Waveguide Filters with Elliptical Function Response: Overview and Results of Different Implementations Jorge A. Ruiz-Cruz, 1 Jose ´ R. Montejo-Garai, 1 Jesu ´ s M. Rebollar, 1 Kawthar A. Zaki 2 1 Departamento de Electromagnetismo y Teorı ´a de Circuitos, Universidad Polite ´ cnica de Madrid, Ciudad Universitaria s/n. 28040 Madrid, Spain 2 Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 Received 5 October 2005; accepted 23 June 2006 ABSTRACT: Some recent implementations of waveguide filters with elliptical response are presented in this paper. The goal is to describe the main aspects involved in the computer- aided design of elliptic waveguide filters, which are commonly used at microwave and milli- meter-wave frequencies by their high selectivity, low insertion loss, and high power-han- dling capabilities. Three different examples based on crosscoupled cavities and the extracted-pole procedure are used to illustrate the main ideas, with their corresponding ex- perimental results. A comparative table summarizes the main features of the presented fil- ters. V V C 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE 17: 63–69, 2007. Keywords: elliptic filters; mode-matching; transmission zeros; circuit synthesis; full-wave opti- mization I. INTRODUCTION Filters at microwave and millimeter-wave frequen- cies are the subject of continuous research driven by the development of new communication systems. The increase in capacity, complexity, and power required by innovative applications has led to two interrelated areas of research: sophisticated filter transfer functions and technologies capable of imple- menting them. The aim of this research is to control the fundamental filter aspects such as high selectiv- ity, power handling, group delay, low in-band inser- tion loss, and so forth. The key is to control these pa- rameters with the lowest degree filter to save mass and volume. Depending on the application, the requirements of linear phase and out-of-band rejection lead to transfer functions characterized by equalization zeros and fi- nite transmission zeros in the stop bands. If the zeros are placed on the real axis or in a complex quad, the group delay can be equalized. On the other hand, the out-of-band rejection is controlled when the zeros are located on the imaginary axis, making the design of filters with very high selectivity possible. One of the most common types of filter transfer functions is the Chebychev one [1]. It is mainly char- acterized by in-band equiripple, with all the zeros of the transfer function located at infinity. In compari- son with the Chebychev filters, the elliptic transfer function supply more degrees of freedom to the de- signer: the response has finite transmission zeros that are suitably located to make the out-of-band rejection fulfill the filter specifications. Therefore, extensive work has been carried out on these types of filters [2–10]. Correspondence to: J. A. Ruiz-Cruz; e-mail: jorgerc@etc.upm.es DOI 10.1002/mmce.20198 Published online 1 December 2006 in Wiley InterScience (www.interscience.wiley.com). V V C 2006 Wiley Periodicals, Inc. 63