Selectivity Versus Noise Trade-Offs in Resistively Driven Passive Switched-Capacitor Infinite Impulse Response Low-Pass Filters

In this article, we derive a practical limit on the maximum achievable selectivity of three commonly used Passive Switched-Capacitor (PSC) Infinite-Impulse Response (IIR) low-pass filter (LPF) topologies driven from a resistive source. We show that filter topology selection and component dimensioning aimed to improve the selectivity of these filters will necessarily degrade the Noise Figure (NF), revealing a selectivity versus NF trade-off. We subsequently capture this in selectivity versus NF graphs. These graphs quantify the limitations on achievable selectivity and NF for each topology given the number of filter poles, and graphically provide guidance in navigating the trade-off between them. The three considered topologies mainly differ in how the sampling capacitor resets, inverts, or holds its voltage between clock periods. We capture the handling of the sampling capacitor as a new design parameter. We derive a singular model to encompass the entire design space consisting of the three topologies, filter order (number of history/integration capacitors), clock frequency, and component dimensions. The model comprises an adjoint network with a state-space description and is used to analyze the filter transfer function (to quantify selectivity), input-and output-referred noise, and NF.