In transient and DC analyses, an iterative method is used to analyse the circuit. Generally, iterative methods start with an initial guess for the solution to a set of equations and then evaluate the equations with that guess. The result of that evaluation is then used to derive a closer estimate to the final solution. This process is repeated until a solution is found that is within the error tolerance required. SIMetrix and SPICE use Newton-Raphson\footnote{Sir Isaac Newton 1642-1727 and Joseph Raphson 1648-1715} iteration which usually converges extremely rapidly. However, there are occasions when this process is either unreasonably slow or fails altogether. Under these circumstances the simulation will abort.

SIMetrix offers superior convergence which has been achieved as a result of the following developments to the simulator core:

  • Automatic pseudo transient analysis algorithm for operating point solution. See below for details.
  • Advanced iteration algorithm reduces numerical noise
  • Enhancements to GMIN and source stepping algorithms to use a variable step size. (The standard SPICE3 variants use a fixed step).
  • Junction GMIN DCOP Convergence Method
  • Proprietary enhancements to transient analysis algorithm.
  • Optional extended and quad precision solvers
  • New matrix solver
  • Improvements to device models.
With these improvements, convergence failure with SIMetrix is extremely rare. However, it is impossible to eliminate this problem altogether and there still remain some circuits which fail.

In this chapter we explain some of the causes of non-convergence and some of the strategies SIMetrix uses to prevent it. Also explained is what to do in the rare event that convergence fails.