A tutorial to switched-capacitor noise analysis by hand

The methods for switched-capacitor (SC) noise analysis published up to this date fall in two groups: one group contains methods suitable for analysis by hand that are not easily applicable to all SC circuits. The other group contains methods that are applicable to all SC circuits, but require matrix manipulations with a computer algebra tool. In this paper, we show a universally applicable hand-analysis method. The main reason why SC noise analysis is so difficult is that noise is sampled on many different capacitors, and when being sampled, its spectrum is aliased. The core idea of making analysis by hand possible is to use an intuitive rather than an algebraic method to derive the continuous-time noise spectra in the different phases. Our method combines charge-equation analysis for the discrete-time aspects with signal-flow-graph analysis for the continuous-time aspects of a circuit. We show in tutorial style how to apply it, and demonstrate that it is very useful for getting insight into SC circuits, deriving simplified expressions, and getting a good correspondence with behavioural simulations using SpectreRF.