SAMPLED-DATA SIMULATION OF PERIODICALLY SWITCHED LINEAR CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 123

made at the boundary of the design objective and yields the advanced
first-order second-moment (AFOSM) method [54].
The accuracy of the method depends upon (i) the accuracy in com-
puting the derivatives of the response with respect to circuit parameters
and (ii) the accuracy of FOSM method. It was shown earlier that com-
putation of the derivatives of the response to circuit parameters can be
made very accurate if the multi-step numerical Laplace inversion algo-
rithms are employed. The accuracy of the method is thereby mainly
determined by that of FOSM method, which is determined by both the
coefficient of variance of circuit parameters, the degree of their corre-
lation, and the characteristics of the circuits. Because only up to the
second-order moments were considered in the derivation of FOSM, the
error of FOSM method will rise if or equivalently the
coefficient of variance of the circuit parameters are large.

6. Noise Analysis

Noise considered here is the small fluctuation of currents or voltages
that are generated within devices themselves. Noise coupled externally,
such as the switching noise generated by digital circuits and electromag-
netic interference, is excluded.
Noise encountered in integrated circuits typically includes thermal
noise, shot noise, and flicker noise among which thermal noise and shot
noise are white in nature. They have constant power spectral density
over a wide frequency range. The power spectral density of flicker noise,
however, is inversely proportional to frequency. The corner frequency of
the flicker noise of MOS devices is in the range of several MHz [2, 1]. Due
to the under-sampling of white noise sources by and the large bandwidth
of periodically switched linear circuits, the total output noise of these
circuits is usually dominated by the noise power folded over from the
sideband components of the white noise sources in the circuits [55]. For
this reason, in what follows only white noise is considered.
The two key issues encountered in time domain noise analysis are (i)
the generation of random noise signals in the time domain and (ii) the
accuracy of numerical integration methods used for solving circuits with
white noise sources.