A Closed-Form Transfer Function for Sample and Hold Master Slave Sampling Filter

A switched capacitor circuit frequently appears in literature in form of sample and hold or master-slave sampling filter. We call this block Sample and Hold Master-Slave Sampling Filter (SH-MSSF). Considering the time varying nature of this circuit it is difficult to predict its behavior, though it looks like a very simple circuit. So there exists no formula describing its function in all of its applications. In this brief, we present a closed-form transfer function, explaining the operation of SH-MSSF, based on state-space analysis. Then by interpolating an infinite number of such transfer functions a continuous-time formula is derived that can exactly model the behavior of this (Linear Periodically Time-Varying) LPTV circuit. The advantage and applicability of such a formula are shown by applying it to three different well-known applications as case studies. The validity of that compact model has been confirmed by comparing it with the simulation results of Cadence Periodic AC (PAC) throughout this brief.