SAMPLED-DATA SIMULATION OF PERIODICALLY SWITCHED NONLINEAR CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 138

also to be kept sufficiently small so that a better starting point, and
subsequently quadratic convergence, can be achieved.
The accuracy of general-purpose analog simulators is limited by the
local truncation error (LTE) of the numerical methods used. Due
to stability constraints, the order of numerical integration algorithms
used by general-purpose analog simulators is low. Most SPICE-like
simulators employ only the first and second-order algorithms (back-
ward Euler and Trapezoidal).
This chapter investigates non LMS-PC algorithms for time-domain
analysis of periodically switched nonlinear circuits, specifically, it ex-
tends the sampled-data simulation algorithm for periodically switched
linear circuits given in the preceding chapter to periodically switched
nonlinear circuits with weakly nonlinearities. In addition, it extends the
two-step algorithm for periodically switched linear circuits to periodi-
cally switched nonlinear circuits to handle inconsistent initial conditions
encountered at switching instants. Both the response and sensitivity of
periodically switched nonlinear circuits at equally spaced time points are
investigated in this chapter. The chapter is organized as follows: Section
1 presents the multi-linear model of nonlinear elements typically encoun-
tered in periodically switched nonlinear circuits. Section 2 derives the
Volterra circuits of periodically switched nonlinear circuits. In Section 3,
a sampled-data simulation algorithm for periodically switched nonlinear
circuits is developed. A two-step algorithm for handling the inconsistent
initial conditions of these circuits is derived in Section 4. Section 5 is
concerned with the sensitivity analysis of periodically switched nonlin-
ear circuits. In Section 6, factors that affect the accuracy and efficiency
of the method are examined. The simulation results of example circuits
are presented in Section 7. The chapter concludes in Section 8.
1. Multi-Linear Theory
A large number of circuits encountered in telecommunication systems
operate at a fixed DC operating point and the signals to be processed
by these circuits are usually of small amplitude. The behavior of nonlin-
ear elements in these circuits can be characterized adequately using the