Deriving technique of equivalent forms from general filter circuits and its application

In the active circuit design it is necessary to consider the designed filter features of the number of elements, element value spread, element sensitivities, and the circuit structure. For example, the desirable circuit structure of the operational transconductance amplifier-C (OTA-C) filter is that all the elements are of equal or near equal value and all the capacitors are grounded. Thus, it is important for the filter design to find the useful method to derive such a desirable equivalent structure. This paper describes the necessary and sufficient condition and a practical procedure to derive an equivalent form from a general active RC circuit or a general LCR circuit. The design examples deriving equivalent voltage controlled current source (VCCS)-C or VCCS-RC circuits from the third-order low-pass LC filter are demonstrated. By this technique it is possible to derive the suitable equivalent circuit for the implementation.