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is usually small and can be considered constant approximately. As
a result,
for and
The following advantages are gained from
this approximation:
LU-decomposition of and subsequent forward and
backward substitutions are no longer needed. This significantly
lowers simulation cost.
The conventional adjoint network approach, similar to that of
ideal switched capacitor networks [79], can be employed conve-
niently to efficiently compute parameter sensitivity and noise, as
will be seen in the following section of the chapter.
A similar approach was proposed in [82, 83] where circuit equation is
discretized in the time domain using backward difference formulae,
usually backward Euler, with the step size equal to the width of
clock phases or smaller. The resultant discrete network equations
are analyzed in Note that both approaches will give a
large error if the clock frequency is comparable to that of the signal
frequency.
As an example, consider the fifth-order elliptic switched capacitor low
pass filter shown in Fig.11.1. The clock frequency is 32 kHz with two
clock phases of equal width. The circuit parameters are tabulated in
Table 11.1. The frequency response of the low pass is shown in Fig.11.2
with its passband shown in Fig.11.3. 0.28 dB ripple in the passband is
observed.
2. Sensitivity Analysis
The importance of small-signal sensitivity analysis was stated earlier
in Chapter 6 when the time domain sensitivity analysis of periodically
switched linear circuits was investigated. This section deals with sen-
sitivity analysis of periodically switched linear circuits in the frequency
domain. The normalized small-change sensitivity is defined as [5]
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