Automatic Tuning

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS, VOL. 55, NO. 5, JUNE 2008 1357

Fully Automated RF/Microwave Filter Tuningby Extracting Human Experience Using

Fuzzy ControllersVahid Miraftab, Member, IEEE, and Raafat R. Mansour, Fellow, IEEE

AbstractThe paper introduces modeling of human experienceby linguistic if-then rules in terms of fuzzy logic controllers fortuning RF/Microwave filters. The approach could be used for anycircuit or system tuning problem that involves human expert infor-mation provided that the expert information could be described interms of linguistic if-then rules. The tuning approach is both the-oretically and practically illustrated in this paper. The tuning isdone in two stages both taking advantage of fuzzy controllers. Thefirst stage uses the phase response of the filter, while the secondstage uses the magnitude response of the filter for adjustment of

the tuning screws. A fully automated experimental setup is imple-mented by high resolution motors with flexible leads to make thetuning possible. 3-pole and 7-pole Chebyshev waveguide filters areused to demonstrate the concept. The measured results prove thevalidity of the method.

Index TermsCircuit tuning, computer-aided tuning, design au-tomation, expert systems, fuzzy control, fuzzy logic systems (FLS),RF/microwave filters.

I. INTRODUCTION

AUTOMATED computer-aided tuning of RF/microwave

filters is challenging and yet useful due to the demandsof fast and cost-effective production lines in the currentfast-growing market [1][3]. The current tuning methods areeither based on optimization or synthesis of the coupling matrixmathematical model. These techniques, however, have theirown shortcomings which are mainly initiated from three basicfacts. First of all, the mathematical model is an approximatemodel and does not directly reflect the effect of the tuningscrews and dispersion. Secondly, there are always manufac-turing tolerances involved, and finally the post-productiontuning lines are usually not fully automated. These shortcom-ings are usually magnified when dealing with more complicatedstructures. As a result, there is still a need for a human operator

who has expertise in the tuning of such structures to further tunethe structure to meet the customer needs. Filters in real-worldapplications are typically tuned manually by human experts(technologists). They have special knowledge/experience with

Manuscript received December 22, 2006; revised August 8, 2007. This workwas supported in part by National Science and Engineering Research CouncilandCOM DEVLtd.,Canada. This paper wasrecommendedby AssociateEditorE. Rogers.

V. Miraftab is with COM DEV Ltd., Cambridge, ON N1R TH6, Canada,R. R. Mansour is with the Electrical and Computer Engineering Depart-

ment, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail:[email protected]).

Digital Object Identifier 10.1109/TCSI.2008.916614

tuning specific-structures. The expert knowledge can often becharacterized in terms of IF-THEN rules.

Fuzzy Logic techniques are the only ways to incorporate lin-guistic rules to duplicate the human way of thinking. Extractinghuman experience and utilizing it in a fuzzy controller can re-place the human operator, thus automating the tuning task.

Fuzzy logic systems (FLS) have been proven to be strongtools and reliable models for tuning and design of microwave

circuits. The feasibility of using FLS in diagnosis and tuningof microwave circuits has been demonstrated in [4], [5]. Thesefuzzy systems are based on objective information i.e., trainingdata pairs, and used for extraction of the circuit model. Use ofhuman expert knowledge in tuning microwave filters was intro-duced in [6] and [7]. The method is based on fuzzy controllerconcept, which actually models the thinking processes an ex-pert might go through in the course of manipulating process.Fuzzy control has been used as one of the most successful ap-plications of fuzzy theory and was introduced by Chang andZadeh in 1972 [8], and Mamdani in 1974 [9]. The fuzzy con-trollers described in [6] are based on numerical data extractedby tracking human expert moves and require enough number of

scenarios for the expert to tune to complete the learning process.The fuzzy controllers in [7], however, are based on linguisticif/then rules extracted from an expert. These fuzzy controllersare capable of including expert rules to accurately tune the filterresponse. Using this approach also gives the flexibility of addingmore expert heuristics in terms of rules. A unique hardwareand software setup is designed to enable the full automation ofthe process. This paper uses the same concept as in [7] experi-menting different and more complex microwave filters showingthe validity and robustness of the approach towards the fully au-tomated tuning. Moreover, the tuning method and design of thefuzzy controllers are theoretically discussed in detail.

The paper uses two levels of fuzzy controllers to tune the

filter. The first level fuzzy controllers do a coarse tuning of thefilter, while the second level fuzzy controllers perform a finetuning procedure to minimize the return loss. The mathematicalconcept is illustrated using a 3-pole filter example. The detailedcomponents of the fuzzy logic controllers are also discussed inthis paper. The approach is successfully tested on an experi-mental 3-pole waveguide filter as well as a 7-pole filter to provethe validity of the approach for higher order filters.

II. EXPERIMENTALSETUP

Fig. 1 shows the diagram for our automated filter tuning. Themotor arms are controlled by our fuzzy logic program. Then, the

motor turns are transferred to the tuning screws. This changes

1549-8328/$25.00 2008 IEEE


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1358 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS, VOL. 55, NO. 5, JUNE 2008

Fig. 1. Automated filter tuning diagram.

Fig. 2. Automated filter tuning setup hardware (3-pole).

Fig. 3. Automated filter tuning setup hardware (7-pole).

the response of the microwave circuit, which is an input to thefuzzy controller. Figs. 25 show the experimental setups for thefilters under test. They are 3-pole and 7-pole bandpass wave-guide filters with adjustable 4-40 tuning screws.

The screws are connected to servo/step motors [10] by customdesigned flexible leads to connect the screws to motor shafts. Wedesigned universal mounting brackets to arbitrarily hold and po-sition the motors on a main aluminum plate. This enables us tohave adjustability in three dimensions to target any position on

a particular device. The motors are controlled using a GraphicalUser Interface (GUI). It contains sliders that are programmed to

Fig. 4. 3-pole microwave filter under test.

Fig. 5. 7-pole microwave filter under test.

turn motors and thus the screws back and forth. Once the move-ment is settled, the network analyzer data containing the scat-tering parameters at the designated channel is read and plotted as

graphs in the GUI. This helps the human operator to go throughthe tuning process by using the GUI only. The GUI is designedto implement the fuzzy logic methods explained in the next sec-tions.

III. TUNINGPROCEDURE

The proposed tuning procedure contains two steps: coarsetuning and fine tuning. The coarse tuning is based on an algo-rithm which looks at the phase and group delay response at thefilter center frequency. A similar approach has been proposed byNess in 1998 [2]. However, Nesss method uses only the groupdelay information to tune both couplings and resonant frequen-

cies, while we use the phase response only to roughly tune theresonators of the filter. We use the group delay response beforestarting the tuning process to measure a phase offset, which willbe explained in the next sections. Nesss method requires that allthe resonators are completely shorted to obtain more accurateresults, which is not usually feasible for practical cases. More-over, microwave filters often need final fine tuning due to manu-facturing tolerances, design imperfections and inaccuracy of themodels.

When all the resonators of a filter are highly detuned, onecan tune each resonator by looking at the phase atcenter frequency. Ideally, the phase toggles from 180 to zerodeg at center frequency when each resonator is tuned. The fine

tuning algorithm is an iterative algorithm to adjust the screwpositions by looking at the return loss response. Both steps are


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MIRAFTAB AND MANSOUR: FULLY AUTOMATED RF/MICROWAVE FILTER TUNING BY EXTRACTING HUMAN EXPERIENCE USING FUZZY CONTROLLERS 1359

Fig. 6. Ideal 3-pole filter example frequency response. (a) in decibels. (b) in decibels. (c) . (d) .

implemented using fuzzy controllers based on linguistic rulesextracted from an expert. In the next sections, the tuning con-cept has been proven followed by the final tuning steps usingthe two types of fuzzy controllers.

IV. COARSE TUNING CONCEPTILLUSTRATION FOR3-POLEFILTEREXAMPLE

In this section, the coarse tuning concept is illustrated by con-sidering the coupling matrix for a 3-pole Chebyshev filter ex-ample with the response shown in Fig. 6

(1)

(2)

Following the coupling-matrix mathematical model [12]

(3)

where

(4)

For this 3-pole filter the matrix is given by

(5)

A. Tuning the First Resonator

The objective is to calculate the phase at the center frequencywhen and are very large (highly detuned resonators).For highly detuned cases of the resonators in this example,we consider the following diagonal values for plotting thefrequency response: . At centerfrequency, , and by assuming where is acoupling value, the smaller terms could be neglected

(6)

Using (1)(4), is calculated as (7) and (8), shown at the

bottom of the page. When all the resonators are highly detuned,by eliminating the lower order terms, (7) could be approximatedas

(9)

(7)

(8)


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Fig. 7. Frequency response of the 3-pole filter when only the first resonator is tuned. (a) in decibels. (b) in decibels. (c) . (d) .

Therefore, the phase is

(10)

Considering the effect of the frequency, the phase could bewritten as

(11)

The group delay could be obtained by taking the derivate ofthe phase with respect to frequency. Using the chain rule

(12)

According to the above equations, around the center fre-

quency, when is very large, group delay is very small.When the first resonator is tuned, for large and

values (highly detuned), (7) could be simplified to

(13)

The phase then could be calculated as

(14)

When the first resonator is tuned, is zero and therefore

the phase becomes 180 deg. Therefore, the first tuning step isto highly detune all the resonators, and tune the first resonator

until the return loss phase at center frequency becomes 180deg. The key assumption here is to have a very large . Thegroup delay around the center frequency could be calculated byconsidering the effect of frequency and taking the phase deriva-tive with respect to frequency

(15)

(16)

Equation (16) illustrates an interesting observation. It indicatesthat the group delay shape is approximately symmetrical aroundthe center frequency. Consider two frequencies of .Then, could be calculated as

(17)

Since is small compared to

(18)

Therefore, the magnitude of is the same for the two frequen-cies and thus the group delay is approximately symmetrical.Fig. 7 shows the corresponding frequency response of the filter.

B. Error Calculation for Tuning the First Resonator

Suppose there is a small error due to not having ideal as-sumptions. Then, instead of getting a phase of , a phase of


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Fig. 8. Frequency response of the 3-pole filter when the first two resonators are tuned. (a) in decibels. (b) in decibels. (c) . (d) .

is obtained, where a is a small positive phase. By ne-glecting the lower order terms and the fact that is zero, (8)could be simplified to

(19)

The phase offset from is then calculated as

(20)

It is interesting to see how much frequency drift this errorwould cause. In the original formulation (5), the A matrix con-tains the term . Considering as zero and finding

at the phase of , the frequency drift (error) could be calcu-lated. This is equivalent to replacing by in (8) and finding

for the phase of . This results in

(21)Solving for

(22)

The phase shift is then calculated by solving the following equa-tion for :

(23)

Therefore

(24)

As an example, for and , .As could be seen from (24), the frequency shift error is verysmall when is large. The same procedure could be obtainedfor tuning the last resonator using the response.

C. Tuning the Second Resonator

Assuming is a relatively large number, while andare small numbers, (7) could be simplified as

(25)

The phase at center frequency is then calculated as

(26)

So, when is large enough (highly detuned), the phase isvery close to zero. This suggests the second step of the tuning,which is leaving detuned and tuning until the phase iszero.

To calculate the group delay around the center frequency, sim-ilar to the previous section procedure, the phase is derived as

(27)


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Fig. 9. Tuning steps using multilevel FL controllers based on linguistic rules.

The group delay is then calculated as

(28)

Using similar explanations, the group delay formula above issymmetrical around the center frequency. Fig. 8 shows the fre-quency response of the filter for the first two resonators tuned.

D. Error Calculation for Tuning the Second Resonator

Suppose there is small phase error of , where is a smallpositive phase. This is normally due to not having a large enough

. This error could be simply using (26)

(29)

The frequency drift could be calculated similar to the previoussection. That is when the phase in (7) is zero. This results to (21)with replaced by . S ince and are b oth very s mall,the first term could only be zero and thus

(30)

Similarly, the phase shift is calculated as

(31)

Interestingly, (30) is very similar to (22) and suggests that thenext adjacent resonator plays a major role. So, the more mis-tuned the adjacent resonator is, the more accurately the currentresonator could be adjusted.

As an example, for and, . As could be seen from (31), the

frequency shift error is very small when is large.This algorithm could be generalized for higher order filters as

well. It is very useful to tune the resonators approximately. The

overall proposed tuning algorithm is shown in Fig. 9, where thecoarse tuning is followed by a fine tuning algorithm.

Fig. 10. Ccontrol block diagram for tuning based on the first type of FLS.

V. TRANSMISSION-LINEEFFECT

As explained in previous sections, the coarse tuning is basedon tuning each resonator to reach a desired phase. However, inpractical cases, we often have a transmission line component atthe input/output ports, which could be part of the circuit or anexternal part imposed by a system. Therefore, it is important totake these effects into account. The resultant and re-sponses get constant phase shifts with the presence of the twotransmission lines. This suggests that these two constant phasesshould be measured at the beginning of the tuning process. Theconstant phase shift, however, does not affect the group delayresponse since it is the phase derivate with respect to frequency.

This phase shift is measured by turning the first and last res-onator screws to obtain group delay symmetry around the centerfrequency. We refer to this as phase reference in this paper.

VI. DESIGNINGFIRSTSTEPFUZZYCONTROLLERS

We follow the procedure described in [11] to design the FLS.Fig. 10 shows the block diagram of the control process to adjustthe screw positions based on the phase response. At each itera-tion the FL controller determines the amount of the screw turnbased on the phase response and the goal.

A. Rules for the First Type of FLS

It is helpful to have the phase response plot for different screw

positions to clarify the procedure. Fig. 11 shows these varia-tions for a sample tuning screw. Depending on the region or


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Fig. 11. Fuzzy regions for the first type of FLS.

TABLE ILINGUISTICFUZZYRULES TOFIND THEPROPERPHASE(EXAMPLE: RULE3- IF

ISNEGAND DELTA ISPB, THEN 1 ISPS)

state we are located, a rule with a specific strength will be fired.The phase offset is measured to be 5 deg for the 3-pole filter.Therefore, for the odd number resonators the phase goal is at

175 deg and for the resonators is 5 deg. For the FLS here,we use two inputs being phase at center frequency and therelative phase changes with respect to the screw movement.The output would be the screw turn with respect to the lastposition. These are basically the parameters that an expert takeinto account when tuning each resonator.

The rules are tabulated in Table I. There are 6 rules dependingon the region we are located at each iteration. If we are far fromthe phase target, we need to apply a larger drive (larger screwchange), while when we are closer to the target, we need to slowdown (smaller screw change).

Note that Delta is not the derivative of the phase function,but it measures the changes from the previous iteration to the

current iteration. It becomes to the derivate only if happensto be very small, which is the case during the last iterations.

B. Fuzzy Sets for the First Type of FLS

In order to continue the design process, we need to assignfuzzy sets or membership functions to each input and outputparameter. As for the FLS, we use triangular membership func-tions for input/output fuzzy sets, max-product inferencing, andcenteroid defuzzification.

Two fuzzy sets are assigned for the phase input; one as posi-tive (POS) and the other one as negative (NEG) with respect tothe target. For the relative phase input, three fuzzy sets are as-signed as positive small (PS), positive (P) and positive big (PB).

The output is the relative change given to the designated screwand has 6 fuzzy sets as positive small (PS), positive (P), pos-

Fig. 12. Input fuzzy sets. (a) Odd number resonators. (b) Even number res-

onators.

Fig. 13. Fuzzy sets for the second input variable.

Fig. 14. Output fuzzy sets.

itive big (PB), negative small (NS), negative (N) and negativebig (NB). The membership function parameters could be ad-justed depending on the system behavior. These fuzzy sets aredepicted in Figs. 1114.

C. Output Calculation

We use the popular centroid defuzzification formula [11] tocalculate the output of the fuzzy logic system

(32)

where is the firing strength (weighting factor) of the th rule,

is the number of the rules, and is the center of gravity of thecorresponding output fuzzy set.


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Fig. 15. Fine-tuning block diagram.

Fig. 16. Fuzzy regions for the second type of FLS.

VII. DESIGNINGSECONDSTEPFUZZYCONTROLLERS

The fuzzy logic system here is similar to the one in theprevious section. However, it has three inputs and one output.Fig. 15 shows the block diagram of the control process for finetuning by small screw adjustments. At each iteration, the FLcontroller determines the amount of the screw turn based on the

magnitude response.When the filter is roughly tuned, the purpose of the expert is

to make some local adjustments around the current state. Thefine-tuning process is not an easy task and may take a very longtime for the expert to finish. One reason is that once one screw istuned, the other screws are no longer at their optimum positionand need to be adjusted too. The other reason is that the responseis very sensitive to small screw turns. The expert looks at themagnitude response and tries to adjust each screw to minimize

magnitude in the pass-band. So, we define the objectivefunction as follows:

(33)

where is the start frequency and is the stop frequency ofthe bandpass filter.

A. Rules for the Second Type of FLS

Fig. 16 shows sample variations of the error objective func-tion for screw position changes. The fuzzy controller tries todecrease the error at a specific state. This process continues onthe other screws and the error objective function improvementsresult to an optimized response. The rules are shown in Table II.

Once all the screws are adjusted approximately for a rela-tively minimum objective function, the process needs to be re-peated since the screws are no longer at their previous minimum,

although we are getting closer to the return loss objective glob-ally. The shape in Fig. 16 is different from one screw to another.

TABLE IITHELINGUISTICFUZZYRULES TOFIND THECURRENTBESTRETURNLOSS INPASS-BAND. (EXAMPLE: RULE6- IF ( 1 0 ISPOS) AND ( 1 IS

NEG)AND ( 1 ISPOS), THEN 1 ISPS)

Fig. 17. Fuzzy sets for the first input.

Fig. 18. Fuzzy sets for the second input.

Fig. 19. Fuzzy sets for the third input.

These shapes are also noisy, which make it a very good candi-date for a fuzzy controller.

B. Fuzzy Sets for the Second Type of FLS

The first input to the FLS is return loss changes at the pre-vious step; the second input is return loss changes at the currentstep; and the third input is screw change at the current step. Theoutput is screw change at the next step. These are the parame-

ters that the expert considers when tuning the filter. For the inputfuzzy sets, we have used two membership functions as positive


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Fig. 20. Fuzzy sets for the output.

Fig. 21. Response of filter without tuning.

Fig. 22. Response after coarse tuning using first type fuzzy controllers.

Fig. 23. 3-pole filter response after 2 fine-tuning iterations.

(POS) and negative (NEG), while the output has four member-ship functions as positive (P), positive small (PS), negative (N),and negative small (NS). Here also triangular membership func-tions, max-product inferencing and centeriod defuzzification isused. Note that we can always increase the number of the fuzzy

sets and alter the rules to improve the fuzzy controller perfor-mance. These fuzzy sets are depicted in Figs. 1720.

Fig. 24. Filter response after 1 iteration of fine-tuning.

Fig. 25. Filter response after 2 iterations of fine-tuning (meets the spec. forRLof 20 dB).

Fig. 26. Filter response after 5 iterations of fine-tuning (meets the spec. forRLof 25 dB).

VIII. RESULTS

The method has been applied to tune experimental 3-pole and7-pole Chebyshev waveguide filters. Figs. 4 and 5 show thesefilters.

A. 3-Pole Filter Tuning

To prove the proposed approach for a case that involves tuningboth resonators and coupling screws at the same time, we con-

sider designing a 3-pole waveguide filter with center frequencyof 15 GHz, bandwidth of 500 MHz, and a return loss of 20 dB.


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Fig. 27. Time response for tuning the resonators.

Fig. 21 shows the response of the filter after fabrication withoutany tuning. As could be seen from the figure, the desired re-

sponse has not been achieved due to manufacturing tolerancesand design imperfections.The coarse tuning fuzzy controllers (first type) give the filter

response as shown in Fig. 22. The fine tuning fuzzy controllers(second type) consider all resonators and coupling screws atthe same time. Fig. 23 shows the filter response after two it-erations of fine-tuning. As could be seen from the figure, theresults closely meet the design specifications. The whole tuningprocess takes approximately 56 min.

B. 7-Pole Filter Tuning

The 7-pole Chebyshev waveguide example is to be tuned at

the center frequency of 11.2 GHz, the pass-band from 10.85 to11.55 GHz, and a return loss of 20 dB. The filter is iris coupledwith WR75 flange size at input and output ports and 440 tuningscrews.

Initially, all the resonators are highly detuned by turning all ofthem clockwise inside the filter. There is no filter response shapewithin the frequency band of interest in this situation. When thecoarse tuning is complete, the return loss becomes around 10dB in the passband. Therefore, there is a need to apply the finetuning steps using the second type fuzzy controllers designed inthe previous sections. Due to hardware limitations, we only hadaccess to the resonator screws of the filter and thus the couplingscrews are all removed from the structure. However, the effect

of the coupling screws along with the resonator screws is con-sidered for the 3-pole filter.

Fig. 24 shows the filter response after 1 iteration of the fine-tuning procedure. One iteration means the second type fuzzy

controller has tuned all the resonators once in sequence. Thereturn loss is very close to the 20-dB return loss target.Fig. 25 shows the filter response after 2 iterations of the fine-

tuning procedure. The return loss is at 23 dB, which meets thedesign specifications for the 20-dB return loss target. The fine-tuning process could be continued to obtain a better return loss.After five iterations the 25-dB target is achieved as shown inFig. 26. The coarse tuning process takes 34 minutes to com-plete with the current setup. Each iteration of the fine tuningprocedure takes about 1 minute to complete resulting in a 56minutes total time for the 20-dB return loss target.

C. The Performance of the Fuzzy Controllers

Fig. 27 shows the time response for tuning each resonatorusing the designed first type fuzzy controllers. It shows thenumber of iterations took for every screw to tune. The timefor each iteration varies depending on the travel of the screw.The overall settling time depends on the speed of the motor,and takes about 30 s for each to complete with the availablesetup. As could be seen from the figures, the fuzzy controller isdesigned to give an under-damped time response. This is foundto be fast and stable at the same time. The tuning speed couldbe further improved by increasing the speed of the motors aswell as optimizing the fuzzy sets. However, this should be donedeliberately to avoid instability. For some applications, the endresults of the fine tuning may not be accurate enough. In these

cases, the objective function for tuning could be changed. Itmay be beneficial to introduce a third fuzzy controller with


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objective functions based on the response over a range offrequency to obtain more accurate results.

IX. CONCLUSION

The paper has demonstrated fully automated RF/microwave

filter tuning using linguistic rules extracted from human ex-pert. The approach takes advantage of fuzzy controller conceptin two steps of coarse and fine tuning. The fuzzy controllershave proven to be very robust in tuning the filter response. Thealgorithm has been tested on experimental 3-pole and 7-poleChebyshev filters. This technique could be easily applied to anyother type of tunable circuit/system where linguistic expert rulesexist. By this method, the tuning time and cost have substan-tially decreased. The results confirm the validity of the proposedmethod.

ACKNOWLEDGMENT

The authors would like to thank Dr. M. Yu to provide themwith the 7-pole waveguide filter. Special thanks go to B. Jolley,Center for Integrated RF Engineering(CIRFE) Laboratory forhis technical assistance in calibration and tuning.

REFERENCES

[1] H. Hsu, H. Yao, and K. A. Zaki, Computer-aided diagnosis and tuningof cascaded coupled resonators filters, IEEE Trans. Microw. TheoryTech., vol. 50, no. 4, pp. 11371145, Apr. 2002.

[2] J. B. Ness, A unified approach to the design, measurement, and tuningof coupled-resonator filters,IEEE Trans. Microw. Theory Tech., vol.46, no. 4, pp. 343351, Apr. 1998.

[3] G. Pepe, F. J. Gortz, and H. Chaloupka, Computer-aided tuning

and diagnosis of microwave filters using sequential parameter extrac-tion, in IEEE MTT-S Int. Microwave Symp. Dig., 2004, vol. 3, pp.13731376.

[4] V. Miraftab and R. R. Mansour, Computer-aided tuning of microwavefilters using fuzzy logic,IEEE Trans. Microw. Theory Tech., vol. 50,no. 12, pp. 27812788, Dec. 2002.

[5] V. Miraftab and R. R. Mansour, A robust fuzzy-logic technique forcomputer-aided diagnosis of microwave filters,IEEE Trans. Microw.Theory Tech., vol. 52, no. 1, pp. 450456, Jan. 2004.

[6] V. Miraftab and R. R. Mansour, Tuning of microwave filters by ex-tracting human experience using fuzzy logic, in IEEE MTT-S Int. Mi-crow. Symp. Dig., 2005, pp. 16051608.

[7] V. Miraftab and R. R. Mansour, Automated microwave filter tuningby extracting human experience in terms of linguistic rules using fuzzycontrollers, in IEEE MTT-S Int. Microwave Symp. Dig., 2006, pp.14391442.

[8] S. S. L. Chang andL. A. Zadeh,On fuzzy mapping andcontrol,IEEETrans. Syst., Man, Cybern., vol. SMC-2, no. 1, pp. 3034, Jan./Feb.1972.

[9] E. H. Mamdani, Application of fuzzy algorithms for the control of adynamic plant, Proc. IEE, vol. 121, no.12, pp. 15851588,Dec. 1974.

[10] SM2315D Smart Motors, AnimaticsCorp., Santa Clara,CA, 2001 [On-line]. Available: http://www.animatics.com/web/sm_2315.html

[11] L. X. WangandJ. M. Mendel, Generatingfuzzyrulesby learningfrom

examples,IEEE Trans. Syst., Man, Cybern., vol. 22, pp. 14141427,Nov./Dec. 1992.[12] A. Atia and A. E. Williams, New type of waveguide bandpass fil-

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Vahid Miraftab(S96M06) was born in 1977. Hereceived the Ph.D. degree in electrical and computerengineering from University of Waterloo, Waterloo,ON, Canada, in 2005.

His doctoral thesis pertained to tuning and designof microwave circuits using fuzzy logic techniques.He has had several internship and co-op industryexperience in different areas of electrical engineeringduring his studies including digital signal processing,electronics, RF and microwaves. He is currentlywith COM DEV Ltd. Cambridge, Cambridge, ON,

Canada. His research interests include intelligent design and tuning of RFcircuits using computational intelligence, design and tuning automation,microwave filter/multiplexer synthesis and design, advanced electromagneticnumerical analysis, and RF passive and active integrated circuits.

Dr. Miraftab holds Canadas National Science and Engineering ResearchCouncil (NSERC) Industrial R&D Fellowship (DRDF) award.

Raafat R. Mansour (S84M86SM90F01) wasborn inCairo, Egypt,on March31, 1955.He receivedtheB.Sc(withhonors)and M.Sc deg from AinShamsUniversity, Cairo, Egypt, in 1977 and 1981, respec-tively, and the Ph.D degree from the University ofWaterloo, Waterloo, ON, Canada in 1986, all in elec-trical engineering.

He was a Research Fellow at the LaboratoiredElectromagnetisme, Institut National Polytech-nique, Grenoble, France, in 1981. From 1983 to1986, he was a Research and Teaching Assistant in

the Department of Electrical Engineering, University of Waterloo. He joinedCOM DEV Ltd. Cambridge, Cambridge, ON, Canada, in 1986, where heheld several technical and management positions in the Corporate Researchand Development Department. He was promoted to Scientist in 1998. InJanuary 2000, he joined the University of Waterloo as Professor in the Elec-trical and Computer Engineering Department. He holds a Research Chairat the University of Waterloo in RF Technologies. He holds several patentsrelated to microwave filter design for satellite applications, and has numerouspublications in the area of electromagnetic modeling and high temperaturesuperconductivity. His present research interests include Superconductivetechnology; microelectromechanical systems technology and computer-aideddesign of RF circuits for wireless and satellite applications.

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