Environmental Engineering Reference
In-Depth Information
Eq.(12.18) reveals that the frequency response of periodically switched
nonlinear circuits can be obtained by summing up that of corresponding
Volterra circuits.
It was shown in Chapter 11 that in the analysis of periodically switched
linear circuits, the difficulties associated with periodically time-varying
topology are handled by decomposing the circuits into a set of linear
time-invariant sub-circuits connected via the initial conditions of the
network variables [8]. Analogously, in distortion analysis of periodically
switched nonlinear circuits, a periodically switched nonlinear circuit can
be considered as a set of nonlinear time-invariant sub-circuits connected
via the initial conditions of the network variables of the circuits.
To simplify presentation, we assume that the characteristics of the
nonlinear elements are mild and their behavior can be depicted ade-
quately using the third-order Taylor series expansion of the nonlinear
characteristics. Further assume that the network variables of periodi-
cally switched nonlinear circuits can also be represented by their third-
order Volterra series expansion. Using modified nodal analysis, the non-
linear time-invariant circuit in phase is characterized by
where and are constant matrices depicting respectively the second
and third-order nonlinear characteristics of the circuits. The elements of
the vectors and are the square and cube of the correspond-
ing elements of respectively. Note that we have used scalar-like
notations for the purpose of their self-explanation.
If the input is changed from
to
where
is a nonzero
constant, Eq.(12.19) becomes
Search WWH ::
Custom Search