Environmental Engineering Reference
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to the single output at frequency of a periodically switched linear cir-
cuit is equal to that of the aliasing transfer functions of the adjoint net-
work from the single input at frequency
to the multiple output at
frequency
The significance of the frequency reversal theorem is that the compu-
tation of the aliasing transfer functions from inputs at frequency
to the output at of
N
requires solving the circuit at multiple frequen-
cies With the frequency reversal theorem,
these aliasing transfer functions can be obtained by solving the adjoint
network
at
only.
6. Examples
Two switched capacitor networks are used as examples in this sec-
tion to assess both the transfer function theorem and frequency reversal
theorem.
Consider the bi-phase stray-insensitive switched capacitor integrator
in Fig.10.7 and its adjoint network shown in Fig.10.8 [81]. The value of
the circuit parameters is given in Table 10.3.
All MOSFET switches are modeled as an ideal switch in series with
a noisy resistor. The operational amplifiers are considered to be ideal.
The transfer and aliasing transfer functions of the circuits are solved
using Watsnap, an interactive computer program for general switched
linear circuits [8] and the results are presented in Tables 10.4 and 10.5.
As can be seen that (i) the magnitude of the transfer function from
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