has been widely misunderstood by many electronics enthusiasts, even
those who have a fairly extensive background in circuit design (that
which does not involve feedback). In fact, there have been instances
of articles being printed in magazines like Popular Electronics,
Radio-Electronics, etc., where the authors got relatively
simple feedback equations wrong due to improper summing of nodes,
necessitating a correction in a later issue based on reader feedback
(a convenient and appropriate word for this comment). This article
discusses feedback in audio circuits to avoid distortion, but the
concepts apply to any frequency of operation. It is possible in
many cases to implement seat-of-the-pants feedback schemes successfully,
but if you need a specific response and guaranteed stability, nothing
short of rigorous mathematical applications will do the job.
March 1958 Radio-Electronics
Wax nostalgic about and learn from the history of early electronics. See articles
published 1929 - 1948. All copyrights hereby acknowledged.
Getting Feedback Straight
it will and won't do in audio amplifiers
By Norman H. Crowhurst*
It's surprising how often feedback is expected to do something
it can't possibly do. For example, I recently met an enthusiast
with an amplifier that put out about 48 watts comfortably and then
ran into severe distortion. He was frantically trying to use feedback
to make the amplifier deliver what he wanted - a full 50 watts.
He couldn't understand why using enough feedback wouldn't push the
output up just this little bit!
Most material on feedback
has been based on a theoretical treatment using the algebra of feedback
theory. This algebra cannot take into account everything at once
- if it did it would become so involved that no ordinary person
could possibly understand it. We use one piece of algebra to tell
us the effect of feedback on the gain of the amplifier, then we
go over the algebra again and find out what its effect will be on
the amplifier's impedances, frequency response and distortion. Each
investigation uses a separate application of the same math. But
this does not prove that the amplifier will do all of these things
in equal manner at the same time. It depends on just what form distortion
(and other things feedback is expected to correct) may take.
Some presentations on feedback have
suggested (with deceptive simplicity) that as feedback tends to
smooth out fluctuation in gain it must flatten the frequency response
- on the basis that deviation from flat in frequency response is
merely deviation in the gain of the amplifier at different frequencies.
Some readers are doubtlessly aware that his oversimplification of
theory can often be the reverse of what really happens. Due to phase
shifts in the amplifier, frequency response can often be accentuated
by feedback, rather than flattened.
Let's take feedback, step by step, starting from a single stage
and using practical examples to see how it can change the response
in each case. Fig. 1 shows some examples of single-stage feedback:
simple cathode circuit current feedback, voltage feedback from plate
to grid on the same stage and the very useful Ultra-Linear circuit
where feedback from plate to screen is provided by taps on the output
Fig. 1 - Three forms of single-stage feedback: a - current
feedback in the cathode; b - plate feedback to grid; c -
Ultra-Linear, plates to screens.
With current feedback in a cathode circuit
the feedback is effective right down to dc at the low end. At the
high end the only modifying factor is the stray capacitance of the
tube and its associated circuit. This eventually deteriorates the
tube's gain and hence also the feedback. So current feedback in
the cathode does not modify the low-frequency response at all, and
the high-frequency response is modified according to the distribution
of tube capacitances.
In plate-to-grid feedback - shown
in Fig. 1-b - a blocking capacitor between the plate and grid keeps
dc from feeding back to the grid and there is stray capacitance
to ground. The blocking capacitor introduces a rolloff at the low
end in the feedback circuit while stray capacitance to ground introduces
a rolloff at the high end.
The low-end roll off causes feedback
to fall off and stage gain to rise to its no-feedback value if no
other rolloff is introduced into the circuit to compensate for this.
The high-end rolloff is the same as that produced without feedback,
but feedback extends the frequency range by the same factor as it
reduces gain. Thus, if feedback reduces gain by 6 db, frequency
range at the high end is extended by a ratio of 2 to 1.
In the Ultra-Linear circuit (Fig. 1-c) the signal fed back from
plate to screen is coupled by the output transformer. At the low
end of the frequency response the transformer introduces a reactance
shunting the plate circuit, due to its primary inductance. When
the tube is operating as a straight pentode, without coupling to
the screen, its source resistance is much higher than with Ultra-Linear
feedback introduced. This means that adding feedback extends the
low-frequency response due to the reduced source impedance the primary
At the high end of the frequency response
the transformer introduces a leakage inductance between plate and
screen so at some point the amount fed back to the screen begins
to fall off. This causes feedback to begin to fall off somewhere
in the higher frequencies. However, this does not show up in practice
because there is a larger leakage inductance between the whole primary
and other windings on the transformer than between the part of the
primary feeding the plate and the part coupled to the screen. So
the other rolloffs in the amplifier circuit go into effect before
the reduction in feedback from plate to screen starts to make itself
Now let's start on feedback over two stages. Take the circuit of
Fig. 2, which represents a driver and output stage with feedback
from the output stage plates to the driver cathodes. Considering
the round-the-loop effect, here we have the coupling capacitors
from driver plates to output grids, and blocking capacitors from
the output plates to the driver cathodes, which contribute to low-frequency
response. At the high-frequency end we have stray capacitances which
can be regarded as shunting the driver and output plates, respectively.
Fig. 2 - A form of feedback using two reactances in feedback
loop at each end of audio response. (Output transformer
not part of feedback circuit.)
Fig. 3 - Sample low-end response curves for Fig. 2. A -
Original rolloff of each time constant; response of amplifier
without feedback; B - open loop response; C - round-the-loop
response with 6-db feedback; D - amplifier response with
6-db feedback (difference between curves A and B); E - round-the-loop
response with 12-db feedback; F - amplifier response with
12-db feedback (difference between curves A and E).
Fig. 4 - Sample high-end response curves for Fig. 2, assuming
loss due to stray capacitance gives identical roll-off with
3-db point at 20 kc for each stage.
Consider the low-frequency response. A first study might
suggest that low-end response could be made absolutely flat. By
making the time constant of the interstage coupling between driver
and output equal to the time constant of the feedback arrangement,
the blocking capacitor in the feedback loop would cause a rise in
frequency response as feedback falls off, while the coupling capacitor
between stages causes a similar roll off in the forward response.
The two having identical frequency characteristics should result
in a flat response. But this assumption ignores one fact.
What happens with phase when there are two or more coupling
elements in the feedback loop? If we use two identical time constants,
as suggested, then more than 6 db of loop feedback starts to show
a peak in the loop response at the low end, due to phase interaction.
But 12 db of feedback shows a peak of about 1.25 db; 18-db feedback
shows a peak of about 3.6 db; 24-db feedback shows a peak of about
6.3 db, and every successive 6 db of feedback shows approximately
3 db more peak.
This effect is independent of how the coupling
arrangements are distributed around the loop. If one coupling element
is in the feedback arrangement, the inverse of the response due
to feedback coupling must be added to this peaking effect. For example,
with 6-db feedback there is a slight peak of a little more than
2 db (curve D, Fig. 3). With 12-db feedback the peak rises to about
7 db (curve F, Fig. 3) and so on, due to the additional boost given
by the coupling element in the feedback part of the arrangement.
At the high-frequency end of the response there is no loss
in the feedback part of the arrangement. Losses due to both groups
of stray capacitance from plate to ground affect the forward response.
The only place where loss would affect feedback is at the cathode
of the driver stage, where there is no loss worth mentioning. Therefore,
assuming the time constant of the stray capacitance from plate to
ground is the same for each circuit, the amount of peaking introduced
by different amounts of feedback in the loop response would apply
without the boost effect due to part of the loss being in the feedback
path. See Fig. 4.
In this circuit (Fig. 2) the feedback
does not include the output transformer, so any frequency response
contributed by the output transformer is added to the response of
the feedback measuring overall response.
The next question is: What happens when we apply feedback
from the output transformer secondary? So far we have discussed
circuits where the factors contributing to rolloff at the low and
high ends are easily separable. But when we consider an output transformer
they are a little more tied up and perhaps not so easy to recognize.
In the output transformers of conventional push-pull amplifiers,
considertion of the low-frequency response, since it is caused by
just the primary inductance shunting the plate resistance of the
output stage, is simple enough. Hence, for low frequencies, performance
is the same whether connected from primary or secondary of
output stage. In fact, by connecting from the secondary, the blocking
capacitor can be eliminated and thus the possibility of achieving
good low-frequency response is somewhat improved.
At the high-frequency end the output transformer contributes two
reactances. There is the plate-to-ground capacitance, to which the
output transformer contributes primary-winding capacitance, and
the leakage inductance between primary and secondary. Since both
of these contribute to high-frequency rolloff, by feeding from the
secondary of the output transformer back to the grid of the output
stage, we have two reactances contributing to high-frequency rolloff.
This means that peaking starts immediately there is more
than a certain amount of feedback, according to the relationship
between the circuit constants. The circuit shown in Fig. 5 never
becomes unstable, no matter how much feedback we use, but we do
run into peaking similar to that produced by the two-stage circuit
of Fig. 2.
If we attempt to feed back over more of the circuit than shown in
Fig. 5. from the output winding of the transformer, it becomes possible
for feedback to push the peaking up to the point where oscillation
begins. This is where real care is needed in the design.
Fig. 5 - Feedback over single stage with output transformer.
Fig. 6 - Basic factors in long-loop-feedback amplifier.
Numbered boxes indicate amplifier stages or phase inverters
without frequency-discriminating components.
The method of tackling this is to arrange the time constants
contributing to rolloff response at both ends of the frequency spectrum
so they are as widely divergent as possible. The best possibility
of increasing the amount of feedback is to make one of the time
constants effect a roll off much closer to the passband of the amplifier
than all the other time constants.
For example, if four
reactances contribute to an ultimate roll off, at each end of the
response, which is a common arrangement, then by having one time
constant at 100 times nearer the amplifier's passband than the remaining
three, 24 db of feedback can be used before peaking begins to show
up at all. And almost 40 db of feedback can be used before the amplifier
becomes unstable. To achieve this range with this particular configuration,
illustrated in basic form by Fig. 6, the roll off point at the low
end for one of the networks could be 100 cycles while the remaining
three should be moved down to 1 cycle. Similarly, at the high end,
one rolloff could be effective at say 10 kc, while the remaining
three should be moved up to 1 mc.
To arrive at what the
ultimate response will be, suppose we use 24-db feedback. The first
acting rolloff is extended by approximately the ratio represented
by 24-db feedback. This corresponds with a ratio of 16 to 1. So
the 100-cycle rolloff is pushed down to about 6 cycles, and the
10-kc roll off is pushed up to about 160 kc, both of which are well
beyond the limits generally recognized as necessary in an audio
Readjusting our figures to finish up with an
amplifier that is just about right for audio, we could make the
rolloff points for the low end 320 cycles with 3.2 cycles for the
remaining three which leaves us with a 20-cycle rolloff for the
low end, and 1,250 cycles with the three additional rolloffs at
125 kc gives us an ultimate rolloff at 20 kc.
Such a combination
provides a satisfactory feedback amplifier for use on audio, but
the trend in most feedback-amplifier designs is to have a much larger
margin, and the figures first given are nearer to those used in
actual design. Once these figures are chosen, we have to stick with
them to get successful performance.
This explains why
it is necessary to insure that some stages respond out to 1 mc to
get satisfactory performance out of the amplifier. A while ago someone
asked why Joseph Marshall added neutralizing to some of the stages
in his Golden Ear amplifier (Radio-Electronics, April, 1954). From
this discussion we see that there can be a good reason for doing
this, although it might appear to be going to extreme limits, until
we realize the fundamentals necessary to achieve stability in a
So much for frequency response and stability
problems. The statements made can be substantiated by the necessary
mathematics and, if any readers are doubtful about them or want
further detailed information for design purposes, they are referred
to my article, "A New Approach to Negative Feedback Design" (Audio
Engineering, May, 1953). But here we want to get on to the question
of sorting out some of the things that the mathematics seem to have
Let's revert to the question introduced at the beginning of the
article. Can feedback actually extend the output of an amplifier?
We could go into a lot of theory on this but probably the best way
to illustrate the matter is to take some typical waveforms from
amplifiers we want to improve.
Fig. 7 - Amplifier output waveform at two levels, where
distortion sets in gradually.
Fig. 8 - How feedback can improve the output in Fig. 7.
Fig. 9 - Amplifier waveform where distortion appears suddenly
as clipping. Feedback cannot help appreciably.
Fig. 7 shows the output waveform
at two different levels for an amplifier where the overloading effect
is not too sudden - it runs into a gradual curvature. This could
be, for example, an amplifier employing power drive, so the output
tubes are driven into positive grid current, and there is power
in the driver stage to supply the necessary grid current. This type
amplifier shows a rounding of the top of the waveform before it
begins to flatten. And this rounding can introduce considerable
distortion before actual clipping begins.
In this kind of
amplifier, feedback can help. The feedback signal can make the driver
give a slightly more peaky waveform to offset the roundings, and
the resultant wave comes closer to the sinusoidal. This is shown
in Fig. 8.
Now look at Fig. 9, which shows sample waveforms
from an amplifier at two different levels, where clipping occurs
quite suddenly. This might be a push-pull amplifier fed by a non-power-driver
stage, so commencement of grid current at the output tubes causes
very abrupt clipping. Since the driver cannot supply any power to
the grids of the output tubes, nothing feedback can do will ever
overcome the clipping. If the driver delivers a small amount of
power that starts to give a little positive grid current in the
output tube, rounding the corners of the clipped waves slightly,
feedback will be able to accelerate the rate at which this power
is provided. So applying feedback makes the output waveform even
more squarely clipped than it is without feedback.
words, feedback stands a chance of improving the waveform of an
amplifier below maximum output but, once clipping starts, feedback
tends to make the clipping sharper rather than to eliminate it.
Another effect of feedback on the overall distortion of
an amplifier seems to get overlooked. At lower levels feedback does
reduce the total harmonic content of an amplifier. But it also changes
the harmonic present, and this change is not always an improvement.
This is best illustrated with some simple figures.
we have an amplifier that introduces a distortion of 5% third harmonic.
This could be due to too high a value for the plate load resistor
for a pentode in an early stage and the percentage might be almost
independent of operating level - 5% third harmonic would appear
on signals of all levels. Now suppose this amplifier has its gain
increased, to make it possible to apply a total overall feedback
of 40 db. This sounds quite good. We should be able to knock the
5% third harmonic down to .05% third harmonic and probably we can.
But we have overlooked something which is illustrated in
Fig. 10. To reduce the third harmonic from 5% to .05% the input
to the amplifier consists of a 100% original input signal, offset
against a 99% fed-back signal. To offset the 5% third harmonic that
the amplifier is going to introduce, the final input signal, made
up by the 100% minus the 99%, must contain a third-harmonic component
almost 5% in value but in opposite phase to the 5% the amplifier
introduces. This 5% of third harmonic goes through the amplifier
as does the original 100% fundamental. Besides offsetting the distortion
produced by the fundamental, it produces some distortion of its
own, to the extent of 5% of 5%, at a harmonic which is the third
of the third. This produces 0.25% of ninth harmonic. So what our
feedback has done is to reduce the original 5% third harmonic to
.05% and at the same time gives us a 0.25% ninth harmonic we never
Measuring this on a distortion analyzer, it
will look as if the feedback has produced an improvement, not quite
as much as we calculated, but quite a good reduction and so we are
happy. But if we listen to the amplifier, it may not sound as much
better as we expected, because 0.25% ninth harmonic can be quite
More than this, we have only considered the
effects of feedback on a single sine wave. When we come to consider
intermodulation products, we find them multiplying up out of all
proportion, and a great variety of intermodulation products is introduced
by an amplifier designed in this manner. The resulting reproduction
sounds extremely muddy, although the figures might appear quite
presentable - an overall distortion figure of 0.25% is not generally
considered to be too bad.
You can't eat your cake ...
Before leaving the question of distortion let's look at
one more aspect. When we apply feedback, sometimes we achieve more
than one purpose. We can make feedback do two or three things at
the same time, but sometimes we use up the feedback on one purpose
so that it is not available for others. This can happen, for example,
where feedback is used to change an impedance.
use a regular type of feedback amplifier to provide a lower source
impedance than its nonfeedback cousin. Next we apply an output load
equal to the source impedance.
We calculate the amplifier
performance on the basis of either no load impedance or the optimum
load impedance for the output tubes used. So it is not really legitimate
to change just the load impedance and expect the same performance
from the feedback amplifier. To find out what really happens we
should recalculate the performance of the amplifier on the basis
of the revised load impedance. What we will probably find is that
the new load impedance allows much smaller output before distortion
starts to be really serious and that feedback has become almost
nonexistent, due to the change in loading impedance reducing the
gain of the output stage.
Just take some figures to illustrate.
Suppose that the optimum load of a certain output stage is 8,000
ohms and its source resistance is 3,000 ohms. By applying 26 db
of feedback, the source resistance can be reduced from 3,000 ohms
to 150 ohms. Now suppose we load the amplifier with a 150-ohm load
(by the same matching transformer used for the 8,000-ohm load).
Let's take the feedback off for a moment and see what happens
by changing the load in this condition. When we take the 8,000-ohm
load off, the gain rises, due to an open-circuit condition, in the
ratio of 11/8. Then, when the 150-ohm load is connected in place
of it, gain is reduced in the ratio of 150/8,150. The net result,
is reduced gain due to the change of load, by a factor of 1/40.
With the 8,000-ohm load the feedback was designed to be
26 db, which is a ratio of 20/1. As the gain has already been knocked
down by a ratio of 40/1, the feedback factor will not be only 0.5,
instead of 20. The amount of feedback resulting from 0.5 fed-back
signal injected in series with the input is only 3.5 db.
This can do little toward reducing distortion. To be precise,
it will reduce distortion by a factor of 2/3. If connecting a 150-ohm
load to the output of this stage produces a distortion of 20%, which
is quite a normal figure for such low loading, feedback reduces
this only to 13.33%, which is still a very high distortion figure.
However, the amplifier will have an apparent source impedance
of 150 ohms, which is what we have used the feedback up for. All
of which reminds us of the old proverb about eating one's cake and
having it too.
Hum and noise reduction
feedback is used for is to reduce amplifier hum and noise. In other
words, to clean up any unwanted sounds not present in the input.
Many users have applied feedback with this object in view,
only to be disappointed in finding either that it has had no effect
whatever or that it has had the reverse effect. Let's just see how
this can be.
First, let's take hum. One point not to be
overlooked is: when adding feedback to an amplifier that must give
full output for a specified input, more gain is necessary, so adding
feedback leaves us with the same gain we had originally. Generally
speaking, hum gets induced in the earlier stages of an amplifier
so, if we're going to apply 20-db feedback, we need 20 db more gain
in the first place, and the hum will get 20 db more amplification
before feedback is applied. Application of feedback then knocks
the hum back to where it started from.
This is assuming
that the hum is injected somewhere within the feedback loop. If
however, as sometimes happens, the hum creeps in outside of the
feedback loop, it is possible for the addition of feedback actually
to increase hum instead of reducing it.
Noise in feedback
amplifiers actually tends to be higher, other things being equal,
than in nonfeedback amplifiers, The reason for this is fairly easy
Fig. 10 - How feedback affects harmonic distortion.
Suppose noise at the input 0 a non-feedback amplifier
is equivalent to 10 μv at the grid of the first stage, which
is intended to accept an input level of 10 mv. If 20 db of feedback
is added to the amplifier, it will need 20 db more gain, and hence
should be able to load with only 1 mv on the first stage grid. But
this grid will still have a noise level of 10 μv. If the feedback
is successful in reducing the noise level by the complete amount
of feedback added, then this reduces the effective noise back to
its original 60-db discrimination. But this depends on every element
in the noise signal being fed back completely out of phase with
the original noise signal.
The lower component frequencies
in noise may be successfully reduced by the 20 db in this way but,
at the upper end of the response, where the random happenings that
constitute noise are of shorter duration, feedback cannot keep pace
with the changes and hence fails to make a reduction of the full
Therefore, the noise level is higher in the feedback
amplifier and it tends to concentrate in the upper frequencies.
Also - if due care has not been paid to eliminating the
peaking effect mentioned earlier-the noise will definitely be colored
by peaks at both ends of the frequency response, resulting in the
familiar hissy, boomy background common with amplifiers using a
large amount of feedback. This is quite independent of the fact
that frequency response throughout the audio range may be quite
Does multi-loop help?
A final question concerns
the relation between single-loop and multi-loop feedback, in all
these points of discussion. In an earlier article, I called attention
to some of the deficiencies of feeding back over the whole amplifier
("Why Feed Back So Far?," Radio-Electronics, September, 1953).
The use of multi-loop feedback does overcome some of these
deficiencies. The short-loop feedback, toward the output end of
an amplifier, stabilizes that part of the amplifier and usually
extends frequency response beyond the audio range to give a satisfactory
margin for application of longer-loop feedback. Also the short-loop
feedback, over a section of the amplifier operating at higher level,
will not aggravate hum or noise troubles in the same way as the
equivalent amount of feedback applied in an overall loop would.
It is advantageous to apply as much feedback as possible
over a shorter loop and minimize the long-loop feedback, if possible,
avoiding any feedback right back to the input stage at all. It is
better to take the feedback to a stage immediately following the
input stage, so the first stage operates at maximum gain and gets
the signal level above the inherent noise of tubes and other things,
before we introduce any feedback.
This last remark applies
especially to high-gain amplifiers or preamps which operate from
low level inputs. Amplifiers designed to operate from high-level
inputs are quite satisfactory with overall feedback, provided precautions
are taken to minimize the possibility of conditional stability.
*Author of Understanding Hi-Fi
Circuits (Gernsback Library).
Posted January 24, 2014