Environmental Engineering Reference
In-Depth Information
To derive the distortion factors of the system in Fig. 7.5, we will now
develop an intuitive method which requires simple algebraic manipulations.
The approach leads to expressions of distortion factors that are a direct
extension of those in (7.16) (7.17) found at low frequency.
As usual, we assume a sinusoidal input tone and that it is
possible to write the output signal as a power series of the source signal
The problem is to find the expression of the closed-loop nonlinear
coefficients
The first coefficient which is responsible for the linear
behaviour, can be simply found. It is equal to the forward-path transfer
function divided by 1 plus the loop-gain transfer function,
Equation (7.47) implies computation of
and
at the frequency of
the input tone (i.e., the fundamental frequency).
To evaluate the higher-order coefficients we have to follow a simple, but
not trivial reasoning. Concentrate our attention to derive the second
harmonic component at the output. It is produced by the nonlinear block
when a signal at the fundamental frequency is presented to its input. Now
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