A Solution to the Approximation Problem for RC Low-Pass Filters

This paper presents a method for investigating the transfer functions of RC low-pass networks. The procedure involves the use of the concept of potential analogy and the technique of conformal transformation. The poles and zeros are arranged in a certain symmetrical fashion in the transformed plane and on this plane the frequency characteristic may be written in closed form. The frequency characteristics obtained by this method have equal-ripple variation inside the pass band. By mathematical manipulations, the several quantities that are essential in describing the quality of each frequency characteristic; i. e., the pass-band tolerance, the stopband-passband ratio and the stop-band attenuation, may be expressed in terms of several geometrical quantities in the transformed plane and the parameters of the transformation function. Thus, the design of this group of network functions may be accomplished by adjusting the geometric dimensions in the transformed plane and the transformation functions. The transformation used here is a function that involves elliptic functions. Some design charts which are helpful in the selections of these values are given.