4
General Properties of Electronic Single-Loop
Feedback Systems
4.1Introduction
In electronic circuits and systems, feedback will be defined as a process whereby a signal proportional to the system’s output is combined with a signal proportional to the input to form an error signal that affects the output. Nearly all analog electronic circuits use feedback — implicitly as the result of circuit design (e.g., as from an unbypassed BJT emitter resistor) or explicitly by a specific circuit network between the output and the input nodes. A circuit can have one or more specific feedback loops. However, in the interest of simplicity, the effects of a single feedback loop on circuits with single inputs will be considered. The four categories of electronic feedback and the feedback that can make an electronic system unstable (deliberately, as in the design of oscillators) or stable will be shown. The effects of feedback on amplifier frequency response, gain, noise, output and input impedance, and linearity will also be discussed.
Op amps will be used to illustrate many properties of single-input–single- output (SISO) feedback systems because all op amps use feedback and they have relatively simple dynamic characteristics. A systems approach will be used in discussing amplifier performance with feedback; little attention will be paid to the nitty-gritty of the electronic components. Block diagrams, signal flow graphs, and Mason’s rule will be used to describe the systems under consideration and the root-locus technique will be used to explore feedback amplifier performance in the frequency domain.
4.2Classification of Electronic Feedback Systems
Figure 4.1 illustrates the general architecture of a SISO feedback system. Reduction of the signal flow graph or the block diagram of Figure 4.1 yields the well-known transfer function:
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© 2004 by CRC Press LLC
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Analysis and Application of Analog Electronic Circuits |
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α |
Kv |
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x |
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β
A
+e
x |
α |
Kv |
y |
+ 
B
β
FIGURE 4.1
Two alternate representations for a single-input–single-output (SISO) linear feedback system.
(A) Signal flow graph notation. (B) Block diagram notation.
Vo |
= |
α Kv |
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(4.1) |
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1− β K |
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V |
v |
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s |
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From this simple result, the following important quantities describing feedback systems can be defined:
• Forward gain = open-loop gain = Kv |
(4.2A) |
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• Loop gain = AL = Kv |
(4.2B) |
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• |
Return difference = RD = 1 − AL |
(4.2C) |
• |
dB of feedback = −20 log 1 − AL |
(4.2D) |
Note that , , Kv, and AL can be scalars or vectors (complex functions of frequency).
A SISO system is said to have negative feedback (NFB) if it has a minus sign associated with either Kv, , or the summer, or with all three elements in the block diagram. Control systems generally use NFB and it is usual to assume a subtraction of Vo at the summer. Electronic systems do not necessarily have a subtraction at the summer; it depends on circuit design. To see if a SISO electronic feedback system has negative feedback, inspect the loop gain. AL(j0) will have a minus sign (be a negative number) if the feedback amplifier is a direct-coupled (DC) negative feedback system. If the amplifier is reactively coupled (RC), then AL(jω) will have a minus sign at mid-frequencies (its phase angle will be −180∞). Feedback amplifier is generally a voltage, but VCCSs are encountered. Considering that feedback can have either sign and the fed-back quantity can be voltage or current, it is
© 2004 by CRC Press LLC