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
of Contents]These articles are scanned and OCRed from old editions of the
ARRL's QST magazine. Here is a list of the
QST articles I have already posted. All copyrights are hereby acknowledged.
See all available
vintage QST articles.
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 the cancellation.
"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 subject.
"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
1 Carter, "Inverse
Feedback Applied to the Speech Amplifier for the Amateur 'Phone Transmitter,"
QST, April, 1937.
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 + ADβ
Solving this for D,
D = d/(1-Aβ)
See Terman, "Feedback Amplifier Design," Electronics, January,1937.
October 17, 2013