Simple Thermal Noise Estimation of Switched Capacitor Circuits Based on OTAs -- Part II: SC Filters

TL;DR

This paper extends a thermal noise estimation method based on the extended Bode theorem to switched-capacitor filters, validating it with analytical and simulation results for basic filter circuits.

Contribution

It introduces a simple, circuit-inspection-based method for thermal noise estimation in SC filters, building on previous work on SC amplifiers.

Findings

Analytical noise estimates match transient simulations closely.

Method simplifies thermal noise analysis without transfer function calculations.

Validated on basic integrator and low-pass filter circuits.

Abstract

In Part I of this paper, we have shown how to calculate the thermal noise voltage variances in switched-capacitor (SC) circuits using operational transconductance amplifiers (OTAs) with capacitive feedback by using the extended Bode theorem. The method allows a precise estimation of the thermal noise voltage variances by simple circuit inspection without the calculation of any transfer functions nor integrals. While Part I focuses on SC amplifiers and track&hold circuits, Part II shows how to use the extended Bode theorem for SC filters. It validates the method on the basic integrator and then on a first-order low-pass filter by comparing the analytical results to transient noise simulations showing an excellent match.