Environmental Engineering Reference
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flicker noise of the operational amplifiers is at 10 Hz. Note
that we have used the same parameters as those in [118] f o r t h e purpose
of direct comparison. There are sixteen white noise sources associated
with MOSFET switches, two white noise sources and two flicker noise
sources related to the operational amplifiers. The output noise power
of the band-pass filter is computed and the results are plotted in Fig.
11.36, together with the simulation results extracted from [118]. The
number of sidebands folded over are 3000, 10000, 30000, 50000, 60000,
and 70000, which correspond to noise band width of 0.384 GHz, 1.28
GHz, 3.84 GHz, 6.4 GHz, 7.68 GHz, and 8.96 GHz, respectively. The
large equivalent noise band width is mainly due to the small channel
resistance of MOSFET switches, small shunt capacitances, and large
unit-gain frequency of the operational amplifiers used in the simulation.
It is seen that our results agree well with those from [118].
The effect of flicker noise is investigated by computing the output
noise power due to the flicker noise sources of the operational amplifiers
only. The output noise power in the base band with 0, 2 and 5 sidebands
folded over, are computed and the results are shown in Fig.11.37. It is
seen that the effect of the flicker noise dominates at frequencies less
than 500 Hz. The output noise power due to the flicker noise sources
saturates when 5 sidebands are considered, indicating that only a few
sidebands are needed. For the purpose of comparison, the output noise
power due to the thermal noise sources with no fold-over is also plotted
in Fig.11.37. It is seen that the contribution of the flicker noise sources
is negligible as compared with that of the thermal noise sources at high
frequencies. This is the reason why flicker noise is generally neglected in
noise analysis of switched analog circuits.
5.
Statistical Analysis
Similar to the first-order second-moment method for statistical analy-
sis of periodically switched linear circuits in the time domain, the mean
and variance of these circuits in frequency domain can also be analyzed
using this approach and the results are given by (11.117) for the mean
and (11.118) for the variance.
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