Fundamentals of Computer-Aided Circuit Simulation

From little more than a circuit-theoretical concept in 1965, computer-aided circuit simulation developed into an essential and routinely used design tool in less than ten years. In 1965 it was costly and time consuming to analyze circuits consisting of a half-dozen transistors. By 1975 circuits composed of hundreds of transistors were analyzed routinely. Today, simulation capabilities easily extend to thousands of transistors. Circuit designers use simulation as routinely as they used to use a slide rule and almost as easily as they now use hand-held calculators. However, just as with the slide rule or hand-held calculator, some designers are found to use circuit simulation more effectively than others. They ask better questions, do fewer analyses, and get better answers. In general, they are more effective in using circuit simulation as a design tool. Why? Certainly, design experience, skill, intuition, and even luck contribute to a designer's effectiveness. At the same time those who design and develop circuit simulation programs would like to believe that their programs are so easy and straightforward to use, so well debugged and so efficient that even their own grandmother could design effectively using their program.

1. Circuit Equation Formulation. - 1. 1 Branch Constitutive Equations. - 1. 2 Nodal Analysis. - 1. 3 Modified Nodal Analysis. - 1. 4 Sparse Tableau Analysis. - 2. Linear Equation Solution. - 2. 1 Gaussian Elimination. - 2. 2 LU Transformation. - 2. 3 LU Transformation Variations. - 2. 4 Determinants. - 2. 5 Accuracy Enhancement. - 2. 6 Iterative Methods. - 3. Sparse Matrix Methods. - 3. 1 Sparse Matrix Storage. - 3. 2 Optimal Ordering. - 4. Nonlinear Equation Solution. - 4. 1 Newton-Raphson Iteration. - 4. 2 Convergence and Termination. - 4. 3 Variations of Newton-Raphson Iteration. - 4. 4 Internal Device Node Suppression. - 5. Numerical Integration. - 5. 1 Introduction to Integration Formulas. - 5. 2 Application of Integration Formulas. - 5. 3 Construction of Integration Formulas. - 5. 4 Truncation Error of Integration Formulas. - 5. 5 Stability of Integration Methods. - 5. 6 Automatic Timestep Control. - 6. Adjoint Networks and Sensitivity. - 6. 1 Adjoint Networks. - 6. 2 Element Sensitivity. - 6. 3 Small-Signal Sensitivities. - 6. 4 Noise and Group Delay Response. - 7. Pole-Zero Evaluation. - 7. 1 Two-Port Transfer Functions. - 7. 2 Muller s Method. - 8. Statistical Analysis. - 8. 1 Distributions. - 8. 2 Tracking and Pivots. - 8. 3 Pivot Sorting Algorithm. - 8. 4 Correlation. - References.