Mathematical Background

Abstract

This chapter attempts to explain the mechanisms of SPICE OPUS in formal terms. You can certainly use a circuit simulator without understanding its mathematical background, just as you can drive a car without knowing what is going on under the hood. This may sound like a good excuse to skip this chapter, in which case many phenomena will just have to go unexplained. For instance, why does SPICE only compute nodal voltages and currents through independent voltage sources? Or why is it that sometimes a simple operating point analysis will last longer than a complex transient? However, advanced users will find this chapter very useful when working with tricky circuits that require manual adjustments of the many simulator parameters available in SPICE OPUS. Questions like the following are tackled.

• When does one switch from the default trapezoidal integration algorithm to Gear integration?

• What exactly is the meaning of all those cryptic warnings and error messages?

• Where is the source of convergence problems and how can one avoid them?

• How accurate are the obtained simulation results?

In order to be as comprehensive as possible, we will proceed systematically from very simple linear resistive networks and later add nonlinear and dynamic behavior.