Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology, 4(), 20, pp. 67-7 SUPPORT VECTOR MACHIE FOR BADWIDTH AALYSIS OF SLOTTED MICROSTRIP ATEA Venmathi A.R. & Vanitha L. 2 Depatment of Electonics Communication Engineeing, Kings Engineeing College, Iungattukottai, Chennai, India, (avenmathi@yahoo.co.in) 2 Depatment of Electonics Communication Engineeing, Si Venkateswaa College of Engineeing, Sipeumbadu, Chennai, India, (vvanetha@yahoo.com) Abstact: In this wok, the Suppot Vecto machine (SVM) is adopted fo analysis of slotted micostip ectangula patch antenna, which is a technique based on the igoous mathematical fundamentals. SVM is one of the most competitive techniques to the popula atificial neual netwoks. In this design pocess, accuacy, computational efficiency of Suppot Vecto Machine is compaed to atificial neual netwok pefomance. It can be concluded that the atificial neual netwok may be eplaced by the Suppot Vecto Machines due to its high appoximation capability and much faste convegence ate. Keywods: Suppot vecto machine, slotted micostip antenna, EM Simulato. ITRODUCTIO In high-pefomance spacecaft, aicaft, missile and satellite applications, whee size, weight, cost, pefomance, ease of installation, and aeodynamic pofiles, ae constaints, low pofile antennas ae equied. To meet these equiements, micostip antennas ae used [ 4]. In the liteatue, atificial neual netwok (A) models have been built fo the design and analysis of micostip antennas [5]. Many new tools fo micowave CAD ae developed duing the past decades. Models ae geneally developed using analytical, electomagnetic simulation, and/o measuement based methods. Accuate and efficient models fo cicuit components ae essential fo costeffective cicuit design. The advantage of neuo computing is that, afte pope taining, a neual netwok completely bypasses the epeated use of complex iteative pocesses fo new cases pesented to it. The single netwok stuctue can pedict the esults fo patch antenna povided that input values ae in the domain of taining values. Suppot Vecto Machines (SVM) and kenel methods, which enable to genealize discete data into the continuous domain have become one of the most popula leaning machines in the last few yeas. In paticula, suppot vecto machines ae based on a judicious and igoous mathematics combining the genealization and optimization theoies togethe and veified to be computationally vey efficient (the so-called Vapnik- Chevonenkis theoy [6] [7]). This leaning machine has found many fuitful applications in science and engineeing. Inset feed micostip antenna with slots in it impoves the antenna bandwidth compaed to antenna without slots of the same physical dimensions [8]. In the pesent wok SVM model is developed to analyze the bandwidth of the example antenna. The Method of Moments (MOM) based IE3D softwae has been used to geneate taining and test data fo the SVM. The pape is oganized as follows: Definition of the poblem in section II, the design and data geneation in section III. Section IV gives the theoy of the SVM. Section V includes esults and conclusions. The esults ae compaed with two eual etwok achitectue, Back popagation(bp) and Radial Basis Function(RBF). 2. DEFIITIO OF THE PROBLEM The fequency of a patch antenna can be inceased by a capacitive o inductive load. In this pape, a two slot micostip antenna has been designed to achieve a wide bandwidth. The poposed SVM model calculates the cut off fequencies f and f2 and hence the bandwidths ( f2 - f) of the example antenna fo diffeent coodinates of the slots i.e., X, Y and X2, Y2. The patch dimensions of the antenna as well as that of slot ae kept constant fo this specific model [8].
68 Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology 3. DESIG AD DATA GEERATIO The ectangula micostip antennas ae made up of a ectangula patch with dimensions width ( W) and length ( L) ove a gound plane with a substate thickness h having dielectic constant [8], [9] As an example an inset feed micostip antennas is designed to esonate at 0 GHz fequency with dielectic constant = 4:7, substate thickness h = :588 mm, L = 6 mm, W = 8:88mm on a gound plane. All dimensions of the antenna ae in mm. The length and the width of the patch ae calculated initially by the elationships in equations ()-(6). νo 2 W = 2 f + νo L = = 2 L 2 f eff ( eff ) W + 0.3 + 0.264 L h = 0.42 h W ( eff 0.258) + 0.8 h + h eff = + 2 2 2 + W /2 () (2) (3) (4) L g = 6(h) + L = 6 (.588) + 6 = 5.528mm (5) W g = 6(h) W = 6 (.588) + 8.88 = 8.40mm (6) Figue shows the geomety of inset feed micostip antenna with two slots in the patch. The patch is enegized electomagnetically using 50 ohm micostip feed line. The length of the cuent path is inceased due to the slot which leads to additional inductance in seies. Hence wide bandwidth is geneated as the esonant cicuits become coupled. The slots aggegate the cuents, which give additional inductance contolled by the patch width. The softwae used to model and simulate the poposed micostip patch antenna is Mento Gaphics IE3D softwae. IE3D is a full wave electomagnetic simulato based on the method of moments. IE3D softwae has been used to calculate the etun loss (S) and hence the cut off fequencies f and f2 of the antenna. Fist the example antenna is designed without slots in IE3D EM Simulato with patch dimensions L = 6, W = 8:88 fo esonating fequency of 0 GHz. The bandwidth fo the antenna is aound 450 MHz. The pesent wok signifies that by intoduction of two slots in the same design, the bandwidth gets enhanced about 25%-45%, i.e., fom 450 to 650 MHz. The same antenna is designed in IE3D Simulato fo diffeent coodinate values of both the slots X, Y and X2, Y2 in the specified ange (X = 0; 0.5 < Y < 4 mm, X2 =0;-0.5 < Y2 < -4mm) keeping patch dimensions, slot dimensions, and h constant and the coesponding cut off fequencies ae ecoded and this data has been used as a taining data and test data fo SVM. 4. SVM, ARTIFICIAL EURAL ETWORK AD RADIAL BASIS FUCTIO ARCHITECTURE 4.. Suppot Vecto Machine (SVM) SVM has poven its efficiency ove neual netwoks and RBF classifies. Unlike neual netwoks, this model builds does not need hypothesizing numbe of neuons in the middle laye o defining the cente of Gaussian functions in RBF [4]. SVM uses an optimum linea sepaating hypeplane to sepaate two set of data in a featue space. This optimum hypeplane is poduced by maximizing minimum magin between the two sets [2]. Theefoe the esulting hypeplane will only be depended on bode taining pattens called suppot vectos. The suppot vecto machine opeates on two mathematical opeations: () onlinea mapping of an input vecto into a high-dimensional featue space that is hidden fom both the input and output. (2) Constuction of an optimal hypeplane fo sepaating the featues discoveed in step. Suppot vectos ae detemined by using the equations 7-2. [0, ] Figue : Inset Feed Micostip Antenna with Two Slots. All Dimensions ae in mm 4.2. Vaiable Definition. Let x denote a vecto dawn fom the input space, assumed to be of dimension m o.
Suppot Vecto Machine fo Bandwidth Analysis of Slotted Micostip Antenna 69 2. Let {ϕ j (x)} fo j= to m, denote a set of nonlinea tansfomations fom the input space to the featue space. 3. m is the dimension of the featue space. 4. {w j } fo j= to m denotes a set of linea weights connecting the featue space to the output space. 5. {ϕ j (x)} epesent the input supplied to the weight w j via the featue space. 6. b is the bias 7. α i is the Lagange coefficient 8. d i coesponding taget output. 4.3. Steps Involved in the Design of SVM. Hypeplane acting as the decision suface is defined as Whee α i dik ( x,) xi 0= (7) K(x,x i ) = ϕ T (x)ϕ(x i ) epesents the inne poduct of two vectos induced in the featue space by the input vecto x and input patten xi petaining to the ith example. This tem is efeed to as inne-poduct kenel. whee ϕ 0 (x) = fo all x w = αidiϕ() xi (8) [ 0 ] ϕ ()(),(),...,() x = ϕ x ϕ x ϕ m x (9) w o denotes the bias b 2. The equiement of the kenel K(x,x i ) is to satisfy Mece s theoem. The kenel function is selected as a polynomial leaning machine. K(x,x i ) = ( + x T x i ) 2 (0) 3. The Lagange multiplies {α i } fo i = to that maximize the objective function Q(α), denoted by α 0,i is detemined. T w α d ϕ() x (4) 0 0, i i i ϕ(x i ) is the image induced in the featue space due to x i. w 0 epesents the optimum bias b 0. 4.4. Back Popagation Algoithm These ae supevised netwoks, and also they equie a desied esponse to be tained. The weights of the netwok ae computed by taining the netwok. Atificial neual netwok with one hidden laye and tained by back popagation taining algoithms is used to design micostip antenna. [2],[3] A stuctue (numbe of layes, numbe of neuons in each laye, neuons activation function, leaning algoithm and taining paametes) is not known in advance. Hence the netwok model is analyzed with diffeent numbe of hidden layes in the stuctue and also the numbes of pocessing elements ae also vaied to acquie the accuacy. Hence it is concluded that thee layes one hidden laye and 25 pocessing elements in the hidden laye is the optimum netwok stuctue fo the poposed poblem 4.5. RBF Algoithm Radial basis function(rbf) netwok is a feed fowad neual netwok with a single hidden laye that uses adial basis activation functions fo hidden neuons. It consists of thee layes of neuons, Input, hidden and output. The hidden laye neuons epesent a seies of centes in the input data space. Each of these centes has an activation function, typically Gaussian. The geneation of the centes and thei widths is done using unsupevised k-means clusteing algoithm.the centes and widths ceated by this algoithm then fom the weights and biases of the hidden laye, which emain unchanged once the clusteing has been done. ( ) () Q() α = α α α d K x, x i i j i i j 2 j= Subject to the following constaints: α idi = 0 (2) 0 αi C fo i =,2,..., (3) 4. The linea weight vecto w 0 coesponding to the optimum values of the Lagange multiplies ae detemined using the following fomula: Figue 2: Achitectue of Suppot Vecto Machine
70 Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology 5. SIMULATIO RESULTS The vaious inputs to the netwok ae coodinates of both slots, i.e., X, X2, Y and Y2. The output of the netwok is bandwidth, i.e., f and f2 cut off fequencies. All the netwoks wee tained with 250 samples and tested with 50 samples. Fo Back Popagation etwok, the taining time is 50 seconds and taining pefomed in 290 epochs. Fo Radial Basis Function (RBF) netwok, the taining time is 40 seconds and taining pefomed in 75 epochs. SVM Classifie takes less time fo taining compaed to othe A netwoks Thus SVM pefoms taining in 3 seconds. The esults simulated using IE3D, Back Popagation etwok, RBF and SVM ae tabulated in Table. Figue 3 shows the compaison between the bandwidth obtained by IE3D, Back popagation, RBF and SVM. Table 2 shows the eo calculated in pecentage fo BP, RBF and SVM compaed with IE3D Simulated esults. Table Compaison of Band Width Results of IE3d, A, RBF and SVM BAD WIDTH I GHz L of slot W of X, Y X 2,Y 2 IE3D BP RBF SVM BW without mm slot mm coodinate coodinate slots in GHZ st slot 2 nd slot 5.2 0.2 0,0.5 0,-0.5 0.595 0.592 0.594 0.593 0.45 5.2 0.2 0,0.7 0,-0.7 0.5902 0.5875 0.588 0.590 0.45 5.2 0.2 0,.0 0,-.0 0.5894 0.58 0.5896 0.573 0.45 5.2 0.2 0,.2 0,-.2 0.5922 0.594 0.59 0.592 0.45 5.2 0.2 0,.5 0,-.5 0.598 0.5874 0.5882 0.5980 0.45 5.2 0.2 0,2.0 0,-0.5 0.5849 0.5884 0.5835 0.5800 0.45 5.2 0.2 0,2.5 0,-2.5 0.6032 0.6029 0.6030 0.6029 0.45 5.2 0.2 0,3.5 0,-3.5 0.649 0.6496 0.6490 0.6492 0.45 5.2 0.2 0,4 0,-4 0.6672 0.6508 0.6549 0.6675 0.45 (X, Y) CO-ORDIATES OF SLOT 2 & SLOT Figue 3: Bandwidth Obtained by IE3D, BP, RBF and SVM Methods fo Diffeent Positions of Slot & Slot 2
Suppot Vecto Machine fo Bandwidth Analysis of Slotted Micostip Antenna 7 conventional patches. The pape concludes that esults obtained using SVM techniques ae quite satisfactoy. Figue 4: Gaph Plotted Between the Pecentage of Eo in the y-axis and Slot Co-odinates in the x-axis Table 2 % of Eo Compaed with IE3d Output ERROR I % X, Y X 2,Y 2 BP RBF SVM coodinate coodinate st slot 2 nd slot 0,0.5 0,-0.5 0.05 0.02 0.03 0,0.7 0,-0.7 0.46 0.36 0.02 0,.0 0,-.0.4-0.03 3.07 0,.2 0,-.2-0.30 0.20 0.03 0,.5 0,-.5.79.66 0.02 0,2.0 0,-2.0-0.60 0.24 0.84 0,2.5 0,-2.5 0.05 0.03 0.05 0,3.5 0,-3.5-0.08 0.02-0.02 0,4 0,-4 2.46.84-0.04 6. COCLUSIO The inset fed micostip patch antenna is a vesatile stuctue which can be modified by the addition of simple slots in the design stuctue to ovecome selected limitations of conventional patch antennas. The antenna can povide impoved bandwidth enhancement, unde cetain conditions, while maintaining many of the desiable featues of REFERECES [] D.M. Poza, Micostip antennas, Poc IEEE 80, 79-8, 992. [2] Vandana Vikas Thakae, Pamod Singhal, Micostip Antenna Design Using Atificial eualetwoks, Wiley Peiodicals, 2009. [3] C. A. Balanis, Antenna theoy, 3d Edition, John Wiley and Sons, Hoboken, J, 997. [4] I. J. Bahl and P. Bhatia, Micostip antennas, Atech House, Dedham, MA, 980 [5] R. K. Misha and A. Patnaik, A techniques in micowave engineeing, IEEE Micowave Mag., 55 60, 2000. [6] V.. Vapnik, Statistical Leaning Theoy, ew Yok: Wiley, 998. [7]. Cistianini, and J. Shawe-Taylo, An intoduction to suppot vecto machines (and othe kenelbasedleaning methods), Cambidge Univesity Pess, 2000. [8] V. V. Thakae P. K. Singhal, Bandwidth Analysis by Intoducing Slots In Micostip Antenna Design Using A, Pogess, In Electomagnetics Reseach M, Vol. 9, 07-22, 2009 [9] Hescovici,., ew consideation in the design of micostipantenna, IEEE Tans. on Antennas Popagat., Vol. 46, o. 6, 807-82, Jun. 998. [0] G. Angiulli, M. Cacciola, and M. Vesaci, Micowave Devices and Antennas Modelling by Suppot Vecto Regession Machines, IEEE Tansactions on Magnetics, Vol. 43, Apil 2007. [] uhan Tuke Tokan, Filiz Gunes, Analysis and Synthesis of the Micostip Lines Based on Suppot Vecto Regession, Poceedings of the 38th Euopean Micowave Confeence [2] Simon Haykin, ]eual etwoks A compehensive foundation, Peason Education Asia, 200. [3] Zhang, Q. J. and K. C. Gupta, eual etwoks fo RF and Micowave Design, Atech House Publishes, 2000.