A method to accurately simulate and detect transition time instants in piecewise linear SMPS circuits

When nonlinear switching circuits like SMPS (Switched Mode Power Supply) designs are simulated using nonlinear circuit simulators like SPICE, the simulation is slow and prone to convergence issues. It is because SMPS designs are stiff circuits having a wide range of time constants. An efficient way to simulate such designs is to first approximate the nonlinear models of diodes and transistors with their piecewise linear (PWL) equivalent models and then simulate them using a piecewise linear simulation method. In this work we present an efficient way of accurately simulating such piecewise linear circuits and finding the transition time instants, using state space modeling. The independent input signals in the SMPS designs can be categorized as sinusoidal, exponential or ramp signals or a combination of these waveforms. In this work, no approximations to the input signal waveforms are considered. The detection of transition time instants where the circuit will transition from one linear region to the next, has been achieved using a combination of Newton Raphson method and state space approach. The results of using this state space solution on a few circuits which are the building blocks of SMPS designs have also been shown.