Sampled-Data Simulation of Periodically Switched Linear Circuits

Summary

Sampled-data simulation, an efficient, accurate, and absolutely stable time domain algorithm for periodically switched linear circuits has been developed in this chapter. We have shown that this algorithm computes response, sensitivity, mean and variance of the response, output noise power in the presence of white noise sources, and the effect of clock jitter of periodically switched linear circuits at time points of a fixed time interval. In computation of the time domain response, only one matrix multiplication and one vector addition are needed in each time step. Once the transition matrix M_k(T) and zero-state response vector P_k(T) are computed to high precision, the response can be obtained with a very high degree of accuracy. The inconsistent initial conditions arising from ideal switching are handled using numerical Laplace inversion based two-step algorithm effectively. In sensitivity analysis, the sensitivity of the response of periodically switched linear circuits to a circuit parameter is computed at time points of a fixed interval. No approximation is made. A drawback of this method in sensitivity analysis is that it yields the sensitivity of the response to one circuit parameter, rather than to all circuit parameters, in one network analysis. It is therefore computationally costly if sensitivities to a large number of circuit parameters are needed. In statistical analysis, the first-order second-moment method that yields the mean and variance of the response of periodically switched linear circuits without multiple analyses of the circuits has been introduced. As compared with Monte Carlo based methods, the method is computationally efficient. Because only up to the second-order moments were considered in the derivation of the first-order second-moment method, the accuracy of the method deteriorates if the coefficient of variance of circuit parameters is large. In noise analysis, white noise signals of a given circuit are represented by a train of pulses with the pulse width set by the noise bandwidth of the circuit and the pulse amplitude set by the output noise power of the circuits due to the noise signals. Using sampled-data simulation, the response of periodically switched linear circuits to both input signals and noise sources can be computed to high precision. The power spectrum of the output noise of the circuit is obtained in a post FFT analysis.