CIRCUIT SIMULATION

Abstract

This text describes in detail the numerical techniques and algorithms that are part of modern circuit simulators, with a focus on the most commonly used simulation modes: DC Analysis and Transient Analysis. After a general introduction in chapter 1, network equation formulation is covered in chapter 2, with emphasis on modified nodal analysis (MNA). The coverage also includes the network cycle space and bond space, element stamps, and the question of unique solvability of the system. Solving linear resistive circuits is the focus of chapter 3, which gives a comprehensive treatment of the most relevant aspects of linear system solution techniques. This includes the standard methods of Gaussian elimination (GE) and LU factorization, as well as some in-depth treatment of numerical error in floating point systems, pivoting for accuracy, sparse matrix methods, and pivoting for sparsity. Indirect solution methods, such as Gauss-Jacobi (GJ) and Gauss-Seidel (GS) are also covered. As well, some discussion of node tearing and partitioning is given, in recognition of the recent trend of increased usage of parallel software on multi-core computers. Solving nonlinear resistive circuits is covered in chapter 4, with a focus on Newton’s method. A detailed study is given of Newton’s method, including its links to the fixed point method and the conditions that govern its convergence. A rigorous treatment is then provided of how this method applies to circuit simulation, leading up to the notion of companion models for nonlinear resistive elements, with coverage of multiterminal elements. As well, a coverage of quasiNewton methods in simulation is provided, which includes the three commonly used homotopy methods for DC Analysis: source stepping, Gmin stepping, and pseudo-transient. Simulation of dynamic circuits, both linear and nonlinear, is covered in chapter 5. This chapter gives a detailed treatment of methods for solving ordinary differential equations (ODEs), with a focus on those methods that have been found useful for circuit simulation. Issues of accuracy and stability of linear multistep methods are covered in some depth. These methods are then applied to circuit simulation, illustrating how the companion models of dynamic elements are derived. Here too, multiterminal elements are addressed, as well as other advanced topics of time-step control, variable time-step, charge conservation, and the use of charge-based models in simulation.