Environmental Engineering Reference
In-Depth Information
feedback has become a key design issue both in analog and digital electronic
circuits and systems.
Feedback applied around an analog network allows gain to be stabilised
(desensitised) with respect to variations in circuit elements, and active device
model parameters. This desensitisation property is crucial in view of
parametric uncertainties caused by device parameters spreads, power supply
variations, temperature changes, aging phenomena, and so on. Feedback
allows the input and output resistances of a given circuit to be suitably
modified in any fashion desired. It improves the linearity of the output signal
by reducing dependence on the parameters of inherently nonlinear active
devices used to implement the open loop circuit. Finally, it can lead to an
increase in the closed-loop bandwidth.
However, all these features are paid for in terms of a proportional
reduction in gain. This is usually a small price to pay, particularly in
applications using operational amplifiers whose dc open-loop voltage gain is
very large (60 dB, at least). Besides, as already mentioned, (negative)
feedback can determine oscillation, hence, frequency compensation is
usually mandatory
2
.
3.1 METHOD OF ANALYSIS OF FEEDBACK CIRCUITS
There are several approaches for analysing feedback circuits [H92],
[PC981]. The most straightforward one is to directly analyse the circuit by
writing the Kirchhoff equations on the small-signal circuit and deriving the
circuit characteristics. However, this approach is computationally tedious, it
does not allow one to disclose the general properties of feedback circuits
which can greatly simplify the analysis and, perhaps more importantly, it
gives no insight into circuit behavior and hardly provides useful design
equations. Thus, alternative approaches have been developed.
Most of the traditional techniques used to analyse feedback amplifiers
start from the idealised block diagram in Fig. 3.1 [G85], [SS91], [C91],
[LS94], where blocks
A
and
f
are the open-loop network (that we may
identify as the open-loop amplifier) and the feedback network, respectively.
Then parameter
A
represents the gain of the open-loop amplifier and
f
is the
feedback factor, i.e. the portion of the output signal fed back to the input.
Signals and represent source, output, feedback and error signals,
respectively. This representation gives only approximate results when
applied to real amplifiers, principally because it assumes unidirectional
blocks. Moreover, it is difficult to take into account the loading effects of the
2
Frequency compensation is treated in Chapter 5 of this topic.
