On Synthesis of Filters

A general classification of reactive ladder filters with real transmission zeros is given which is based on the extreme frequency behavior of port impedances and on types of design polynomials of the characteristic and effective transmission functions. It is shown that this classification provides an ordered algorithm for automatic realization of ladder structures which can be used to construct a logical development of appropriate computer programs. The bilinear frequency transformation is extended to all filter classes for a synthesis procedure entirely in the transformed plane. Accuracy limitations of this method are discussed and reasons for them are pointed out. A recently developed method of filter synthesis is proposed, which does not require high accuracy working in a computer because it operates throughout with simple factors which are never multiplied into polynomials. A design example of a through-supergroup filter is offered which demonstrates limitations of standard synthesis procedures.