1636 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 5, MAY 2005 Synthesis and Design of In-Line -Order Filters With Real Transmission Zeros by Means of Extracted Poles Implemented in Low-Cost Rectangular -Plane Waveguide José R. Montejo-Garai, Jorge A. Ruiz-Cruz, Jesús M. Rebollar, Manuel J. Padilla-Cruz, Antonio Oñoro-Navarro, and Isidro Hidalgo-Carpintero Abstract—In this paper, an extension to the extracted pole technique for synthesizing -order filters with -transmis- sion zeros at real frequencies is presented. In addition, a new bandpass rectangular waveguide -plane low-cost configuration filter for high-power low-loss application (patent pending) that implements a filtering function with finite real frequency trans- mission zeros is proposed. This structure operates as a resonant cavity in transmission at central frequency of the bandpass and simultaneously introduces a controlled transmission zero out of the bandpass. Since every double-controlled electrical behavior cavity introduces a transmission zero, it is possible to introduce as many transmission zeros as the order of the filtering function. In order to validate the synthesis procedure and the new structure, different filters have been designed: a second-order filter with two transmission zeros, a third-order filter with one transmission zero, a fourth-order filter with two transmission zeros, and finally, an eighth-order filter with two transmission zeros. The last two have been manufactured, showing an excellent agreement between the measurement and theoretical simulation. Index Terms—Extracted pole, filter, -plane, transmission zero. I. INTRODUCTION T HE INCREASE in capacity, complexity, and RF power used in satellite communications and broadcast repeaters has brought about the use of sophisticated filter transfer func- tions. Regarding the out-of-band rejection, a more and more de- manding specification is required at present for innovative ap- plications. It is also mandatory not to use high-degree filters to fit these specifications in order to save mass and volume. Filters incorporating finite transmission zeros at real frequencies make it possible to design transfer functions with very high selectivity. In addition, symmetrical or asymmetrical out-of-band rejections can be obtained if the positions of the zeros are suitably chosen. Equally important, pseudo-low-pass and pseudo-high-pass fil- ters can be designed if all the transmission zeros are located ei- ther on the higher or on the lower rejection band. Another ap- Manuscript received September 23, 2004. This work was supported by the Comisión Interministerial de Ciencia y Tecnología Spain under Project TIC2001-3430 and by Alcatel Espacio S.A under a contract. J. R. Montejo-Garai, J. A. Ruiz-Cruz, and J. M. Rebollar are with the Depar- tamento de Electromagnetismo y Teoría de Circuitos, Esculea Técnica Superior Ingenieros Telecomunicación, Universidad Politécnica de Madrid, Ciudad Uni- versitaria S/N, 28040 Madrid, Spain (e-mail: jr@etc.upm.es). M. J. Padilla-Cruz, A. Oñoro-Navarro, and I. Hidalgo-Carpintero are with the Passive RF Department, Alcatel Espacio, Tres Cantos, 28760 Madrid, Spain. Digital Object Identifier 10.1109/TMTT.2005.847053 plication of the asymmetrical response is to compensate the dis- tortion arising in the manifold multiplexers. Given a filter specification, the first task is to generate the transfer function that in the more general case can be expressed as the ratio of two finite-degree polynomials with complex co- efficients. The evaluation of this mathematical response must fit with the out-of-band rejection specifications and the return losses in the bandpass. Therefore, in the more general case, transmission zeros can be implemented in an -order filtering function. There are two different approaches to designing responses with finite transmission zeros at real frequencies: • general folded cross-couplings [1] can be used, intro- ducing a direct coupling between the source and load of the structure [2], [3]; • to extract poles in a ladder network configuration [4]. If cross-couplings are used, the designer does not have spe- cific control over the positions of the zeros because there is no one-to-one correspondence between the zeros and cross-cou- plings. For this reason, this kind of structure is very sensitive and difficult to adjust. However, by implementing the extracted-pole technique, every transmission zero is controlled independently. This is a very important asset from the engineering point-of- view in order to minimize the sensitivity of the network for mass production. The basic synthesis theory of filters with extracted poles for symmetrical responses was developed in [5] and later general- ized in [1] for asymmetrical responses. Recently, different tech- niques using frequency-independent reactances to replace the phase shifters have been proposed for the case of one or two transmission zeros located at the input and output [6], [7]. In this communication, an extension is made to extract the maximum number of transmission zeros in -order filters with either sym- metrical or asymmetrical response. Since all transmission zeros are located at finite real frequencies, it is significant to empha- size that it will be required to fit the value of the insertion loss at an infinite frequency by means of an impedance change. In addition to the synthesis, we present a new structure to implement extracted poles in a rectangular waveguide -plane configuration. It operates as a resonant cavity in transmission at central frequency of the bandpass and simultaneously intro- duces a controlled transmission zero out-of-band. Considering 0018-9480/$20.00 © 2005 IEEE