Use of transformations in active BP filter designs

In this paper transformations, which are very often used in design of active filters, are summarized, and used for revealing the relations between different classes of active filter sections. Among various transformations we distinguish: frequency transformations and network transformations. As frequency transformation examples we consider the well known "low-pass to band-pass" (LP-BP) and less known "lossy low-pass to bandpass "(LLP-BP) frequency transformation. As examples of network transformations, which are performed by network elements substitution we consider (i) "lossy" LP-BP network transformation: to obtain BP filter it substitutes each resistor of the LP prototype filter by a series RC circuit, and each capacitor by a parallel RC circuit; and (ii) complementary transformation: passive network in negative feedback loop is transformed into passive network in positive feedback loop of operational amplifier.