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Audiophile Myths About Amplifier Negative Feedback Debunked

by Bruno Putzeys July 18, 2020

Feedback is an ubiquitous and unavoidable basic technique that keeps the world running. It is only controversial in audio, and then only specifically in power amplifiers. As more respected manufacturers are coming out of the closet concerning their heavy and happy use of feedback, the myth is increasingly on the back foot.  Here we present a pseudo-interview to help answer questions about feedback which is a fascinating and complex topic that lies at the core of successful design.

Q: What is Negative Feedback and what is it good for?

A: When you stand up without falling over, that’s feedback. Your inner ear has a kind of gyroscope that tells you where down is, and instructs your feet to move your center of gravity when it looks like the direction of down is changing. That’s combined with visual input from your eyes, so people whose inner ear balance doesn’t work can still stand up straight. That is, until they close their eyes and their feedback turns off. Then they keel over.

People use feedback constantly when they drive. You stay in your lane by looking at the lines and steering the car to stay between them. No sane person would suggest that driving with your eyes closed makes you a better driver.

Feedback is part of the physics of life. Paper planes only fly true because the slightest turn gets rewarded by an opposite push from the flowing air. Feedback just means that what is going to happen next is in some way influenced by what’s happened before.

Feedback is everywhere. All we do as engineers is use that perfectly natural phenomenon to help us get difficult stuff done.

Amplifier Feedback YouTube Discussion with Bruno Putzeys

Q: Like amplifiers.

A: Right. Let me guide you into this softly. Here’s an op amp gain stage, wired as a noninverting amplifier.

 image1.png

Do you remember this from school?

Let’s unpack this circuit for a bit. The plus and minus signs on the op amp symbol are shorthand to say that the voltage at the minus input is subtracted from the voltage at the plus input, and then amplified:

 image2.png

The circle with a plus in it is called a summing node. When there’s also subtractions taking place we’ll draw pluses and minuses next to the inputs to make that clear.

The two resistors form an attenuator. If the two resistors have the same value, the network multiplies the signal by one half. Let’s put that in a box too. A is the gain of the amplifier, B is the “gain” of the attenuator.

 image3.png

The grey formula says that the output of the summing node is the input voltage minus the attenuated output voltage. The red formula says that output voltage is that same thing multiplied by the gain of the amplifier. The number A is the “open loop gain” in control theory lingo.

Q: Let me stop you right there, I’ve heard some of this before and this is where engineers start talking about open loop gain, closed loop gain, and simply loop gain and they’re hoping we’re not going to confuse those three.

A: Fair point. We can call A gain before feedback.

We now have a formula for the output voltage Vo, but the expression itself contains Vo. That’s an equation and if we want to know what Vo is, we’ll have to solve it.

image4.png

At school we also learned, for an op amp, to assume that A is infinite. With A just about infinite, the output of the summing node has to be just about 0. So the task of amplifier A is to steer the output voltage such that the voltage differential between the two inputs stays at zero. Like the driver’s task is to steer the car so that the difference between its position and that of the middle of the lane is zero.

When you do that, the one in the denominator becomes negligible and the output simply becomes the input times 1/B. That number, 1/B, is the gain after feedback (“closed loop gain” officially). 1/B=2 in our example of course.

That’s a first answer to your question: what is feedback good for. It allows us to build a circuit that does the precise opposite of whatever it is that you put in the feedback loop. That’s useful because with passive parts you can make an accurate attenuator but you can’t make gain. With transistors you can’t do a precise amount of gain but you can make a lot of it. Put the two in a feedback loop and you get an amplifier with a very precisely defined gain.

Same thing for filters. With resistors and capacitors you can only build half of all possible filter types. By adding an op amp you can now also do the other half.

Q: That doesn’t seem too evil to me and I don’t think many audiophiles mind feedback being used that way. Recordings are made with mic preamps, mixing desks and converters that are stuffed with op amps. The best DACs and phono stages use them.

A: Mind you, “op amp” does not have to mean “chip”. Some of the best op amps are still made from loose parts. But whether they’re made with discrete transistors or on a silicon chip, the op amp is the fundamental building block of all high performance audio circuits. But you’re right, most folks are happy with that when it comes to their signal source. It’s only when we’re talking power amplifiers that all of a sudden there’s a culture war going on.

Q: I guess they’d say that using feedback to control gain is one thing, and using it to reduce distortion is another.

A:  Feedback always does both. When you’re building a filter, you want it to be independent of the tolerances in your op amp. It only works because feedback takes the op amp’s errors out of the equation. It doesn’t matter what you intended.

All you want a power amp to do is to gain up your signal as accurately as possible and nothing else. A linear power amplifier (by which I mean class A, AB or B) is just a discrete op amp with a bigger than usual power stage.

Q: Can you put the distortion into the picture?

A: Yes. Let’s make the power stage explicit and also add in the distortion created by the power stage.

 image5.png

Normally speaking the power stage is a kind of follower circuit whose gain C is around 1. We treat the distortion as a separate input. It’s a simplification that makes it a lot easier to understand what’s going on.

Working backwards from the output we can write Vo by first adding Ve and then continuing through the amp, the input and then back to Vo through the attenuator:

 image6.png

Move all Vo’s to the left:

image7.png

Divide both sides by 1+ABC and rearrange:

image8.png

The result is what we had before, except we now also have a separate term with Ve in it. The output voltage is the input voltage times something plus the error voltage times something else.

That’s beautiful because it means that this circuit treats the input signal and the distortion differently. As A increases, Vi gets multiplied by something that gets ever closer to one over B. Meanwhile, Ve gets reduced by approximately A times B times C. This number (“loop gain”) is the amount of feedback.

Q: So where’s the bad news?

A: The bad news is that making A large is not trivial. It is a bloody hard problem in fact. This analysis only shows is how wonderful life would be if A were large. It doesn’t say how.

That’s where reviewers and armchair experts go wrong. They think feedback is an easy fix, a cheat almost. All you need to do is crank up A real high right? Sure, all you need to do to win the London Marathon is to run really fast and keep going. Go tell that to Sir Mo Farah.

Q: Sorry- just explain, what’s so hard about adding gain? If you can’t make an amp with enough gain, can’t you just add another one?

A: Have you tried that?

Q: I have.

A: Did it work?

Q: No, it went unstable.

A: Bingo.

Feedback responds now to what happened before. It’s about time.

The output stage isn’t infinitely fast. If you don’t want the feedback loop to overreact, you want the gain stage A to react gently at first and only add further course corrections when it sees the power stage respond.

Control systems engineers like to use simple signals to test the stability of a feedback loop. A step function, say. We perturb the system with a Ve that jumps from zero to one and then stays there. Then we watch the system steer the output back to zero.

Q: That sounds reasonable. After all, the distortion must first happen before the feedback loop can do something about it.

A: And ultimately it can’t respond any faster than it can command the output stage.

image9.png

I’ve pared the circuit down a bit. I’ve removed the input signal and the summing node with it. Then I’ve combined the gain of the attenuator into the amplifier triangle alongside the minus sign from the summing node. It’s called negative feedback for a reason.

It’s not a terrific drawing but I’ve tried to show there’s a delay between the power stage’s input and output. Because of that delay alone, the gain stage A needs to respond gently at first.

What kind of circuit does this? Let’s remove all traces that aren’t directly connected to the gain stage A:

image10.png

At a short time scale, a large input only produces a moderate output. Over the short run, A is small. But after a while a nearly zero input produces a sizeable output. So over the long run A must get quite large.

Another way of saying this is that fast, high frequency swings are amplified much less than slow, low frequency swings.

We call a circuit like this an integrator, symbolized by that weirdly elongated S.

 image11.png

The frequency response of an integrator drops by a factor 10 every time the frequency goes up by a factor 10. On a dB scale and a logarithmic frequency scale we get a straight line that slopes downward by 20dB per decade. Or, less accurately, 6dB per octave. That’s saying that whenever you multiply a frequency with the gain you get at that frequency, you always get the same number. That includes the frequency where the gain is 1. That frequency is called the Gain Bandwidth Product.

Q: That number will tell us how quickly the distortion gets compensated I assume. But it doesn’t take away the fact that at t=0 the distortion went unchallenged entirely.

A: Whatever happens, stays happened. Very fast or high frequency errors don’t get corrected.

Here’s what the loop does to distortion:

 image12.png

We can still use our old equations, so long as we remember that the numbers A and C (and in some cases B) are frequency dependent, so you need to calculate it for every frequency and make a plot. Then you find that the distortion ends up high pass filtered.

The amount of feedback is not a single number but one that drops with frequency. That’s important when you’re trying to relate how much feedback an amp has with how it sounds.

Q: Well I did notice that a lot of amps show a rise in distortion as frequency goes up.

A: Actually all of them do. The game is to try to keep distortion as low as possible in the audio band. Real distortion isn’t super fast so to a degree the loop has some time to catch up with it while it happens. But the basic fact remains that A has a natural tendency to come down with frequency and I for one have a natural desire to make A as large as possible.

The problem is that we can’t just push GBW. GBW has to stay below the bandwidth of the power stage or we risk overreaction or worse, instability. So far I treated C like it was 1 for simplicity’s sake but it isn’t. I’m still simplifying but let’s say the power stage is a first order lowpass filter:

 image13.png

The point where the combined gain ABC goes from a first order slope to a second order slope should be below unity gain, otherwise the phase shift will tip the circuit into oscillation.

Q: What I don’t get is this. Power transistors in the 70’s were slow. And you’re basically saying that if the power stage isn’t fast, you can’t get a lot of feedback. But it was exactly in the 70’s that you’d see these amps with ridiculously large amounts of feedback.

A: No you didn’t. That’s where it all went pear-shaped. The confusion was really simple. Here’s a typical gain plot for those days:

 image14.png

People would look at the number on the left of the graph and say wow 80dB that’s a lot. But hang on, you barely get 20dB at the end of the audio band. That’s not much at all.

Reports of amplifiers with lots of feedback in the 70’s were Bigfoot sightings. “I’ve seen an amp with a ton of feedback and I’ve got a fuzzy photograph to prove it.” People thought they were listening to a high feedback amplifier, didn’t like what they heard, concluded feedback was bad and a myth was born. By the start of the 80’s, it was gospel.

Q: Huh.

A: 80dB at 20Hz is trivial. 80dB at 20kHz, now that would have been an achievement. It would also have corresponded to a GBW of 200MHz.

Q: A 200MHz power stage wouldn’t even be possible today, would it?

A: A handful of headphone amps come close, but for a serious power amp it’s not on the cards.

Q: Is a lot of feedback even possible?

A: It is, but speeding up the power stage is only going to get you so far. We need to get out of the GWB straitjacket entirely.

We said that feedback high-pass filters the distortion. But does it have to be first order? Can’t we make that a second order? Well seen from that angle it’s not a hard one to answer. Just take that formula 1/(1+ABC) we had earlier and equate that with a second-order high-pass filter. Solve for AB, and see if you end up with something you can build.

 image15.png

Conceptually we start by imagining we’ve solved the problem, that we’ve got an amplifier that filters distortion according to the red curve. That only leaves us to work out what’s inside. How much feedback does it need to produce that behavior. The answer is the blue curve. It has a second order slope, which is no surprise. But somewhere before it hits unity gain it slows down to a first order slope. I didn’t need to invent this. It’s just what the math says it should do. Now build it and Bob’s your uncle.

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Recent Forum Posts:

everettT posts on July 21, 2020 22:01
jeffca, post: 1405740, member: 48611
Who does this Bruno Putzeys think he is? One of the greatest amp designers on the planet?

Hey, egg head, amp design is based upon belief that it's good, not science and mathematics. You and your equations & science make my head hurt.

You should be using tubes because that pleasant, orange glow let's you know that the music must sound good. Even better if it has giant meters.

This class D stuff you are pushing lacks the warmth and musicality that you can only get from pentodes that are producing a ton of wonderful distortion and noise. In making a straight wire with gain, you have destroyed everything that is wonderful about amplifiers.

So, Bruno, calm down! Make amps the fantastic, old fashioned way and everything will be grand. No one needs an audio amplifier that is audibly perfect.

Keep America great! Trump

jeffca posts on July 21, 2020 21:45
Who does this Bruno Putzeys think he is? One of the greatest amp designers on the planet?

Hey, egg head, amp design is based upon belief that it's good, not science and mathematics. You and your equations & science make my head hurt.

You should be using tubes because that pleasant, orange glow let's you know that the music must sound good. Even better if it has giant meters.

This class D stuff you are pushing lacks the warmth and musicality that you can only get from pentodes that are producing a ton of wonderful distortion and noise. In making a straight wire with gain, you have destroyed everything that is wonderful about amplifiers.

So, Bruno, calm down! Make amps the fantastic, old fashioned way and everything will be grand. No one needs an audio amplifier that is audibly perfect.

Keep America great! Trump 2020
Gmoney posts on July 18, 2020 08:44
gene, post: 1404865, member: 4348
Here is the long form of the Amplifier Feedback article for those that wish to dive deeper:
https://www.audioholics.com/audio-amplifier/amp-myths-negative-feedback
Clearly a better understanding! Thanks Gene.
gene posts on July 18, 2020 04:15
Here is the long form of the Amplifier Feedback article for those that wish to dive deeper:
https://www.audioholics.com/audio-amplifier/amp-myths-negative-feedback
Gmoney posts on May 19, 2020 00:40
Pogre, post: 1391948, member: 79914
I couldn't tell by his accent!

I forgot he was from Oxford.
Oh no you didn’t just go there, Stephen Hawkins was an inspiration to other’s with total Paralysis from his Debilitating disease to his very end of his life. He like many other’s who didn’t take a Cowards way out by taking his own life. Haven’t met the man in person but I have followed his work and his Accomplishments in life and his Field of science was nothing short of astonishing. If I could only have his Courage. His Constitution of Will surely is a standard set. The man had a wonderful Spirit of life.
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