Efficient and Accurate Analysis of a Substrate Integrated Waveguide (SIW) Rat-Race Coupler Excited by Four U-Shape Slot- Coupled Transitions

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1 4 ACES JOURNAL, Vol. 30, No., JANUARY 05 Efficient and Accurate Analysis of a Substrate Integrated Waveguide (SIW) Rat-Race Coupler Excited by Four U-Sape Slot- Coupled Transitions R. Dedast-Heydari,K. Forooragi, and M. Naser-Mogadasi Department of Electrical Engineering, Science and Researc Branc Islamic Azad University, Teran, Iran dedasteydari@gmail.com, mn_mogaddasi@yaoo.com Department of Electrical Engineering Tarbiat Modares University (TMU), Teran, Iran KEYVAN_F@modares.ac.ir Abstract In tis paper, te bandwidt of one SIW rat-race (ybrid ring) coupler as been increased up to 30% by four U-sape slot-coupled transitions witout disadvantages due to transmission line loss, radiation and design complexity. Te SIW coupler structure as been analyzed by te mode matcing metod tat uses te cylindrical vector expansion to minimize computational time and memory occupation. Trougout -5 GHz bandwidt, return loss and isolation as well as pase differences in output ports ave been presented. It is observed tat te numerical results are in good agreement wit simulation and experimental measurement. Index Terms Boundary conditions, coaxial cables, Cylindrical Vector Waves (CVWs), Dyadic Green s Functions (DGFs), rat-race (ybrid ring) coupler, Substrate Integrated Waveguide (SIW), transition, U-sape slots. I. INTRODUCTION Substrate Integrated Waveguide (SIW) structures are also known as laminated waveguide or post-wall waveguide structures. Tey are used as a concept for te design of microwave and millimeter-wave waveguide structures and components []. SIWs are based on te equivalence between well-known metallic waveguide structures (usually a Rectangular Waveguide (SIRW)) and waveguide structures on a dielectric substrate using rows of metal posts (vias). Many passive components, suc as filters, antennas, circulators, couplers, transitions, etc., are based on SIW or similar tecnologies, and tey ave been studied in [-9]. Witout any doubts, te transitions between excitation section and SIRW are mostly a critical element to get optimized S-parameters. Several transitions for te SIRW were presented [0-5] over te last few years, like transformers to rectangular waveguides, single layer transitions from microstrip lines to SIRWs, uniplanar CPW transitions, GCPW transitions. However, tese structures ave drawbacks suc as not compatible wit planar circuits, incompatible wit low-loss SIRWs, radiation and design complexity and fabrication. Terefore, a new design of transition is necessary in order to simplify te structure and improve bandwidt. Recently, several papers [6-] ave applied a Cylindrical Vector Wave expansion (CVW) to study te simplified -D case and te full 3-D case. Tese mode expansions allow an efficient full-wave analysis of SIW structures for metallic and dielectric posts. Neverteless, tere is a need in using efficient metod of mode matcing to analyze wideband SIW structures; for instance, SIW couplers. Te single-layer SIW rat race coupler basically as been proposed in [3], utilizing te transition from microstrip lines to SIW rat-race Submitted On: October 3, 03 Accepted On: October 4, ACES

2 DEHDASHT-HEYDARI, ET.AL: EFFICIENT AND ACCURATE ANALYSIS OF A SUBSTRATE INTEGRATED WAVEGUIDE (SIW) 43 arms. Accordingly, tere was not mentioned anyting about output pases (0 and 80 degrees) and te analysis of te coupler. Tis coupler as limited bandwidt (about 0% in X-band and 7% in Ka-band) and its dimensions sould optimize to obtain furter bandwidt. In tis paper, a simple SIW transition structure is designed for GHz frequency (over 50% relative bandwidt) in Section II. Te coaxial cables are accompanied wit U-sape slots to excite te signal inside te SIRW. As an application, a SIW ybrid ring coupler as been modified wit tis new SIW transition to increase te bandwidt over tan 30% and carry out a lower loss and profile coupler. Te design and optimization procedure of te coupler ave been presented in Section III. In Section IV, te proposed coupler as been analyzed and te vector wave functions ave been used for te coupler. By imposing boundary conditions on eac post and transfer te obtained equations to te matrix, te unknown coefficients ave been determined and scattering parameters of te proposed rat-race coupler to be calculated. To confirm te efficiency and accuracy of te metod, te coupler calculated parameters ave been compared wit simulated and measured results in Section V. II. DESIGN OF U-SHAPE SLOT- COUPLED TRANSITION Te structure of U-sape slot-coupled transition is sown in Fig.. Te structure is similar to conventional SIW, wic is excited wit coaxial cable directly wit no need to use microstrip line transition. Te sole difference is in rectangular U-sape slots above te substrate plate were te inner conductors of coaxial cables are connected to te top plate. In te first step, we simulated a two port SIW waveguide witout coaxial probes for single-mode (i.e., TE0 mode) in te operating frequency range of GHz wit CST microwave studio. In te next step, it is necessary to use te transition from two coaxial probes to te SIW waveguide. We ave seen in te CST package tat by using a slot coupling for probe feeding to SIW transition, te input resistance increases wit te tickness of SIW substrate but decreases wit slot lengt. Tis trade off can be acieved by adjusting te lengt and sape of te slot. Terefore, te transition bandwidt can be maximized by matcing te input resistance as nearly as to te caracteristic impedance of te probe feeding. Fig.. Te back-to-back U-sape slot-coupled transition structure (all dimensions are in millimeters). From optimization in CST for different slot sapes along wit different lengts, we realized tat te best configuration to maximize te relative bandwidt of te transition can be exploited by U- sape slots rater tan te oter sapes (e.g., E- sape slots). Terefore, te two U-sape slots are designed to enance te bandwidt of te SIW structure excited by coaxial cables witout radiation from te slots or design complication as well as te bandwidt of te structure wit waveguide ports excitation. Entrance of te coaxial probes and te dimensions of U-sape slots are critical for te return loss performance of te SIW ybrid ring in te next section. A lot of simulations ave been made to optimize te transitional performance using CST, wic te optimized dimensions are demonstrated in Fig.. By applying tese coupling slots over te top plate of SIW transition, te TEM waves from coaxial cables convert to TE0-like modes and enter into SIW structure. Tus, te performance of tis proposed structure is te same as te structure wen excited only wit waveguide ports. Tis agreement is illustrated in Fig.. As sown in te figure, te S and S of te structure in fundamental mode wen excited wit coaxial cable and U-sape slot-coupled are similar to waveguide port excitation. We use tis similarity in our analysis in Section IV.

3 44 ACES JOURNAL, Vol. 30, No., JANUARY 05 Fig.. S-parameters of SIW structure wit waveguide port excitation and U-sape slotcoupled transition. III. DESIGN AND OPTIMIZATION PROCEDURE OF SIW HYBRID RING (RAT-RACE) COUPLER Te optimized SIW ybrid ring (rat-race) structure as been sown in Fig. 3. Te dimension of te proposed coupler as been obtained based on te following procedure:. In te previous section, we ave designed a new SIW transition wic is applied for excitation of our coupler. As sown in Fig. 3, te SIW coupler arms consist of four U-sape slots and coaxial connectors.. According to [3] for manufacturing considerations, te distances between te four arms sould be increased one wavelengt in comparison to conventional distances between te coupler arms. Te spatial angles between te four ports ave been sown in Fig We ave cosen te logical and possible ranges for inner radius (r), 3r 9 and outer radius (r3), 0 r3 0 of te coupler. In addition, four matcing posts ave been used for improving te impedance matcing of te coupler [3]. Te initial radius (r) of te matcing posts is in 3.5 r 9.5 range. By coosing tree radiuses from above ranges, our initial coupler as been prepared for analysis. Te SIW rat-race coupler analysis as been presented in detail in te next section. 4. After calculating te coupler S-parameters form analysis, we ave optimized te coupler wit IWO optimization algoritm [4]. Te parameters under optimization are r, r, r3 and te matcing posts diameters. In our optimization, te operating frequency band was over GHz, but because of considering all goal functions, i.e., return loss, isolation, insertion loss and pase differences of te coupler; simultaneously te maximized bandwidt as been met 30% relative bandwidt, wic is over -5 GHz for our optimized dimensions in Fig. 3. To te best of our knowledge, tis relative bandwidt as not been obtained for te SIW rat-race coupler by literatures up to now, and te proposed SIW rat-race coupler is a good candidate for te wideband applications because te relative bandwidt of te coupler can be sifted in te interested band by canging and optimizing te dimensions. Also, because of using te probe feeding instead of te microstrip line transition, our coupler is low loss and profile. Te experimental measurements confirm our claim in Section V. Fig. 3. Te SIW ybrid ring coupler structure (r=4.5 mm, r=6.5 mm and r3=5.5 mm). IV. SIW HYBRID RING (RAT-RACE) COUPLER ANALYSIS In tis section, we analyze te SIW ybrid ring (rat-race) coupler wit mode matcing algoritm for tese reasons: a. Our analysis minimizes memory computation and time consumption rater tan te oter

4 DEHDASHT-HEYDARI, ET.AL: EFFICIENT AND ACCURATE ANALYSIS OF A SUBSTRATE INTEGRATED WAVEGUIDE (SIW) 45 full wave package like CST and HFSS. b. As mentioned in te previous section, after calculating te S-parameters of te coupler from our analysis, we can optimize te dimensions of te coupler to acieve te iger bandwidt wit optimization algoritms troug Matlab code, wereas te optimization of te SIW coupler takes a very long time in CST or HFSS. Furtermore, after many optimizations in CST or HFSS, te goal functions for tis SIW coupler is not capable of reacing to our desired bandwidt. c. It is wortwile mentioning tat our code can generally be andled for te SIW passive structures wic require bandwidt enancing and te analyzed and optimized algoritm ave been applied for te proposed SIW coupler as a good example in our effort. According to Section II, because te coaxial cable TEM waves are converted to TE modes troug te U-sape slots, to analyze te fields in te SIW Hybrid ring (rat-race) structure, we substitute four U-sape slots and coaxial cables wit rectangular waveguide port excitations (magnetic source in tis paper). Now, we can examine te incident and scattered magnetic fields from eac metallic post included vias of four rectangular arms, four matcing posts wit radius (r), vias of inner radius (r) and vias of te outer radius (r3) of te SIW coupler. In general, an arbitrary total magnetic field H(r) can be expressed as: Htotal () r H H, () were H is incident wave from a magnetic source ( M s ) and H is scattering magnetic wave from eac via. Calculating H, we need tis equation: H j G MdV () m s, V were G m is a magnetic Green s function of te second kind, wic for parallel plate waveguide troug using residue teorem in cylindrical coordination and [5,6], explicit form is given by: ˆˆ G (, r r) ( rr) m k N N z ( m0 ) j4 m0 nn km [ Pn( km, kz,, z) P n( km, kz,, z) Qn( km, kz,, z) Q n( km, kz,, z)], (3) and 0 if m 0 m0. if m 0 In (3), we define two vector wave functions Pn( km, kz,, z) and Qn( km, kz,, z) as te equivalence of magnetic fields. Calculating tese functions, lets assume tis armonic scalar potential n() r : () jkz ( z n ) Hn ( km) e n () r, (4) jkz ( z n ) Jn( km) e () were H n and J n indicate n-order Hankel s function of te second kind and n-order Bessel s function respectively. Also, k k k, kz m /, k 00r and is te eigt of substrate. In tis manner, m and n are te cylindrical modes in vertical ( direction) and azimutally ( direction) respectively. Te relation between Pn( km, kz,, z) and Qn( km, kz,, z) is as follows: P(,,, ) ( ( ) ˆ n km kz z n r ), (5.a) Qn( km, kz,, z) Pn( km, kz,, z), (5.b) k were ˆ is unit normal vector on te lateral surface of eac cylindrical metallic post of te ybrid ring coupler. Similarly, P n( km, kz,, z) and Q n( km, kz,, z) can be acquired from (5.a) and (5.b) by intercanging witin (4). We can write scattering waves for TM and TE modes as Cylindrical Vector Wave (CVW) expansions: Pvia N N z TM lmn,, n m z l m n0 TE lmn,, n( m, z,, )], H () r [ C P( k, k,, z) (6) D Q k k z were indexl denotes to te number of te SIW coupler vias. To determine unknown coefficients TM TE ( C lmn,,, D lmn,,), te boundary conditions sould be imposed for te surface of eac via; for metallic (PEC) vias: n( EE) 0 (7) in surface of eac PEC wit radius ai, were ( EE) (/ j ) ( H H) and a i is eac metallic via radius of te coupler as te radiuses of te four matcing posts are twice of te oter vias in Fig. 3. z m z

5 46 ACES JOURNAL, Vol. 30, No., JANUARY 05 By operating (7), te unknown coefficient TM / TE TM TE vector can be expressed as: F [ C, D ] lmn,, lmn,, lmn,, TM / TE F,,0.. [ U] [ S], (8). TM / TE F lmn,, were U and S are interaction matrix between te vias and excitation vector respectively. After determining te coefficients from (8), we use te admittance matrix of rectangular waveguide [7] wic is replaced wit coaxial cable and U-sape slot coupling: i j Yi, j j ZiZ j Gm( ri, rj) dsidsj, (9) j i Zi H () r dsi i j were and are magnetic field modal vector and Z i, Z j are wave impedance for eac waveguide port. If we regard cross section of te SIW coupler waveguide port in te x-direction wit te equivalent widt of waveguide port a eqv and y-direction wit te substrate eigt, for TE i j mode, or in (9) is obtained as: TE p nˆ a eqv ( m n ) m m n (0) [ cos( x)sin( y) xˆ n m n sin( x)cos( y) yˆ ]. Similarly for TM mode, / TM ( mn) p nˆ a eqv ( m n ) n m n () [ cos( x)sin( y) xˆ m m n sin( x)cos( y) yˆ ]. In (0) and (): m, n 0,,,3,..., m n 0 is excluded, and if k 0 k, if k 0 were n ˆ p denotes te unit normal vector to te waveguide port. From te knowledge of te admittance matrix, te scattering matrix of te SIW coupler can simply be computed [8]. V. RESULTS AND DISCUSSION Te proposed algoritm in Section IV as been implemented in Matlab code. Te TE0 mode propagation is considered for all te waveguide ports of te analyzed SIW coupler. Attaining to 0.0 error of te coupler parameters, N =7 and N z = cylindrical modes in (3) and (6) ave been selected, and te obtained results are validated wit te simulation and experimental conclusions. In our attempt, te substrate material and te tickness are Rogers R04003 wit r =3.55 and =0.83 mm in te order mentioned. Figure 4 depicts a manufactured SIW rat-race coupler wit te dimensions wic ave been acquired in Section III. Te coupler S-parameters from te analysis, CST time domain solver and measurement are sown in Figs. 5 and 6. From Fig. 5 (a), te return losses (S ) and isolations (S 4) are less tan -8 db and -0 db over -5 GHz (30% relative bandwidt) respectively. In addition, te insertion losses between te output ports, ports and 3, are divided equally from db to -3 db in Fig. 5 (b). As sown in Fig. 6, trougout -5 GHz, te pase differences between ports and 3 for inpase are in te range of to 0 +., wen port 4 is excited and for out-of-pase are from 80-4 to , wen port is excited. Obviously, very good agreement as been obtained from our metod, simulation and measurement wic tis matter confirms accuracy of te proposed analysis. Fig. 4. Te potograp of te manufactured SIW rat-race (ybrid ring) coupler.

6 DEHDASHT-HEYDARI, ET.AL: EFFICIENT AND ACCURATE ANALYSIS OF A SUBSTRATE INTEGRATED WAVEGUIDE (SIW) 47 (a) (b) Fig. 6. Te pase difference responses: (a) inpase response, and (b) out-of-pase response. (b) Fig. 5. Comparison of te SIW ybrid ring coupler S-parameters: (a) return loss (S ) and isolation (S 4), and (b) insertion losses (S and S 3). (a) To prove te efficiency of our analysis, te coupler as been compared wit HFSS and CST frequency domain solver as well as CST time domain solver. In te case of analysis, HFSS and CST frequency domain solver, te allowed error for te S-parameters convergence of te coupler is % and we ave used 50 frequency points for te output results. After calculating te all frequency points, te run time ratio of te analysis is related to HFSS is / and CST frequency domain solver is /0, wile to CST time domain solver is /.5 ratio. So, our metod as te best efficiency and te CST time domain solver efficiency is muc closer to te analysis rater tan HFSS or CST frequency domain. Table as reported te simulation time of te proposed coupler from te analysis, CST and HFSS. Table : Simulation time on a Core i5 wit 4-GB RAM (azimutally mode numbers=7, vertically mode numbers=) Structure Type SIW Hybrid ring (rat-race) coupler Vias Number CST CPU Time Time Domain HFSS Frequency Domain Analysis 50 Frequency Points s 50s 0s

7 48 ACES JOURNAL, Vol. 30, No., JANUARY 05 VI. CONCLUSION Tis paper presents a novel SIW transition as an application for te SIW ybrid ring (rat-race) coupler under analysis. By using U-sape slotcoupled transitions, te relative bandwidt of te rat-race coupler as been increased up to 30% wit low loss, low profile and ig isolation in te operated frequency. Tis ybrid ring coupler as been analyzed wit an efficient and accurate metod of mode matcing to calculate te scattering matrix. Te output parameters of te analyzed and optimized coupler ave been justified wit full wave simulation and experimental results. Witout losing te generality of te analysis, our metod is a good candidate for te relative bandwidt improving (up to 30 percent) of te oter passive SIW structures. REFERENCES [] K. Wu, D. Deslandes, and Y. Cassivi, Te substrate integrated circuits-a new concept for ig-frequency electronics and optoelectronics, In Proc. 6 t International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Service TELSIKS 003, vol., pp. P-III-P-X, 003. [] Z. Q. Xu, P. Wang, J. X. Liao, and Y. Si, Substrate integrated waveguide filter wit mixed coupled modified trisections, IET Electronic Letter, vol. 49, pp , Marc 03. [3] H. Min-Hua and L. Ceng-Siou, Novel balanced bandpass filters using substrate integrated alfmode waveguide, IEEE Microwave and Wireless Component Letters, vol. 3, pp , February 03. [4] Z. Li, M. S. Maani, and R. Abari, Experiment of substrate integrated waveguide interconnect measurement for ig speed data transmission application, Microw. Opt. Tecnol. Lett., vol. 54, no., pp , February 0. [5] F. Giuppi, A. Georgiadis, A. Collado, and M. Bozzi, Active substrate integrated waveguide (SIW) antenna wit pase-sifterless beamscanning capabilities, IEEE MTT-S Int. Microwave Symp. Dig., pp. -3, June 0. [6] E. Ofli, R. Valdieck, and S. Amari, Novel E- plane filters and diplexers wit elliptic response for millimeter-wave applications, IEEE Trans. Microw. Teory Tec., vol. 53, no. 3, pp , Marc 005. [7] W. M. Abdel-Waab and S. Safavi-Naeini, Low loss double-layer substrate integrated waveguideybrid branc line coupler for mm-wave antenna arrays, IEEE Antennas and Propagation International Society Symposium (APSURSI), pp , 0. [8] K. Song, F. Zang, F. Cen, and Y. Fan, Wideband millimetre-wave four-way spatial power combiner based on multilayer SIW, Journal of Electromagnetic Waves and Applications, vol. 7, nos. 3, 75-79, 03. [9] Y. Liu, X. H. Tang, and T. Wu, SIW-based low pase-noise millimeter-wave planar dual-port voltage-controlled oscillator, Journal of Electromagnetic Waves and Applications, vol. 7, nos. 8-9, , 0. [0]T. Kai, J. Hirokawa, and M. Ando, Transformer between a tin postwall waveguide to a standard metal waveguide, In IEEE Antennas Propagation Society Symp. Dig., pp , June 00. []D. Deslandes and K. Wu, Integrated microstrip and rectangular waveguide in planar form, IEEE Microw. Wireless Compon. Lett., vol., no., pp , February 00. []N. Jain and N. Kinayman, A novel microstrip mode to waveguide mode transformer and its applications, In IEEE MTT-S Int. Microwave Symp. Dig., pp , May 00. [3] Y. Huang, K. L. Wu, and M. Elert, An integrated LTCC laminated waveguide-to-microstrip line T- junction, IEEE Microw. Wireless Compon. Lett., vol. 3, no. 8, pp , August 003. [4] S. Lin, A. E. Faty, and A. Elserbini, Development of a novel UWB vivaldi antenna array using SIW tecnology, Progress In Electromagnetics Researc, PIER 90, , 009. [5] R. Kazemi, A. E. Faty, S. Yang, and R. A. Sadegzade, Development of an ultra-wide band GCPW to SIW transition, IEEE Radio and Wireless Symposium (RWS), pp. 7-74, January 0. [6] E. D. Caballero, H. Esteban, A. Belenguer, and V. Boria, Efficient analysis of substrate integrated waveguide devices using ybrid mode matcing between cylindrical and guided modes, IEEE Trans. Microw. Teory Tec., vol. 60, no., pp. 3-43, February 0. [7] A. Belenguer, H. Esteban, E. Diaz, C. Baciller, J. Cascon, and V. E. Boria, Hybrid tecnique plus fast frequency sweep for te efficient and accurate analysis of substrate integrated waveguide devices, IEEE Trans. Microw. Teory Tec., vol. 59, no. 3, pp , Marc 0. [8] E. Arnieri and G. Amendola, Analysis of substrate integrated waveguide structures based on te parallel-plate waveguide green s function, IEEE Trans. Microw. Teory Tec., vol. 56, no. 7, pp , July 008. [9]B. Wu and L. Tsang, Full-wave modeling of

8 DEHDASHT-HEYDARI, ET.AL: EFFICIENT AND ACCURATE ANALYSIS OF A SUBSTRATE INTEGRATED WAVEGUIDE (SIW) 49 multiple vias using differential signaling and sared antipad in multilayered ig speed vertical interconnects, Progress In Electromagnetics Researc, PIER 97, 9-39, 009. [0] M. Casaletti, R. Sauleau, and M. Ettorre, Efficient analysis of metallic and dielectric posts in parallelplate waveguide structures, IEEE Trans. Microw. Teory Tec., vol. 60, no. 0, pp , October 0. [] E. Arnieri and G. Amendola, Metod of moments analysis of slotted substrate integrated waveguide arrays, IEEE Trans. Antennas Propag., vol. 59, no. 4, pp , April 0. [] H. Zairi, H. Baudrand, A. Garsalla, and A. H. Garb, An efficient iterative metod for analysis of a substrate integrated waveguide structures, Microw. Opt. Tecnol. Lett., vol. 5, no., pp , January 00. [3] W. Ce, K. Deng, E. K. N. Yung, and K. Wu, Hplane 3-dB ybrid ring of ig isolation in substrate integrated rectangular waveguide (SIRW), Microw. Opt. Tecnol. Lett., vol. 48, no. 3, pp , Marc 006. [4] A. R. Merabian and C. Lucas, A novel numerical optimization algoritm inspired from weed colonization, Ecological Informatics, vol., , 006. [5] C. T. Tai, Generalized vector and dyadic analysis: applied matematics in field teory, series on Electromagnetic Waves, Piscataway, IEEE Press, 99. [6] C. T. Tai, Dyadic green s function in electromagnetic teory, series on Electromagnetic Waves, Piscataway, IEEE Press, 993. [7] R. E. Collin, Field teory of guided waves, series on Electromagnetic Waves, Piscataway, IEEE Press, 993. [8] D. M. Pozar, Microwave engineering, 3 rd edition, Jon Wiley & Sons Inc., 005. Ramin Dedast-Heydari was born in Esfaan-Iran, in 983. He received te B.Sc. and M.Sc.degrees in Electrical Eng. in 005 and 008 from te Said Sattari and Saed Universities, Teran-Iran, respectively. He currently is pursuing is P.D. tesis wit te Science & Researc Branc, Islamic Azad University, Teran-Iran. His principal fields of interest in researc are UWB antennas, microwave and millimeter wave circuits, and numerical electromagnetism metods. Keyvan Forooragi received te M.Sc. degree in Electrical Engineering, te Licentiate of Tecnology degree and te P.D. degree in Electrical Engineering in 99 from Calmers University of Tecnology, Gotenburg, Sweden. He worked as a Researcer at Calmers University of Tecnology from 99 to 99. In 99, e joined te Department of Computer and Electrical Engineering, Tarbiat Modares University. Presently e is a Full Professor wit te Communication Group. His researc interests include electromagnetic teory and computational electromagnetic and antenna teory. Moammad Naser-Mogadasi was born in Save, Iran, in 959. He received te B.Sc. degree in Communication Eng. in 985 from te Leeds Metropolitan University, UK. From 987 to 989, e was awarded a full scolarsip by te Leeds Educational Autority to pursue an M.Pil. studying in CAD of Microwave Circuits. He received is P.D. in 993, from te University of Bradford, UK. He was offered ten a two years Post Doc. to pursue researc on Microwave cooking of materials at te University of Nottingam, UK. In 995, Naser-Mogadasi joined Islamic Azad University, Science & Researc Branc, Iran, were e currently is an Associate Professor and Head of Postgraduate Studies. His main areas of interest in researc are Microstrip antenna, Microwave passive and active circuits, RF MEMS. He as so far publised over 40 papers in different journals and conferences.