On the evaluation of the exact output of a switched continuous-time filter and applications

In this paper, a study of the operation of switched continuous-time filters (SCTFs), defined as continuous-time filters with elements that are alternatively switched on and off in the signal path, is conducted. A well-known example is the use of switched resistors to multiply their value, but the universe of applications is wider. First, a detailed calculation of the output of an SCTF in the frequency domain, which allows the examination of any SCTF in a general framework, is presented. This result particularly explains the resistor multiplication effect. Three application examples using switched elements are presented and examined as SCTFs: a nonideal sample & hold, a switched active filter that is tuned by varying the duty cycle of the switching, and a switched G_m-C filter to implement a chopper amplifier. In all cases, the theoretical background allows the examination of circuit behavior and limitations, and the analysis is supported by measurements or transient simulations.