Switched-capacitor filter design using the bilinear z-transform

A general synthesis technique is described for obtaining a switched-capacitor (SC) filter from an active
RC
prototype. The response of the SC filter is related to that of its prototype by the bilinear
z
-transform. This allows the filtering and sensitivity properties of the prototype to be preserved for the SC circuit. It also enables the designer to realize such economical and low-sensitivity circuits as the FDNR and gyrator filters. Finally, it permits the processing of signals at much higher frequencies than do previously known circuit design techniques.