Miniaturized Microstrip Filter Design Using Active Learning Method

Transcription

1 ADIOEGIEEIG VOL. O. 4 DECEMBE 857 Miniaturized Microstrip Fiter Design Using Active Learning Method Payman EZAEE Majid TAYAAI einhard KÖCHEL Dept. of Eectrica Engineering Iran University of Science and Technoogy armak Tehran Iran Microwave Group Christian-Abrechts-University of Kie Kie 44 Germany pre@tf.uni-kie.de m_tayarani@iust.ac.ir rk@tf.uni-kie.de Abstract. eating couping and externa quaity factor of a fiter to the physica parameters of the structure which is the fina step of any fiter design is usuay compicated due to geometrica compexities of the fiter or in the case of microstrip resonators due to the ack of the exact soution for the fied distribution. Therefore common approach is using time consuming fu wave simuations. In this paper active earning method (ALM) which is a fuzzy-based modeing technique deveoped by a procedure agorithmicay mimics the information-handing process of the human brain is proposed to overcome this drawback. Modeing steps of an unknown function using ALM wi be described using an iustrative exampe. Afterwards the modeing approach wi be impemented to mode couping factor between two couped spira resonators (Ss) for two different couping structures and externa quaity factor of the same resonator. Accuracy of the extracted surfaces is vaidated using two different criteria. Using the extracted surfaces; a four poe Chebychev bandpass fiter was designed and fabricated. Good agreement between the measured response and simuation vaidated the accuracy of the extracted surfaces again. Comparing the fabricated S fiter with a square open oop resonator (SOL) one demonstrates more than 7% of fiter area reduction. Keywords Active earning method couping factor computation externa quaity factor computation soft computing techniques spira resonator.. Introduction Due to the increasing compexity and variety of microwave structures the number of design variabes is on the rise. Athough Maxwe s equations are satisfied in a eectromagnetic structures but sti a ot of different structures coud be found without any anaytica soution which motivated designers using numerica methods. Time consuming process of these fu wave simuations prompted designers to the use of circuit-based modes which are not precise as EM-based modes are but they are fast enough. The main idea of this paper is to introduce a method for microwave structure modeing with different modeing parameters which benefits from EM-based modeing techniques accuracy circuit-based modeing fastness but does not suffer from the huge amount of cacuations. In this regard the abiity of soft computing techniques in modeing compicated probems may provide such a usefu faciity. Among the soft computing techniques the abiity of fuzzy inference method in soving compicated eectromagnetic probems such as; microwave fiter tuning [] [] EMC probems [] resonant frequency computation [4] [5] aso antenna modeing [6] [7] has been proved in various pubications. Artificia neura network (A) which is aso a we-known soft computing technique has been used recenty in microwave fiter design [8]. Athough the modeing steps of these methods seem to be very simiar to the human ogica-thinking the amount and compexity of mathematics which is used even in ordinary fuzzy-based modeing techniques [9] [] is usuay forgotten. ALM which is a reativey new soft computing technique [] [] does not suffer from the mathematica compexity of fuzzy agorithms time consuming training process of A-based techniques aso difficuty of the interpretation of the embedded knowedge in the trained As. This method is simiar to the way which human being ooks at any phenomena acquires data from it extracts knowedge about the observed events and finay the decision he makes about the tota system. In ALM any muti-input singe-output (MISO) system is supposed to be as the combination of some singe-input singe-output (SISO) one. Behavior of each SISO system which is a curve and a spread reated to it is extracted by the ink drop spread (IDS) method versus the corresponding independent variabes. Then using an appropriate combination rue of inference the genera behavior of the system is understood. Considering the simpicity interpretabiity fastness and accuracy of the ALM method in this paper a quite genera ALM-based approach for couping and externa quaity factor computation is proposed. The paper is organized as foows. Basic definitions of ALM carifying the modeing steps using an iustrative exampe and its

2 858 P. EZAEE M. TAYAAI. KÖCHEL MIIATUIZED MICOSTIP FILTE DESIG USIG ACTIVE LEAIG METHOD genera formuation are described in section. Section is devoted to the impementation of ALM for couping and externa quaity factor modeing of Ss versus two and three important physica parameters respectivey. In section 4 extracted couping and externa quaity factor surfaces are impemented to design a four poe Chebychev S fiter then comparison of the dimensions of the designed S fiter and an open oop resonator one iustrates the amount of miniaturization provided by the S configurations. Finay concusions are presented in section 5.. ALM Definition ALM is mainy characterized by its intuitive patternbased processing which is based on the hypothesis that humans interpret information in the form of pattern-ike images rather than numerica or ogica forms. Confronting any new experiment creates a new pattern in the brain. Therefore each pattern represents a simpe concept and by the combination of these basic patterns compicated subjects can be expressed and understood. Fig. shows the fow diagram of the method. According to this fow diagram ALM uses the foowing steps to mode an unknown system or function versus the tota number of independent variabes that affect its behavior or output vaue. At first sampe data are gathered by any numerica method or measurement technique. In the second step which is usuay caed projection step a the gathered data are projected on each x i -y pane where x i is the ith input variabe and y stands for the output. In this step we are trying to imagine that the system is composed of some SISO one. If the system was reay a SISO one the projected data woud provide a narrow unique path but because of the effect of other inputs a spread is detectabe around each narrow path. This spread shows the effect of other input variabes on the corresponding x i -y pane. It can be easiy deduced that the narrower this spread; the effects of other input parameters on the output computation are ess. In the third step the IDS agorithm is run for each initia data point in the corresponding x i -y pane to extract the behavior of each SISO system. In the IDS method we assume each data point in each x i -y pane as a ight source which has a cone shaped beam width. When the vertica distance from this point increases its pattern spreads and interferes with the pattern of other data points which are now other sources of ight. Indeed these cones are three dimensiona membership functions which show the degree of confidence to other points near data points. If the mixed patterns are potted on the corresponding input-output pane in grayscae a pattern wi be constructed as shown in Fig.. The process of grayscae representation of the data in each x i -y pane is caed IDS. Start Gathering input-output data Projecting the gathered data on each x i -y pane unning IDS agorithm Extracting narrow path for each x i -y pane Extracting spread reated to each of the extracted narrow paths Generating the appropriate Fuzzy rues Cacuating the output Measuring the error using predefined threshod Yes Is the error ess Save the mode than the threshod? o Divide the data domains of the Stop variabes to more sections or add intermediate data points Fig.. Fow diagram of ALM for modeing an unknown function. In the fourth step behavior of each SISO system is extracted from the IDS pattern using (). k ymax x k dx y dx y () yymin yk where ( x) is the extracted narrow path for the input parameter x. d(a b) is the vaue of darkness in point (ab). This vaue is for the darkest points which are the most confident points in the pane and is for the ightest ones. In the fifth step for each extracted narrow path a spread is cacuated using (). This parameter indicates the effect of the corresponding input in overa system output. x max y d x y min y d x y () In the sixth step according to the number of divisions for each input variabe appropriate fuzzy rues of inference wi be produced. As an exampe if for a two-input function each input domain is divided into two sections there are four inference rues as foows. Fig.. A typica IDS pattern. k k : If : If x x k k k k k k ()

3 ADIOEGIEEIG VOL. O. 4 DECEMBE 859 where ψ ij is the jth narrow path for the ith input variabe and A ij denotes the jth membership function for the ith input variabe. Finay the mode output is obtained by aggregating the narrow paths. For a two-input function with two divisions for each variabe mode output is cacuated as foows. y is (4) or or or where or is the union operator and β ij denotes the weight of the jth narrow path for the ith input variabe. The vaue of β is determined from the spread and the degree of truth of the antecedent part in (). It is cacuated as foows. k k A A k A A k / i ; j ; k ij ij A k A A k A ; k A A (5) In the eighth step the output of the constructed mode is compared with the origina output by a predefined threshod error. If the mode is not accurate enough the input domains wi be divided in more sections and if it is necessary intermediate data points wi be added to the previous ones. The active earning method is run again to reduce the error of the mode. In order to extract the behavior of the system in the shaded area of Fig. (b) it is ony necessary to consider x in the interva [- ] of the part B and x in the interva [.5] of the part C. As it can be seen in Fig. 4 for the mentioned interva of x in the part C a wide spread is detectabe therefore no information about the output can be eicited from this projected data. On the other hand in the mentioned interva for the x in the part B there is a thin spread which means a high correation between x and the output. Therefore part B effectivey eicits the system feature of the shaded area. In order to extract the behavior of the system in the tota variation range of the inputs a data of parts A to D shoud be utiized. For each of these parts the reated narrow path which expains the behavior of the corresponding SISO system and the reated spread which expains the effect of other inputs on the extracted narrow path are obtained using IDS agorithm as shown in Fig. 5. Y X =[.5] x B Y X =[- ] x Fig. 4. Projected data on the corresponding x i -y pane for the parts B and C. Spread C. A Two-Input Function Modeing by ALM In order to expain the modeing process of ALM we use a two-input function that has an input-output reationship as shown in Fig. (a). For the simpicity of expanation each input domain is divided into two parts as shown in Fig. (b). Therefore four SISO systems are generated i.e. A B C and D. In this figure A ij is the jth membership function for the ith input variabe. Projected data of parts B and C on the corresponding x i -y pane are shown in Fig. 4. Y(Output) A A X X Spread Fig. 5. IDS pattern of four SISO systems. ed curves are extracted narrow paths. Spreads which are the width of the dark area in the y direction are aso visibe in these figures..5 5 x x.5 Beongingness Fig.. (a) Input-output reationship of a two-input function and (b) input domains divisions and corresponding membership functions. Fig. 6. Extracted input-output reationship. Finay using extracted narrow paths and spreads the output of the system is computed using (4) as shown in

4 86 P. EZAEE M. TAYAAI. KÖCHEL MIIATUIZED MICOSTIP FILTE DESIG USIG ACTIVE LEAIG METHOD Fig. 6. It shoud be mentioned that the utiized membership functions for this modeing have cosine form as foows. where x is variabe. x a cos b a x a cos b a for x : a b for x : a b. ALM for Three-Input Systems In this section the ALM formuation for modeing of an unknown function with three independent variabes which are referred to as x x and x is described. Suppose each input domain is divided into m m and m partitions respectivey. Therefore the number of IDS units is cacuated as foows. L m i i j i j ji (6) (7) where L is the tota number of IDS units and i denotes the number of IDS units for the input variabe x i. L aso denotes the number of inference rues. Some of these inference rues are as shown in (8). : If x : If : If x : If x x m m and x and x and x and x m m Finay a the extracted narrow paths spreads and membership functions are used for output mode computation (9). y is βψ or...or βikψik or...or β ψ k... i where β ik is cacuated as foows. i i i k. (8) (9) ik ik. () ik In this equation Γ ik is cacuated using (). A A A... A... ik A ik A m m A A m m () where is the intersection operator of the fuzzy sets. It shoud be emphasized that the fow diagram of Fig. is vaid for ALM modeing of an unknown function with any required number of input variabes.. Couping and Externa Quaity Factor Modeing Using ALM In the foowing subsection couping and externa quaity factor are briefy described and some references are addressed concerning common approach to open oop fiter design using couping factor matrix. In the next subsection ALM is impemented for modeing these two factors for a distinct S. Extracted ALM-based couping and externa quaity factor surfaces are utiized in section 4 as a fiter design too.. Brief Definition of Couping and Externa Quaity Factor Couping factor which is the most important quantity in designing any narrow band fiter can be cacuated using the foowing equation. fe - fm K = () f + f where f e and f m are even and odd resonant frequencies of the two couped resonators which occur at the frequencies where S has its minimum vaue []. Fig. 7(a) and 7(b) show two different structures of the couped Ss. e Fig. 7. Couped Ss (a) mixed couping and (b) magnetic couping. (c) Typica tapped-ine feeding structure for a S. Another important quantity in the fiter design is externa quaity factor (Q ext ). This factor can be described as the couping of a resonator to an externa circuit. For every resonant circuit Q ext can be computed by the aid of unoaded quaity factor (Q U ) and oaded quaity factor (Q L ) as it is shown in () [4]. = -. () Qext QL QU A typica tapped ine feeding structure which is used to excite a S has been shown in Fig. 7(c). Q ext of this structure is modeed in the foowing subsection. Eary after the first introduction of SOLs in [5] different couping structures and a fiter design exampe using couping coefficient approach was described in []. The same process has been appied to other kinds of open oop resonators such as trianguar [6] pentagona [7] hexagona [8] and even Ss. The fina step of the approach which has been described in [] and impemented in [6]-[8] is devoted to the cacuation of required couping factors through the use of time consuming m

5 ADIOEGIEEIG VOL. O. 4 DECEMBE 86 fu wave simuators. In these references the probem of externa quaity factor computation for a kinds of open oop resonators was negected. To avoid this time consuming process of couping factor computation and to introduce an approach for determination of the feed ine physica parameters according to the required externa quaity factor use of ALM is proposed.. Modeing Steps In this subsection the effect of substrate height (h) in the range of [.5 mm mm] and spacing between resonators (S) in the range of [. mm. mm] on the mixed and magnetic couping factors (Fig. 7(a) and 7(b)) is modeed using the discussed modeing technique. Afterwards the effect of feed ine ength (L f ) feed ine position (D f ) and feed ine width (W f ) on the Q ext is modeed for the structure shown in Fig. 7(c). In this modeing L f D f and W f are within the range of [ mm mm] [ mm] and [. mm.8 mm] respectivey. In order to carify the modeing steps a distinct S with the foowing dimensions is used; W =.7 mm g =.6 mm L = 5.6 mm and d =. m. Seected substrate permittivity for these modeings is 9.8. In the Q ext modeing the substrate height is seected to be.7 mm. The foowing steps have been carried out to construct the ALM-based couping and externa quaity factor surfaces: Mixed and magnetic couping factors have been cacuated using Ansoft HFSS- for 6 points within the variation range of the modeing parameters i.e. h and S. These are the required initia input data for the construction of couping factor mode. In the same way Q ext of Fig. 7(c) has been cacuated using Ansoft HFSS- for data points within the variation range of W f L f and D f. These data points are the required initia inputs for the construction of Q ext mode. Concerning the mixed and magnetic couping factor modeing the variation range of h and S has been divided into and 8 sections respectivey. Concerning the Q ext modeing the variation range of W f L f and D f has been divided into 4 5 and sections respectivey. Initia data of each section have been projected on the corresponding x i -y pane and reated IDS patterns have been constructed for each SISO system. Using the constructed IDS patterns the narrow path and spread of different SISO systems have been computed by the aid of () and () respectivey. Finay the mode output has been cacuated using (9). In this cacuation extracted narrow paths and spreads and the cosine form membership functions (6) which are aocated to each of the independent variabes according to the number of divisions have been used. Fig. 8 shows the extracted ALM-based couping factor surfaces for the mixed and magneticay couped Ss. According to the number of independent variabes for the Q ext modeing which are three ones we need a four dimensiona space for representation of the resuts in one figure which is not possibe. In this regard Fig. 9(a) - 9(c) show the extracted Q ext surfaces versus two of the modeing parameters. In each of these figures one of the independent variabes has been set to three different vaues and the other ones sweep their own range of variations. Fig. 8. ALM-based extracted couping surfaces for the couped Ss (a) mixed couping (b) magnetic couping. Fig. 9. Extracted Q ext for the structure of Fig 7(c) (a) D f = (top) D f = mm (midde) D f = mm (bottom) (b) W f =. mm (top) W f =.5 mm (midde) W f =.8 mm (bottom) and (c) L f = mm (top) L f = 7 mm (midde) L f = mm (bottom). esoution of the extracted couping factor surfaces is.5 mm for each of the independent variabes. For the extracted Q ext surfaces resoution is equa to.5 mm. mm and. mm for L f D f and W f respectivey. Considering the above resoution each of the mixed or magnetic couping surfaces consists of 6 points and the extracted quaity factor consists of 4 9 points. ALM needs a few minutes for modeing each of these mixed and magnetic couping surfaces and ess than haf an hour for modeing externa quaity factor versus its three independent variabes whie Ansoft HFSS- needs 9 minutes for each point of these couping factor surfaces and minutes for each point of the externa quaity factor surfaces. In other words Ansoft HFSS- needs more than years for computing each of the couping factor surfaces

6 86 P. EZAEE M. TAYAAI. KÖCHEL MIIATUIZED MICOSTIP FILTE DESIG USIG ACTIVE LEAIG METHOD and 7 years for computing externa quaity factor data. This comparison ceary shows the abiity of the ALM method in providing a vanishingy fast modeing too with a high resoution of the extracted data for couping and externa quaity factor computations within a wide variation range of the independent variabes which seems amost impossibe by the fu wave approach. It shoud be emphasized that the modeing approach and modeing simpicity remains unchanged when the number of modeing variabes increases because in this modeing technique every compex system is broken down into its simper aspects to acquire usefu information in a more comprehensibe form. In order to verify the mode accuracy the error between the target function (fu-wave-based extracted data) and the constructed mode (ALM-based extracted data) was measured using two different criteria i.e. the fraction of variance unexpained (FVU) and correation coefficient (CC) which are defined as foows. CC FVU y y yˆ y y y yˆ yˆ y y yˆ yˆ (4) (5) where y and ŷ denote the th data point of the output vector and the constructed mode respectivey. is the tota number of the output vector. Couping Factor ALM-Based Extracted Fu Wave Simuation S [mm] Couping Factor ALM-Based Extracted Fu Wave Simuation S [mm] Fig.. ALM-based extracted couping curves and fu wave simuation (a) h =.75 mm cut of Fig. 8(a) and (b) h =.7 mm cut of Fig. 8(a). FVU is proportiona to the mean square error. As the mode accuracy increases the FVU approaches zero and CC approaches one. To consider the accuracy of the extracted surfaces two different cuts of Fig. 8(a) as an exampe are considered (h =.75 mm and h =.7 mm). These two cuts are shown in Fig. by soid ines whie the corresponding fu-wave-based extracted data are demonstrated by dashed ines. As it is seen they are in good agreement. Computing FVU and CC resuts in FVU =.9 and CC =.9999 for Fig. (a) and FVU =.5 and CC =.9999 for Fig. (b). These vaues show the modeing accuracy of the proposed approach. Accuracy of the extracted surfaces is vaidated again in the next section by a fiter design exampe. 4. Fiter Design In order to show the accuracy of the extracted couping and externa Q surfaces a four poe Chebychev bandpass fiter was designed and fabricated. equired physica parameters of the structure were reated to the couping and externa Q of the fiter using ALM-based extracted surfaces. Center frequency and the fractiona bandwidth of the fiter are.765 GHz and 5% respectivey. The couping matrix and Q ext are as foows M Q 9. ext (6) Physica structure of the fiter is shown in Fig.. Dimensions of the resonators are W =.7 mm g =.6 mm L = 5.6 mm and d =. mm (Fig. 7). The fiter is fabricated on a substrate of ogers TMMi with a reative permittivity of 9.8. In order to satisfy the center frequency of the fiter substrate thickness is seected equa to.7 mm. Considering the physica structure of the fiter the first and the ast two resonators are mixed couped whie the second and the third resonators are magneticay couped. Therefore the spacing between the mixed couped resonators i.e. S and S 4 (Fig. ) is determined easiy using h =.7 mm cut of Fig. 8(a) which is shown in Fig. (b) with the soid ine. This curve resuts in S = S 4 =.55 mm. In the same way considering h =.7 mm cut of Fig. 8(b) resuts in S =.5 mm. Using ALM-based extracted Q ext surfaces for Q ext = 9. various tripets of (L f W f D f ) are cacuated. Among these different choices L f W f and D f were seected 5 mm.4 mm and.6 mm respectivey. The simuated and measured responses of the fiter are demonstrated in Fig.. As it is seen they are in good agreement. Fig.. Fabricated S fiter. In order to show the miniaturization degree of the S fiter in comparison with an ordinary open oop resonator one a SOL fiter with the same degree and neary the same eectrica characteristics (center frequency equa to.64 GHz and fractiona bandwidth equa to 4%) was de-

7 ADIOEGIEEIG VOL. O. 4 DECEMBE 86 signed and fabricated on the same substrate. The fabricated fiter and responses are shown in Fig.. The tota active area of this fiter (excuding feed ines) is 4.97 cm whie this area is.4 cm for the S one (Fig. ). It shows more than 7% of miniaturization for the S fiter in comparison with the SOL one. variation range of required fiter characteristics such as center frequency and bandwidth. Sampes of extracted ALM-based couping factor surfaces for the eectricay couped SOLs have been represented in Fig mm S [db] S [db] Frequency(GHz) (a) S -Simuation -5 S -Measured S -Simuation S -Measured Frequency(GHz) (b) Fig.. Measured and simuated response of the spira fiter (a) ampitude of the S (in-band response is shown inset) and (b) ampitude of the S (in-band response is shown inset). Design process of the SOL fiter is simiar to the expained procedure of the S fiter design. In this regard we impemented ALM to mode couping and externa quaity factor. Modeing parameters of the externa quaity factor were feed ine ength feed ine width and feed ine position. Couping factor was aso modeed for two different couping structures i.e. eectric and magnetic couping. In this modeing three different parameters were considered which are spacing between resonators resonator ength and substrate permittivity. Successfu ALM-based modeed couping and externa quaity factor in the case of SOLs and Ss shows the abiity of ALM in modeing different resonant structures. Considering three different parameters in couping factor modeing of the couped SOLs in comparison with two ones for the couped Ss vaidates the capabiity of ALM in extending the number of modeing parameters. These surfaces provide a fast and usefu too for SOL fiter design in a reativey wide S [db] S [db] Frequency(GHz) (b) S -Simuation -5 S -Measured S -Simuation S -Measured (a) Frequency(GHz) (c) Fig.. (a) Fabricated square open oop resonator fiter (b) ampitude of the S (in-band response is shown inset) and (c) ampitude of the S (in-band response is shown inset). 5. Concusions In this paper a nove approach based on ALM has been proposed to mode couping and externa quaity factor of Ss. Spacing between resonators and substrate height were the couping factor modeing parameters and feed ine ength feed ine width and feed ine position were the externa quaity factor modeing parameters. The

8 864 P. EZAEE M. TAYAAI. KÖCHEL MIIATUIZED MICOSTIP FILTE DESIG USIG ACTIVE LEAIG METHOD modeing was carried out within a wide range of modeing parameters surprisingy fast and accurate. Accuracy of the extracted surfaces was verified using two different error measures. Using the ALM-based-extracted couping and externa quaity factor surfaces one four poe Chebychev bandpass fiter was designed and fabricated. Good agreement between the measured and fu wave simuated response of the fiter vaidated the accuracy of the extracted surfaces again. The same process using ALMbased-extracted couping and externa quaity factor surfaces was carried out to design a SOL fiter. Good agreement between the measured and fu wave simuated response of the fiter shows the accuracy of the method and its generaity in modeing different resonant structures. Comparison between these two fiters determined more than 7% of area reduction for S fiters. The proposed modeing approach for couping and externa quaity factor is genera and can be used for other kinds of couping configurations other resonators or other feeding structures with the same degree of simpicity. It is aso possibe to consider more than three parameters in the proposed modeing approach simpy if we add initia required data of the new parameters to the previous ones. [] TAYAAI M. KAMI Y. Quaitative anaysis in engineering eectromagnetic; an appication to genera transmission ines. IEIEC Transactions on Eectronics vo. E84-C no. p [4] GUEY K. SAIKAYA. esonant frequency cacuation for circuar microstrip antennas with a dieectric cover using adaptive network-based fuzzy inference system optimized by various agorithms. Progress in Eectromagnetics esearch PIE 7 7 p [5] GUEY K. SAIKAYA. Concurrent neuro-fuzzy systems for resonant frequency computation of rectanguar circuar and trianguar microstrip antennas. Progress in Eectromagnetics esearch PIE 84 8 p [6] OSTADZADEH S.. SOLEIMAI M. TAYAAI M. A fuzzy mode for computing input impedance of two couped dipoe antennas in the echeon form. Progress in Eectromagnetics esearch PIE 78 8 p [7] OSTADZADEH S.. SOLEIMAI M. TAYAAI M. A fuzzy mode for computing back-scattering response from ineary oaded dipoe antenna in the frequency domain. Progress in Eectromagnetics esearch PIE [8] KABI H. WAG Y. YU M. ZHAG Q-J. High-dimensiona neura-network technique and appications to microwave fiter modeing. IEEE Transactions on Microwave Theory and Techniques vo. 58 no. p [9] TAKAGI T. SUGEO M. Fuzzy identification of systems and its appication to modeing and contro. IEEE Transactions on Systems Man and Cybernetics 985 vo. SMC. 5 no. p (a) ε r (b) S [] TAKAGI T. SUGEO M. A fuzzy ogic approach to quaitative modeing. IEEE Transactions on Fuzzy Systems 99 vo. no. p [] SHOUAKI S. B. HODA. ecursive fuzzy modeing based on fuzzy interpoation. Journa of Advanced Computationa Inteigence 999 vo. no. p [] SHOUAKI S. B. HODA. Fuzzy interpretation of human inteigence. Internationa Journa of Uncertainty Fuzziness and Knowedge-based Systems 999 vo. 7 no. 4 p (c) S Fig. 4. (a) Eectricay couped SOLs. Extracted couping surfaces for the eectricay couped SOLs shown in Fig. (4-a) (b) L = 6 mm (top) L = 9 mm (midde) L = mm (bottom) (c) ε r = (top) ε r = 4 (midde) ε r = (bottom) and (d) S =.8 (top) S =.6 (midde) S =.5 (bottom). S is the normaized spacing between resonators (S = S/L). eferences [] MIAFTAB V. MASOU.. Computer-aided tuning of microwave fiters using fuzzy ogic. IEEE Transact. on Microwave Theory and Techniques vo. 5 no. p [] MIAFTAB V. MASOU.. A robust fuzzy-ogic technique for computer-aided diagnosis of microwave fiters. IEEE Transactions on Microwave Theory and Techniques 4 no. vo. 5 p (d) r [] HOG J. S. LACASTE M. J. Couping of microstrip square open-oop resonators for cross-couped panar microwave fiters. IEEE Transactions on Microwave Theory and Techniques 996 vo. 44 no. p [4] IZZI P. A. Microwave Engineering: Passive Circuits. Prentice- Ha 988. [5] HOG J. S. LACASTE M. J. Canonica microstrip fiter using square open-oop resonators. IET Eectronics Letters 995 vo. no. p.. [6] CHAIMOOL S. KEDSUMAG S. AKKAAEKTHALI P. A nove microstrip bandpass fiter using trianguar open-oop resonators. In Proceedings of the 9 th IEEE Asia Pacefic Conference on Communication. Penang (Maaysia) p [7] OMAI I.. A. SOAES J. M. A. ABDALLA H. Compact microstrip bandpass fiter with enhanced stopband performance. In Proceedings of the th IEEE Internationa Microwave and Optoeectronics Conference. Savador (Brazi) 7 p [8] MAO. J. TAG X. H. WAG L. DU G. H. Miniaturized hexagona stepped-impedance resonators and their appications to fiters. IEEE Transactions on Microwave Theory and Techniques 8 vo. 56 no. p

9 ADIOEGIEEIG VOL. O. 4 DECEMBE 865 About Authors... Payman EZAEE was born in Kermanshah Iran in 98. He received the B.Sc. and M.Sc. degrees both in Eectrica Engineering from Iran University of Science and Technoogy (IUST) Tehran Iran in and 5 respectivey and is currenty working toward the Ph.D. degree in Eectrica Engineering. His research interests incude soft computing techniques in compicated eectromagnetic probems microwave inear and noninear circuit design microwave measurement techniques and metamateria structures. Majid TAYAAI was born in Tehran Iran in 96. He received the B.Sc. degree from Iran University of Science and Technoogy Tehran Iran in 988 the M.Sc. degree from Sharif University of Technoogy Tehran Iran in 99 and the Ph.D. degree in communication and systems from the University of Eectro-Communications Tokyo Japan in. From 99 to 99 he was a esearcher with the Iran Teecommunication Center where he was invoved with noninear microwave circuits. Since 99 he has been a member of the facuty with the Department of Eectrica Engineering Iran University of Science and Technoogy Tehran Iran where he is currenty an Assistant Professor. His research interests are quaitative methods in engineering eectromagnetic eectromagnetic compatibiity (EMC) theory computation and measurement techniques microwave and miimeter-wave inear and noninear circuit design microwave measurement techniques and noise anaysis in microwave signa sources. einhard KÖCHEL (IEEE Feow) received the Dip.- Ing. degree in Eectrica Engineering in 975 and the Dr.- Ing. degree in 98 from the Technica University Braunschweig Germany. From 98 to 986 he was a Principa Scientist at the Phiips esearch Laboratory Hamburg Germany. In 986 he joined the Technica University Hamburg-Harburg where he was a Fu Professor in microwave eectronics unti ovember 99. Since December 99 he has hed the Chair in Microwave Engineering at the University of Kie Kie Germany where he serves as Dean of the Department. His research interests incude active and passive microwave components utrawideband technoogy microwave measurement techniques industria microwave sensors and radar. He has pubished more than 4 papers in reviewed journas and at scientific conferences. He was Guest Editor of the book Sensors Update Vo.7 (Wiey-VCH) and the specia issue on utrawideband of the IEEE TASACTIOS O MICOWAVE THEOY AD TECHIQUES vo. 54 Apri 6. He has authored 9 patents. Dr. Knöche is active in the IEEE. He serves on the TPC of the IEEE Microwave Symposium (IMS) and is the Chair of the Technica Committee MTT-6 on Microwave Systems. He was the Genera Chairman of the German Microwave Conference 8. He is a Feow of the IEEE for contributions to microwave systems and sensors for industria process contro. He is a member of USI Commission A and a member of the German Institute of Eectrica Engineers VDE-ITG. He was recipient of the VDE best-paper award 978 the European Microwave Prize 98 and the TSH-Technoogy Transfer Award in.