## Contents

PREFACE

1 LINEAR RESISTIVE CIRCUIT ANALYSIS

1.1 Introduction

2 ANALYSIS USING TRANSFORMS

2.1 Introduction

2.2 The Laplace transform and its applications

2.3 Automatic equation formulation

2.4 Multiport and multiterminal networks

2.5 Frequency domain analysis

2.6 Symbolic function generation

2.7 Linear system description by nodal formulation

3. NONLINEAR DC ANALYSIS

3.1 Introduction

3.2 Two-terminal companion model

3.3 Equation formulation

3.4 Nonlinear circuit analysis algorithm

3.5 Other nonlinear elements

3.6 Convergence aspects of nonlinear DC analysis

3.7 DC analysis of electronic circuits

4. TRANSIENT ANALYSIS OF ELECTRONIC CIRCUITS

4.1 Introduction

4.2 Statement of the problem

4.3 The backward Euler formula and its application

4.3.1 Approximation of the derivative

4.3.2 Application of the backward Euler formula

4.3.3 Analysis of nonlinear dynamic circuits

4.4 Accuracy, stability and stiffness

4.5 Multistep integration formulae

4.6 Implementation considerations

4.7 Some specific applications

4.8 Device modelling

4.8.1 Model generation

4.8.2 Classification of models

4.8.3 Model structure and related topics

5. SENSITIVITY ANALYSIS

5.1 Introduction

5.2 Tellegen's theorem

5.3 Computation of sensitivities in linear resistive networks

5.5 Sensitivities with respect to excitations

5.6 Second order sensitivities

5.7 Sensitivities in nonlinear circuits

5.8 Sensitivity in the frequency domain

5.8.1 Sensitivity of currents and voltages

5.8.2 Sensitivities of amplitude and phase responses

5.8.3 Sensitivities of networks containing transmission lines

5.8.4 Sensitivities with respect to conductances

5.8.5 Sensitivities of circuits without current dependencies

5.9 Time domain sensitivity analysis

5.10 Large signal sensitivity analysis of linear circuits

6. TOLERANCE ANALYSIS AND DESIGN

6.1 Introduction

6.2 Basic terms and definitions

6.3 Tolerance analysis methods

6.3.1 Worst-case analysis

6.3.2 The method of moments

6.3.3 The Monte Carlo method

6.4 Tolerance design

7. ELECTRONIC CIRCUIT OPTIMIZATION

7.1 Introduction

7.2 Basic terms and definitions

7.3 Newton's method

7.4 Application of Newton's method

7.4.1 Coefficient matching

7.4.2 DC operating point design

7.4.3 Chebyshev optimization

7.4.4 The least p-th approximation

7.5 Constrained optimization

7.6 Quasi-Newton methods

7.7 Multiple criteria optimization

7.8 Optimization by simulated annealing

8. LOGIC SIMULATION

8.1 Introduction

8.2 Logic state modelling

8.2.1 Two-state logic

8.2.2 Three-state logic

8.2.3 High impedance state

8.2.4 Multiple state logic

8.2.5 Hazard states

8.2.6 Signal strengths

8.3 Delay models

8.3.1 Zero delay model

8.3.2 Pure delay model

8.3.3 Ambiguous delay model

8.3.4 Inertial delay mode

8.4 Gate models

8.5 Simulation algorithms

8.5.1 Compiled simulation

8.5.2 Interpreted simulation

8.5.3 Event-driven simulation

8.5.4 Scheduling events

8.5.5 Zero delays

8.6 Fault models and fault simulation

8.6.1 The single-stuck fault model

8.6.2 Fault simulation

8.6.3 Parallel fault simulation

8.6.4 Deductive fault simulation

8.6.5 Concurrent fault simulation

8.7 Functional simulation and hardware description languages

9. MIXED-SIGNAL SIMULATION

9.1 Introduction

9.2 Signal conversion

9.2.1 Analogue to logic interface

9.2.2 Logic to analogue interface

9.2.3 Insertion of interface models

9.3 Synchronisation of logic and circuit simulators

9.3.1 The lockstep algorithm

9.3.2 Optimistic simulation

9.3.3 Hybrid synchronization algorithms

9.3.4 Initialization

APPENDIX 1 SPICE

APPENDIX 2 VHDL

REFERENCES

INDEX