A general approach to continuous-time Gm-C filters

A general topology for transconductance-capacitor (G(m)-C) filters is presented that permits any continuous-time analog G(m)-C filter to be analysed via a matrix-description. Based on these matrices, explicit formulas are derived for the transfer function and the sensitivities valid for any G(m)-C filter topology. The approach leads to a useful relationship between the passive capacitor network of the filter and the degree of its transfer function. The matrix-based approach is formulated especially for efficient use in computer-aided analysis and design of G(m)-C filters, but 'hand designs' of G(m)-C IFLF and LF filters are given as illustrative examples. A new, more general definition of G(m)-C state-space filters is proposed. Connections between the state matrices for voltage- and current-mode state-space G(m)-C filters are formulated and two canonical transformations are defined that convert state-space filters into direct state-space ones, i.e. those having only grounded capacitors. Copyright (C) 2003 John Wiley Sons, Ltd.