A Simplified Cascade Synthesis of RC Transfer Functions

This paper presents a new cascade synthesis of RC transfer functions with an unspecified multiplying constant. The method is based on a topological identity for cascaded RLC twoports and a theorem on the realization of RC voltage transfer functions with a prescribed termination. Proofs of the topological identity and the realizability theorem are given. The minimal realization of a class of biquadratic transfer functions is investigated, and some sufficient conditions for a fiveelement realization are found. The use of these results in the present synthesis procedure yields a relatively simple realization of RC transfer functions having one pair of complex zeros and any number of real zeros in the left half-plane. Several numerical examples are given, and comparisons are made with the results obtained by other well-known methods.