Analog Design Centering and Sizing

Contents......Page 5
List of Figures......Page 10
List of Tables......Page 17
Preface......Page 19
1.1 Integrated Circuits......Page 21
1.2 Analog Circuits......Page 24
1.3 Analog Design......Page 26
1.4 Analog Sizing......Page 33
2.1 RC Circuit......Page 38
2.4 Nominal Design/Performance Optimization......Page 39
2.5 Yield Optimization/Design Centering......Page 41
3.1 Parameters......Page 46
3.2 Parameter Tolerances......Page 47
3.3 Range-Parameter Tolerances......Page 48
3.4 Statistical Parameter Distribution......Page 50
3.5 Univariate Normal Distribution......Page 51
3.6 Multivariate Normal Distribution......Page 53
3.7 Transformation of Statistical Distributions......Page 58
3.8 Generation of Normally Distributed Sample Elements......Page 62
3.9 Global and Local Parameter Tolerances......Page 63
3.10 Performance Features......Page 64
3.11 Numerical Simulation......Page 65
3.12 Performance-Specification Features......Page 66
4.1 Sensitivity-Based Analysis......Page 68
4.1.3 Significance of Parameters......Page 70
4.1.6 Exercise......Page 71
4.2.2 Finite-Difference Approximation......Page 72
4.3.2 Scaling to the Covered Range of Values......Page 73
4.3.4 Scaling by Equalization of Sensitivities......Page 74
4.5 Multiple-Objective Optimization......Page 75
4.5.1 Smaller or Greater Performance Vectors......Page 76
4.5.3 Pareto Front......Page 78
4.6 Single-Objective Optimization......Page 80
4.6.2 Performance Targets......Page 82
4.7.1 Worst-Case Analysis......Page 83
4.7.2 Worst-Case Optimization......Page 87
4.8.1 Yield......Page 89
4.8.2 Acceptance Region Partitions......Page 91
4.8.4 Yield Analysis......Page 94
4.8.5 Yield Optimization/Design Centering......Page 95
4.8.6 Tolerance Assignment......Page 99
4.8.7 Beyond 99.9% Yield......Page 100
5. WORST-CASE ANALYSIS......Page 103
5.1 Classical Worst-Case Analysis......Page 104
5.1.1 Classical Worst-Case Parameter Vectors......Page 106
5.1.3 Discrete Parameters......Page 107
5.2 Realistic Worst-Case Analysis......Page 108
5.3 Yield/Worst-Case Distance – Linear Performance Feature......Page 111
5.4 General Worst-Case Analysis......Page 113
5.4.2 General Worst-Case Performance Values......Page 116
5.5 Yield/Worst-Case Distance – Nonlinear Performance Feature......Page 117
5.5.1 Yield Approximation Accuracy......Page 118
5.6 Exercise......Page 123
6.1 Statistical Yield Analysis......Page 125
6.1.1 Monte-Carlo Analysis......Page 127
6.1.2 Importance Sampling......Page 128
6.1.3 Yield Estimation Accuracy......Page 129
6.2.1 Tolerance Interval......Page 133
6.2.2 Tolerance Box......Page 134
6.2.3 Tolerance Ellipsoid......Page 136
6.2.4 Single-Plane-Bounded Tolerance Region......Page 139
6.2.5 Corner Worst Case vs. Realistic Worst Case......Page 144
6.3.1 Problem Formulation......Page 146
6.3.2 Lagrangian Function......Page 149
6.3.3 First-Order Optimality Condition......Page 150
6.3.4 Second-Order Optimality Condition......Page 151
6.3.6 Worst-Case Statistical Parameter Vector......Page 153
6.3.7 Worst-Case Distance......Page 154
6.3.8 Geometric Yield Partition......Page 155
6.3.9 Geometric Yield......Page 156
6.3.10 General Worst-Case Analysis/Geometric Yield Analysis......Page 159
6.3.11 Approximate Geometric Yield Analysis......Page 160
6.4 Exercise......Page 161
7.1.1 Acceptance-Truncated Distribution......Page 162
7.1.2 Statistical Yield Gradient......Page 163
7.1.3 Statistical Yield Hessian......Page 165
7.1.4 Solution Approach to Statistical-Yield Optimization......Page 166
7.1.6 Deterministic Design Parameters......Page 167
7.2.1 Worst-Case-Distance Gradient......Page 170
7.2.2 Solution Approaches to Geometric-Yield Optimization......Page 173
7.2.3 Least-Squares/Trust-Region Solution Approach......Page 174
7.2.5 Linear-Programming Solution Approach......Page 179
7.2.6 Tolerance Assignment, Other Optimization Parameters......Page 180
A.3 Mean Value......Page 181
A.8 Variance/Covariance Matrix......Page 182
A.9 Calculation Formulas......Page 183
A.11 Exercises......Page 184
B.2 Variance Estimator......Page 185
B.5 Expectation-Value-Estimator Variance......Page 186
B.7 Exercises......Page 187
C.1 Unconstrained Optimization......Page 188
C.2 First-Order Unconstrained Optimality Condition......Page 189
C.3 Second-Order Unconstrained Optimality Condition......Page 190
C.4 Constrained Optimization......Page 191
C.5 First-Order Constrained Optimality Condition......Page 192
C.6 Second-Order Constrained Optimality Condition......Page 194
C.7 Bounding-Box-of-Ellipsoids Property (37)......Page 196
References......Page 198
L......Page 208
W......Page 209
Z......Page 210