1. Introduction. 1.1 Integrated Circuits. 1.2 Analog Circuits. 1.3 Analog Design. 1.4 Analog Sizing. 2. Tolerance Design: Example. 2.1 RC Circuit. 2.2 Performance Evaluation. 2.3 Performance-Specification Features. 2.4 Nominal Design. 2.5 Yield Optimization/Design Centering. 3. Parameters & Tolerances, Performance & Specification. 3.1 Parameters. 3.2 Parameter Tolerances. 3.3 Range-Parameter Tolerances. 3.4 Statistical Parameter Distribution. 3.5 Univariate Normal Distribution. 3.6 Multivariate Normal Distribution. 3.7 Transformation of Statistical Distributions. 3.8 Generation of Normally Distributed Sample Elements. 3.9 Global and Local Parameter Tolerances. 3.10 Performance Features. 3.11 Numerical Simulation. 3.12 Performance-Specification Features 4. Analog Sizing Tasks. 4.1 Sensitivity-Based Analysis. 4.2 Performance-Sensitivity Computation. 4.3 Scaling Parameters and Performance Features. 4.4 Nominal Design. 4.5 Multiple-Objective Optimization. 4.6 Single-Objective Optimization. 4.7 Worst-Case Analysis and Optimization. 4.8 Yield Analysis, Yield Optimization/Design Centering. 5. Worst-Case Analysis. 5.1 Classical Worst-Case Analysis. 5.2 Realistic Worst-Case Analysis. 5.3 Yield/Worst-Case Distance - Linear Performance. 5.4 General Worst-Case Analysis. 5.5 Yield/Worst-Case Distance - Nonlinear Performance. 5.6 Exercise. 6. Yield Analysis. 6.1 Statistical Yield Analysis. 6.2 Tolerance Classes. 6.3 Geometric Yield Analysis. 6.4 Exercise. 7. Yield Optimization/Design Centering. 7.1 Statistical-Yield Optimization. 7.2 Geometric-Yield Optimization. A Expectation Values. A.1 Expectation Value. A.2 Moments. A.3 Mean Value. A.4 Central Moments. A.5 Variance. A.6 Covariance. A.7 Correlation. A.8 Variance/Covariance Matrix. A.9 Calculation Formulas.A.10 Standardization of Random Variables. A.11 Exercises. B Statistical Estimation of Expectation Values. B.1 Expectation-Value Estimator. B.2 Variance Estimator. B.3 Estimator Bias. B.4 Estimator Variance. B.5 Expectation-Value-Estimator Variance. B.6 Estimator Calculation Formulas. B.7 Exercises. C Optimality Conditions of Nonlinear Optimization Problems. C.1 Unconstrained Optimization. C.2 First-Order Unconstrained Optimality Condition. C.3 Second-Order Unconstrained Optimality Condition. C.4 Constrained Optimization. C.5 First-Order Constrained Optimality Condition. C.6 Second-Order Constrained Optimality Condition. C.7 Bounding-Box-of-Ellipsoids Property.
Here is a compendium of fundamental problem formulations of analog design centering and sizing. It provides a differentiated knowledge about the many tasks of analog design centering and sizing. In particular, coverage formulates the worst-case problem. The book stands at the interface between process technology and design technology, detailing how the two are required to reach a solution. It presents a mathematically founded description based on numerical optimization and statistics. This volume will enable analog and mixed-signal designers to assess CAD solution methods that are presented to them as well as help developers of analog CAD tools to formulate and develop solution approaches for analog design centering and sizing.