A New Method of Solving the Accuracy Problem in Filter Design

Abstract

A very important problem in network design by modern synthesis methods is the apparent loss of significant digits which occurs at every stage of the conventional synthesis process and the consequent need to perform all calculations with a very large number of digits. This paper shows how a transformed variable (obtained by a well-known bilinear transformation of the frequency variable) can be used at all stages of the synthesis process. Attention is concentrated upon those band-pass filters which provide a loss which has prescribed poles and is equal ripple in the pass band. Two separate methods are described; one, which is the classical design method adapted for the transformed variable, is suitable for the conventional symmetrical and antimetrical filters and the other, which is a method of iterating the coefficients of the open-circuit input impedance in terms of the transformed variable, is suitable for two new types of parametric filters. Computer programs based on these methods and using only eight-digit working have been used to design large (degree as high as eighteen) narrow-band band-pass filters; the error in the final element values was judged to be always less than one hundredth of one per cent.