Environmental Engineering Reference
In-Depth Information
The order of Volterra series expansion in depicting nonlinear circuits.
The order of interpolating Fourier series in approximation of the input
of high-order Volterra circuits.
Simulation window.
Error propagation.
We examine each of them in detail.
6.3.1 The Order of Taylor Series Expansion
The order of the Taylor series expansion of nonlinear elements depends
upon the characteristics of the nonlinearities, the amplitude of the input
signal, and the tolerance of the error of approximation. When the
Taylor series expansion is employed to characterize the nonlinear
element, the truncation error is given by
where is the displacement from the operating point and
As an example, consider a forward biased diode characterized by
where
and
are the forward biasing voltage and current of the diode,
respectively,
is the saturation current, and
is the thermal voltage.
Let
where
and
are the DC and AC components of
respectively. Expanding
in Taylor series at the DC operating
point gives
where is the AC component of If the 4th-order Taylor series
expansion is used, the truncation error is estimated from
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