Image Parameter Square-Frequency Filter Design

By homographic or bilinear transformations of the square frequency plane, it is shown that the image propagation behavior of filters of reactive impedances can, on normalization to the bandwidth, be described independently of the relative bandwidth. A graphical filter design method, similar to the Kosowsky approximation method for filters of narrow relative bandwidth, is hence made available as an accurate method for any relative bandwidth. For relating critical frequencies of lattice impedances to the peaks of infinite attenuation, results combine the simplicity of the Kosowsky (approximate) formulas with complete accuracy for all relative bandwidths. Methods of treating reflection loss are given. In terms of the transformed square frequency variable, the image propagation behavior of any filter represents a whole class of filters from which, by homographic transformations, individual members may be formed as band-pass, high-pass, low-pass, or all-pass filters.