A general approach to continuous‐time Gm‐C filters

A general topology for transconductance‐capacitor (Gm‐C) filters is presented that permits any continuous‐time analogGm‐Cfilter to be analysed via a matrix‐description. Based on these matrices, explicit formulas are derived for the transfer function and the sensitivities valid for anyGm‐Cfilter 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 Gm‐C filters, but ‘hand designs’ ofGm‐CIFLF and LF filters are given as illustrative examples. A new, more general definition ofGm‐Cstate‐space filters is proposed. Connections between the state matrices for voltage‐ and current‐mode state‐spaceGm‐Cfilters 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.