Environmental Engineering Reference
In-Depth Information
1. Switch off the critical controlled source setting
P
= 0.To achieve the
direct transmission term,
compute the transfer function between the
input and output Condition
P =
0 requires an open circuit
(short circuit) to replace the branch containing the controlled source if
P
is
associated with a controlled current (voltage) source.
2. Set the input source to zero. This means short-circuiting the voltage
source or opening the current source. Replace the critical controlled voltage
(current) source by an independent voltage (current) generator of value
P.
The
return ratio, T,
coincides with the resulting controlling quantity changed
in sign, (i.e., evaluate and multiply it to
P).
3. Set the critical parameter to infinitely large Since the
controlled variable must be finite, this is equal to setting The
asymptotic gain,
is the transfer function between the input and the
output under this special condition.
A comparison of (3.1) with (3.7) suggests that, for those cases where the
direct transmission term, is negligible, the return ratio equals the product
between the amplifier gain and the feedback factor (i.e.,
T = fA
)
.
For this
reason we will use the terms return ratio and loop gain almost
interchangeably, although this is not exactly true. The term in (3.7)
can be viewed as a corrective term, which modifies (3.1) when the loop gain
is not very large compared to unity. Under this condition, (3.1) and its
consequences are no longer valid. Thus (3.7) is a more general, and
insightful relation, for computing the closed-loop gain than (3.1). The
asymptotic gain equals the reciprocal of the feedback factor
Term represents the transfer function of a feedback amplifier under the
ideal condition of infinite loop gain. Thus, for well-designed feedback
circuits, exhibiting low values of and high values of
T,
the transfer
function of the feedback circuit is well approximated by The reader can
recognise in this observation the basis for the customary paper-and-pencil
analysis of feedback configurations employing ideal operational amplifiers.
In order to illustrate the use of the Rosenstark theory and to give an idea
of its strength and simplicity, let us apply the method to a common Z
configuration whose load determines an intrinsic feedback. The circuit,
reported in Fig. 3.3a, is the same as that analysed in Chapter 2 (the source
and the load resistances are coincident with resistance and
respectively). The small signal model, in which for simplicity the bulk
transconductance,
and the transistor output
resistance, have
been
neglected, is shown in Fig. 3.3b.
