Design and Evaluation of Shifted-Companion-Form Active Filters

Abstract

Two techniques for designing a class of low-sensitivity, follow-the-leader, feedback-type active filters have been introduced by Hurtig and Laker-Ghausi. The FLF configuration consists of a cascade of second-and/or first-order sections, with feedback from each section back to the first. This paper presents an approach for designing FLF-type realization for all classes of filter functions. The technique is based on a shifted-companion form of the associated-state equations. Some salient features of Hurtig's primary resonator block, Laker-Ghausi's follow-the-leader feedback, and the shifted-companion-form techniques are presented below. (i) Hurtig's PRB realizes any all-pole (no finite transmission zeros) filter function. This includes the low-pass, high-pass, and symmetrical bandpass filters without finite zeros. Explicit design equations are available, and the individual sections in the array are identical. (ii) Laker-Ghausi's FLF realizes any symmetrical (including finite transmission zeros) bandpass filter function. The sections are not constrained to be identical, which allows optimization using this degree of freedom. Finite zeros are realized by a summation technique. (iii) The SCF realizes all types of filter functions, i.e., low-pass, high-pass, bandpass, all-pass, or band-reject filters. Explicit design equations are available. The first section can differ from the rest, thus allowing some optimization with standardization. Feed-forward as well as summation techniques can be used to realise the finite zeros. Two bandpass design examples using SCF, PRB, and/or Laker-Ghausi FLF techniques are given and compared with the low-sensitivity coupled (leapfrog) biquad, the conventional cascade biquad, and the passive ladder filter designs. The comparison shows that the passive filter gives