Negative feedback and linearity in receivers (was 'Re: [HBR] HBR-11/2000. Comments?')

[Walt Hutchens]

Another too-long post ... 

> I like to think of the effect of negative feedback as not really
> widening bandwidth but rather equalizing gain at all frequencies.
> Plus you can use the feedback to shape response if you pay careful
> attention to phase margin. 

The way to think of negative feedback is that, within an error of 
roughly 1/n (where n is the ratio by which gain is reduced by the 
feedback loop) negative feedback sets the relationship between the 
output and the input.   For example, an amp with 10% distortion at 
a certain power level with the gain reduced 10X by feedback will be 
down close to 1% distortion.   

All you've lost is voltage gain -- the POWER gain you had is still 
there.   You might have to make up the voltage gain with another 
stage, but two audio stages is plenty in nearly any superhet 
receiver.   

For amplifiers in receivers the feedback usually is a resistive 
voltage divider so that for our purposes the frequency response of 
the amplifier is flat.  However we don't care about the flatness of the 
frequency response because for comm work we're not going to use 
anything much outside the range 250-3000 cps anyhow. 

Flattening the frequency response isn't a reason to use negative 
feedback in a communications receiver.

The reason for negative feedback in comm work lies in the 
reduction of amplitude distortion, in particular, of the generation of 
harmonics (which any waveform distortion translates to) and of 
intermodulation distortion (what two independent waveforms do to 
each other when amplifed together in an amplifier that is non-
linear).   

Harmonic generation and intermod distortion make voices harder to 
understand.   We may not care about (probably don't WANT) wide 
frequency range in a communications receiver but voices being 
easy to understand -- THAT we care about. 

A good-sounding receiver is the result of minimizing distortion 
stage-by-stage in every stage between the antenna and the 
loudspeaker. 

In the stages of a receiver prior to the final detector, distortion is 
minimized first by keeping signals as small as possible (just 
enough to be well over the internal noise of the tube) and second 
by using newer, wider range tubes.   The 6EH7 can't be beaten for 
RF and IF amp service up to 30 Mcs or so.  It was designed for TV 
IF work at 40 Mcs and the specs on intermod at various bias 
(AGC) voltages are outstanding.

Negative feedback has sometimes been used in RF and IF stages 
to improve linearity but because of problems with phase shift in 
stages using tuned circuits, the feedback usually takes the form of 
an unbypassed cathode resistor.  In a receiver with AC on the 
filaments this must be done with care -- maybe just in the final IF 
stage -- because hum modulation can easily be introduced.   

(Collins used a capacitive voltage divider from the plate circuit to 
give negative feedback in some grounded grid SSB power 
amplifiers; that is the only other negative feedback application I'm 
aware of.)

Do not be intimidated by the modern tubes and do not assume that 
you'll have to lower the gain.   Be careful about layout and wiring 
practices (another topic for another time) and they'll usually work 
okay.  Problems with high gain RF/IF stages are the main reason 
one should build one or two well tested designs before striking out.

Mixers should be linear -- either operated with the smallest 
possible signals or using beam deflection-types.

(Though the mixing process itself is inherently non-linear, mixers 
CAN be linear on the signal path -- that is, twice the signal means 
twice the mixer output.  That's the kind of linearity we're talking 
about.)  

When using modern tubes and circuits,  HF receivers are often 
better off without an RF Amp.   True vintage designs -- 6K8, 
6SA7or 6BE6 mixers for example -- do need an RF amp, as do low 
gain mixers with a high-loss filter (the Collins mechanical filters ...) 
if good weak signal performance is desired.

The second detector is actually just another mixer and like the 
others, needs to be linear on the signal path.   Diodes work if the 
signal is large however this makes linearity in the final IF stage 
more of a challenge.  For SSB/CW I think the best choices are the 
6BN6/6BY6 gated beam tubes OR one of the beam deflection 
tubes, 7360-6AR8-6JH8-6ME8.

Any of these six tubes can be used in a product detector that's 
both got high gain (so you can run the IF well within its linear 
range) AND has ample dynamic range for the variation in signal 
strength that's to be expected after the AGC does its work.  Other 
mixer circuits will also work (triodes, the pentagrid converters ...) 
but linearity is harder to acheive.  The acid test is when receiving a 
strong signal if you turn off the BFO the audio output signal should 
go down 30-40 db or so.  (Product detector = mixer ... mixing is 
multiplication ... if one input goes away then the output should be 
zero.)  Any residual signal with the BFO of is an error, that is, non-
linearity.  However  I believe all of these product detectors will need 
some kind of behind-the-panel adjustment to give this level of 
performance.

For AM the choice is more complicated because if you use a diode 
you need a larger signal than for the more sensitive product 
detector circuits meaning more gain ahead of the detector.  A plate 
detector works well (good match gain-wise to a high gain product 
detector) but requires specific attention to linearity.   Again, a 
trimming adjustment may be needed to get top performance.

The volume control comes next -- finally, a component for which 
linearity isn't an issue!   

Shaping of the audio frequency response -- lower and upper limits --
should be done outside the amp feedback loop; as a practical 
matter than means doing it between the second detector and the 
audio amp.

You cannot avoid distortion below whatever is the low frequency 
cutoff of the amp -- for example, maybe your amp will go down to 
100 cps.  You want this as low as possible; it's wise to set 
coupling cap/grid resistor combinations to go down to 10 cps or so, 
thus leaving your cheap output transformer to set the true lower 
limit.  Then you start to roll off the amp input below 500 cps so you 
never feed the amp signals it can't digest.  

Hams are often horrified to see amplifier time constants set for a 10 
cps rolloff -- all those LOWS!   But you're just reducing distortion of 
signals caused by loss of gain (i.e. reduced feedback) and 
transformer core saturation (increased distortion) at 100 or 200 
cps; you aren't going to let anything even close to 10 cps get there.

You don't want to hear very much above 2500 cps because there's 
not much voice intelligence up there but lots of noise.   Though a 
narrow IF filter will do much of the job (for SSB and CW) you'll want 
to roll it off some more after the detector because the post-
selective filter IF stages will introduce some higher frequency noise.

The audio amplifier needs plenty of gain -- a triode and pentode in 
either of the possible orders will do it if you have a few volts at the 
detector output.   Then you use negative feedback to cut the gain 
down to what you actually need to drive your loudspeaker.  

How much gain do you need?  Well, suppose you have 3 volts at 
the detector output -- that would be in the usual ballpark.   3 volts 
at the speaker voice coil would be over a watt for an 8-ohm 
speaker: With a reasonably efficient speaker that's enough to 
cause pain if you're in the same room.   In other words, an overall 
AF amp voltage gain in the ballpark of one will be fine; normally 
you'll use the volume control to set it much lower than that. If the 
output tube has a plate resistance of 4800 ohms then the 
impedance ratio is 600 and the turns ratio 24:1 so the voltage gain 
from amp input to output plate would be 24.  If the product of the 
two stage voltage gains is 1000 then the feedback loop can cut the 
gain from 1000 to 24, thus reducing distortion by 1000:24 or a 
factor of about 41.  Any half-way well designed amp with its 
distortion reduced by over 30 db is going to sound fine.  

The feedback should go from the voice coil to the cathode of the 
input stage of the amplifier.  I usually adapt the circuit of the 15-
watt high-fi amplifer in the RCA tube manual, however you cannot 
use quite so much open-loop gain without getting into problems 
unless you use a high-fidelity output transformer.  The usual cheap 
1 or 2 watt output transformer has too much phase shift to work 
well at the gain level of that amp. which is a pentode-pentode 
configuration.  It's much easier to use a triode-pentode (12AX7-
6AQ5, for example) or the reverse -- 6U8-pp 12AU7.   Either has 
ample gain for communications needs with fewer problems.

Low noise hi fi tubes -- 7199, 6922, and such -- aren't needed in HF 
communications receivers because comm audio stages don't have 
to have the extreme dynamic range of a high fi amp.  When 
atmospheric noise may be S-3 on a really good day and the whine 
from computer power supplies 20 over, we do not need to be able 
to hear musicians turning pages between the cannon volleys in the 
1812 Overture.  Perfectly ordinary tubes run at the gain levels 
needed in comm work will be dead silent.

You may have amplifier stability problems above the range of 
frequencies you want amplified. I've had trouble with oscillations in 
the 50 kcs range.  Bypassing can be used inside the loop to roll off 
the open-loop gain rapidly above 10 kcs or so to kill these.  When 
the amp seems to be working correctly it's well to run it at full 
power on a voice or music signal and look around with a scope. 
You can sometimes get instability only on transients or only at 
certain signal levels and you may not hear anything beyond 
"Sometimes it doesn't sound quite right." 

(While you are poking around with the scope it is interesting to 
feed in a sine wave large enough to develop something close to 
maximum power output and look at how the distortion plays out, 
stage by stage.  Since most distortion in an amp is usually in the 
power stage due to tube and transformer limitations at high power, 
the signal in the earlier stages will be sort of pre-distorted the other 
way by the feedback, so when it goes through the output stage it 
comes out close to right.)

I had a heck of a time taming the 6U8-pp 6AQ5 amp in the one-
month HBR.   But it sure is a fine-sounding receiver!

If you're not a believer and you do as I usually do and hook up and 
adjust the feedback after everything else is working, you will be 
convinced.  Even a receiver that sounds good without feedback will 
be substantially cleaner-sounding when you add the feedback.

Of course, this assumes that all the pre-audio stages are linear.   
"Garbage in, garbage out" -- the AF amp can't mend what was 
broken by earlier stages.

A receiver need not be complex to be designed according to these 
principles.  In fact it's easier to do it right with fewer tubes because 
you're less likely to wind up with too much gain causing 
overloading of later stages.   The HBRs get away with having too 
much gain by giving you manually adjustable gain controls in 
several places; these will normally be operated well below 
maximum.  Handbook hollow state designs have less excess gain; 
those of the 60's will give a good account of themselves.  

However, nearly all of the common designs will benefit from use of 
a better audio amplifier.  The HBR 13C is the only receiver for 
which the schematic is handy that uses feedback in the audio amp 
and that one isn't end to end. 

Walt Hutchens
Ruining for a pound what others could fix for a shilling, for over 60 
years.  (KJ4KV)