This paper describes a numerical design procedure of element values of RC polyphase filters with equal minima in stopband and equal ripple in passband. Determination of element values of RC polyphase filters with equal-ripple characteristic have not been solved to the best knowledge of the authors. There found a paper tackling with the problem; however, it can only give sub-optimal solutions via numerical calculation [3]. We propose a numerical element value design procedure for RC polyphase filters with equi-ripple gain in both stopband and passband by using the coefficient matching method. Some design examples are given.

Element value spread of an equal-ripple RC polyphase filter depends heavily on the order of zero assignment. To find the optimum design, we must conduct exhaustive design for all the possible zero assignments. This paper describes two circuit transformations on equal-ripple RC polyphase filters, which preserve their transfer functions, for reducing circuit design efforts. Proposed Method I exchanges (R,C) values to (1/C,1/R) for each stage. This gives a new circuit with different zero assignment for each stage of its original circuit. Method II flips over the original circuit and exchanges the resulting (Ri,Ci) values for (Cn-i+1,Rn-i+1) for each i-th stage. Those circuit transformations can reduce a number of circuit designs down to 1/4 of the straight-forward method. This considerably reduces a burden for exhaustive design for searching the minimum element value spread condition. Some design examples are given to illustrate the proposed methods.