Overview of SPICE-like circuit simulation algorithms

A tutorially orientated account of the principles underlying circuit level simulation forms the basis for discussing reliability of circuit level simulation. An outline of equation formulation and time discretisation of the equations is followed by consideration of stability of the numerical integration methods. The precision of simulation, which also depends on the integration methods used, is then discussed, with particular reference to the analysis parameters of the SPICE simulator. A descriptive account of the Newton-Raphson method of solving the nonlinear algebraic equations, derived from the discretised differential equations, is then presented again with relation to SPICE parameters. The reasons for convergence failure in both transient and DC simulation are related to the underlying principles of simulation and possible ill conditioning of the circuit. The paper includes some simple simulation examples of problematic situations