Active RC filters containing periodically operated switches

The state-variable approach to inductorless filters that utilize resistors, capacitors, gyrators, controlled sources or negativeimpedance converters (NIC), and switches suitable for integration is described. By using the state equations of active networks in the standard form, it is shown that multiplications of resistances, gyration conductances, transfer coefficients of controlled sources, and NIC in active network can be achieved by means of the switching technique. From these results, the relations between the input and the output at signal frequency of active filters containing periodically operated switches are derived at the steady state for the case where the switching frequency is much higher than the signal frequency. The results show that the cutoff and the center frequencies of active filters are adjustable by changing the ratio of the on duration in a period to the period of switching. The experimental results of low-pass, bandpass, and high-pass filters are shown along with the theoretical curves.