Fast MOS circuit simulation with a direct equation solver

An approach to MOS circuit simulation is presented. This approach considers most of the important circuit parameters, such as input slew rate, loading capacitance, overlapping of inputs, incomplete charging or discharging of output nodes, back gate bias effect, and the Miller effect. A general-purpose MOS circuit primitive is proposed. This circuit primitive captures most of the important parameters in MOS circuits. The transient response of the primitive is analytically found by recognizing the unique properties of the Ricatti equation model for the primitive. The analytical solution of differential equation provides a high accuracy. In addition to the popular ramp approximation of rising and falling edges, more general piecewise linear waveform approximation is also allowed. Simulation results for a benchmark 50-stage CMOS inverter chain and a CMOS XNOR gate show that the speed of a simulator using this approach is comparable with state-of-the-art switch level simulators and up to two orders of magnitude faster than SPICE for transient analysis with less than 1% error