Noise and clock jitter analysis of sigma-delta modulators and periodically switched linear networks

Abstract

This thesis investigates general computer-aided noise and clock jitter analysis of sigma-delta modulators. The circuit is formulated at electrical circuit level. Modulators with either switched-capacitor, switched-current, or continuous-time loop-filters can be analyzed. The methods and algorithms are also applicable to pe4riodically switched linear networks, such as switched-capacitor and switched-current filters.

Thermal noise is an important source limiting circuit resolution, but traditional frequency domain noise analysis is not applicable to sigma-delta modulators. Noise analysis of sigma-delta modulators has not been presented before. In this thesis we give a new time domain method. It is applied to thermal noise analysis and dithering analysis.

Clock jitter is another major major source that results in performance degradation of analog sampled-data circuits.Despite the fact that clock jitter is usually random, previous methods were restricted to periodic jitter analysis. They are based on classical switched-capacitor methods that analyze the circuit by exploiting its periodic switching nature. The introduction of random jitter destroys the periodic swtching pattern, and classical methods are not applicable. To overcome this problem, we present a new varying-step sampled-data method for analysis of linear time invariant circuits. It is applied to clock jitter analysis of periodically switched linear networks and sigma-delta modulators. No restrictions on the jitter waveform were imposed. It can handle either periodic or random clock jitter analysis.

Transition matrix and input-transfer vector play important roles in circuit theory. Evaluations of their time derivatives are needed for the special sampled-data method. In this thesis, direct computation methods for the derivative matrices and vectors are presented. They are based on circuit theory concepts and aimed at numerical comutation.

The theories have been implemented in a computer program, and validated on numerical examples. Comparisons are made with exact analysis, physical measurements, or experimental observations. The algorithms are efficient, and transient analysis of a typical sigma-delta modulator for several hundred thousand clock cycles is obtained in the order of minutes.