Design and Evaluation of Shifted-Companion-Form Active Filters

Recently, Hurtig 1,2 introduced a low-sensitivity, multiple-loop-feedback active RC filter configuration for the realization of greater-thansecond-order voltage transfer functions. The configuration has been found to exhibit greatly improved stability over cascaded designs. For symmetrical bandpass filters, Hurtig's structure [called the primary resonator block (PRB) configuration] consists of a cascade of identical biquadratic bandpass sections (i.e., same pole-frequency and pole-Q) with feedback from each section (except the first) back to the first section. More recently, Laker and Ghausi 3,4 extended Hurtig's configuration to include symmetrical bandpass filters with finite transmission zeros, e.g., elliptic-type filters. In Laker and Ghausi's approach [called the follow-the-leader feedback (FLF) technique], different pole-Q values can be allowed for the biquadratic bandpass sections. For the PRB technique, Hurtig has given a set of explicit equations expressing the biquadratic bandpass transfer function and the feedback factors in terms of the coefficients of the all-pole prototype lowpass transfer function. 2 In the FLF approach, Laker and Ghausi used a coefficient-matching technique. Because of the nonuniqueness of solutions in the FLF approach, Laker and Ghausi further proposed a method of choosing the pole-Q values for an optimum design. In this paper, we present yet another approach based on a shiftedcompanion form of state variable representation of the voltage transfer function for the design of symmetrical bandpass and band-reject filters with this structure.