INCONSISTENT INITIAL CONDITIONS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 82

the detection of the existence of impulses at switching instants. The de-
termination of the existence of impulses at switching instants is critical
to the analysis of circuits with internally controlled switches as impulses
generated at switching instants are usually high enough to change the
states of other switches in the circuits. The chapter is summarized in
Section 7.

1. Inconsistent Initial Conditions
It was shown in Chapter 2 that the full-transistor model is capable of
capturing the rapidly time-varying transient characteristics of circuits.
Simulation based on the full-transistor model, however, is costly. The
use of this model is warranted only if the transient behavior of the cir-
cuit in the vicinity of switching instants is critically needed. Analysis
based on the voltage-modulated resistor model, on the other hand, is
much less expensive computationally. The large ratio of the ON and
OFF resistances of the voltage-modulated resistor model, however, gives
rise to stiff systems that have ill-conditioned circuit matrices and require
excessive simulation time. This drawback can be eliminated if the ideal
switch model that has zero resistance in the ON state and infinite re-
sistance in the OFF state is employed. Ideal switching, however, may
cause an abrupt change in nodal voltages due to impulsive capacitor cur-
rents, as shown in Fig.2.3. Similarly when inductors are encountered,
ideal switching may give rise to an abrupt change in loop currents, re-
sulting in impulsive inductor voltages. As a result, not only the value of
branch currents and nodal voltages immediately before switching may
differ from that immediately after switching, impulses are also generated
at switching instants. Difficulties arising from ideal switching include :

i) Impulses and discontinuities encountered at switching instants can
not be handled by conventional linear multi-step predictor-corrector
algorithms as these algorithms usually require the continuity of net-
work variables.

ii) Because switched circuits change their topology at switching instants,
and (immediately before switching) can not be used to