Foreword XIII -- Preface XV -- Acknowledgements XXXIX -- List of Figures XLI -- List of Tables LI -- List of Glossary and Abbreviations LV -- List of Mathematical Symbols LXI PART I: Engineering, Circuit Design, Flow and Methods 1 Introduction: What Makes an Engineer a Good Designer? 3 -- 1.1 Key Problems in Circuit Design 7 -- 1.1.1 Brute-Force Design-NoWay! 11 -- 1.2 Engineering Techniques 15 -- 1.2.1 GroundWork and Anticipation 15 -- 1.2.2 Iterative Refinement 16 -- 1.2.3 Composition in Design 17 -- 1.2.3.1 Construction vs. optimization 17 -- 1.2.4 TeamWork and Divide-and-Conquer 19 -- 1.2.5 Automation and Tools 20 -- 1.2.6 Re-Use in Designs 21 -- 1.2.7 Summary 22 -- 1.3 Key Elements and Aspects in Circuit Design 23 -- 1.3.1 Datasheets, Conditions, and Trade-Offs 24 -- 1.3.1.1 Trade-off examples 26 -- 1.3.1.2 Datasheet contents 28 -- 1.3.2 Modeling Is Key 35 -- 1.3.3 Design, Debugging, and Tools 41 -- 1.3.4 Simulation Aspects 48 -- 1.3.5 Total Yield and Partial Yield 49 -- 1.3.6 Robust Designs 54 -- 1.4 Design Flow Inputs and Outputs 56 -- 1.5 Questions and Answers 60 -- 2 Manual Analog-Centric Design Style(s) 63 -- 2.1 Biasing and Transistor Sizing 66 -- 2.2 Specification Margin Approach: Fast but Risky 70 -- 2.3 TheWorst-Case Approach 75 -- 2.4 Worst-Case Corner Finding 78 -- 2.4.1 Worst-Case Corner Example and Heuristics 81 -- 2.4.2 Advanced OFAT Methods 84 -- 2.4.3 Advanced Fitting Methods and Adaptive Search Methods 87 -- 2.5 Monte Carlo and Mismatch 96 -- 2.6 Moving to a Robust Circuit Design 101 -- 2.7 An Efficient General Design Strategy 103 -- 2.7.1 Desirable Improvements 106 -- 2.7.2 Mr. Murphy and Mr. Beckmesser 109 -- 2.8 Design with Pictures Part One 110 -- 2.8.1 CMOS RF-PA Example 110 -- 2.8.2 Worst-Case Search Showdown 121 -- 2.9 Questions and Answers 128 -- 2.10 Rules for Corner Analysis 130 -- 2.11 Summary onWorst-Case Corner Search 131 PART II: Basic Statistical Design Techniques 3 Classical Monte-Carlo and Data Analysis for Yield 135 -- 3.1 Corners vs. Monte-Carlo 140.
6 Advanced Sampling Methods 253 -- 6.1 When to Use What? 255 -- 6.2 Advanced Monte-Carlo Sampling Schemes 257 -- 6.2.1 Cartesian Grid Sampling 261 -- 6.2.2 Latin Hypercube Sampling LHS 264 -- 6.2.3 Discrepancy of Point Sets 268 -- 6.2.4 Low-Discrepancy Sampling LDS 272 -- 6.2.5 Sequences versus Sets 282 -- 6.2.6 Summary and Comparison of Sampling Methods 283 -- 6.3 Design with Pictures Part Four 292 -- 6.3.1 Experiments on Small Testcases 293 -- 6.3.2 LHS and LDS for Contribution Analysis 295 -- 6.4 Synthetic Monte-Carlo: Bootstrap 295 -- 6.4.1 Bootstrap Application Examples 298 -- 6.5 Fast Monte-Carlo by Sample Sorting 299 -- 6.5.1 Advanced Features and Example Run 301 -- 6.6 Questions and Answers on Sampling and Sorted Monte-Carlo 309 -- 7 Fast and High-Yield Estimation Techniques 315 -- 7.1 Worst-Case Distance (WCD) Analysis 318 -- 7.1.1 Worst-Case Distance Analysis by Hand 320 -- 7.1.2 Worst-Case Distances for Yield Approximation 325 -- 7.1.3 Classical WCD Analysis 326 -- 7.1.4 Problems inWorst-Case Distances 329 -- 7.1.5 Contribution Analysis versus WCD 336 -- 7.2 Fast k ` Sigma Corner Estimation 337 -- 7.3 Importance Sampling IS 339 -- 7.4 Sigma-Scaling Method SSS 340 -- 7.5 Design with Pictures Part Five 346 -- 7.5.1 Contribution versus WCD for a Comparator 347 -- 7.5.2 WCD in a Complex Filter 349 -- 7.5.3 Sorted MC in a Complex Filter 360 -- 7.6 Questions and Answers on Advanced Statistical Methods 361 -- 7.7 Summary of Advanced Statistical Analysis for Yield 364 -- 7.7.1 Different Methods on Difficult Mathematical Cases 365 -- 7.7.2 Different Methods on Circuits 370 -- 8 Optimization Techniques for Circuit Design 379 -- 8.1 When to Use What? 381 -- 8.2 Introduction to Optimization; When to Optimize? 385 -- 8.2.1 Optimization Pre-requisites and Limitations 388 -- 8.2.2 Classifications of Optimization 391 -- 8.3 How Successful OptimizersWork 396 -- 8.3.1 Newton and Quasi-Newton 398 -- 8.3.2 Parameter Setup Hints and Stopping Criteria 401 -- 8.3.3 Hill Climbing Techniques and Global Optimization 403.
3.2 Questions and Answers: Test Yourself 145 -- 3.3 Important Definitions and Concepts 147 -- 3.4 Expected Values 152 -- 3.5 Estimates, Bias Error, and Confidence Intervals 154 -- 3.6 Basic Data Analysis for Normal Gaussian Data 157 -- 3.6.1 The Yield Estimation Problem 161 -- 3.6.2 Sample Yield vs. CPK 165 -- 3.6.3 Confidence Interval-Based Autostop for MC 168 -- 3.7 Questions and Answers 173 -- 4 Monte Carlo and Non-Normal Data 175 -- 4.1 Examples of Non-Normal Distributions 176 -- 4.2 Identification of Non-Normal Distributions 179 -- 4.3 Non-Normal Data Analysis via Generalized CPK 180 -- 4.4 Analyzing Real Production Data 186 -- 4.5 Yield Estimation for Non-Normal MC Data via CGPK 189 -- 4.6 Questions and Answers 191 -- 4.7 Rules You Have to Know for Monte Carlo 192 -- 4.8 Design with Pictures Part Two 194 -- 4.8.1 Normal versus Student-t versus IH Distribution 195 -- 4.8.2 Calculations with Random Numbers 200 PART III: Advanced Statistical Design Techniques 5 Multivariate Statistical Analysis for Design Insights 205 -- 5.1 Multivariate Probability Density Functions 210 -- 5.2 Correlation 213 -- 5.3 Regression and Multivariate Modeling 216 -- 5.3.1 Variable Screening and Model Choice 220 -- 5.3.2 Variance Contribution Analysis 222 -- 5.4 Adaptive Sampling and High-Dimensional Models 227 -- 5.5 Multivariate CPKs 229 -- 5.5.1 Total CPK Estimation via Correlations 230 -- 5.5.2 Total CPK Estimation via Blocking Min 234 -- 5.6 Design with Pictures Part Three 236 -- 5.6.1 Latched Comparator Sensitivity Analysis 237 -- 5.6.2 More on Covariance & Co. 245 -- 5.7 Questions and Answers 248.
8.3.4 Do Real-World Circuit Designs Have Local Minima? 406 -- 8.3.5 Advanced Techniques Beyond (Quasi- )Newton 408 -- 8.4 How to Support Optimization 411 -- 8.4.1 Goal Definition 412 -- 8.4.2 Worst-Case Corners and Worst-Case Distance in Optimization 415 -- 8.4.3 Sizing Rules 417 -- 8.4.4 Optimization Shortcuts 419 -- 8.5 Design with Pictures Part Six 421 -- 8.5.1 Deeper Dive on Quadratic Problems 421 -- 8.5.2 Men versus Machine? Construction versus Optimization? 425 -- 8.6 Questions and Answers 427 -- 8.7 Summary: Why OptimizationWas So Hard? 430 -- 9 Advanced Front-End Design Methods 435 -- 9.1 Task-Driven Adaptive Statistical Analysis 437 -- 9.2 Yield Optimization and OverallWorst-Case Search 439 -- 9.2.1 Methods for OverallWorst-Case Search 441 -- 9.2.1.1 Example and heuristics for overall worst-case search 442 -- 9.2.1.2 Worst-case corner effort reduction methods 448 -- 9.2.2 Fast Full-Yield Optimization with Heuristics 450 -- 9.2.2.1 How the worst-cases may change during an optimization 452 -- 9.2.3 Advanced Yield and Surrogate-Based Optimization 455 -- 9.3 Connecting Design Methods 456 -- 9.3.1 Script-Supported Design 458 -- 9.3.2 The Split Monte Carlo Method 459 -- 9.3.3 The Eye Opener 461 -- 9.3.4 The Spec Inverter 462 -- 9.3.5 The Automatic Optimization Parametrizer 464 -- 9.3.6 The Circuit Terminator 465 -- 9.4 Design with Pictures Seven 467 -- 9.4.1 OverallWorst-Case Search in Action 467 -- 9.4.2 Comparator Yield Optimization 468 -- 9.4.3 What to Do after an Optimization? 472 -- 9.4.4 Optimization with InaccurateWorst-Case Distances 475 -- 9.5 Questions and Answers 477 -- 10 The Fully Assisted Variation-Aware Design Flow 479 -- 10.1 IP Reuse and Design Support 480 -- 10.1.1 IP Tools 481 -- 10.1.2 Technology-Independent Design 483 -- 10.2 Cockpit Number One: Augmented Schematic 487 -- 10.2.1 Designing with Constraints 491 -- 10.2.2 Design Tools 493 -- 10.3 Cockpit Number Two: Variation-Aware Driver Seat 495 -- 10.3.1 Task-Driven Design Flow 499 -- 10.3.2 Physical Aspects and Sign-Off 501.
10.3.2.1 Advanced layout techniques 504 -- 10.3.2.2 Parasitic analysis 506 -- 10.3.2.3 Layout-dependent effects LDE 508 -- 10.3.2.4 Post-layout speed-up techniques 510 -- 10.4 Summary 511 -- 10.5 Design with Pictures Eight 512 -- 11 Conclusion and Outlook 519 -- 11.1 Advances in Corner Analysis and Modeling 522 -- 11.2 Advances in Verification and Statistics 524 -- 11.3 Advances in Optimization and Synthesis 527 -- 11.3.1 Hierarchical Optimization 529 -- 11.3.2 Circuit Synthesis 530 -- 11.4 Business Drivers and Trends 534 -- 11.4.1 Design and IP 536 -- 11.4.2 Computing Trends 538 -- 11.5 Future Analog Design 539 -- 11.5.1 Enabling the Next Revolution 541 -- 11.6 LastWords 547 Appendix 551 Index 569 About the Authors 575.
Circuit Design = Science + Art! Designers need a skilled ""gut feeling"" about circuits and related analytical techniques, plus creativity, to solve all problems and to adhere to the specifications, the written and the unwritten ones. You must anticipate a large number of influences, like temperature effects, supply voltages changes, offset voltages, layout parasitics, and numerous kinds of technology variations to end up with a circuit that works. This is challenging for analog, custom-digital, mixed-signal or RF circuits, and often researching new design methods in relevant journals, conference proceedings and design tools unfortunately gives the impression that just a ""wild bunch"" of ""advanced techniques"" exist. On the other hand, state-of-the-art tools nowadays indeed offer a good cockpit to steer the design flow, which include clever statistical methods and optimization techniques. Actually, this almost presents a second breakthrough, like the introduction of circuit simulators 40 years ago! Users can now conveniently analyse all the problems (discover, quantify, verify), and even exploit them, for example for optimization purposes. Most designers are caught up on everyday problems, so we fit that ""wild bunch"" into a systematic approach for variation-aware design, a designer's field guide and more. That is where this book can help! Circuit Design: Anticipate, Analyze, Exploit Variations starts with best-practise manual methods and links them tightly to up-to-date automation algorithms. We provide many tractable examples and explain key techniques you have to know. We then enable you to select and setup suitable methods for each design task - knowing their prerequisites, advantages and, as too often overlooked, their limitations as well. The good thing with computers is that you yourself can often verify amazing things with little effort, and you can use software not only to your direct advantage in solving a specific problem, but also for becoming a better skilled, more experienced engineer. Unfortunately, EDA design environments are not good at all to learn about advanced numerics. So with this book we also provide two apps for learning about statistic and optimization directly with circuit-related examples, and in real-time so without the long simulation times. This helps to develop a healthy statistical gut feeling for circuit design. The book is written for engineers, students in engineering and CAD / methodology experts. Readers should have some background in standard design techniques like entering a design in a schematic capture and simulating it, and also know about major technology aspects
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