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6.3.2 The Order of Volterra Series Expansion
The order of Volterra series expansion in depicting the nonlinear cir-
cuits depends upon the nonlinear characteristics of the circuits and the
error of approximation. Consider a nonlinear resistor characterized by
where and are the voltage and current of the resistor in phase
respectively, and are constants. Representing and in
their Volterra series expansions to the order of 3 and substituting the
results into (7.50) yields
Eq.(7.51) reveals that the nonlinear resistor can be represented by three
linear resistors, together with added voltage sources quantifying the non-
linear effect. If the 4th-order Volterra series expansion is considered, we
will have
The difference is the last equation in (7.52) that accounts for the effect
of the 4th-order nonlinear characteristic. Eq.(7.51) will be considered
adequate if the difference between the response of the circuit with the
3rd-order Volterra series expansions and that with the 4th-order Volterra
series expansions considered is negligible.
6.3.3 The Order of Interpolating Fourier Series
The solution of the first-order Volterra series is accurate provided that
and
are computed to high precision. The error in solving
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