25 MICROWAVE FILTERS WITH MULTIPLE CROSS-COUPLINGS AND MAXIMUM NUMBER OF CONTROLLED ATTENUATION POLES G. Lojewski*, N. Militaru*, M.G. Banciu** *University POLITEHNICA of Bucharest E-mail: george.lojewski@munde.pub.ro **National Institute of Materials Physics E-mail: gbanciu@infim.ro Abstract–In this paper a novel configuration of microwave planar filters, with multiple cross- couplings and with a number of poles of attenuation NZ equal to the order N of the filter, is investigated. The position of the poles on the frequency axis can be controlled, allowing the design of band-pass filters with improved selectivity with respect to the adjacent channels. The new configurations were designed and verified by em-field simulation. The responses of the designed filters are in good agreement with the specification, confirming the possibilities of designing microwave band-pass filters of a relatively low order with moderate losses and with improved performances. Keywords: band-pass filters, attenuation poles, cross- couplings, coupling matrix 1. STRUCTURE OF THE INVESTIGATED FILTERS It is well known that poles of attenuation in the transfer characteristic of a band-pass filter can be obtained only in the presence of one or more cross-couplings between the elements of the filter. The number of attenuation poles NZ cannot be greater than the order N of the filter, i.e. the number of resonators in the filter. The maximum number of poles, NZ = N, can be obtained only if the topology of the filter allows not only cross-couplings between resonators and/or between resonators and the lines, but also a direct coupling between the two access lines (Fig. 1). a) b) c) d) Fig. 1. Different types of band-pass filter topologies (here, case of N = 4 resonators): a) the in-line topology; b) with cross-couplings; c) with cross-couplings and with multiple couplings to the access lines; d) with cross-couplings, multiple couplings to access lines and with a direct coupling between these lines. The generalized coupling matrix M, describing a topology like that shown in Fig. 1, has N + 2 rows and columns. It contains, in a normalized form, all the coupling coefficients between different resonators, the couplings between resonators and access lines represented by the corresponding loaded Q’s of the resonators, the possible direct coupling between input and output represented by the characteristic admittance of the corresponding inverter. This matrix M contains also the offsets of the individual resonators with respect to the central frequency of the filter, in a normalized form. All these key parameters of the filter can be derived from M, through a straightforward de-normalization procedure [1]. The normalized matrix M corresponding to some given specifications can be obtained through a basic synthesis procedure, presented in [1], [2]. The object of this paper is to investigate the practical possibilities of implementing topologies like that of Fig. 1, in a simple, cost-effective planar technology like microstrip. The analysis was focused on the fourth-order filters, because the quadruplet with cross- couplings between resonators was intensively studied in the last years [3]. In order to obtain four attenuation poles an extra coupling has to be realized directly between the input and output lines, beside the cross-coupling possibilities offered by such a quadruplet. 2. DESIGN OF A FOURTH-ORDER FILTER, WITH FOUR PRESCRIBED POLES OF ATTENUATION To illustrate the design procedure, a band- pass filter was designed, with the next main specifications: • central frequency 3 GHz; • bandwidth 75 MHz (2.5%); • 50 Ohms terminal impedances;