Environmental Engineering Reference
In-Depth Information
which shows that a relative variation in the open-loop system A corresponds
to a relative variation in the closed-loop system (1
+fA
) times lower.
In real cases, unfortunately, blocks
A
and
f
are made up of active and
passive components, and generally they cannot be assumed to be
unidirectional. Of course, to take into account the electrical nature of real
amplifiers a straightforward nodal analysis can be applied, but the approach
is tedious because it requires the simultaneous solution of numerous
equations even for medium-complexity circuits. A commonly used approach
models the amplifier and the feedback network with their proper two-port
models, each having as their input and output variables both the port voltage
and port current [G85]. This leads to an explosion of cases that depend on
the specific kind of amplifier and feedback network implemented. The
approach can also take into account the non-unidirectional nature of real
blocks, but in this case the two-port model increases in complexity and the
final analysis, though accurate, becomes extremely elaborate [GM93]. As a
result, there are several limitations to this approach. The two-port network
which models the block must be selected judiciously. The computation of
closed-loop parameters (transfer function and input and output resistances) is
tedious, especially if block
A
is a multistage amplifier or a multi-loop
feedback is implemented. Moreover, the method is straightforwardly
applicable to only those circuits that implement a
global feedback
(a
feedback between the input and the output) [PG981], whereas many
feedback amplifiers exploit only
local feedback
3
.
Other methods to analyse feedback amplifiers are based on Mason
s
signal flow graph (SFG) theory [M53], [M56], [MZ60], [C91], [MG91]:
they can either be derived from it, or related to it [R74], [C90], [B91],
[MG91]. The implicit drawback of the uncritical application of the classical
signal flow analysis is that we almost completely lose our understanding of
circuit behavior, and as a consequence, we have greater difficulties in
carrying out the design. This drawback is overcome by approaches that can
be derived from signal flow analysis, such as the Rosenstark method [R74],
the Choma method [C90], and the Blackman theorem [B43]. The Rosenstark
and the Choma methods primarily focus on the evaluation of the closed-loop
transfer function. The Blackman theorem -intrinsic to the other two
methods- involves the computation of the input and output resistance of a
feedback amplifier. Both the Rosenstark and Choma procedures together
with the Blackman theorem give circuit designer a very powerful tool for the
analysis and design of feedback amplifiers. Indeed, not only do they achieve
exact
relationships by describing the closed-loop amplifier efficiently and in
'
3
Local feedback occurs when the input and output terminals of the feedback
network do not coincide respectively with the output and input terminals of the
amplifier.
