Yield and reliability in microwave circuit and system design

This reference is for anyone involved with microwave design. It tackles the practical aspects of microwave statistical design and introduces statistical design techniques that encompass many different applications. This presentation focuses on two main example areas - microwave circuits and systems - but any application with a complex relation between design variables and performance and design variable uncertainty can benefit from statistical design.

Foreword	p. xiii
Preface	p. xv
Acknowledgments	p. xvii
Chapter 1 Introduction	p. 1
1.1 The Economics of Yield and Reliability Design	p. 1
1.2 Background Terminology and Scope	p. 3
1.3 The Design and Development Process	p. 5
1.4 Design and Development for Manufacturability	p. 6
1.5 Testing Model	p. 7
1.5.1 Specifications	p. 8
1.5.2 Elements of the Test Model	p. 9
1.5.3 Failure Mechanisms	p. 10
1.6 Manufacturing Model	p. 10
1.6.1 Definition of High Yield	p. 13
1.6.2 Ways To Achieve High Yield	p. 13
1.6.3 Parameter Aging and Environmental Model	p. 13
1.7 Design	p. 14
1.7.1 Single-Point Optimization Design Approach	p. 14
1.7.2 Extending Single-Point Procedures With Statistical Design	p. 16
1.8 Sources of Parameter Value Uncertainty	p. 17
1.9 When To Use Statistical Circuit Design	p. 19
1.9.1 Voltage Divider	p. 19
1.9.2 Low-Frequency Operational Amplifier	p. 20
1.9.3 High-Frequency Amplifier	p. 21
1.10 Examples of Statistical Circuit Design	p. 21
1.10.1 Butterworth Filter	p. 22
1.10.2 A 2- to 6-GHz Feedback Amplifier	p. 23
1.10.3 Satellite-Receiver System	p. 23
1.10.4 Tunable Active Filter	p. 25
1.10.5 Summary of Examples	p. 25
1.11 Conclusion	p. 25
1.12 Important Ideas From Chapter 1	p. 26
Chapter 2 Yield	p. 29
2.1 Introduction	p. 29
2.2 Two Ways To Describe Yield	p. 29
2.2.1 Mathematical Viewpoint: Calculating Yield	p. 30
2.2.2 Geometric Viewpoint: Seeing Yield	p. 30
2.3 Parameter Space and Performance Space	p. 30
2.3.1 Parameter Vector, P	p. 30
2.3.2 Parameter Space, P	p. 31
2.3.3 The Performance Space M, and the Measurement Vector M	p. 32
2.3.4 Design Specification, S	p. 33
2.3.5 Acceptable Performance Region, M[subscript a]	p. 34
2.3.6 Performance Function G(P)	p. 34
2.3.7 Acceptability Region in Parameter Space, P[subscript a]	p. 36
2.3.8 Example--A Voltage Divider	p. 37
2.3.9 Tolerance Region, T	p. 37
2.4 Parameter Statistics	p. 38
2.4.1 Random Variables	p. 39
2.4.2 Probability Density Function, f[subscript p](P)	p. 40
2.4.3 Average or Nominal Value	p. 41
2.4.4 Variance	p. 42
2.4.5 Higher-Order Moments	p. 43
2.4.6 Uniqueness	p. 43
2.4.7 Multiple Random Parameters and Their Joint PDF	p. 43
2.4.8 Covariance Matrix	p. 45
2.4.9 Independent and Uncorrelated Random Parameters	p. 45
2.4.10 Higher-Order Statistics	p. 47
2.5 Geometric Approach to Yield Calculation	p. 48
2.5.1 The General Geometric Approach	p. 49
2.5.2 Yield With Uniform Independent Parameters	p. 51
2.5.3 Example--A Voltage Divider	p. 52
2.6 Mathematical Approach to Yield Calculation and Yield as a Multidimensional Integral	p. 53
2.7 Conclusion	p. 54
2.8 Important Ideas From Chapter 2	p. 54
Chapter 3 Calculating Yield	p. 57
3.1 Introduction	p. 57
3.2 Monte Carlo Integration	p. 59
3.2.1 Fundamental Theorem of Monte Carlo	p. 59
3.2.2 Ratio of Volumes Interpretation	p. 60
3.2.3 The Definite Integral of a Binary Function	p. 62
3.3 Monte Carlo Approach to Yield Calculation	p. 63
3.3.1 Confidence Intervals	p. 65
3.3.2 Variance Reduction	p. 66
3.3.3 Importance Sampling	p. 68
3.4 Geometric Approach to Yield Calculation	p. 70
3.5 The Parts of Yield Calculation	p. 71
3.5.1 Background	p. 71
3.5.2 n-Dimensional Geometry and Convex Sets	p. 71
3.5.3 The Yield-Calculation Elements	p. 72
3.6 Combining the Parts: Yield-Calculation Methods	p. 77
3.6.1 Regionalization	p. 77
3.6.2 Simplical Approximation	p. 79
3.6.3 Efficient Simplical Approximation	p. 80
3.6.4 Ellipsoidal Region Approximation	p. 84
3.6.5 Radial Approximation	p. 85
3.6.6 Polynomial Approximation With Cuts	p. 86
3.6.7 Dynamic Constraint Approximation	p. 90
3.6.8 Monte Carlo	p. 92
3.7 Conclusion	p. 94
3.8 Important Ideas From Chapter 3	p. 95
Chapter 4 Statistical Sensitivity	p. 101
4.1 Introduction	p. 101
4.1.1 Classic Sensitivity	p. 102
4.1.2 Interpretation of Sensitivity	p. 102
4.1.3 Sensitivity in Optimization	p. 103
4.1.4 Manufacturing Sensitivity	p. 103
4.1.5 Three Sensitivity Concepts	p. 104
4.2 Illustrative Problems	p. 105
4.3 Review of Sensitivity Studies	p. 108
4.3.1 Single-Point Sensitivity	p. 109
4.3.2 Multiparameter Sensitivity	p. 110
4.3.3 Large-Change Sensitivity	p. 111
4.3.4 Multiparameter Large-Change Sensitivity	p. 112
4.3.5 Performance Variance Reduction, Taguchi Methods	p. 113
4.4 Manufacturing Sensitivity	p. 117
4.4.1 Performance Statistical Sensitivity	p. 117
4.4.2 Yield Statistical Sensitivity	p. 122
4.5 Performance Variance Sensitivity	p. 124
4.6 Performance Variance Factor	p. 125
4.7 Statistical Sensitivity Calculation	p. 126
4.7.1 Performance and Yield Factor	p. 127
4.7.2 Average Performance and Yield Sensitivity Calculation	p. 128
4.8 Statistical Sensitivity Management and Reduction	p. 129
4.8.1 Sensitivity Management	p. 129
4.8.2 Sensitivity Reduction	p. 131
4.9 Examples	p. 132
4.9.1 Lug Nut	p. 132
4.9.2 Salen and Key Filter	p. 134
4.10 Conclusion	p. 137
4.11 Important Ideas from Chapter 4	p. 139
Chapter 5 Yield Optimization	p. 143
5.1 Introduction	p. 143
5.1.1 The Optimization Problem	p. 144
5.1.2 Classification of Optimization Methods and Goals	p. 146
5.2 Single-Point (Nominal) Performance Optimization	p. 147
5.2.1 Objective (Error) Function Formulation	p. 147
5.2.2 Gradient Methods	p. 149
5.2.3 Direct-Search Methods	p. 151
5.2.4 Brinkmanship Design	p. 155
5.3 Statistical Optimization	p. 156
5.3.1 Design Centering	p. 156
5.3.2 Statistical-Optimization Error Function	p. 160
5.3.3 Yield-Optimization Approaches	p. 160
5.4 Deterministic Methods for Yield Optimization	p. 161
5.4.1 Simplical Approximation	p. 161
5.4.2 Multicircuit	p. 163
5.5 Sampling-Based Methods for Yield Optimization	p. 164
5.5.1 Statistical Exploration	p. 164
5.5.2 Parametric Sampling	p. 166
5.5.3 Radial Exploration	p. 168
5.6 Yield Factor Histograms	p. 169
5.7 Sensitivity Reduction	p. 175
5.8 Conclusion	p. 175
5.9 Important Ideas From Chapter 5	p. 176
Chapter 6 Statistical Modeling and Validation	p. 179
6.1 Introduction	p. 179
6.2 Survey of Statistical Modeling	p. 181
6.3 Elements of Statistical Modeling	p. 185
6.4 Statistical Characterization	p. 187
6.5 Verification	p. 188
6.5.1 Tests for Multivariate Statistical Equivalence	p. 188
6.5.2 The Generalized Kolmogorov-Smirnov Test	p. 188
6.5.3 Nearest Neighbor Test	p. 189
6.5.4 Multivariate Verification of FET Data	p. 189
6.5.5 Summary of Multivariate Statistical Verification	p. 191
6.6 Statistical-Model Development and Extraction	p. 192
6.6.1 Design Scenario Using the "Average" Device	p. 192
6.6.2 Moments	p. 193
6.6.3 Graphical Methods for Statistical Modeling: Frequency and Cumulative Frequency Distributions	p. 194
6.6.4 Truth Model	p. 195
6.6.5 Design Centering, Yield, and the Truth Model	p. 195
6.6.6 Statistical-Interpolation Model	p. 197
6.6.7 Summary of Statistical-Model Development	p. 199
6.7 Proposed Framework for Statistical Modeling	p. 200
6.7.1 Step 1: Characterization	p. 201
6.7.2 Step 2: Deterministic-Model Error Analysis	p. 202
6.7.3 Step 3: Statistical-Model Development	p. 203
6.7.4 Step 4: Extraction and Verification	p. 203
6.7.5 Step 5: Database Updating	p. 203
6.8 Conclusion	p. 204
6.9 Important Ideas From Chapter 6	p. 204
Chapter 7 Examples and Case Studies	p. 209
7.1 Introduction	p. 209
7.2 Example--A Comprehensive Design Using a Lowpass Filter	p. 209
7.2.1 Comments	p. 209
7.2.2 An Extended-Design Methodology	p. 210
7.2.3 The Statistical-Design Methodology in Practice	p. 211
7.2.4 Summation	p. 218
7.3 Example--A 2- to 6-GHz GaAs MMIC Feedback Amplifier	p. 218
7.3.1 Comments	p. 218
7.3.2 Preliminary Information	p. 218
7.3.3 Statistical-Parameter Model	p. 222
7.3.4 Statistical Optimization and Analysis	p. 222
7.3.5 Results	p. 223
7.4 Example--A Satellite-Communications System	p. 223
7.4.1 Comments	p. 223
7.4.2 Preliminary Information	p. 227
7.4.3 Statistical System-Design Methodology	p. 227
7.4.4 Analogue--Two Amplifiers and a Filter	p. 228
7.4.5 Analogue--A Satellite Receiver	p. 230
7.4.6 Summation	p. 230
7.5 Case Study--A 0.5- to 2.5-GHz MMIC Gain Block	p. 234
7.5.1 Comments	p. 234
7.5.2 Preliminary Information	p. 234
7.5.3 Amplifier Design	p. 235
7.5.4 Statistical-Response Prediction With the Database Model	p. 236
7.5.5 Summation	p. 238
7.6 Case Study--Small-Signal Yield Analysis	p. 238
7.6.1 Comments	p. 238
7.6.2 Preliminary Information	p. 238
7.6.3 Approach	p. 239
7.6.4 Sensitivity Equations and Coefficients	p. 240
7.6.5 Analogue--A Broadband Low-Noise MMIC Distributed Amplifier	p. 242
7.6.6 Summation	p. 245
7.7 Case Study--A 7- to 11-GHz Low-Noise MMIC Amplifier	p. 246
7.7.1 Comments	p. 246
7.7.2 Preliminary Information	p. 246
7.7.3 CAD-System Overview	p. 248
7.7.4 A Three-Stage 7- to 11-GHz Low-Noise Amplifier	p. 249
7.7.5 Summation	p. 253
7.8 Case Study--Design to Cost	p. 253
7.8.1 Comments	p. 253
7.8.2 Preliminary Information	p. 253
7.8.3 Design-to-Cost Framework	p. 255
7.8.4 Results	p. 255
Appendix A Monte Carlo Confidence-Interval Tables	p. 261
Index	p. 271

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