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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.
APPENDIX 6.A: Computation of
and
In this appendix, we develop efficient and accurate algorithms for computing the
vectors
and
introduced in this chapter.
1.
Computation of
Consider the circuit
Laplace transform of (6.A.1) is given by
It is seen that the response of the circuit is To compute for an arbitrary
T
with a high degree of accuracy, a multi-step numerical Laplace inversion approach
similar to that for computing and given in the preceding chapters is
taken here. The time interval in which we are interested in the behavior of the circuit
is first divided into multiple small sub-intervals of equal width such that the error
of numerical Laplace inversion over each sub-interval is sufficiently small. The first
sub-interval is given by (0,
Using numerical Laplace inversion, we obtain the
response of the circuit at
In the second step, the time origin is shift from
to
The circuit in this
step is depicted by
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