Synthesis of Sub-optimal RC Filters

Abstract

In the design of filters, the main emphasis has been on the realization of ideal ‘brick wall’ characteristics of normalized low pass filter. Many attempts in this direction were aimed to achieve LC filters being lossless. But now inductorless filters are becoming attractive because resistors and capacitors are comparatively cheaper, simpler and more close to ideal than inductors, particularly, where low frequencies are encountered. A major breakthrough in this direction has been after the advent of integrated circuits.

In this paper, well known Butterworth response is approximated by means of a physically RC realizable transfer function. Only passive components are used as these yield cheaper, more exact and least sensitive networks. The designed filters are only sub-optimal as RC transfer functions can not have their derivatives zero at ω=0. The performance of these RC filters is comparable with the Butterworth LC filter, both in frequency and time domains. An experimental verification for the same has been done by the practical fabrication for second and third order filters. A general design rule for filters of higher order is stated. The designed networks are particularly suitable for low frequency applications.