диафрагмированные волноводные фильтры / 5c4634c7-e678-4a23-ac92-4a1b852263ec

in Section III, where the vectors , , and include the physical design parameters, the extracted circuital parameters, and the objective circuital parameters of both filters, respectively.

It should be noted that the objective coupling matrices are obtained from the ideal prototype filters that would have been used for optimization of the filters if they were isolated, instead of starting with the model of the complete diplexer structure as is usually done. In fact, the mutual interaction of both filters in the diplexer is reflected in the Jacobian matrix of the modeling function which cannot be almost diagonal, since the variation of the physical dimensions of one filter modifies the electromagnetic behavior of the other filter. Therefore, (30) must be used to calculate the initial Jacobian matrix. However, after this calculation, the Jacobian matrix is updated without additional evaluations of the modeling function, using the scheme of Section III-A.

The diplexer used to test the optimization method consists of two sixth-order -plane filters connected by an -plane T-junction as depicted in Fig. 9 with the following specifications:

• Channel 1:

—center frequency: 28.75 GHz;

—bandwidth: 0.5 GHz;

—return loss in the passband: 25 dB.

• Channel 2:

—center frequency: 30 GHz;

—bandwidth: 1 GHz;

—return loss in the passband: 25 dB.

•Waveguide section: WR28 (7.112 mm 3.556 mm).

•Thickness of metal inserts: 100 m.

TABLE III

INITIAL DESIGN PARAMETERS OF THE DIPLEXER

The initial design of the diplexer is synthesized following the method proposed in [24]. This method starts from the optimized design of the two filters and then fixes the distances from the reference planes of the T-junction to the reference plane of each filter (indicated as and in Fig. 9). The geometrical dimensions of the initial design are given in Table III, and the full-wave electromagnetic analyzed response of this initial design is shown in Fig. 10. The mutual interaction between the filters through the T-junction produces high return losses, as is observed in the response. The optimization method modifies the parameters of the filter in order to compensate for this mutual interaction and recover the frequency response of the isolated original filters. The process optimizes the couplings and the resonant frequencies of each filter, but not the distances between the filters and the T-junction (i.e., and remain constant during the optimization routine).

Fig. 10. Scattering parameters of the initial design of the diplexer.

TABLE IV

OPTIMIZED DESIGN PARAMETERS OF THE DIPLEXER

passband of each channel) were calculated in every electromagnetic simulation.

The second column of Table II shows the performance comparison of this process and the equivalent optimization using a conventional gradient-based method as in the example of the isolated filter. In this case, the optimum can be reached using both optimization techniques, but the computation time is reduced to only 0.83% using the proposed method. It should be noted the large reduction of the number of evaluated frequency sweeps due to the Jacobian update scheme, compared to the explicit computations of the gradient of the error function using a forward differences method.

V. CONCLUSION

In this paper, an efficient method for the direct electromagnetic optimization of microwave passive devices, based on the extraction of a rational model from a reduced number of data samples of the frequency response, has been described. Some particular advantages of this method is the possibility to approximate nonrational responses and the adaptive update of the mapping between the circuital model parameters and the dimensions of the physical device. The current implementation restricts the application of the method to lossless networks due to two limitations:

•the use of the lossless Feldtkeller equation;

•the analytical method used to synthesize a coupling matrix.

However, the usual approach for synthesizing microwave devices requires only the use of lossless models, as losses are introduced in a last step after the proper optimization.

Two numerical application examples have shown remarkable improvements in computation efficiency. This reduction of the total time required for the optimization is achieved in two ways. First, the number of required optimization iterations is greatly reduced. Second, the number of needed data samples at each iteration is minimized thanks to the use of Cauchy’s method. One of the examples consists of the optimization of a complete diplexer, showing the flexibility of the method, that can be applied to structures different from isolated filters.

Fig. 11. Scattering parameters of the optimized design of the diplexer.

The geometric dimensions after optimizing the diplexer are shown in Table IV, and the scattering parameters of the modified design are presented in Fig. 11, where the equiripple response is almost completely recovered. As expected, the most modified geometrical dimensions are those located closer to the T-junc- tion, in order to compensate the reactive load that each filter presents to the other. The complete optimization process of the 26 parameters took only ten iterations and the total number of full-wave electromagnetic simulations executed was 37 (11 for the initial design and the ten iterations and 2 13 for the computation of the initial Jacobian, since there are 13 geometrical parameters in each filter). Only 22 frequency samples (11 in the

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Alejandro García-Lampérez (S’98) was born in Madrid, Spain, in 1976. He received the Ingeniero de Telecomunicación (M.S.E.E.) degree from the Universidad Politécnica de Madrid (UPM), Madrid, Spain, in 2000, and is currently working toward the Ph.D. degree at the UPM.

Since September 1999, he has been with the Microwave and Radar Group, Departamento de Señales, Sistemas y Radiocomunicaciones (SSR), UPM, where he carried out his graduate work on techniques for the design of microwave filters. His

research activities and interests are in the area of passive microwave devices design and simulation and application of numerical methods to electromagnetic problems.

Sergio Llorente-Romano (S’01) was born in Madrid, Spain, in 1977. He received the Ingeniero de Telecomunicacíon (M.S.E.E.) degree from the Universidad Politécnica de Madrid (UPM), Madrid, Spain, in 2000, and is currently working toward the Ph.D. degree at UPM.

Since September 1999, he has been with the Microwave and Radar Group, Departamento de Señales, Sistemas y Radiocomunicaciones (SSR), UPM, where he carried out his graduate work on techniques for the simulation and design of filters

and diplexers in waveguide technology. His research activities and interests are in the area of numerical methods applied to electromagnetic problems related to the design of microwave devices.

Magdalena Salazar-Palma (M’89–SM’01) was born in Granada, Spain. She received the Ingeniero de Telecomunicación and Ph.D. degrees from the Universidad Politécnica de Madrid (UPM), Madrid, Spain.

She is currently a Profesor Titular with the Departamento de Señales, Sistemas y Radiocomunicaciones, Escuela Técnica Superior de Ingenieros de Telecomunicación, UPM. She has taught courses on electromagnetic-field theory, microwave and antenna theory, circuit networks and filter theory, analog and

digital communication systems theory, numerical methods for electromagneticfield problems, as well as related laboratories. She has developed her research within the Grupo de Microondas y Radar in the areas of electromagnetic-field theory, computational and numerical methods for microwave structures, passive components, and antenna analysis; design, simulation, optimization, implementation, and measurements of hybrid and monolithic microwave integrated circuits; and network and filter theory and design. On numerous occasions, she has been a Visiting Professor with the Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY. She has authored three books and has authored or coauthored a total of 15 contributions for chapters and papers in books published internationally, 30 papers in international journals, and 140 papers in international conferences, symposiums, and workshops, plus a number of national publications and reports. She has served in different academic committees at the department, school, and university level. She has delivered a number of invited presentations, lectures, and seminars. She has lectured on several short courses, some of them in the frame of European Community Programs. She has participated as a researcher or director in 45 research projects and contracts, financed by international, European, and national institutions and companies. She has assisted the Comisión Interministerial de Ciencia y Tecnología (Spain National Board of Research) in the evaluation of projects. She is serving as reviewer of the Grant Project Office of the Italian Ministero dell’Universita e della Ricerca Scientifica e Tecnologica (Ministry of Universities and Scientific and Technological Research). She has also served in several evaluation panels of the Commission of the European Communities. She was Topical Editor for the disk of references of the triennial Review of Radio Science for three times. She has been a member of the Editorial Board of three scientific journals.

Prof. Salazar-Palma is a Registered Ingeniero de Telecomunicación in Spain. She is an associate editor for the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS (AWPL). She is a correspondent of the International Union of Radio Science (URSI). She has served as vice-chairman and chairman of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S)/IEEE Antennas and Propagation Society (IEEE AP-S) Spain joint chapter and chairman of the IEEE Spain Section. She is currently the IEEE Spain Section membership development officer. She has been a member of the IEEE Region 8 Nominations and Appointments Committee. She is currently the chairperson of the IEEE Region 8 Conference Coordination Subcommittee. She has been a member of the IEEE Ethics and Member Conduct Committee. Since 2001, she has been a member of the IEEE Women in Engineering Committee (WIEC). She has acted as liaison between the IEEE Regional Activities Board and the IEEE WIEC. She is currently the chairperson of the IEEE WIEC. She is a member of the Technical Program Committee of several international and national symposiums and reviewer for different international scientific journals, symposiums, and editorial companies. She has received two individual research awards and, together with the rest of her department, another research award, all from national institutions.