Analog Circuit Simulators for IC Designers

• Year: 2020
• Tongue: English
• Leaves: 414
• Category: Library

✦ Table of Contents

Preface
List of Abbreviations
Common Symbols and Their Meaning
Contents
About the Author
Chapter 1: Introduction
1.1 Background
1.2 The Arrival of Simulators
1.3 This Book
Chapter 2: Overview of Numerical Methods
2.1 Differential Equations: Difference Equations
2.1.1 Initial Value Problems
2.1.2 Euler’s Methods
2.1.3 Trapezoidal Method (Trap)
2.1.4 Second-Order Gear Method (Gear2)
2.1.5 Summary
2.1.6 Solution Methods: Accuracy and Stability
2.1.6.1 Accuracy
2.1.6.2 Stability
2.2 Nonlinear Equations
2.2.1 Newton-Raphson
2.3 Matrix Equations
2.3.1 Basic Matrix Formulation Based on N Unknowns
2.3.2 Matrix Solvers
2.3.2.1 Gauss Elimination
2.3.2.2 LU Decomposition
2.3.2.3 Iterative Methods
2.3.2.4 Summary
2.4 Simulator Options Considered
2.5 Summary
2.6 Codes
2.6.1 Code 2.7.1
2.7 Exercises
References
Chapter 3: Modeling Techniques
3.1 CMOS Transistor Model
3.1.1 CMOS Transistor Basics
3.1.2 CMOS Transistor Physics
3.1.3 MOSFET Capacitance Modeling Details
3.1.4 BSIM Models
3.1.4.1 Basic Model
3.1.4.2 BSIM6
3.2 Bipolar Transistors
3.2.1 General Behavior
3.2.2 Ebers-Moll Model
3.2.3 Gummel-Poon Model
3.2.4 Hi-Current Model (HiCUM)
3.2.5 VBIC Model
3.3 Model Options Considered
3.4 Transistor Models Used
3.4.1 CMOS Transistor Model 1
3.4.2 CMOS Transistor Model 2
3.4.3 Bipolar Transistor Model 3
3.5 Summary
3.6 Exercises
References
Chapter 4: Circuit Simulators: Linear Case
4.1 Introduction
4.2 Historical Development
4.3 Matrix Equations
4.3.1 Passive Element
4.3.2 AC Simulation
4.3.3 Active Elements
4.3.3.1 Independent Sources
4.3.3.2 Dependent Sources
4.3.4 Summary
4.4 Matrix Building: AC Simulation
4.4.1 Noise Analysis
4.4.2 Stability Analysis
4.4.3 S-Parameter Analysis
4.4.4 Transfer Function Analysis
4.4.5 Sensitivity Analysis
4.4.6 Odd Cases: Things to Watch out for
4.5 DC Linear Simulation
4.6 Transient Linear Simulation
4.6.1 Forward Euler
4.6.2 Backward Euler
4.6.3 Trapezoidal Method
4.6.4 Second-Order Gear Method
4.6.5 Stiff Circuits
4.6.6 Local Truncation Error
4.6.7 Odd Cases: Things to Watch out for
4.7 Simulator Options Considered
4.8 Summary
4.9 Codes
4.9.1 Code 4.2
4.9.2 Code 4.3
4.9.3 Code 4.4
4.9.4 Code 4.5
4.9.5 Code 4.6
4.9.6 Code 4.7
4.9.7 Code 4.8
4.9.8 Code 4.9
4.9.9 Code 4.10
4.10 Exercises
References
Chapter 5: Circuit Simulation: Nonlinear Case
5.1 Introduction
5.2 DC Nonlinear Simulation
5.2.1 Solution Techniques
5.2.1.1 Nonlinear Model Implementations
5.2.1.2 Bandgap Circuit
5.2.2 Convergence Criteria
5.2.2.1 Convergence Issues
5.2.3 Odd Cases: Things to Watch Out for
5.3 Linearization Techniques
5.4 Transient Nonlinear Simulation
5.4.1 Fixed Timestep
5.4.1.1 Example Circuits with Uniform Timesteps: Purely Resistive Case
5.4.1.2 Example Circuits with Uniform Timesteps: Dynamic Case
5.4.2 Adjustable Timestep
5.4.2.1 Timestep Adjustments
5.4.2.2 Summary
5.4.2.3 Example Circuits with Timestep Control: Purely Resistive Case
5.4.2.4 Example Circuits with Timestep Control: Dynamic Case
5.4.2.5 Benefits of Timestep Control
5.4.3 Convergence Issues
5.4.3.1 LTE Criterion Guidelines
5.4.3.2 Global Truncation Error
5.4.3.3 Pseudo-Transient Method for Convergence Aid
5.4.4 Nonlinear Capacitors
5.4.5 Break Points
5.4.6 Transient Accuracy: Summary
5.5 Periodic Steady-State Solvers
5.5.1 Shooting Methods
5.5.2 Harmonic Balance Methods
5.5.3 Envelope Analysis
5.5.4 Perturbation Techniques
5.5.5 Periodic S-parameter, Transfer Function, Stability Analyses
5.5.6 Quasi-Periodic Steady-State Analyses
5.5.7 Specific Circuit Examples
5.5.8 Odd Cases: Things to Watch Out for
5.5.9 Accuracy: How to Determine
5.5.10 Simulator Options Considered
5.5.11 Summary
5.6 Codes
5.6.1 Code 5.1
5.6.2 Code 5.2
5.6.3 Code 5.3
5.6.4 Code 5.4
5.6.5 Code 5.5
5.6.6 Code 5.6
5.6.7 Code 5.7
5.6.8 Code 5.8
5.6.9 Code 5.9
5.7 Exercises
References
Chapter 6: Epilogue: Simulators in Practice
6.1 Model Verification Strategies with a New Process Technology
6.1.1 DC Response Curves
6.1.2 Vth Extraction
6.1.3 ft Characterization
6.1.4 Gate-Source and Gate-Drain Capacitance Characterization
6.1.5 Summary
6.1.6 Example of Faulty Model Behavior
6.1.7 Corner Simulation Strategy
6.1.8 Monte Carlo Simulations
6.2 Small Block Simulations
6.2.1 Analog Circuit Simulation Strategy
6.2.2 Small Digital Circuit Simulation Strategy
6.3 Large Block Simulations
6.3.1 Analog-Digital Co-simulation Strategies
6.3.2 Summary
6.4 Exercises
References
Chapter 7: Mathematics Behind Simulators
7.1 Network Theory
7.1.1 Sparse Tableau Analysis
7.1.2 Nodal Analysis
7.1.3 Modified Nodal Analysis
7.2 Numerical Solution Techniques of Differential Equations
7.2.1 ODE Solution Methods
7.2.1.1 Initial Value Problems
7.2.1.2 Classification of Linear Multistep Methods
7.2.1.3 Stability of Linear Multistep Methods
7.2.1.4 Timestep Control Algorithms
7.3 Newton-Raphson Theory
7.3.1 Basic Derivation for Arbitrary Dimensions
7.3.2 Common Difficulties and Workarounds
7.4 Shooting Method Theory
7.5 Harmonic Balance Theory
7.6 Matrix Solvers: Brief Theory
7.6.1 Gauss-Jordan Elimination
7.6.2 LU Decomposition
7.6.3 Iterative Matrix Solvers
References
Appendix A Complete Python Code Lists for All Examples
A.1 Introduction
A.1.1 Variables
A.1.2 Basic Structure
A.1.3 Netlist Syntax
A.1.4 Control Statements
A.2 AnalogDef.py
A.3 Models.txt
Index