General Description of State-Space Continuous-Time G_m-C Filters

摘要

A general approach to analysis continuous-time analog G_m-C filters and equalizers, based on matrix description, is presented. A general transfer function formula for any G_m-C filter structure are given. The considerations accompanying this approach lead to useful relationships between the passive network of the filter and its transfer function. Based on these con- siderations, a new definition of continuous-time state-space G_m-C filters is given. Moreover, connections between state matrices for voltage- and current-mode state-space G_m-C filters are formulated and two canonical transformations of state-space filters into direct state-space ones, i.e. those having grounded capacitors only, are defined. Another two classes of G_m-C filters, i.e. reducible and quasi-state-space structures are also considered.