-chat is given in Fig.. This figue is a compaison of an oiginal Smith-chat and modified Smith-chat, which calculated fom the geomety of a micostip antenna fo a wieless AN system with opeating fequency at.45 GHz. Fig. shows that the ect of amic pemittivity will lead to a modification of the Smith chat. - j.5 - j. - j1. Oiginal Smith chat Modified Smith chat Intenational Jounal of The ompute, The Intenet and Management, Vol. 11, No.3, 3, pp

5 Fig. : Oiginal Smith chat compaed with modified Smith chat fo coax-fed ectangula micostip patch antenna opeating at.45 GHz, =4.53, =5 Ω, H=.3cm, =.78cm, W=.85cm. 3 INPUT IMPEDANE OF THE fequency; and f is the esonant fequency. MIOSTIP PATH ANTENNA It can be witten as [1]: A micostip antenna may be excited o fed by diffeent types of tansmission lines, fo example coaxial, micostip, o coplana. Two diffeent types of feed ae shown in Figs. 3 (a) and (b). The adiating elements may be fed diectly, with electical continuity between the conducto of the tansmission line and the conducting patch. On the othe hand, the micostip patch antenna fed by a tansmission line behaves as a complex impedance in = ( + jx), which depends mainly on the geomety of the coupling between the tansmission line and the antenna. H W W W (a) (b) Gound plane Fig. 3: Geomety of a ectangula micostip patch antenna (a) coax feed. (b) diect feed The input impedance of the stuctue shown in Fig. 3 is given by [1]: ( f ) f f f f T = + j X 1+ f f f f 1+ f f f f T T () whee is the esonant esistance including the influence of the finging field at the edges of the patch; f is the opeating = πf H πx cos W T (1) whee is the amic pemittivity. T is the quality facto associated with system losses, which include adiation fom the wall ( ), osses in the dielectic ( D ) and osses in the conducto ( ). is calculated by [1]: T T = + + () D whee, and ae given below D c = (3) 4 f H 1 D = (4) Tgδ ( W ).786 f ao H = fo coppe; f in GHz Pa (5) ) whee ao (W is the impedance of an ai filled micostip line of width (W) and thickness (H). ao (W ) is evaluated by setting =1. The impedance of a dielectic filled line can be witten as [1]: a ( W) 6π W 1 = H, W H > 1 ( + 1) π 1 W n +.94 H 38

6 Micostip Antenna fo Wieless AN Applications (6) () = () + () + (), e1, e, (31) and W ( πh ) ( H ) + W H π H W W P a = W W + n π exp +.94 H π H, W H (7) To take the ect of coax-feed pobe (Fig. 3) into account, it is necessay to modify the input impedance by an inductive eactance tem [11], given by X 377 fh = n c fd c π (8) whee c o is the velocity of light in vacuum and d o is the diamete of the pobe. f = f mn c = m n + W e ff (9) whee W is the ective width, is the ective length and is the amic pemittivity which is a function of dimension (W,, H) [1]: ( ) ( ) = (3) whee () epesents the total amic capacitance of the patch in the pesence of a dielectic of elative pemittivity and ( ) epesents the total amic capacitance of the patch in the pesence of ai, () can be witten as whee, () is the amic main field of the patch capacitance without consideing the finging field. e, () is the amic edge field of the patch capacitance with consideing the finging field fo each side of the patch, which can be expessed by [1]: () W (), stat, = = (3) Hγ nγ m γ nγ m whee,stat () epesents the static main capacitance of the patch without consideing the finging field and γ n and γ m ae in the fom: 1 fo i = γ i = (33) fo i Assuming that the edge-field of the esonato has an x- and y- dependent field distibution, the amic finging capacitances ae then given in the geneal fom by [1]: e1, e, ( ) ( W, H, ) = 1 W ( W, H ) H 1 1 = γ n c, ( ) (34) 1, H, = 1 1 = W γ m c H H,, (35) whee (W,H, ) is the chaacteistic impedance of the micostip line [1], [13]. Intenational Jounal of The ompute, The Intenet and Management, Vol. 11, No.3, 3, pp

7 If the ect of the stip thickness is neglected, ( W, H, ) W W = ( ) n H H W (36) Howeve, in the poposed model, moe accuate expession fo the chaacteistic impedance [3] is consideed. It is given by: 377 ( W, H, = 1) = n π ( W H ) = 6 + ( 6) f π f ( W H) + 1+ ( W H) ( W H) (37) exp ( ) W H (38) To evaluate,the following simple equation fom [14] is adopted [1]: ( W ) = W H (39) To obtain ( ), can be eplaced by in all of the above equations. To take the ect of the finging field at the cones and the dielectic inhomogeneity [1] of the ectangula micostip patch antenna, the W and can be calculated fom the following elation: ( W ) +.3 ( W ). 58 = Weq W + whee W eq is the equivalent width (4) W eq 1πH = (41) a ( W ) ( W ) Similaly, we can calculate W fom equation (4) and (41) by eplacing,, W eq, W with W, W, eq, espectively. 4 ANTENNA SYSTEM IN WIEESS OMMUNIATION APPIATIONS (ISM BAND):DESIGN ONSIDEATIONS In this section, the applications of the modified Smith-chat on the ectangula micostip patch antenna design ae illustated. The esults of modified Smithchat model ae compaed with the esults by using the method in [1], [16]. They ae also compaed with measued values [15] concening the fundamental mode (m =, n = 1). In Table 1, the esults on esonant fequency ae pesented. It can be seen that the esults of the poposed model ae bette than those pedicted by [1] and [16] and ae in good ageement with expeiment [15]. Figs. 4 and 5 show the input impedance fo a patch antenna opeating at 4.5 GHz and 3.7 GHz, espectively. The poposed model esults ae compaed with the computed esults in [1] and measued data of [1]. The esults indicate that the poposed model gives esults close to the expeimental data. It can also be obseved that the pesent esults ae bette than those pedicted in [1]. The eason is that, in the poposed model, the fequency-dependent chaacteistic impedance is moe compehensively addessed included in the algoithm so that possible eos in the high fequency ae educed. 4

8 Micostip Antenna fo Wieless AN Applications Table 1. ompaisons of measued and calculated esonant fequency of a ectangula micostip patch antenna ( =.33) Dimension (cm) esonant Fequency ( f,ghz ) W H Measue [15] James [16] Abboud [1] Model j1. j GHz popose calculate measue - j GHz - j1. Fig. 4: Input impedances of coax-fed ectangula micostip patch antenna Intenational Jounal of The ompute, The Intenet and Management, Vol. 11, No.3, 3, pp

9 =.55,Tg =., H=.159cm, =.17cm, =5 Ω, mode (m=,n=1), =.1cm, σ d W=.1cm, X j1. =.13cm. j GHz 3.9 GHz popose calculate measue -j.5 -j1. Fig. 5: Input impedances of coax-fed ectangula micostip patch antenna =4.53,Tg =.5,H=.3cm, =.65cm, =5 Ω, mode (m=,n=1), =1.74cm, σ d W=.31cm, X =.55cm. 5 DESIGN OF MIOSTIP ANTENNA FO A WIEESS AN APPIATION BY USING MODIFIED SMITH-HAT EPESENTATION To design a micostip antenna fo wieless AN applications, designes must know an opeating fequency of wieless AN systems. In the United States, the Fedeal ommunications ommission (F) govens adio tansmissions, including those employed in wieless ANs. Othe nations have coesponding egulatoy agencies. Wieless ANs ae typically designed to opeate in potions of the adio spectum whee the F does not equie the end-use to puchase license to use the aiwaves. In the U.S. most wieless ANs boadcast ove one of the ISM (Instumentation, Scientific, and Medical) bands. These include 9-98 MHz, GHz, GHz, and GHz. Fo wieless ANs to be sold in a paticula county, the manufactue of the wieless AN must ensue its cetification by the appopiate agency in that county. In this section, the poposed Smith-chat is utilized to design a ectangula micostip antenna fo wieless AN applications. Fo the pesent design, the ectangula micostip antenna has a substate with dielectic constant ( ) of 4.53 and the antenna is a coax-fed type. The size of the patch is.85 cm (w).78 cm ( l ) (at f =.45 GHz) and a thickness of h =.3 cm. Fig. 6 shows the input impedance fo this patch antenna model. 4

10 Micostip Antenna fo Wieless AN Applications j1. j GHz. 51 GHz - j.5 - j1. Fig. 6: Input impedances of coax-fed ectangula micostip patch antenna opeating at.45 GHz =4.53,Tg σ =.,H=.3cm, d =.5573cm, =5 Ω, =.78cm, W=.85cm, = cm, mode (m=,n=1). X 6 ONUDING EMAKS The use of modified Smith-chat is poved to be a method epesenting the fequency-dependent chaacteistics of micostip antennas fo wieless AN applications. The pesent study demonstates the feasibility of a cohesive pesentation of the dispesion (lossy and lossless) chaacteistics of a micostip line, which is compatible fo AD ots. elevant simulations show that the input impedances calculated fom the model ae moe accuate than those fom the Abboud s model by compaing to the measue, as illustated with an example of a patch antenna. In summay, the technique descibed in this pape offes a stategy fo potaying the fequency-dependent chaacteistics of micostip antennas via a modified Smith-chat epesentation fo wieless AN applications. EFEENES [1] M. Kobayashi, A dispesion fomula satisfying ecent equiement in Intenational Jounal of The ompute, The Intenet and Management, Vol. 11, No.3, 3, pp

11 micostip AD, vol. 36, pp , Aug [] P. Pamanick and P. Bhatia, An accuate desciption of dispesion in micostip, Micowave J., vol. 6, no. 1, pp. 89-9, Dec [3] E. Hammestad and O. Jensen, Accuate models fo micostip compute aided design, IEEE MTT-S Int. Micowave Symp. Dig., New Yok, NY, June 198, pp [4] E. Yamashita, K. Atsuki, and T. Veda, An accuate dispesion fomula of micostip line fo compute-aided design of micowave integated cicuits, IEEE Tans. Micowave Theoy Tech., vol. MTT-7, pp , Dec [5] M. Kischning and. H. Jansen, Accuate model fo ective dielectic constant with validity up to millimete-wave fequency, Electon. ett., vol. 18, pp. 7-73, Jan [6] A. K. Vema and. Kuma, New empiical unified dispesion model fo shielded-, suspended-, and compositesubstate micostip line fo micowave and mm-wave applications, IEEE Tans. Micowave Theoy Tech., vol. MTT-46, pp , Aug [7] A. K. Vema and. Kuma, A new dispesion model fo micostip line, IEEE Tans. Micowave Theoy Tech., vol. MTT-46, pp , Aug [8]. S. Walke, apacitance, Inductance and osstalk Analysis, Nowood, MA: Atech House, 199. [9] J.. Feeman, Fundamentals of Micowave Tansmission ines, John Wiley & Sons, Inc., NewYok, [1] F. Abboud, J. P. Damiano, and A. Papienik, Simple model fo the input impedance of coax-fed ectangula micostip patch antenna fo AD, IEE Poc. H, Micowaves, Antenna & Pogag., vol. 135, pp , [11] M. D. Deshpande and M.. Bailey, Input impedance of micostip antenna, IEEE Tans. Antennas Popagat., vol. 3, pp , Dec [1] K.. ave and E.. offey, Theoetical investigation of the micostip antenna, Technical epot 99. Physical Science aboatoy, New Mexico State Univesity, as uces (New Mexico), [13] K.. Gupta,. Gag, and I.J. Bahl, Micostip lines and slotlines, (Atech House, Dedham, 1979) [14] M.V. Schneide, "Micostip lines fo micowave integated cicuits", Bell System Technical Jounal, vol. 48, pp , [15] E. hang, S.A. ong and W.F. ichads, "An expeimental investigation of electically thick ectangula micostip antenna", IEEE Tans. Antenna Popagat., vol. AP- 34,pp ,1986. [16] J.. James, P.S. Hall and. Wood, Micostip antenna theoy and design, Stevenage,U.K., Pete Peeginus td,