Numerical oscillation, or ringing, is an undesired artifact of the Trapezoidal integration method. The oscillations appear as bounded point-to-point ringing which persists without any, or very little, damping. The presence of point-to-point ringing can adversely affect convergence, and in extreme cases, the ringing can be so severe that the actual simulation results are incorrect.

The oscillations associated with the Trapezoidal integration method can occur for a number of reasons, but the most common events leading to numerical oscillations are:

  • step changes in the current through an inductor.
  • step changes in the voltage across a capacitor.
  • step changes in the conductance of a device, for example, a switch.

The problem is illustrated in the following waveform, which shows the current through a capacitor.

The most common method used to eliminate numerical oscillations is to use the Gear integration method. The disadvantage of this approach is that the Gear integration method is typically slower and less accurate than the Trapezoidal integration method, and for some simulations, such as simulations of resonant oscillators, the Gear method will actually suppress desired oscillations.

A better alternative for eliminating the numerical oscillations is to use the SUPOSC option. This option is on by default. This approach uses sophisticated techniques to detect the occurrence of point-to-point ringing, and performs suppression only when the problem is present.

The effect of the SUPOSC option is shown below. The blue trace shows the first half of the above oscillatory current waveform, and the other two traces show how the numerical oscillations are removed using the Gear integration method (red trace) and the SUPOSC option (green trace). Both methods are equally affective at eliminating the point-to-point ringing; however the SUPOSC method retains the superior speed, accuracy, and stability of the trapezoidal integration method.