Environmental Engineering Reference
In-Depth Information
Consider a single-input single-output periodically switched linear cir-
cuit
N
shown in Fig. 10.6. Its adjoint network is also shown in the
figure. Write (10.25) in the time domain
where the subscripts and identify the network variables of the output
and input branches, respectively. Because
and
Eq.(10.39) becomes
Representing the responses of
N
and
using (3.5), substituting the
inputs of
N
and
into (10.40), and making use of the time reversal
characteristic of
we obtain
Because
the output of
N
at frequency
is given by
where is the aliasing transfer function from the volt-
age input at frequency to the voltage output at frequency
Further utilizing the relationship between
and
gives
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