Please explain feedback to an ignoramus

[SY]

I think Jan is just defining "amount of feedback" as beta, which is (in my understanding) more properly called "feedback factor."

 

[DPH]

I think Jan is just defining "amount of feedback" as beta, which is (in my understanding) more properly called "feedback factor."

That's definitely the math being applied. Infinite OLG with 6 dB of feedback makes my head hurt, though. (Infinite - 6 dB) I'm much more okay with.

Edit to add: I wish I could find a link online that covers the very, very basics we're talking about. I have my "intro to circuits" textbook from freshman/sophomore year of EE, but we built up to it. "Art of Electronics" might not be a bad intro for the OP--it's an invaluable resource and very approachable.

 

[DF96]

Is "6dB of feedback" a well defined concept? If so, a textbook can tell us if it means 'reduce the closed-loop gain by 6dB' or 'feed back 0.5 of the output to the summing point'. These two definitions converge in the limit of infinite loop gain.

Actually, 6dB is about the worse possible figure to choose to illustrate the point. This is because 1-0.5=0.5 . Better to ask about '20dB of feedback'. I think most of us would understand that to mean 'closed-loop gain reduced by 20dB'. It certainly does not mean 'feedback factor = 0.1'. It may mean '1 + ff factor X open loop gain = 10'.

By this time the OP may be permanently confused!

 

[SY]

If he is, then a nice read of Bruno Putzeys's paper "The F Word" (available at Jan's Linear Audio website) will clarify things.

 

[dudleyperkins]

If anyone is familiar with chemical engineering, a good analogy for feedback is a distillation column using reflux.
Some product is fed back to the column, (some output is fed back to the input). Result:- less product (lower gain) but improved purity (lower distortion). Hope this helps with the principal of feedback, which like many things, is a trade off to improve the final quality.

 

[chopchip]

Yes, but this is a beginner. You can't feed them with a fire hose.

now THIS is understanding!

 

[GoatGuy]

Is "6dB of feedback" a well defined concept? If so, a textbook can tell us if it means 'reduce the closed-loop gain by 6dB' or 'feed back 0.5 of the output to the summing point'. These two definitions converge in the limit of infinite loop gain.

Actually, 6dB is about the worse possible figure to choose to illustrate the point. This is because 1–0.5=0.5 . Better to ask about '20dB of feedback'. I think most of us would understand that to mean 'closed-loop gain reduced by 20dB'. It certainly does not mean 'feedback factor = 0.1'. It may mean '1 + ff factor X open loop gain = 10'.

By this time the OP may be permanently confused!

You're right (and also … unaccountably confused too!). For instance, taking the semantically worst figure (–6 dB) for an amplifier having an open loop gain OLG of 10× (+20 dB), feeding back ½ does not converge on a net gain of +20 - 6 = +14 db!

Instead, it converges on a gain of only 1.6× or +4.4 dB. (Try it for input of 2 volts…

2 volts - 1.667 volts = 0.333 volts net input to amp
0.333 V × 10 (OLG) = 3.33 volts 'output' to be tapped by feedback loop
3.33 V × 0.5 (purported feedback amt) = 1.667 volts back to sum junction

See? So 3.333 output ÷ 2.000 input = 1.667× net gain = +4.4 dB.

If we actually want –6 dB of gain drop … AKA '6 dB NFB', using my abstraction of “magic / OLG”, where magic = 1.0 for target –6 dB… then output feedback fraction to summing point on input is: 1 ÷ 10 = 0.1.

Again:

2 volts - 1.000 volts = 1.000 volts net input to amp
1.000 V × 10 (OLG) = 10.00 volts net output to be tapped for FB
10.00 V × 0.1 (magic/gain) = 1.000 volts back to sum junction

Yes, it might be the worst case, but it also demonstrates that feeding back 'half of output' is a hopelessly confused concept. The not so confused idea though is “an amount of feedback that reduces overall gain some number of decibels”.

And this … is magic / OLG!
where magic requires that table (because it is hard to compute!)

GFB 'magic'
–0.0 0.00
–1.0 0.12
–2.0 0.26
–3.0 0.41
–4.0 0.58
–5.0 0.78
–6.0 1.00
–7.0 1.24
–8.0 1.51
–9.0 1.82
–10.0 2.16
–11.0 2.55
–12.0 2.98
–13.0 3.46
–14.0 4.01
–15.0 4.62
–16.0 5.31
–17.0 6.08
–18.0 6.94
–19.0 7.91
–20.0 9.00
–21.0 10.21
–22.0 11.58
–23.0 13.12
–24.0 14.84
–25.0 16.77

(bold ones are the values DF96 was talking about… and GoatGuy)

GoatGuy

PS... one last one. OLG is 100x = +40 dB of some amp. We want to really tame it with -20 dB of NFB. Choosing line #-20.0 --> 9.00 magic# in the table, work the math. INPUT is 2.5 volts (arbitrary)

2.500 V - 2.250 V = 0.250 V at input with feedback amount removed
0.250 V × 100 (OLG) = 25.0 V at output, from which to tap feedback
25.00 V × (9 magic / 100 OLG) = 2.250V feedback ... to first line

Net gain is 25.0 / 2.50 = 10x = +20 dB
Net NFB is OLG (+40 dB) - CLG (+20 dB) = "20 dB NFB" in parlance of us audio dudes and dames.

'magic' DF96. Divided by OLG equals proportion of output to actually feed back to input (inverted, of course).

______

Lightbulb moment... The "hardness" of computing "magic" turns out to be straight forward doing some algebra. One formula to rule them all:

magic = [(1 - 10^(-NFB/20)) / 10^(-NFB/20) ]

Where NFB is in conventional / conversational positive dB. The formula is OLG free, and it produces the 'magic' table without any iterative converging hoohah. Sigh... this reminds me of the 'beta' equations. Oh well...

 

[DF96]

The formula is OLG free, and it produces the 'magic' table without any iterative converging hoohah.

Yes, algebra usually beats repeated arithmetic (except for those cases which have no closed form solution).

 

[ruffrecords]

Here you go:

https://drive.google.com/file/d/0B_n67A1hN3qtbHBvdmVuWGt0dUE/view?usp=sharing

I wrote it a long time ago and it does have some silly types in it, for example the + in equation 2 should be an = sign.

Cheers

Ian

 

[GoatGuy]

Some paper!

Here you go:

https://drive.google.com/file/d/0B_n67A1hN3qtbHBvdmVuWGt0dUE/view?usp=sharing

I wrote it a long time ago and it does have some silly types in it, for example the + in equation 2 should be an = sign.

Cheers

Ian

Nice paper, Ian. For a student of engineering, as crisp as you would want it to be. For the average bloke, might be somewhat “math-y”. If I could suggest something for the appendix, it would be the key “most useful couple of equations” in descending-usefulness order. Again… thanks!

GoatGuy

 

[kstagger]

some history: https://www.wpi.edu/about/history/feedback.html

Black's invention solved a problem that had hindered the advance of long-distance telephone service. To get telephone signals to travel over long spans, one had to amplify them several times, with each amplification introducing new distortions. Black's insight was that by feeding part of the signal back into the amplifier, in negative phase, and comparing it to the original signal, the distortion could be greatly reduced.

Black's technical accomplishment was important enough to earn him eternal recognition (as just one example of the honors he received, he was inducted into the Inventors Hall of Fame, along with Robert Goddard '08). But the story of his discovery is also the stuff of legend. In 1927 he was taking the Hudson River ferry to his office when he suddenly thought of the solution to the distortion problem he'd been absorbed in for some weeks. Having nothing else to write on, he sketched his idea on a page of The New York Times that had been printed quite faintly. He signed and dated his notes and then had a colleague do the same when he got to work. That page from the Times, pictured above, is now in the AT&T archives.

also from the AT&T archives: https://www.youtube.com/watch?v=iFrxyJAtJ7U

 

[rayma]

now THIS is understanding!

Just the voice of experience.