Environmental Engineering Reference
In-Depth Information
The variables associated with the capacitor in the corresponding sensi-
tivity network are the sensitivity current
and sensitivity voltage
The capacitance remains the same. The constitutive equation
of the capacitor in the sensitivity network is the same as that in the
original circuit. An ideal current source is added in parallel with
the capacitor. It is the input of the sensitivity network. The substitu-
tion for the capacitor in the corresponding sensitivity network is given
in Fig.11.7. Similarly, one can derive the substitutions for other basic
elements in corresponding sensitivity networks. The results are shown
in Fig.11.7.
To compute the sensitivity of the response of a periodically switched
linear circuit
N
with respect to capacitor
C,
the corresponding sensitiv-
ity network
is needed. The input of
is a current source connected
in parallel with
C
of current
Because
therefore
This is equivalent to have an infinite number of current sources of value
connected in parallel
with the capacitor, as depicted in Fig.11.8. Each of these current sources
generates an output that also contains an infinite number of frequency
components. The complete output of at frequency is obtained
by summing up the contributions of all the added current sources at
frequency
where
is the aliasing transfer functions from the current
source at frequency
to the output of
at frequency
A care-
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