Transfer functions for sharp cut-off filters with an equalized phase response
Branko D. Rakovich, B.M. Djurich · International Journal of Electronics · 1976
A method is presented for determining transfer functions of sharp cut-off low-pass and band-pass filters having small pass-band magnitude and group delay distortion. It is similar to the conventional approach in the sense that the minimum phase shift filter section and the all-pass phase equalizer section are designed separately and then connected in cascade. Unlike the latter, however, the present technique does not use the smallest possible order of function to realize the minimum phase-shift part of the network, but some redundant elements are permitted in order to simplify the design of phase-equalizer section. To this end, the prescribed magnitude rosponse is approximated by use of a recently introduced class of monotonic pass-band filters, referred to as LSM filters. It is shown that this leads to a reduction in the overall complexity of the network when compared with conventional Cauer filter and phase-equalizer combination. Also, the relative sensitivity of the resulting network taken with respect to different circuit parameters is considerably decreased, which is of great importance, especially in the design of active filters. If the frequency range over which the group delay equalization is required does not cover the entire pass-band the result obtained by the present method can be used as an initial solution in an iterative process aimed at providing further reduction in the overall network complexity.