Optimising two commonly used active-filter building blocks using the complementary transformation

In the paper, the minimisation of the gain-sensitivity product (g.s.p.) for two important active-filter types that are finding widespread use in voiceband communication systems, in the form of hybrid-integrated filter building blocks, is considered. The first comprises a twin I for zero realisation: this is incorporated in the positive-feedback loop of a single operational amplifier and is referred to as the twin-T s.a.b.b. The known conditions for minimum g.s.p. for the twin-T s.a.b.b. are briefly recapitulated and expanded. The second comprises a differential scheme for zero realisation, and combines positive and negative feedback. It is referred to as the single-amplifier biquad (s.a.b.). The paper shows that the two circuits are closely related by the complementary transformation, and that conditions for minimum g.s.p. in both cases are identical