790 M. İLARSLAN, S. DEMIREL, H. TORPI, A. K. KESKIN, M. F. ÇAĞLAR, OPTIMIZATION OF FILTER BY USING SUPPORT VECTOR Optmzaton of Flter by usng Support Vector Regresson Machne wth Cuckoo Search Algorthm Mustafa İLARSLAN 1, Salh DEMIREL 2, Hamd TORPI 2, A. Kenan KESKIN 2, M. Fath ÇAĞLAR 3 1 Turksh Ar Force Academy, 34149, Yeşlyurt, Istanbul, Turkey 2 Dept. of Electroncs and Communcaton Engneerng, Yıldız Techncal Unversty, Turkey 3 Dept. of Electroncs and Communcaton Engneerng, Süleyman Demrel Unversty, Turkey m.larslan@hho.edu.tr, salhd@yldz.edu.tr, torp@yldz.edu.tr, kkeskn@yldz.edu.tr, mfcaglar@gmal.com Abstract. Heren, a new methodology usng a 3D Electromagnetc (EM) smulator-based Support Vector Regresson Machne (SVRM) models of base elements s presented for band-pass flter (BPF) desgn. SVRM models of elements, whch are as fast as analytcal equatons and as accurate as a 3D EM smulator, are employed n a smple and effcent Cuckoo Search Algorthm (CSA) to optmze an ultrawdeband (UWB) mcrostrp BPF. CSA performance s verfed by comparng t wth other Meta-Heurstcs such as Genetc Algorthm (GA) and Partcle Swarm Optmzaton (PSO). As an example of the proposed desgn methodology, an UWB BPF that operates between the frequences of 3.1 GHz and 10.6 GHz s desgned, fabrcated and measured. The smulaton and measurement results ndcate n concluson the superor performance of ths optmzaton methodology n terms of mproved flter response characterstcs lke return loss, nserton loss, harmonc suppresson and group delay. Keywords Cuckoo Search Algorthm, optmzaton, ultrawdeband, band-pass flter, Support Vector Regresson Machne (SVRM). 1. Introducton In mcrowave and wreless systems, 3.1-10.6 GHz ultra-wdeband (UWB) communcaton band, whch has been dedcated by the Federal Communcatons Commsson (FCC) snce February 2002 [1], has a sgnfcant role because of ts hgh data-rate, large channel capacty, low power consumpton, mmunty to multpath nterference and coexstence wth other wreless systems. Wth these advantages, UWB communcaton systems contnue to attract attenton as a popular research feld n both academa and ndustry. It s ncontestable that one of the essental components n UWB RF front-end modules s the band-pass flter (BPF) and hence, BPF desgn takes a crtcal role n UWB communcaton. Band-pass flters are vtal buldng blocks whch allow a sgnal to pass at requested frequences and repel the rest of frequences n recever and transmsson systems. In RF and mcrowave communcaton systems, compactness, low nserton loss at the transmsson band and hgh suppresson at the rejecton band are crucal parameters n order to desgn a well-suted BPF [2]. Dfferent knds of UWB BPF desgn methods and technologes have been nvestgated for many years n the lterature [3-11]. As a flter realzaton technology, mcrostrps are thoroughly employed because of ther low cost, easy fabrcaton and ntegraton [12], [13]. Accurate and fast UWB BPF desgn s a dffcult optmzaton problem as each part of the crcut hghly affects the frequency response of the flter to a certan extent. Snce there are no analytcal models of elements, 3D EM smulators should be used n the desgn process whch thereby consumes a lot of tme and CPU resources. In ths paper, an accurate and faster methodology for desgnng a mcrostrp UWB BPF s demonstrated. Ths method uses the very popular Support Vector Regresson Machne (SVRM) [14-16] whch s traned by 3D EM smulator results of the desred mcrostrp shapes gven as the basc desgn blocks and then combnes the blocks to construct the BPF wthn an effcent and robust optmzaton process n accordance wth the requred desgn objectves. Thus, ths method not only avods the slowness of 3D EM smulators, but s also as accurate as these smulators. Moreover, the easy mplementaton of dfferent knds of shapes and technologes lke strp lnes s one of the promnent features of ths novel desgn methodology. As an applcaton example, an UWB BPF s desgned by usng three base fundamental shapes; Shunt Stub (SS), Etched Square Stub () and Defected Ground Structure (DGS). SWRM and Cuckoo Search Algorthm (CSA) are utlzed together n the analyss and desgn of the BPF. In recent years, Cuckoo Search Algorthm has become very popular as a new optmzaton method amongst the academc communtes of varous engneerng dscplnes [17], [18]. It was frst proposed by Xn-She Yang and Suash Deb n 2009 and ts performance was tested by
RADIOENGINEERING, VOL. 23, NO. 3, SEPTEMBER 2014 791 usng standard test functons. The results were superor when compared wth other popular meta-heurstc optmzaton methods lke Genetc Algorthm (GA) and Partcle Swarm Optmzaton (PSO). In ths study, the tranng data sets for the desred bass shapes are created frst by usng the 3D Computer Smulaton Technology Mcrowave Studo (CST MWS) and then the SVRM model of each shape s constructed wth these data sets. Then, the output of the obtaned SVRM models are fed nto the CS optmzaton algorthm untl the BPF desgn s optmzed accordng to the desgn goals. The performance of the CSA s compared wth the standard Meta-Heurstcs; Genetc Algorthm (GA) and Partcle Swarm Optmzaton (PSO) methods. Fnally, the desgned UWB BPF s fabrcated and measured. Ths paper s composed of 5 sectons: After the ntroducton, the next secton states the characterstcs and desgn of the base elements and the SVRM model buldng. In the thrd secton, the Cuckoo Search Algorthm (CSA) s presented for optmzng the defned cost functon by makng use of the SVRM models. The desgn procedure and fabrcaton of the UWB BPF s gven n Secton 4 and fnally, Secton 5 s for the concluson. 2. Base s In ths study, 3 knds of resonator types whch are llustrated n Fg. 1-3 are used as the base elements for the UWB BPF desgn. DGS r DGS W up W DGS up Fg. 3. Defected Ground Structure wth mcrostrp lne base element. Shunt Stub (SS) behaves lke hgh pass, Etched Square Stub () works lke band stop, whle Defected Ground Structure (DGS) shows band stop and low pass characterstcs. Operatonal parameters of the resonators are manpulated by ther geometrcal dmensons wthn the lmtatons of the flter. These lmtatons could arse from the desgn objectves such as compactness and the frequency response of the flter. In the desgn, RO-4350 materal whch has a delectrc permttvty (ε r ) of 3.48, substrate thckness (h) of 1.52 mm, copper thckness (t) of 35 μm and a tangent loss (tanδ) of 0.002 s utlzed as the substrate. 3. Desgn Synthess and Optmzaton Process W SS Fg. 1. Shunt stub base element. up n W up W n SS W Fg. 2. Etched Square stub base element. 3.1 Mathematcal Bases of Support Vector Regresson Gven the tranng dataset ( x, y ), = 1,2,, where y R and s the sze of the tranng data, Support Vector Regresson Machne (SVRM) attempts to construct a contnuous mappng functon f ( x ) from the ndependent p-dmensonal nput varable vector x to the dependent output varable y by lnearly combnng the results of a nonlnear transformaton of the nput samples: ( ) n sv ( ) (, ) 1 f x K x x b (1) where n sv s the number of the Support Vector (SV)s, 0, 0 are Lagrange multplers and b s bas parameter, K s a kernel functon whch performs the nonlnear transformaton and n practce, s drectly defned. The measure of how well a sample s ftted by the functon f s gven by a so-called ϵ- nsenstve loss functon [14] descrbed by L( f( x) y) y f( x) max 0, y f( x) (2)
792 M. İLARSLAN, S. DEMIREL, H. TORPI, A. K. KESKIN, M. F. ÇAĞLAR, OPTIMIZATION OF FILTER BY USING SUPPORT VECTOR where ϵ s the radus of the regresson tube and the dstance among the predcted and target values for the tranng samples s defned as the emprcal rsk as follows: 1 R L( x, y, f). (3) emp 1 Therefore, n SV regresson, the goal s to mnmze R emp. In order to make support vector regresson, mnmzaton of the emprcal rsk formulaton (3) s transformed nto maxmzaton of equaton (4). Usng the standard Lagrange multplers technque, the aforementoned mnmzaton problem can be transformed nto Constraned Quadratc Programmng (CQP) n whch the followng functon must be maxmzed wth respect to the Lagrange parameters (α, α) [14]: MaxmzeW (, ) nsv nsv nsv 1 j j K x xj 2, 1 y j 1 1 ( )( ) (, ) ( ) ( ) subject to: 0 C, 0 C, 1 1 (4) (5) where ndex represents support vector elements of the tranng data and ndex j represents rrelevant elements remanng from the tranng data. The parameter C 0 measures the trade-off between the capabltes of f ( x ) to approxmate the nput samples and the error of the new samples. The CQP can be solved usng standard optmzaton technques subject to the condtons gven by (5) and the result n Lagrange multpler pars (, ). The parameter b can be computed by means of so-called Karush-Kuhn-Tucker condtons [14], [15], [16]. Snce the nsenstve loss functon gven by (2) apples the ϵ- tube selecton process to the tranng dataset ( x, y), = 1,2,...,, thus only for the samples satsfyng f( x) y, the Lagrangan multplers (, ) may be nonzero, and for the samples of f( x) y, the Lagrangan multplers (, ) vansh. The samples ( x, y), = 1,2,, n that come wth non-vanshng coeffcents are called Support Vectors (SV). Therefore, we sv obtan a sparse expanson of the Lagrangan multplers (, ) n terms of the nput varable vector x. In other words, we perform generalzaton between the whole nput x - and output y- domans usng only a small subset of the tranng data that ensures enormous computatonal advantages [14]. 3.2 3D EM Smulaton-based SVRM Mcrostrp Modelng In order to obtan accurate and fast desgn UWB BPF, the SVRM model of basc elements s employed. Blackbox models of each element are created, ncludng geometrcal dmensons of elements as nput parameters and S parameters of element as output parameters. Input varable vectors of SS, and DGS models are defned as; W,, f, W,,W, up up n n,w,, f and W, SS SS DGS,W,, r, f, respectvely. Output parameters of the DGS up up element models are the same; S, S, S, S, the magntude and phase of S parameters. Snce the SVRM model 11 11 21 21 has one output, a parallel operaton s run to compose the element models. Therefore, each element model contans four machnes whch have the same nput because of the four output parameters. Radal kernel functon s exploted for the SVM regresson whch s descrbed by, x 2 x K( x, x) e (6) where γ s the varance of the kernel functon and wll be chosen n the tranng phase. The tranng dataset of base elements s obtaned by CST Mcrowave Studo wthn the physcal ranges gven n Tab. 1. Base SS DGS Input Mn. Max. Data Interval Varables Value Value Number W SS (mm) 0.2 1 0.2 5 l SS (mm) 3 5 0.2 11 f (GHz) 0.2 25.2 1 26 W (mm) 0.5 1 0.1 5 l (mm) 0.5 1 0.1 5 W up (mm) 1.7 2 0.1 4 l up (mm) 1 1.3 0.1 4 W n (mm) 1 1.4 0.2 3 l n (mm) 0.5 0.7 0.1 3 f (GHz) 0.2 25.2 1 26 W DGS (mm) 0.2 0.5 0.1 4 l DGS (mm) 5 7 0.4 6 W up (mm) 1 2 0.2 6 l up (mm) 2 4 0.2 11 r (mm) 0.2 0.5 0.1 4 f (GHz) 0.2 25.2 1 26 Tab. 1. Dmensonal range of Base s for tranng data. Total tranng data number of neural network for each frequency of SS, and DGS are 55, 3.600 and 6.336, respectvely. Furthermore, n Tab. 2, the accuracy of the models, the Support Vector numbers of S 21, are compared γ C ϵ SS DGS S 21 SVs Number S 11 (%) S 11 (%) S 21 (%) S 21 (%) 0.001 10000 0.05 32 99.8 99.8 99.9 99.6 0.001 10000 0.07 23 99.5 98.1 99.4 99.2 0.001 10000 0.1 14 98.9 97.2 99.0 98.7 0.001 10000 0.05 1617 99.7 98.8 99.6 98.9 0.001 10000 0.07 1272 99.3 98.6 99.1 98.8 0.001 10000 0.1 820 98.1 97.9 98.3 98.5 0.001 10000 0.05 2915 99.2 98.1 99.0 97.5 0.001 10000 0.07 2002 98.5 97.2 97.9 96.6 0.001 10000 0.1 1223 97.2 96.1 96.8 96.0 Tab. 2. Accuracy wth respect to SVRM parameters.
RADIOENGINEERING, VOL. 23, NO. 3, SEPTEMBER 2014 793 for dfferent ϵ nsenstve loss parameters. Tab. 2 gves the used SVRM parameters, selecton tube radus ϵ, number of the SVs and the resulted accuracy for the SVRM model of the S parameters for 7 GHz. The numbers of SVs used to tran the SVRM model for SS, and DGS are 14, 820 and 1223 respectvely, wth the accuracy of at least 96.0%. The smulaton results show that SVRM models of the elements are not only as accurate as the 3D EM smulaton model, but also approxmately 280 tmes faster than the CST model GA, there s essentally only one parameter, P a n CS as the populaton sze (the number of avalable host nests, n) s fxed, makng t very easy to mplement and fast to converge. 3.3 Cuckoo Search Algorthm Smlar to other meta-heurstc optmzaton algorthms, t s a bo-nspred optmzaton algorthm based upon the oblgate brood parastsm of some cuckoo speces n nature whch lay ther eggs n the nests of other host brds. The Cuckoo Search whch dealzes such breedng behavor was proposed by Xn-She Yang and Suash Deb n 2009 and snce then, t has been appled extensvely to varous engneerng optmzaton problems lke antenna array optmzaton [19], data fuson n wreless sensor networks [20], and to mult-objectve desgn optmzaton problems lke relable embedded system desgn [21]. It was also hybrdzed wth quantum computng prncples [22] and wth power seres [23] to obtan better performance. In the CS, each egg n a nest represents a soluton, and a cuckoo egg represents a new soluton. The am s to use the new and potentally better solutons (cuckoos) to replace a not-so-good soluton (egg) n the nests. In the smplest form, each nest has one egg. The CS s bult upon the followng three dealzed rules: Each cuckoo lays one egg at a tme and dumps ts egg n a randomly chosen nest; The best nests wth hgh-qualty eggs wll carry over to the next generaton; The number of avalable host nests, n s fxed, and the egg lad by a cuckoo s dscovered by the host brd wth a probablty P a (0,1). Dscoverng means that some set of worst nests (eggs) wll be thrown away and ther correspondng solutons wll be dscarded from further calculatons. Yang and Deb also dscovered that the random-walk style search s better performed by Lévy flghts rather than by smple random walk. Many studes have shown that the flght behavor of many anmals and nsects has demonstrated the typcal characterstcs of Lévy flghts [17-24]. Lévy flght s defned as a random walk wth the steplengths based on a heavy-taled probablty dstrbuton whch enables CS to explore the whole soluton space effectvely. An mportant advantage of CS algorthm s ts smplcty. In fact, compared wth other populaton or agent-based meta-heurstc algorthms such as PSO and Fg. 4. Flow chart of the conventonal Cuckoo Search Algorthm. Fg. 4 s the flow chart ndcatng the man steps of the regular CS algorthm mplementaton [24]. 3.4 Cost Functon Evaluaton and Updatng Process In mcrowave crcut desgn, two port structures could be demonstrated as cascaded connectons of sub-structures. Thus, crcuts can be solved by usng ABCD parameters of each sub-structure. The total ABCD matrx of a crcut whch s composed of cascaded n two-ports s descrbed by; A B A1 B1A2 B2 An Bn... C D C1 D 1 C2 D 2 Cn D. (7) n In our case, UWB BPF could be consdered by connecton of each basc element n cascade form. The frequency response of the flter s calculated usng (7) and the ABCD parameters of base elements are transformed from S parameters [25] whch are obtaned by SVRM models per the elements dmensons and frequency. There are 2 of SS, 3 of and 4 of DGS n our BPF desgn makng the n = 9. Therefore, the ABCD matrx of the flter s as follows (8-9) n An Bn T Cn D (8) n A B 1 2 4 T T T T... T 3 9 SS 1 DGS 1 1 DGS 1 SS 2 C D (9) Flter
794 M. İLARSLAN, S. DEMIREL, H. TORPI, A. K. KESKIN, M. F. ÇAĞLAR, OPTIMIZATION OF FILTER BY USING SUPPORT VECTOR S parameter of the flter s acqured usng nverse transformaton equatons [25]. Meanwhle, there s no need to nvestgate full S parameters of base elements. The SVRM model results, whch gve us S 11 and S 21 of each elements, are enough to calculate ABCD parameters because of the recprocty S 11 = S 22 and S 12 = S 21 [25]. In the desgn process, the optmal dmensons of the elements for the requred UWB flter response are nvestgated by usng the CS algorthm and SVRM models together under the analytcal combnaton of ABCD parameters subject to cost functon whch s defned as follows (10) Cost Func.. +. +., (10) 1 1 1 2 2 3 3 1 S 11 f1 1 S 21 f2 1 S 11 f3, (11), (12) 2 (13) 3 where f 1 s pcked as 0.2-3.1 GHz to provde suppresson at a lower band (11), f 2 s selected as 3.1-10.6 GHz to obtan pass band characterstcs (12) and f 3 s taken between 10.6-20 GHz to suppress the second and thrd harmonc of the flter (13). Moreover, ω 1, ω 2, ω 3 (10) are chosen as 2/10, 1, 1/10, respectvely. Optmzaton comes to the end when the teraton number s maxmzed or the cost value s mnmzed. 4. Desgn and Comparson of UWB Bandpass Flter In ths secton, the UWB band pass flter desgn process s descrbed and then the results of a specfc desgn example are dscussed. Frst, tranng data sets of bases elements are obtaned wth a 3D EM smulator n order to form fast and accurate SVRM models of SS, and DGS wthn ther physcal lmtatons. Later, these models are employed n the CSA optmzaton process n order to obtan the requred flter specfcatons whch nclude rejecton and pass band characterstcs. The cost functon of CSA s determned usng analytcal calculatons of ABCD parameters for cascade-connected base element SVRM models. The CSA optmzaton process concludes when the teraton number or cost value reaches ts lmts. If the 3D model of basc elements s utlzed nstead of fast SVRM models, the duraton of the optmzaton process would be extremely long. The desgn procedure of the flter s shown n Fg. 5. RO-4350 materal as mentoned n Secton 2 s used for fabrcaton of the desgned flter crcut. The am s to desgn an UWB BPF that has an operatonal bandwdth between 3.1 GHz and 10.6 GHz. In order to acheve that, the dmensons of base elements of the flter are adjusted usng the optmzaton process. After the optmzaton, the Base SS DGS Fg. 5. General desgn procedure for the BPF. Fg. 6. Scaled flter drawng wth grd background. Input Varables 1. 2. 3. 4. W SS (mm) 0.6 0.8 - - l SS (mm) 4 4.2 - - W (mm) 0.6 0.7 0.6 - l (mm) 0.7 0.6 0.7 - W up (mm) 2 1.7 2 - l up (mm) 1.1 1.2 1.1 - W n (mm) 1.2 1 1.2 - l n (mm) 0.6 0.5 0.6 - W DGS (mm) 0.3 0.4 0.3 0.2 l DGS (mm) 5.4 5.8 6.2 5 W up (mm) 1.6 1 1 1.6 l up (mm) 2.4 3.8 3.8 2.4 r (mm) 0.2 0.3 0.3 0.2 Tab. 3. Soluton of the base elements.
RADIOENGINEERING, VOL. 23, NO. 3, SEPTEMBER 2014 795 20 x 10-10 15 (a) Group delay (ns) 10 5 0 In-Band (b) Fg. 7. Photographs of the fabrcated UWB BPF: (a) top layer, (b) bottom layer. desgned crcut s manufactured and measured. The total sze of the flter whose scaled drawng and the actual pcture can be seen n Fg. 6 and Fg. 7 respectvely s about 2.5 cm 1.5 cm. The actual dmensons of each base element used n the desgn are gven n Tab. 3. The smulaton and actual measurement results are n parallel wth each other as gven n Fg. 8. It s understood from the results that nserton loss, whch ncreases wth frequency, s better than -2 db over the whole transton band and there s extra loss at the end of the transton band because of the SMA connectors utlzed n the ports. Moreover, there s good suppresson whch s better than 10 db untl 25 GHz whch contans the second and thrd harmonc at the rejecton band. Return loss s under -10 db at pass band. In addton, the low and hgh cut-off regons of frequency response show that the flter has good sharpness. Furthermore, the desgned flter has a flat group delay over the whole operaton band, as can be seen n Fg. 9. In the CS optmzaton process, number of host nest (sze of populaton), and fracton probablty (P a ) s chosen as 50 and 0.25, respectvely as they provded the best results. 10 0-5 0 5 10 15 20 25 Frequency (GHz) Fg. 9. Measured group delay of the desgned UWB BPF. In order to compare t wth other Meta-Heurstcs, the PSO optmzer s constructed wth the populaton (partcle number) equal to 50, max/mn velocty of ±0.1 and learnng factors set to 2.0, respectvely. Smlarly, the GA optmzer has a populaton (chromosome) of 50, crossover probablty of 0.8, and mutaton probablty of 0.1. The cost results of 30-tme tres and 120 teraton of CSA and other standard Meta-Heurstc algorthms and benchmarkng at 120 th teraton for best try wth the correspondng executon tmes for the same flter are shown n Tab. 4. Algorthm Worst (max) Best (mn) Average (mean) Executon Tme (s) CSA 2.687 0.266 0.813 131 GA 4.999 0.677 2.017 180 PSO 2.158 0.301 1.110 136 Tab. 4. Comparson of the CSA performance wth the Standard Meta-Heurstc Algorthms. A desktop computer wth Intel Core 7 CPU, 2.20 GHz Processor, 8 GB RAM s used for the desgn and optmzaton process. At end of the optmzaton, the teraton number reaches 65 and the cost value of the operaton s equal to 0.266. It s clear from Tab. 4 that CSA has a superor performance wth respect to other popular Meta-Heurstcs. S Parameter (db) -10-20 -30-40 -50-60 S 21 CST Result S 21 Measured S 11 CST Result S 11 Measured -70 0 5 10 15 20 25 Frequency (GHz) Fg. 8. Smulated and measured S parameters of the desgned UWB BPF. 5. Conclusons In ths paper, a novel desgn methodology whch uses fast and accurate SVRM models of base elements based on a 3D EM smulator s presented to desgn and analyze an UWB BPF. The outputs of the bult SVRM models are used as nput by a straghtforward, smple and effcent CS algorthm under the rules of crcut theory to solve the flter response. The desgned flter s manufactured and measured to show that the actual results are n concdence wth the smulaton results. Furthermore, the performance of the CS algorthm s compared wth other popular methods lke GA and PSO to demonstrate the effcency of the CS algo-
796 M. İLARSLAN, S. DEMIREL, H. TORPI, A. K. KESKIN, M. F. ÇAĞLAR, OPTIMIZATION OF FILTER BY USING SUPPORT VECTOR rthm. The suggested methodology could be used for dfferent knd of element shapes and flter types. Consequently, the proposed desgn methodology could be consdered as an mportant contrbuton to the mcrowave desgn lterature. References [1] Federal Communcatons Commsson, Revson of Part 15 of the commsson's rules regardng ultra wdeband transmsson system frst report and order. Tech. Rep., ET Docket 98-153, FCC02-48, FCC, Feb. 2002. [2] MATTHAEI, G. L., YOUNG, L., JONES, E. M. T. Mcrowave Flters, Impedance-matchng Networks, and Couplng Structures. Norwood: Artech House, 1980. [3] OSKOUEI, H. D., FOROORAGHI, K., HAKKAK, M. Guded and leaky wave characterstcs of perodc defected ground structures. Progress In Electromagnetcs Research, PIER 73, 2007, p. 15 27. [4] WU, B., LI, B., SU, T., LIANG, C. H. Equvalent-crcut analyss and lowpass flter desgn of splt-rng resonator DGS. 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Mustafa ILARSLAN was graduated from the Mddle East Techncal Unversty of Ankara n 1989, wth a B.Sc. degree n Electrcal & Electroncs Engneerng. He receved M.Sc. degree n Electroncs Engneerng from the Osmangaz Unversty of Esksehr, Turkey. He has been the drector of Aeronautcs and Space Technologes Insttute of TurAFA located n Istanbul, Turkey snce March 2011. Hs research nterests are arcraft and spacecraft avoncs, systems engneerng, radar and EW systems and technologes. Salh DEMIREL has receved M.Sc. and Ph.D. degrees n Electroncs and Communcaton Engneerng from Yıldız Techncal Unversty, Istanbul, Turkey n 2006 and 2009, respectvely. He has been currently workng as an Assstant Professor n the same department. Hs current research nterests are among of mcrowave crcuts especally optmzaton of mcrowave crcuts, broadband matchng crcuts, devce modelng, computer-aded crcut desgn, mcrowave amplfers.
RADIOENGINEERING, VOL. 23, NO. 3, SEPTEMBER 2014 797 Hamt TORPI has receved M.Sc. and Ph.D. degrees n Electroncs and Communcaton Engneerng from Yıldız Techncal Unversty, Istanbul, Turkey n 1990 and 1996, respectvely. He has been currently workng as an Assstant Professor n the same department. Hs current research nterests are n the areas of multvarable network theory, devce modelng, computer-aded mcrowave crcut desgn, monolthc mcrowave ntegrated crcuts, and antennas. A. Kenan KESKIN has receved M.Sc. degree n Electroncs and Communcaton Engneerng from Yıldız Techncal Unversty, Istanbul, Turkey n 2012. He has been currently workng as a Research Assstant and studyng as a Ph.D. student n the same department. Hs current research nterests are mcrowave crcuts, computer-aded crcut desgn, UWB antennas, ground penetratng radars. M. Fath ÇAGLAR, receved hs B.Sc. degree n Electroncs and Communcaton Engneerng from the Istanbul Techncal Unversty n 1996 and M.Sc. degree n Electroncs and Communcaton Engneerng from the Suleyman Demrel Unversty, n Isparta, n 1999. He had hs Ph.D. degree from the Yıldız Techncal Unversty n Istanbul n Communcaton Engneerng n 2007. Hs current research nterests are among of RF/mcrowave crcuts, especally modelng of mcrowave crcuts, computer-aded crcut desgn and Artfcal Neural Networks.