SAMPLED-DATA SIMULATION OF PERIODICALLY SWITCHED LINEAR CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 119

The algorithm of (6.34) has the following properties:

For fixed T , and are constant. They can be com-
puted in a pre-processing step prior to the start of simulation, the
sensitivity of the circuit at time points of a fixed time interval can be
computed efficiently in two matrix-vector multiplications and three
vector additions. The algorithms that compute

and

are given in Appendix 6.B of this chapter.

To compute must be available a priori.

No approximation is made in the derivation of the method. The
method is thus exact. To yield accurate sensitivity numerically,
and their derivatives to circuit parameters must be
computed to high precision. This is accomplished by using the multi-
step numerical Laplace inversion, as detailed in Appendix 6.B of this
chapter.

The algorithm computes the sensitivity to a single element in one

analysis of sensitivity network. For different circuit elements,

and must be re-computed. The method becomes costly if
sensitivities to a large number of circuit parameters are needed.

4. Inconsistent Initial Conditions of Sensitivity
Networks
Similar to the inconsistent initial conditions encountered in analysis
of the time domain response of periodically switched linear networks,
discontinuity may occur at switching instants of sensitivity networks.
We need to compute from Since sensitivity networks
are periodically switched linear circuits, the two-step algorithm effective
for computing the consistent initial conditions of periodically switched
linear circuits is applicable. In what follows, we detail this algorithm.
To compute from a forward step of step size T

is taken from is computed using (6.34) in the

forward step.