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Feedback systems are usually designed with the
familiar single-loop block diagram in mind, that is, the major loop feedback path is designed to
have a transmission function such that the specified gain is achieved in the presence of noninfinite
major loop gain. Various nonidealities, such as unavoidable minor loops and direct forward
transmission, make the single-loop block diagram progressively less useful, especially at higher
frequencies.
In conventional analysis, attention is
usually focused on the loop gain T, which is calculated by injection of a
test signal into the forward path.
There are two deficiencies in the
conventional approach:
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The right answer for T is obtained
only if the test signal is injected at an "ideal point," such as at an ideal
dependent generator, which doesn't exist in a real circuit. |
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2. |
Nonidealities are ignored, as is tacitly
conceded in represenation of the forward and feedback signal paths by arrows
to exclude reverse transmission. |
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The General Feedback Theorem (GFT)
overcomes both deficiencies and provides additional benefits.
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1. |
The loop gain T is calculated by
injection of both voltage and current test signals at a nonideal
injection point. |
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2. |
Calculations are performed on
the complete circuit model without the constraint of unidirectional paths. |
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3. |
No assumptions or
approximations are made, so the nonidealities are included. If the voltage
and current test signal injections are made at the error signal summing
point, effects of the nonidealities can be evaluated separately. |
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The GFT dissects the closed-loop gain
into three of four constituent transfer functions, each of which is obtained
directly in terms of the circuit elements, which makes it possible for the
results to be used backwards for design. This is the principal objective of
DESIGN-ORIENTED ANALYSIS, The Only Kind of Analysis Worth Doing. |
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The GFT defines a "natural" block
diagram model that is identical in format to the single-loop model that is
conventionally assumed, thus providing a link between general feedback theory
and a detailed circuit diagram analyzed in terms of factored pole-zero transfer
functions. The natural block diagram emerges as a result of the analysis,
not as an initial assumption.
Although the GFT
can be employed in symbolic analysis, it is also computer-friendly. Intusoft’s ICAP/4 design
simulator product line includes GFT Templates, and also a
User’s Manual written by Dr. Middlebrook. The User’s manual can also be
downloaded directly from this website. The User chooses the injection configuration,
which is where to inject either one or two test signals, and the GFT Template then quickly makes
available Bode plots of all the simulated and post-processed transfer functions. A reduced Template
produces the loop gain only, and reads out the phase and gain margins.
In the CD, the GFT is illustrated on a
two-stage feedback amplifier having various nonidealities, including loading interactions at all
points, direct forward transmission, and two minor loops. Another illustration investigates the
potential instability of a Darlington Emitter/Source Follower.
The GFT applies to any transfer function,
including not only voltage and current gains, but transfer gains and input and output impedances. It
can also represent the Extra Element Theorem (EET) to spotlight exactly how one or two selected
elements affect the system performance.
The GFT can be applied to any system representable by a linear model, such as switching power
converters, servo systems, and is especially useful in analog high-frequency ICs where the
nonidealities eventually control the performance.
This CD contains a 3 hour live
presentation of a Professional Education Seminar by Dr. Middlebrook, recorded at the IEEE Applied
Power Electronics Conference (APEC) , Anaheim, California, on February 22, 2004.
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