Noise, sensitivity, and distortion analysis of switched analog circuits

Abstract

This thesis deals with the analysis of noise, sensitivity, and distortion of analog circuits containing externally clocked switches in the frequency domain.

The phasor representation of the network variables of multi-phase periodically switched linear (PSL) circuits is introduced. Tellegen's theorem for RSL circuits in phase domain is derived and the theory of the adjoint network of PSL circuits is developed. Two novel theorems, namely, frequency reversal theorem and transfer function theorem are introduced and their usefulness in computing the aliasing transfer functions of PSL circuits is investigated. The theory of the adjoint network is applied to noise analysis of PSL circuits and an algorithm that is orders of magnitude faster than the conventional brute-force method is obtained.

The developed Tellegen's theorem is further applied to sensitivity analysis of PSL circuits. The frequency-domain sensitivity of PSL circuits is obtained. The sensitivity network of PSL circuits is also introduced and its usefulness in sensitivity analysis is compared with that of the adjoint network approach. To analyze switched nonlinear circuits in frequency domain, time-varying Volterra functional series and multi-frequency transforms. The complete spectrum of nonlinear time-varying systems is obtained. The theory is applied to distortion analysis of multi-phase periodically switched nonlinear circuits. Both the harmonic and intermodulation distortion are analyzed.

The theories presented in this thesis have been implemented in three computer programs that compute the noise and sensitivity of periodically switched linear circuits, and the distortion of periodically switched nonlinear circuits.