circuits seem simple enough intuitively, at least for simple systems.
It is easy, though, for someone not comfortable with algebraic manipulations
to arrive at the wrong conclusion for how a given feedback constant
figures into the calculation. Such was the case with an article
published in the ARRL's QST magazine, when many readers
wrote to the author accusing him of making an erroneous claim regarding
using feedback to cancel out an unwanted harmonic in an amplifier.
The criticism turned out being justified. Here is a statement of
the error and an explanation of the proper approach which was printed
a couple months later.
July 1937 QST
Wax nostalgic about and learn from the history of early electronics. See articles
QST, published December 1915 - present (visit ARRL
for info). All copyrights hereby acknowledged.
Note on Reduction of Distortion and Noise
with Inverse Feedback
A few of our readers have disagreed with some of the conclusions
reached, with respect to optimum inverse feedback conditions for
reduction of distortion and hum, in the article describing the construction
of a speech-amplifier-modulator unit in April QST.1 Since
the criticisms are all of the same nature, we have selected for
publication a letter from J.R. Davey, New York, which gives a rather
complete explanation of the operation of the inverse feedback circuit
in this respect:
"The section of the article headed 'Curing
Distortion and Noise' contains several statements which I believe
to be incorrect. The author begins this section by showing how a
5-volt third harmonic in the 20-volt fundamental output of the amplifier
used as an example is eliminated by using a feedback ratio of 1:10.
A feedback ratio of 1:10 and a stage gain of 10 would actually cut
the distortion and noise introduced in the stage to one-half its
original value, and not eliminate it completely.
author also applies the same reasoning to the hum elimination problem,
reaching the general conclusion that the feedback ratio should be
the reciprocal of the gain of the stage. Here again this actually
gives a reduction of 50 per cent in noise, distortion and the effective
gain of the stage. The statement that it this ratio is exceeded
overcompensation would result, and that the distortion would increase,
is quite incorrect. As the negative feedback is increased, the noise,
distortion, and effective gain all continue to decrease. To get
complete cancellation of the noise and distortion would require
infinite negative feedback and consequently zero gain. The error
in the reasoning is that it neglects the fact that as soon as the
noise or distortion is cancelled out in the output by some means,
there is no longer any signal component to feed-back and continue
"There also appears to be an inconsistency
in that there is first mentioned the possibility of overcompensation
and then later that the theoretical ratio of gain of stage is a
minimum value and that larger amounts may be used. The actual feedback
ratio used in designing an amplifier depends on how much gain it
is economical to lose, how much feedback can be used without excessive
positive feedback and oscillation at the extremes of the frequency
range, and the amount of noise, distortion, or potential supply
variations which are being compensated for. There is a feedback
ratio in each case beyond which there is no point in going, either
because of loss of gain, phase difficulties, or because a closer
approach to the desired response characteristic would not be warranted.
usual type of nomenclature used in feedback amplifiers is given
in Fig. 1. It is to be found in numerous publications treating the
"The reduction of gain caused by the feedback is
1/(1-Aβ).2 This is also the reduction in noise and
distortion produced in the stage.3 The characteristic
with feedback approaches that of the feed- back or β circuit.
When, as in this article, β = -1/A, the factor 1/(1-Aβ)
The above factor is demonstrated below in obtaining
the table given on page 47, April QST:
"The actual case of
the author's distortion example is shown in Fig. 2. The 5-volt third
harmonic produced in the amplifier is reduced one-half, to 2.5 volts,
but not eliminated. If Aβ should be made as high as 15 to 20,
then much more reduction of distortion (1/16 and 1/21) would be
obtained. I have no doubt that the amplifier as described works
very well, but there appears to be no foundation for the desirable
feedback ratio of 1/gain of stage."
1 Carter, "Inverse Feedback Applied
to the Speech Amplifier for the Amateur 'Phone Transmitter," QST,
2 When the feedback is negative,
as is the case here, β is negative. - Editor.
The amount of distortion fed back to the grid circuit is equal to β
times the resultant distortion in the plate circuit; i.e., the distortion
remaining in the output with feedback present. The resultant distortion
is the algebraic sum of the original distortion without feedback
and the amplified feedback distortion. Letting D = resultant distortion
with feedback and d = original distortion without feedback.
D = d + ADβ
Solving this for D,
D = d/(1-Aβ)
See Terman, "Feedback Amplifier Design," Electronics, January,1937.
October 17, 2013