Behavioral Modeling of a C-Band Ring Hybrid Coupler Using Artificial Neural Networks

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1 RADIOENGINEERING, VOL. 19, NO. 4, DECEMBER Behavioal Modeling of a C-Band Ring Hybid Couple Using Atificial Neual Netwoks Edem DEMIRCIOGLU 1, Muat H. SAZLI 1 R&D Satellite Design Depatment, Tuksat AS, Golbasi, 06830, Ankaa Electonics Engineeing Depatment, Ankaa Univesity, Tandogan, 06100, Ankaa edemicioglu@tuksat.com.t, sazli@eng.ankaa.edu.t Abstact. Atificial Neual Netwoks (ANNs) gained impotance on the RF micowave (MW) design aea and behavioal modeling of MW components in the past few decades. This pape pesents a cost effective neual netwok (NN) appoach to ovecome design, modeling and optimization poblems of an 180 o ing hybid couple opeating in C-Band. The poposed NN model is tained by data sets obtained fom electomagnetic (EM) simulatos and neual test esults ae compaed with simulato findings to detemine the netwok accuacy. Moeove, necessay tade-offs ae applied to impove the netwoks pefomance. Finally coelation factos, which ae defined as compaison citeia between EM-simulato and poposed neual models, ae calculated fo each tade-off case. Keywods Atificial Neual Netwoks (ANNs), Ring Hybid Couple (RHC), C-band, optimization, behavioal modeling. 1. Intoduction EM-simulatos ae the design and optimization tools which include specific algoithms and mathematical methods dedicated to solve RF cicuit poblems. In ecent decades, an ANN, knowledge-aided design (KAD), appoach has been developed fo the modeling and optimization of RF MW components. A neual model fo a device o cicuit can be established by using data sets which ae acquied by measuement and simulation esults, though a pocess called taining. Once the netwok is tained, this netwok can be used fo cicuit design to povide instant answes fo tasks it leaned. Successful implementations of linea and nonlinea device tuns neual applications into a eseach aea fo the modeling of vaious MW components [1, ], and MW cicuit design [3, 4, 5]. Recent woks have shown that NN can accuately model components, such as micostip inteconnects [1, 3], vias [3, 5], spial inductos [4], FET devices [1, 6], powe tansistos and powe amplifies [7], coplana waveguide components [3], packaging and inteconnects [8], micostip cicuit design [9], MW filte design [10], etc. This pape discusses the neual modeling of an 180 o RHC fo efficient and obust behavioal estimations unde necessay tade-offs. RHC design paametes ae obtained by confomal mapping based appoximation fomulas. Then Ansoft Designe, which employs Method of Moments (MoM) as the EM poblem solve, is used as EM-simulato to analyze and optimize the hybid design. Subsequently EM-simulato data sets ae utilized fo establishing ANN. Finally neual modeling and simulato esults ae compaed fo each case. Both neual design and EM - ANN compaisons ae simulated in MATLAB by a.33 GHz Intel Xenon x64 pocesso with.33 GHz, 4.00 GB RAM Ring Hybid Couple Design A 3 db, 180 Ring Hybid Couple, also called as the "at-ace couple", is a high-powe capable, fou-pot device, optimized to sum two in-phase combined signals with essentially no loss o to equally split an input signal with no esultant phase diffeence between outputs and inputs. The fouth pot is match teminated. A ing hybid has many applications in RF micowave wold such as mixes, phase shiftes, amplifies, etc. Fig. 1 demonstates an 180 o ing hybid couple whee detailed equations and opeation pocess can be found in the liteatue [11]. Fig o Ring hybid couple.

2 646 E. DEMIRCIOGLU, M. H. SAZLI, BEHAVIORAL MODELING OF A C-BAND RING HYBRID COUPLER USING The simplest and most effective way of epesenting MW components chaacteistic is the scatteing paametes commonly known as S-paametes. The effective dielectic constant and chaacteistic impedance of a ing hybid couple, which is designed using the micostip substate, can be calculated using well-known confomal mapping based appoximation methods such as Wheele, Schneide o Hammestad and Jensen [1, 13]. Wheele Appoximation: The analysis and synthesis equations ae deived based on confomal mapping appoximations of the dielectic bounday with paallel conducto stips sepaated by a dielectic sheet [14]. The chaacteistic line impedance fo wide micostip which has width ove depth atio of (W/d > 3.3) can be expessed as: O 1 ZWd L(,, ) (1) W 1 1 e W 1 e ln4 ln( ( 0.94)) ln d d d 16 The effective dielectic constant fo wide stips which have width ove depth atio of (W/d > 1.3) is given as: eff E D 1 ew 1 e whee D ln 0.94 ln (3) d 16 1 W 1 W and E ln( e ) d d. (4) The chaacteistic impedance fo naow micostip with (W/d 3.3) can be stated as: O 4d 4d ZWd L(,, ) ln ln ln (5) ( 1) W W 1 The effective dielectic constant fo naow micostip with (W/d 3) depending on the chaacteistic impedance is given as following equation. 1 O ln ln eff. (6) Z L The effective dielectic constant which is independent of the chaacteistic impedance, fo naow micostip (W/d 1.3) is given as; 1 A eff (7) A B whee d 1 W A ln 8 ( ) W 3 d and E () (8) B ln ln. (9) 1 Schneide Appoximation: In this appoach, effective dielectic constant and the chaacteistic impedance fomulas ae obtained by ational function appoximation with accuacy of ±.5% fo 0 W/d 10 which is the ange of impotance fo most engineeing applications [15]. 1 d W W ln 8, fo 1 W 4d d O ZL 1 W, (10), fo 1 eff W d d (1 ) d d W W eff (11) d 110 W Hammestad Appoximation: The chaacteistic impedance and effective dielectic constant equations povides eos at least less than those caused by physical toleances and is bette than 0.01% fo W/d 1 and 0.03% fo W/d 1000 [16]. ZL1 (,, ) ( W, d Z ) L W d (1) whee O d d ZL 1( W, d) ln fu 1 W W f d W, (13) u 6 ( 6) exp( ( ) ), (14) 1 1 d ( W, d, ) 1 10 eff W 4 1 ( / 5) 1 4 ab, (15) u u u au ( ) 1 ln( ) ln1 ( ), (16) 49 u b( ) (17) 3 whee u = W/d and η 0 =10π. In this wok, the mathematical appoximations ae employed to analyze the vaious tansmission line chaacteistics and these analysis esults ae inseted in RHC synthesis pocess. Mathematically obtained design paametes ae utilized and some tuning optimizations ae applied though EM-simulato fo accuate design. The simulations ae epeated fo a vaiety of substate pemittivity and height, ing adius and opeating fequency values. 3. Atificial Neual Netwoks (ANNs) ANNs ae infomation pocessing systems, which ae utilized to lean the input-output elationship chaacteistics

3 RADIOENGINEERING, VOL. 19, NO. 4, DECEMBER of the device unde consideation. The ANNs design is inspied fom the human bain s ability to lean fom obsevations. NNs must be fist tained to model electical behavio of linea and nonlinea complex components o systems. These tained neual models can be used to design, model and optimize the focused device by poviding fast simulation answes compaed with computationally loaded numeical solutions, o toughly obtained analytical and limited expeimental esults [17]. The ANN achitectues and leaning algoithms ae the most impotant factos fo developing neual models. The selected achitectue and algoithm vay depending on the focused poblem. The multilaye pecepton neual netwoks (MLPNNs) offe limited complexity and common appoximation capabilities. Thus they ae the most widely used NN achitectues [18, 19]. In this study, MLPNN models with feed-fowad netwok achitectues and vaious taining algoithms ae utilized to solve the modeling poblem of passive micowave devices, which ae stipline and micostip line type ing hybid couples. such as S 11, S 1, S 13, and S 14 pesent the device esponse. Sample data geneated using EM simulations will be used in taining pocess. Once NN is tained, then the neual model can be used fo pedicting the output values coesponding to input vaiables. In NN testing stage, an independent set of input-output samples, called testing data which coves the whole definition space and equally distibuted ove the egession suface between taining data, is used to test the neual model accuacy. When the netwok outputs ae continuous functions of the inputs, modeling poblem is known as egession o function appoximation, which is the most common case in micowave design aea. 3.1 Multilaye Pecepton Neual Netwoks (MLPNNs) Models MLPNNs consist of an input laye, one o moe hidden layes of computation nodes, and an output laye. The input signal popagates though the netwok in a fowad diection, on a laye-by-laye basis. MLPNNs have been applied successfully to solve some difficult and divese poblems by taining them in a supevised manne with a highly popula algoithm known as the eo back-popagation algoithm [0]. Fig. epesents the MLPNN achitectue. Fig.. MLPNN achitectue. Neual models can be constucted to estimate the linea and nonlinea devices behavio. In this study, the geneated ANN is applied to behavioal modeling of a linea ing hybid couple. Input paametes of the ing hybid ae defined as simulation fequency, ing hybid adius, substate height, and pemittivity. Then scatteing paametes Fig. 3. ANN illustation of the discussed modeling poblem. Fig. 3 epesents the poposed neual model fo the micostip line type ing hybid couple modeling poblem, which is elatively complex compaed with single input modeling poblems. The netwok outputs ae the ing couple S-paametes S 11, S 1, S 13, S 14, which clealy demonstate the fundamental chaacteistics of a symmetical MW device. The model inputs ae taken as dielectic substate height d, dielectic substate pemittivity ε, simulation fequency ange f, ing hybid couple adius ad. 3. Backpopagation Taining Algoithms Standad backpopagation is a gadient descent algoithm, as is the Widow-Hoff leaning ule, in which the netwok weights ae moved along the negative of the gadient of the pefomance function. Popely tained backpopagation netwoks tend to give easonable answes when pesented with inputs that they have neve seen. Typically, a new input leads to an output simila to the coect output fo input vectos used in taining that ae simila to the new input being pesented. This genealization popety makes it possible to tain a netwok on a epesentative set of input/taget pais and get good esults without taining the netwok on all possible input/output pais. Once the netwok weights and biases ae initialized, it is eady fo taining. Levenbeg-Maquadt (LM) taining algoithm is a least-squaes estimation method based on the maximum neighbohood idea. LM pesents adequate chaacteistics in convegence time and ability to handle small netwoks. The peeminent aspects of Gauss-Newton technique and steepest-descent method ae combined in this algoithm without many of thei limitations. The eo function can be expessed as below [1].

4 648 E. DEMIRCIOGLU, M. H. SAZLI, BEHAVIORAL MODELING OF A C-BAND RING HYBRID COUPLER USING and m i (18) i1 i ( ) ( di i). (19) Ew ( ) e( w) gw ( ) e w y y whee g(w) is the function containing individual eo tems, y di is the desied value of the output neuon i, and y i is the actual output of that neuon. It is pesumed that, g(w) and its Jacobian J g matix ae known at point w. Jacobian matix contains the fist deivatives of the netwok eos with espect to biases and weights. The weight vecto w is calculated while the eo function is minimized. The subsequent weight vecto w k+1 can be deived fom the peceding weight vecto w k as given below. w w w (0) k 1 k k T T 1 and w ( J g( w ))( J J I) (1) k g k g g whee k is the numbe of iteations, J g is the Jacobian matix of g(w k ) which is computed by taking deivative of g(w k ) with espect to w k, λ is the Maquadt paamete and I is the identity matix. Conjugate Gadient of Polak-Ribièe (CGP) taining algoithm updates the weight and bias values accoding to conjugate gadient backpopagation poposed by Polak-Ribièe, on condition that, netwok weights, inputs and tansfe functions have deivative functions. In this algoithm, the line seach is used to locate the minimum point and the seach diection is computed fom the new gadient in subsequent iteations. The seach diection in each iteation can be detemined by updating the weight vecto []. w k 1 w k p () k whee pk gk kp, (3) k1 T gk 1gk k (4) T g g k1 k1 T T T and gk 1 gk g. (5) k1 Gadient Descent (GD) taining algoithm is a fistode optimization tool which finds the local minimum of the function using gadient descent. This line seach minimization pocedue smoothen the descent diection in the steepest descent method. The weights and biases ae updated in the diection of the negative gadient of the pefomance function [3]. Conjugate Gadient of Fletche-Reeves (CGF) taining algoithm updates weight and bias values by the Fletche-Reeves conjugate gadient fomulas [4]. This algoithm employs the nom squaed of the pevious gadient and the nom squaed of the cuent gadient to pefom the update pocedue and evaluate the weight and bias values [4]. Scaled Conjugate Gadient (SCG) taining algoithm combines the model thust egion appoach used in LM. SCG offes avoiding time consuming line seach pocess, in contast to conventional conjugate scaled algoithms which equie line seach in all iteations. This line seach is computationally expensive, because it equies that the netwok esponse to all taining inputs to be computed seveal times fo each seach [5]. Resilient Popagation (RP) taining algoithm povides faste convegence than othe algoithms and eliminates hamful effects of the magnitudes of the patial deivatives. Then the RP algoithm detemines the diection of the weight update by using the sign of the deivative and detemines the size of the weight change by a sepaate update value. The magnitude of the deivative has no effect on the weight update [6]. 4. Simulation Results MLPNN achitectues ae tained with vaious backpopagation algoithms fo stipline and micostip line types of hybid couples data. Then, neual model impovement is accomplished by alteing taining algoithms and netwok input paametes of substate dielectic and height, couple adius and fequency. Moeove taget pefomance and epoch numbes of the taining pocess ae vaied to find the optimum achitectue. The accuacy and eliability of the geneated netwoks ae measued using the Peason Poduct-Moment coelation coefficient γ which is selected as success citeia between NN and simulato esults. ( xi x)( yi y) (6) ( x x) ( y y) i whee x i is the simulato scatteing paamete value, y i is the MLPNN computed value, x is the simulated sample mean and y is the MLPNN computed sample mean. The design paametes of the micostip ing hybid couple is defined in the ange of.33 ε 10., mm d mm, mm ad mm, 3 GHz f sim 8 GHz, 4.45 GHz f cen GHz. Additionally, stipline type ing hybid couple has design paametes anges of.33 ε 10., mm d mm, mm ad mm, 3 GHz f sim 7 GHz, 4.16 GHz f cen 6.3 GHz. The simulation fequency sweep is defined by f sim and cente fequencies of hybid couples ae given by f cen. Fig. 4 illustates the instantaneous scatteing esults of the stipline type couple modeled by a LM tained netwok which utilizes 1000 sample pais in taining and test pocesses whee equal numbe of pais is taken fo both pocesses. Each sample pai includes S-paametes vs. equally distibuted fequency points between -7 GHz unde fixed stipline substate popeties such as ad, d and ε. Thus the NN model includes single input with fou output neuons. Resonance fequency and 3dB coupling points can be monitoed to detemine the ing hybid opeating i

5 RADIOENGINEERING, VOL. 19, NO. 4, DECEMBER fequency band. The applied NN to solve the stipline example is a single input, multiple outputs netwok with one hidden laye. Adequate neuons ae employed in the hidden laye to find optimum esults. As shown in Tab. 1, the esults obtained by NN ae high enough to accuately model the stipline hybid couple. S11 [db] S13 [db] F [GHz] F [GHz] S1 [db] S14 [db] F [GHz] EM-simulato ANN model F [GHz] Fig. 4. Stipline type RHC (f cen = 4.16 GHz) scatteing paametes: EM simulato vs. NN model. Scatteing Paametes Coelation facto fo single hidden laye S S S S Tab. 1. Coelation factos fo stipline hybid design. This concludes that a single hidden layeed NN achitectue with Levenbeg-Maquadt taining algoithm is adequate to solve the single input and multiple outputs modeling poblem as a consequence of input laye simplicity. Subsequent step in modeling poblem will be moe complicated fo NN utilization. A micostip line type RHC modeling is aimed to be solved by the neual model. This neual implementation can be used as genealized design, modeling and optimization tool, when boadened netwok input paametes such as hybid adius, opeating fequency and substate popeties ae utilized. Multiple input vaiations adapt the poposed netwok to a modeling and optimization tool which can be used to find scatteing values of any RHC design that falls into taining ange. Thus the necessay coase and fine tunings fo design optimization can be achieved by paametic neual model without having to edo the fullwave EM-simulato. In micostip case, fou input paametes ae alteed in ode to each the optimum output esults. Numbe of hidden layes and neuons in these layes ae adjusted in accodance with applied leaning algoithms to achieve the best test esults. The oveall data set includes 500 data samples which cove the whole input paametes ange. Test set contains half the data samples and these testing samples ae equally distibuted ove the egession suface between the taining samples. Neual models ae tested with vaying numbe of taining and test sets. Initial tials have shown that as the data sets ae inceased poposed netwoks can handle modeling poblem with highe accuacy. Then the numbe of hidden layes is enhanced and multi-hidden layeed netwok is tained by the same taining set until aimed esults ae acquied. All netwoks ae tested with the same sets. Accoding to the computed esults, tade-offs such as coelation coefficients and computation time between single hidden layeed and multi hidden layeed netwoks ae done. Vaiations on numbe of neuons in hidden layes, epoch numbe and taget pefomance ae also applied to obtain detailed tade-offs fo NN applications. Taining algoithms ae compaed by the citeia s of conveging speed and accuacy, memoy needs and coelation esults. Fig. 5 7 epesent the neual modeling esults of a micostip RHC opeating at cente fequency of 456 MHz. Netwoks compising single to fou hidden layes ae analyzed to each the finest scatteing estimations. Two and thee layeed netwoks offe moe adequate esults though single and fou hidden layeed netwoks pesent undefitting and ovefitting espectively. Constucted NNs ae tained with the Levenbeg Maquadt algoithm which conveges fast and povides accuate esults. Howeve it equies a lot of memoy to un, thus additional NN simulations with othe taining algoithms ae employed to find optimal taining algoithm and impove NN estimations fo the poposed modeling poblem. Fig. 5 illustates the etun loss paamete of the modeled couple. S11 [db] S11 esults: EM simulation vs NN -35 NN 1 hid NN hid -40 NN 3 hid NN 4 hid Fequency [GHz] Fig. 5. S 11 esults: EM simulato vs. NN esults fo LM (f cen = 456 MHz). S1 [db] S1 esults: EM simulation vs NN -1 NN 1 hid -14 NN hid NN 3 hid NN 4 hid Fequency [GHz] Fig. 6. S 1 esults: EM simulato vs. NN esults fo LM (f cen = 456 MHz).

6 650 E. DEMIRCIOGLU, M. H. SAZLI, BEHAVIORAL MODELING OF A C-BAND RING HYBRID COUPLER USING Additionally, Fig. 6 and Fig. 7 epesent the though pot scatteing paametes. poblem. Howeve LM algoithm conveges much slowe than othes fo elatively lage netwoks. -1 S14 esults: EM simulation vs NN -16 S11 esults: Taining algoithms compaison S14 [db] -4-5 NN 1 hid -6 NN hid NN 3 hid NN 4 hid Fequency [GHz] S11 [db] LM GD SCG CGF RP CGP Fequency [GHz] Fig. 7. S 14 esults: EM simulato vs. NN esults fo LM (f cen = 456 MHz). Numbe of neuons in each hidden laye is vaied fo the impovement of LM taining algoithm esults. Finally tuned netwoks with highest accuacies ae pesented in Tab. compliant with the coelation factos (CF). Scatteing Paametes CF fo single hidden layeed NN CF fo two hidden layeed NN CF fo thee hidden layeed NN CF fo fou hidden layeed NN S S S S Tab.. Coelation factos fo MLPNN tained by LM algoithm. Futhemoe, coelation factos ae computed among successful leaning algoithms which applied to solve the modeling poblem and gouped in Tab. 3 accoding to highest coelation facto values. Scatteing Paametes LM CGP GD CGF SCG RP S S S S Tab. 3. Compaison of coelation factos fo successful algoithms. Fig illustate the compaison of NN taining algoithms fo the RHC opeating at the cente fequency of 569 MHz. The plots ae zoomed into the fequency ange of 4 GHz 6.5 GHz in ode to demonstate the small neual solution vaiations. The modeled RHC povides adequate etun loss esults as shown in Fig. 8. Fig. 8 and Fig. 10 clealy show the estimation capabilities of NNs tained by algoithms achieving highly successful appoximations. As shown Fig. 10 in Levenbeg Maquadt, esilient backpopagation, and conjugate gadient of Polak Ribièe algoithms offe the peeminent estimation values among othe successful algoithms fo the RHC modeling Fig. 8. Compaison of taining algoithms fo S 11 (f cen = 569 MHz). S1 [db] S1 esults: Taining algoithms compaison -5 LM GD SCG -5.5 CGF RP CGP Fequency [GHz] Fig. 9. Compaison of taining algoithms fo S 1 (f cen = 569 MHz). S13 [db] S13 esults: Taining algoithms compaison -35 LM GD -40 SCG CGF RP CGP Fequency [GHz] Fig. 10. Compaison of taining algoithms fo S 13 (f cen = 569 MHz) In Tab. 4, the taining algoithms with less successive appoximation values ae compaed. The quasi-newton method, gadient descent with momentum appoach, one step secant and vaiable leaning ate backpopagation taining algoithms povide elatively appalling coelation factos. Tab. 5 and 6 illustate the computation time measuements fo taining algoithms unde the same activation functions, numbe of hidden layes and neuons ae given.

7 RADIOENGINEERING, VOL. 19, NO. 4, DECEMBER In each model measuement, 3 hidden layes with 0 neuons ae tained fo 000 epochs. The fou inputs and fou outputs netwok with many hidden layes causes the LM algoithm taining time incement. Scatteing Paametes BFG GDM GDX OSS S S S S Tab. 4. Coelation factos fo elatively low successful algoithms. LM CGP GD CGF SCG RP Tab. 5. Computation time in seconds fo successful algoithms. BFG GDM GDX OSS Tab. 6. Computation time in seconds fo less successful algoithms. 5. Conclusions In this wok, the MLPNNs ae employed as a design, modeling and optimization tool fo C-Band ing hybid couples. Well-known confomal mapping based mathematical appoximations mentioned in Section ae exploited fo the theoetical component design phase. Then the theoetical foundations ae simulated and some tunings ae applied using the EM-simulato to geneate necessay taining and test data sets. A paametic neual model is stated using ing hybid adius, opeating fequency points, substate popeties such as dielectic pemittivity and thickness. Optimum netwoks ae geneated by vaying numbe of hidden layes, neuons in these layes and taining algoithms. Finally, obtained netwoks ae used fo modeling and optimization such that once the ANN is tained fo given input data anges then the paametic model can be used to find scatteing values of any design that falls into given ange. Thus the fine and coase tunings fo design optimization, which is initially done by EMsimulato, can be succeeded by ANN evolvement within simulation ange. As the numbe of input paametes is inceased, sufficient numbe of new hidden layes must be added to the netwok achitectue to ovecome the poblem complexity. Howeve complex achitectues with many hidden layes and neuons have a vital dawback of high computation time and memoy need. Moeove the tansfe functions of the hidden laye neuons ae vaied in ode to achieve desied output values using accuate neual applications. These tade-offs must be done when the neual models ae ealized to solve micowave modeling poblems. Time and memoy equiements fo both the fullwave EM-simulato and neual solutions must be compaed to detemine pecise scatteing paametes. The neual taining algoithms ae also evaluated to optimize the netwok outputs. Convegence speed, memoy needs and accuacy ae the main assessment constaints of the taining algoithms. Thus the most accuate and fast conveging algoithms ae selected to tain the netwoks unde adequate neuon and hidden laye numbes condition. Consequently, neual solutions of RF micowave design and optimization poblems offe many advantages compaing to EM-simulatos which equie high level pocessos to ovecome the backgound calculations complexity. Impoved time consumption in numeic computations and cost ae the main dawbacks in EM-simulatos. Thus paametic neual models can be applied fo design optimization inside taining ange without having to edo the time and pocesso consuming fullwave EM-simulato analyses. This may foce neual solutions as an altenative design, modeling and optimization way of micowave devices unde the adequate selection of taining algoithms and netwok achitectues. Refeences [1] WANG, F., ZHANG, Q. J. Knowledge based neual models fo micowave design. IEEE Tansactions on Micowave Theoy and Techniques, 1997, vol. 45, no. 1, p [] CREECH, G. L., PAUL, B. J., LESNIAK, C. D., JENKINS, T. J., CALCATERA, M. C. Atificial neual netwoks fo accuate micowave CAD applications. IEEE Intenational Micowave Symposium Digest, San Fancisco, CA, 1996, p [3] WATSON, P. M., GUPTA, K. C. Design and optimization of CPW cicuits using EM-ANN models fo CPW components. IEEE Tansactions on Micowave Theoy and Techniques, 1997, vol. 45, no. 1, p [4] ZAABAB, A. H., ZHANG, Q. J., NAKHLA, M. S. Neual netwok modeling appoach to cicuit optimization and statistical design. IEEE Tansactions on Micowave Theoy and Techniques, 1995, vol. 43, no. 6, p [5] WATSON, P. M., GUPTA, K. C., MAHAJAN, R. L. Development of knowledge based atificial neual netwok models fo micowave components. IEEE Intenational Micowave Symposium Digest, Baltimoe, MD, 1998, p [6] KOTHAPALLI, G. Atificial neual netwoks as aids in cicuit design. Micoelectonics Jounal, 1995, vol. 6, p [7] HARKOUSS, Y., ROUSSET, J., CHEHADE, H., BARATAUD, D., TEYSSIER, J. P. Modeling micowave devices and cicuits fo telecommunications system design. In Poceedings of IEEE Intenational Confeence on Neual Netwoks. Anchoage (USA, AK), 1998, p [8] VELUSWAMI, A., NAKHLA, M. S., ZHANG, Q. J. The application of neual netwoks to EM based simulation and optimization of inteconnects in high speed VLSI cicuits. IEEE Tansactions on Micowave Theoy and Techniques, 1997, vol. 45, no. 5, p [9] HORNG, T., WANG, C., ALEXOPOULOS, N. G. Micostip cicuit design using neual netwoks. IEEE Intenational Micowave Symposium Digest, Atlanta, GA, 1993, p [10] BURRASCANO, P., DIONIGI, M., FANCELLI, C., MONGIARDO, M. A neual netwok model fo CAD and

8 65 E. DEMIRCIOGLU, M. H. SAZLI, BEHAVIORAL MODELING OF A C-BAND RING HYBRID COUPLER USING optimization of micowave filtes. IEEE Intenational Micowave Symposium Digest, Baltimoe, MD, 1998, p [11] RIZZI, P. A. Micowave Engineeing Passive Cicuits. Pentice Hall, [1] BAHL, B., GUPTA G. Micostip Lines and Slotlines. Atech House, 1996 [13] SVACINA, J. New method fo analysis of micostip with finitewidth gound plane. Micowave and Optical Technology Lettes, vol. 48, no., 006, p [14] WHEELER, H. A. Tansmission-Line Popeties of Paallel Stips Sepaated by a Dielectic Sheet. IEEE Tansactions on Micowave Theoy and Techniques, 1965, vol. 13, no., p [15] SCHNEIDER, M. V. Micostip lines fo micowave integated cicuits, The Bell System Technical Jounal, 1969, vol. 48, p [16] HAMMERSTAD, E., JENSEN, Ø. Accuate models fo micostip compute-aided design. Symposium on Micowave Theoy and Techniques, 1980, p [17] SELVAN, P. T., RAGHAVAN, S. Multilaye pecepton neual analysis of edge coupled and conducto-backed edge coupled coplana waveguides. Pogess in Electomagnetics Reseach B, 009, vol. 17, p [18] KAYA, S., TURKMEN, M., GUNEY, K., YILDIZ C. Neual models fo the elliptic- and cicula-shaped micoshield lines. Pogess in Electomagnetics Reseach B, 008, vol. 6, p [19] TURKMEN, M., YILDIZ C. Quasi-static models based on atificial neual netwoks fo calculating the chaacteistic paametes of multilaye cylindical coplana waveguide and stip line. Pogess in Electomagnetics Reseach B, 008, vol. 3, p. 1-. [0] WANG, F., DEVABHAKTUNI, V. K., XI, C., ZHANG, Q. J. Neual netwok stuctues and taining algoithms fo RF and micowave applications. Intenational Jounal of Micowave and Millimete-Wave Compute-Aided Engineeing, 1999, vol. 9, no. 3, p [1] LEVENBERG, K. A method fo the solution of cetain nonlinea poblems in least squaes. Quately of Applied Mathematics, 1963, vol. 11, p [] POLAK, E., RIBIERE, G. Note su la convegence de methods de diections conjuguees. Reveu Fancaise d Infomatique et de Recheche Opeationnelle, 1969, p [3] HAYKIN, S. Neual Netwoks A Compehensive Foundation. Pentice Hall, [4] FLETCHER, R., REEVES, C. M., Function minimization by conjugate gadients. The Compute Jounal, 1964, vol. 7, p [5] MOLLER, M. F. A scaled conjugate gadient algoithm fo fast supevised leaning. Neual Netwoks, 1993, vol. 6, p [6] REIDMILLER, M., BRAUN, H., A diect adaptive method fo faste backpopagation leaning: The Rpop algoithm. In Poceedings of the IEEE Intenational Confeence on Neual Netwoks. San Fancisco (USA), 1993, p About Authos... Edem DEMİRCİOGLU was bon in Mugla, Tukey. He eceived his B.Sc. degee fom Yildiz Technical Univesity in 004 and M.Sc. degee fom Syacuse Univesity in 006. He is woking as a senio specialist in R&D Satellite Design Depatment of Tuksat AS and pusuing his doctoal studies in Electonics Depatment of Ankaa Univesity. His eseach inteests include satellite payload systems, atificial intelligence applications in EM and biomedical topics. Muat H. SAZLI was bon in 1973 in Elazig, Tukey. He eceived the B.Sc. (with highest honos) and M.Sc. degees fom Electonics Engineeing Depatment, Ankaa Univesity, in 1994 and 1997, espectively. He eceived the Ph.D. degee in electical engineeing fom Syacuse Univesity in 003. He was the ecipient of Outstanding Teaching Assistant Awad fom Syacuse Univesity in 00. He is cuently an assistant pofesso and vice chaiman of Electonics Engineeing Depatment of Ankaa Univesity. His aeas of inteest include tubo coding and decoding, neual netwoks and thei applications, wieless communications.