Environmental Engineering Reference
In-Depth Information
Assuming
and
as dependent or output variables we can express them
as a function of the two other independent or source variables,
and
Since
solving for
yields
and by substituting (3.4) into (3.3a), the transfer function of the closed-loop
amplifier results
Of course, to evaluate we have to relate weights with circuit
elements. Term can be found by setting the control parameter to zero and
evaluating the transfer function between input and output under this
condition. Term is the transfer function between the output and the
controlled variable, setting the input source, to zero. Term can be
computed via the transfer function between the source variable and the inner
variable, when the controlled variable, is set to zero, which in other
words means setting control parameter, P, equal to zero. Term gives the
relation between the independent and the controlled inner variables setting
control parameter, P, and input variable, to zero. Finally, it is worth
noting that, as apparent from Fig. 3.2, product represents the loop gain
of the network, also more properly termed the return ratio.
Equation (3.5) is only one of the many mathematical representations of a
linear circuit, which also depends on the particular choice of parameter P.
Note, however, that unless P is selected as feedback factor f , which is not
always transparent in feedback architectures, expressions for the loop gain
and the open loop gain of the feedback amplifiers remain obscure. In the
following we utilise (3.5) as a starting point to derive the Rosenstark,
Choma, and Blackman procedures.
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