Amplifier Design 709negative feedback loop is in essence a type of quality
control wherein the system output is compared with
what is desired for it to be. Any difference as a result of
this comparison is injected back into the system in such
a way as to force a correction of system behavior. A
highly simplified example is as follows. Consider a dc
voltage-amplifier for which it is desired that the voltage
gain be 10; that is, an output voltage ten times as large
as the input signal but with the opposite polarity. One
might proceed on good faith and employ the latest elec-
tronic design techniques, consult manufacturer’s speci-
fications on the best available active devices, design,
and finally construct an amplifier that, according to the
best available information, possesses an open loop
transfer function at low frequencies of 10. In fact, in
order to be on the safe side, one may follow the same
procedure yielding a value of 20 and precede the
device by an adjustable attenuator set at an absolute
value of ½ or whatever is required to obtain an overall
transfer function of 10 when the system is first tested.
Unfortunately, the active devices employed are at the
mercy of the operating voltages supplied to them (line
voltage variations, etc.), ambient temperature variations,
age, and weather elements in general. To a lesser
degree, the same may be said of the passive elements
involved. A, the open loop transfer function may
possess a nominal value of 10 but it is constantly
changing from moment to moment being at times larger
and at other instants smaller than the intended value.
There exists nothing in the system to monitor its overall
operation. Alternatively, one might, following the same
procedures outlined before, design an amplifier having
an open loop transfer function whose nominal value is
100 and enclose this with a negative feedback loop to
obtain a nominal closed loop transfer function, Ac, of
10. Mathematically,
By substituting nominal values, one can solve for B:
B is found to require the properties of a simple atten-
uator or voltage divider. The next step would be to
construct this divider from precision resistors
possessing very small voltage and temperature coeffi-
cients of resistance. The feedback loop is then closed,
making use of this stable attenuator. The resulting
system has a nominal closed loop transfer function,
Ac=10, a nominal loop gain, AB=9, and a nominal
gain reduction factor of 10. What has been accom-
plished? Suppose that the original open loop amplifier
whose nominal transfer function was 10 had variations
or changes in A that were about ±20% and the new
amplifier that was constructed employing the same
technology has similar variations under open loop
conditions. Now compare the ratio of the variations to
the nominal values with and without feedback; that is,
'A/A is to be compared with 'Ac/Ac. Knowing that
Ac=A/(1 –AB) and by employing the techniques of
differential calculus one finds thatConsequently,The application of negative feedback has produced a
system that has a nominal transfer function of 10 with
a variation of ±2%; whereas before, in the absence of
feedback, there existed a system having a nominal
transfer function of 10 with a variation of ±20% under
the same conditions. The price paid for this improve-
ment amounted to trading off a higher open loop gain
for the sake of a more stable value of gain.
Negative feedback affects many amplifier properties
other than gain stability. Negative feedback increases
amplifier bandwidth, reduces most but not all forms of
distortion, modifies amplifier input and output imped-
ances, and can be beneficially employed in shaping
frequency response characteristics. Examples of these
features are given in the next section.
Negative feedback is not, however, a panacea. It can
not turn a bad amplifier into a good one. It may make a
good amplifier into a better one. It should always be
remembered that the derivations and conclusions
obtained above are based on linear or nearly linear oper-Ac A
1 – AB=----------------10– 100–
1 + 100 B----------------------=1 +10 100 B=
100 B 9=B^9
100---------='Ac 'A
1 – AB^2=-----------------------'Ac
Ac---------'A
1 – AB^2-----------------------A
1 – AB----------------= ------------------------'A
A-------^1
1 – AB= u----------------r20%^1
10= u----- -= r2%