A general approach to continuous-time G_m-C filters

摘要

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.