Energy-based control of numerical errors in time-domain simulation of dynamic circuits

In this paper, we consider the accuracy of integration algorithms such as the implicit Euler and the trapezoidal methods, which are largely employed in the time domain circuit analysis. These algorithms require one to make hypotheses on the intersample shape and on the "energy content" of the sampled waveforms. For example, the implicit Euler algorithm supposes functions to be piecewise constant, When these hypotheses are violated, some errors are introduced by the integration process into the solution waveform. We consider the energy of the sampled functions, and through energy balance equations, estimate the accuracy of the integration algorithm. Furthermore, we propose an implicit algorithm to determine an adequate integration time step during numerical time domain analysis. This algorithm is based on a global energy balance equation and not on the conventional estimation of the local truncation error. It avoids the "cut and try" mechanism used in SPICE to determine the time step that satisfies the desired error tolerance.