Environmental Engineering Reference
In-Depth Information
The loop-gain transfer function of the integrator in Fig. 9.16, can be
obtained from that of a CFOA with a resistive feedback as calculated in the
previous section, by replacing
with
At frequencies higher than the two dominant poles, remembering the
expression of
the transfer function (9.30a) can be simplified into
Assuming a safely compensated CFOA with pole higher than the
transition frequency, we get the same gain-bandwidth product given by
(9.26) setting As a consequence, the compensation procedure is equal
to the one already studied for a purely resistive feedback. This is simple to
understand: for high frequencies such as those in the vicinity of the transition
frequency we can assume the feedback capacitance,
to be short-circuited,
and the CFOA in unity gain configuration.
To evaluate the loop-gain transfer function of the differentiator in Fig.
9.17, we have to substitute resistor with capacitor in the CFOA with
resistive feedback. In an ideal CFOA, whose resistance at the inverting input
is also nominally equal to zero, capacitance would be outside the loop
gain, and would not play any part. However, real CFOAs have a finite buffer
output resistance. Moreover, capacitance determines another high-
frequency pole in the loop-gain transfer function. It can be shown that the
loop-gain transfer function becomes
