Environmental Engineering Reference
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where
and
denote the phasors of the
frequency component of
at frequencies
and
respectively. The contribution of
to the fundamental component at
is given by
3.2 The Second-Order Volterra Circuit
The input of
denoted by
is given by (12.25) and can be
written as
where and are the phasors
of and respectively. Among the
frequency components of only those at contribute to
the second-order harmonic. In saying so, we have assumed that
and
will not be the multiples of
for any
This is often
the case in reality as
is usually much higher than
The second-
order harmonic
of the output is obtained by summing up the
response of
at frequency
with an input at frequencies
where
is the aliasing transfer function of
with the
input at the frequency
and the output at the frequency
The complete solution of
in the time domain, denoted by
with
the input given by (12.31), is given by
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