Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems: (425 The Springer International Series in Engineering and Computer Science)

The existence of electrical noise is basically due to the fact that electrical charge is not continuous but is carried in discrete amounts equal to the electron charge. Electrical noise represents a fundamental limit on the performance of electronic circuits and systems. With the explosive growth in the personal mobile communications market, the need for noise analysis/simulation techniques for nonlinear electronic circuits and systems has been re-emphasized. Even though most of the signal processing is done in the digital domain, every wireless communication device has an analog front-end which is usually the bottleneck in the design of the whole system. The requirements for low-power operation and higher levels of integration create new challenges in the design of the analog signal processing subsystems of these mobile communication devices. The effect of noise on the performance of these inherently nonlinear analog circuits is becoming more and more significant. This text presents analysis, simulation and characterization techniques and behavioural models for noise in nonlinear electronic circuits and systems, along with practical examples. The book treats the problem within the framework of, and using techniques from, the probabilistic theory of stochastic processes and stochastic differential systems. This book should be of interest to RF/analog designers as well as engineers interested in stochastic modelling and simulation.

Table of Contents:
1. Introduction.- 2. Mathematical Background.- 2.1 Probability and Random Variables.- 2.2 Stochastic Processes.- 2.3 Filtering of Stochastic Processes with Linear Transformations.- 2.4 Matrix Algebra, Linear Differential Equations and Floquet Theory.- 2.5 Stochastic Differential Equations and Systems.- 3. Noise Models.- 3.1 Physical Origins of Electrical Noise.- 3.2 Model for Shot Noise as a Stochastic Process.- 3.3 Model for Thermal Noise as a Stochastic Process.- 3.4 Models for Correlated or non-White Noise.- 3.5 Summary.- 4. Overview of Noise Simulation for Nonlinear Electronic Circuits.- 4.1 Overview.- 4.2 Noise Simulation with LTI Transformations.- 4.3 Noise Simulation with LPTV Transformations.- 4.4 Monte Carlo Noise Simulation with Direct Numerical Integration.- 4.5 Summary.- 5. Time-Domain Non-Monte Carlo Noise Simulation.- 5.1 Formulation of Circuit Equations with Noise.- 5.2 Probabilistic Characterization of the Circuit with Noise.- 5.3 Small Noise Expansion.- 5.4 Derivation of a Linear Time Varying SDE Model for Noise Analysis.- 5.5 Derivation of Linear Time Varying ODEs for the Autocorrelation Matrix.- 5.6 Solution of the Linear Time Varying ODEs for the Autocorrelation Matrix.- 5.7 Numerical Computation of the Autocorrelation Matrix.- 5.8 Alternative ODEs for the Autocorrelation Matrix.- 5.9 Time-Invariant and Periodic Steady-State.- 5.10 Examples.- 5.11 Summary.- 6. Noise in Free Running Oscillators.- 6.1 Phase Noise and Timing Jitter Concepts.- 6.2 Phase Noise Characterization with Time Domain Noise Simulation.- 6.3 Phase Noise: Same at All Nodes.- 6.4 Kaertner’s Work on Phase Noise.- 6.5 Alternative Phase Noise Characterization Algorithm.- 6.6 Non-White Noise Sources and Phase Noise.- 6.7 Phase Noise of Phase-Locked Loops.- 6.8 Summary.- 7. BehavioralModeling and Simulation of Phase-Locked Loops.- 7.1 PLLs for Clock Generators and Frequency Synthesizers.- 7.2 Behavioral Models of PLL Components.- 7.3 Behavioral Simulation Algorithm.- 7.4 Post Processing for Spurious Tones and Timing Jitter/Phase Noise.- 7.5 Examples.- 7.6 Summary.- 8. Conclusions and Future Work.- References.- Index>.