Environmental Engineering Reference
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where
and
are the phasors
of
at frequencies
and
respectively.
These phasor quantities are needed in solving
as to be shown in the
following section.
3.3 The Third-Order Volterra Circuit
The input of contains two components. The first component
contains frequency components
and
Among them, only those at
contributes
to the third-order harmonic at
The input at
however,
affects the fundamental. Note that it was assumed that
and
will not be multiples of either
or
for any
Based
on these observations, we conclude that
needs to be solved with the input at frequencies
and the output at the frequency
for its contribution
to the third-order harmonic at
needs to be solved with the input at frequencies
and the output at the frequency
for its contribution
to the fundamental at
In computing the input of the solutions of at and
at are needed. and therefore need to be solved at all
relevant side band frequencies with the output at these frequencies.
however, needs only to be solved with the input at specific fre-
quencies because only the response at the fundamental frequency
and that at the third-order harmonic frequency
are of interest.
The output of
at
due to
is obtained from
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