## Fundamentals of Computer-Aided Circuit SimulationFrom 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. |

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### Contents

1 CIRCUIT EQUATION FORMULATION | 1 |

13 Modified Nodal Analysis | 10 |

14 Sparse Tableau Analysis | 12 |

2 LINEAR EQUATION SOLUTION | 17 |

22 LU Transformation | 21 |

23 LU Transformation Variations | 23 |

24 Determinants | 29 |

26 Iterative Methods | 33 |

54 Truncation Error of Integration Formulas | 101 |

55 Stability of Integration Methods | 107 |

56 Automatic Timestep Control | 112 |

6 ADJOINT NETWORKS AND SENSITIVITY | 125 |

62 Element Sensitivity | 126 |

63 SmallSignal Sensitivities | 131 |

64 Noise and Group Delay Response | 134 |

7 POLEZERO EVALUATION | 137 |

3 SPARSE MATRIX METHODS | 37 |

32 Optimal Ordering | 45 |

4 NONLINEAR EQUATION SOLUTION | 53 |

42 Convergence and Termination | 58 |

43 Variations of NewtonRaphson Iteration | 66 |

44 Internal Device Node Suppression | 74 |

5 NUMERICAL INTEGRATION | 87 |

52 Application of Integration Formulas | 92 |

53 Construction of Integration Formulas | 96 |

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### Common terms and phrases

adjoint network admittance matrix approach approximation Backward Euler bipolar transistor Branch Constitutive Equations branch relation branch voltages Capacitor circuit simulation Circuit Theory Circuits and Systems column computed considered Constitutive Equations convergence derivative diagonal diode eigenvalue equivalent circuit Euler approximation evaluated fill-ins Forward Euler Gaussian elimination Gear-Shichman formula Hsieh IEEE IEEE Trans illustrated in Figure Inductor Integration Formulas junction limiting LINEARIZED CIRCUIT EQUATIONS LU transformation Markowitz Modified Nodal Analysis Muller's method Newton-Raphson iteration Nodal Admittance Matrix nodal analysis nodal equations node voltages non-zero terms Norton equivalent current nth step Numerical Integration NZLC output parameter pivot polynomial problem procedure Program RC circuit represents resistor RHS e+ S.W. Director sensitivity small-signal solving Sparse Matrix sparse tableau stability storage system of equations systems of linear TABLE Taylor series technique threaded list timestep h Transient Analysis Trapezoidal formula truncation error values variables variation vector voltage source y-parameters zero