Without feedback, the amplifier has a certain gain vs frequency curve.
With feedback, it has a different gain vs frequency curve.
The feedback curve will be always below (less gain) the no feedback curve.
In the middle frequencies, the difference between the two gains is the amount of feedback.
This amount will usually decrease near the frequency extremes, though.
NFB is trading gain for linearity. 6dB of gain is traded for lower THD.
Amplifier causes distortion. The output of the amplifier is distorted in waveform relative to the input waveform.
Small portion of the output is taken, inverted (it's inverted by the amplifier as part of normal operation) and summed with the input, or to a node near the input.
When summing two waves of opposite phase, the original (undistorted) wave is partly cancelled out (diminished in amplitude). Also, the errors in the feedback signal (distortion) are summed to the input.
The errors are however of opposite phase as the errors that the amp makes, so it cancels out part of the errors the amp will make.
This is maybe a bit clumsy explanation but hope it helps at least some.
Amplifier causes distortion. The output of the amplifier is distorted in waveform relative to the input waveform.
Small portion of the output is taken, inverted (it's inverted by the amplifier as part of normal operation) and summed with the input, or to a node near the input.
When summing two waves of opposite phase, the original (undistorted) wave is partly cancelled out (diminished in amplitude). Also, the errors in the feedback signal (distortion) are summed to the input.
The errors are however of opposite phase as the errors that the amp makes, so it cancels out part of the errors the amp will make.
This is maybe a bit clumsy explanation but hope it helps at least some.
Let's say you have input signal that has two frequency components both at 0dB level; 1kHz and 10khZ.
The amp has poor frequency response open loop, so in the output, let's say the 1k is +20dB and the 10k is +10dB.
Then feedback is applied.
Inverted signal (portion of output) is summed to the input. 1k signal is bigger in output, so when summing the inverted FB to the input, 1k signal is cancelled out more.
10k is much smaller, so it is cancelled out less when summed to the input.
So, new input is now such that the 1k part is smaller than the 10k part. When they go thru the amp, they come out close to the original signal (both at the same level).
So NFB can be used to extend freq response, both higher and lower.
In reality of course all this happens almost concurrently, this is just a thought experiment.
The amp has poor frequency response open loop, so in the output, let's say the 1k is +20dB and the 10k is +10dB.
Then feedback is applied.
Inverted signal (portion of output) is summed to the input. 1k signal is bigger in output, so when summing the inverted FB to the input, 1k signal is cancelled out more.
10k is much smaller, so it is cancelled out less when summed to the input.
So, new input is now such that the 1k part is smaller than the 10k part. When they go thru the amp, they come out close to the original signal (both at the same level).
So NFB can be used to extend freq response, both higher and lower.
In reality of course all this happens almost concurrently, this is just a thought experiment.
The open loop gain. With no feedback, let's say your amplifier has a gain of 50. You apply feedback and the gain is now 25. Then you have a 2:1 gain reduction, which is 6dB.
It gets slightly more complicated with real-world amps that don't have a constant gain with frequency, or feedback networks that also change with frequency, but for most back-of-envelope calculations at midrange frequencies, you can use the simple way for a starting point.
If you have 6dB feedback, that means that 1/2 of the output signal is fed back to the input in opposite phase. (6dB is a factor 2 and the feedback uses 1/feedback factor therefor 1/2).
The result is that the amp gain is lowered. In a perfect world, with an amp that has infinite gain before feedback, the gain is now 6dB. With a practical amp, it will be less.
Let me give a numerical example rather than math stuff.
Let's say we have an amp that has a gain (no feedback) of 20 times. Assume an output voltage of 20V. Therefor, the input voltage required is 1V. OK?
Now we take 1/2 of the output voltage (6dB feedback) and subtract that from the input signal.
The amp gain itself is still 20 x so the effective input signal, Vin - 1/2 of Vout, still needs to be 1V. Because we subtract 1/2 x 20 = 10V the input signal now needs to be 11V to get the same 20V output! The gain of the feedback amp is now 20/11 is almost 2 (1.82) , which it would be if the open loop gain would be huge, that should be evident now.
What is this good for? Well, let's say that the amp open loop gain is not perfect 20 x but wobbles between 20 and say 24. That gain wobble happens because of tolerances in parts, loading conditions, different frequencies etc.
We know that at gain = 20, the feedback amp has a gain of 20/11. With an open loop gain of 24, the feedback amp gain becomes (left as an exercise for the reader ;-) 24/13 = 1.85. So we see that any change in open loop gain from the hypothetical 20 to 24 (20%) is now reduced to just 1.6% (difference between 1.82 and 1.85). And the bigger the open loop gain the smaller the feedback variation will be.
The beauty is that this goes for EVERYTHING that causes that wobbling gain. It reduces gain variation due to load so looks like the amp now has a very low output resistance (high damping factor). It reduces variation during a signal cycle which means it reduces distortion. It reduces frequency-dependent gain variations so it extends the frequency response both on the low and on the high side.
It's great invention, really!
Jan
The result is that the amp gain is lowered. In a perfect world, with an amp that has infinite gain before feedback, the gain is now 6dB. With a practical amp, it will be less.
Let me give a numerical example rather than math stuff.
Let's say we have an amp that has a gain (no feedback) of 20 times. Assume an output voltage of 20V. Therefor, the input voltage required is 1V. OK?
Now we take 1/2 of the output voltage (6dB feedback) and subtract that from the input signal.
The amp gain itself is still 20 x so the effective input signal, Vin - 1/2 of Vout, still needs to be 1V. Because we subtract 1/2 x 20 = 10V the input signal now needs to be 11V to get the same 20V output! The gain of the feedback amp is now 20/11 is almost 2 (1.82) , which it would be if the open loop gain would be huge, that should be evident now.
What is this good for? Well, let's say that the amp open loop gain is not perfect 20 x but wobbles between 20 and say 24. That gain wobble happens because of tolerances in parts, loading conditions, different frequencies etc.
We know that at gain = 20, the feedback amp has a gain of 20/11. With an open loop gain of 24, the feedback amp gain becomes (left as an exercise for the reader ;-) 24/13 = 1.85. So we see that any change in open loop gain from the hypothetical 20 to 24 (20%) is now reduced to just 1.6% (difference between 1.82 and 1.85). And the bigger the open loop gain the smaller the feedback variation will be.
The beauty is that this goes for EVERYTHING that causes that wobbling gain. It reduces gain variation due to load so looks like the amp now has a very low output resistance (high damping factor). It reduces variation during a signal cycle which means it reduces distortion. It reduces frequency-dependent gain variations so it extends the frequency response both on the low and on the high side.
It's great invention, really!
Jan
Last edited:
Yes, when the feedback is negative as it usually is, but since it can also be positive, I would prefer to be exact which one is considered.
I would disagree. I am used to understand the amount of NFB as the amount of gain reduction due to NFB.
If open loop gain is 20 dB and 6 dB NFB is used, then the gain is reduced to 14 dB.
Actually the same as SY and frank1 explained, but with different numbers and words.
Last edited:
My dear colleague… I think you scrambled that explanation pretty handily. Other earlier posters made/make it clear.
gain reduction = 20 log₁₀( open loop gain / close loop gain );
Oddly, this is one of the harder things to get a handle on “empirically”: if you try to make an approximating loop spreadsheet, it can 'go wild' easily (tho' circuits don't).
Ultimately though there is a cute set of “magic numbers” that can be determined empirically using real-world amplifiers and either oscilloscopes or good A/C multimeters, and lots of protection for your body. Or a converging spreadsheet too.
Anyway… there's one key formula to know:
dB gain loss (stated GFB) = “magic” / open loop gain.
where “magic” is from this table:
magic 0.00 = 0.0 db
magic 0.13 = –1.0 db
magic 0.26 = –2.0 db
magic 0.42 = –3.0 db
magic 0.59 = –4.0 db
magic 0.78 = –5.0 db
magic 1.00 = –6.0 db
magic 1.24 = –7.0 db
magic 1.52 = –8.0 db
magic 1.82 = –9.0 db
magic 2.17 = –10.0 db
magic 2.55 = –11.0 db
magic 2.98 = –12.0 db
magic 3.47 = –13.0 db
magic 4.01 = –14.0 db
magic 4.63 = –15.0 db
magic 5.31 = –16.0 db
magic 6.08 = –17.0 db
magic 6.94 = –18.0 db
magic 7.91 = –19.0 db
magic 9.00 = –20.0 db
magic 10.22 = –21.0 db
magic 11.59 = –22.0 db
magic 13.12 = –23.0 db
magic 14.84 = –24.0 db
magic 16.78 = –25.0 db
magic 18.95 = –26.0 db
Remember: unless you're good with some tough formulæ, these "magic values" are quite useful.
The magic value of 9.0 gives –20 dB gain drop (feedback effect).
If open-loop gain is 50, then
9.0 ÷ 50 = 18% of output (negated) fed back to input.
If open-loop gain is 100, then
9.0 ÷ 100 = 9% of output (negated) fed back to input
That's why the “magic” is called “magic”. The amount of feedback to achieve some particular GFB amount does depend on the open loop gain and the “magic” constant.
_______
The bigger problem of course is figuring out how to turn all this into resistor values. Note that most SET and PP designs use the secondary of the output transformer, which of course being a 'step down' device, performs some of the “magic”-divided-by-openloop gain function. That … and it is usually not negated and summed to the input, but is “added in” as cathode lift to the first stage's first gain tube whether its a triode or pentode. The mathematics of this is really hard to summarize…
But let's just say that one can just implement a variable resistor scheme to make for 'adjustable NFB', and play with it a bit to empirically “find” a most-pleasing value. Then remove the pot, and replace it with the same value resistor.
Good luck!
GoatGuy
(PS: the above table was found or determined by writing a program that ended up checking 20,000 values of magic from 0.001 to 19.999 in 0.001 steps. Each evaluation in turn performed 1,000 iterative loops to converge on a value for the decibel loss that was accurate to 1% or better. This is why I coined the term "magic". Hard to calculate, but once you get the numbers, a constant that can be used easily.
Last edited:
Do the math. This is only true when the open loop gain is infinite. Did you check my example? Anything wrong with that?
Jan
True, that's the definition of the gain reduction. But that is not necessarily the 6dB he mentioned. It ONLY is 6dB (in this example) if the open loop gain is infinite. Please tell me where my numbers example went wrong. I went out of my way to make it as simple as possible, so you should be able to pinpoint any errors easily.
In fact, the reason that fb cannot reduce distortion to zero is exactly because the open loop gain is never infinite. If it was, the gain would indeed be exact, and all distortion vanished. Do the numbers.
Jan
Member
Joined 2009
Paid Member
the basic premise of "I want to apply 6 dB of feedback" isn't how actual engineers go about using negative feedback
in this forum's Audio amplifier design context that really is already the superstitious, audiophool formulation of those who don't "trust" high negative feedback, likely want to "preserve euphonic harmonic structure" are using other illogical formulations
maybe advanced for the OP? http://linearaudionet.solide-ict.nl/sites/linearaudio.net/files/volume1bp.pdf
in this forum's Audio amplifier design context that really is already the superstitious, audiophool formulation of those who don't "trust" high negative feedback, likely want to "preserve euphonic harmonic structure" are using other illogical formulations
maybe advanced for the OP? http://linearaudionet.solide-ict.nl/sites/linearaudio.net/files/volume1bp.pdf
I just love it when a simple question gets asked on this forum
... and I have never seen magic invoked within the first two pages!
I'm outta here!
Jan
Last edited:
See that last bit (do the numbers) is exactly what I am doing, and why we must have a language difference between our (very probably same) concepts.
To me, when someone says, 6 dB of NFB, it means exactly the same as lowering effective gain to (1/2 = -6 dB) of its original non-fed-back open loop value. The term (again, to me) does not mean taking 1/2 the output and feeding it back into the input. It can't.
The amount of output to feed back to the input (negated of course) is an amount that is what I claim: magic_factor / open_loop_gain.
The magic_factor accomplishes the desired NFB amount, when reduced by open loop gain.
So, for an actual -6 dB of NFB for an amplifier having 100x, exactly 1.00 (magic) / 100 (gain) = 0.01 or 1.0% of the output fed back to input. Try it. It works.
And 1.0% isn't -6 dB of anything. It is the factor needed for this hypothetical amplifier to produce the desired 50% overall gain reduction. It also makes no claim in how much amplification-error reduction will be realized.
Peace on... and of course do the calculations!
GoatGuy
PS: jan.didden … you might want to consider your infinite gain eigenidea somewhat more closely.
I know (having also taken UCBerkeley EE 107 - the op-amp special course), that the infinite gain scenario is mathematically ideal for eliminating amplification errors (distortion), as well as asymptotically realizing perfect-value component choices. This we agree upon. However, unless one is willing to do the lim( … ) math, real-world math is a lot messier. Again, not to beat a dead horse, but why I abstracted the feedback amount to be k/Ao (k = magic_factor from iterative converging Taylor series calcs.)
GoatGuy
I know (having also taken UCBerkeley EE 107 - the op-amp special course), that the infinite gain scenario is mathematically ideal for eliminating amplification errors (distortion), as well as asymptotically realizing perfect-value component choices. This we agree upon. However, unless one is willing to do the lim( … ) math, real-world math is a lot messier. Again, not to beat a dead horse, but why I abstracted the feedback amount to be k/Ao (k = magic_factor from iterative converging Taylor series calcs.)
GoatGuy
Ehgads. Poor OP.
(The pedants have struck, the pedants have struck!) (Not that they're at all being malicious
OK, ok ok ok
I can take a hint.
To answer poor OP, negative feedback is the routing of some portion of an amplifier's output, phase inverted, back to the input, to 'mix' with the input, diminishing how much of that input gets thru the amplifier. In so doing, errors in amplification AKA 'distortion' is also reduced along with overall gain.
Anything more complicated than that requires math. And the math is pedantic in the end. As are the definitions, as are the outcomes. As are the misconceptions, the pedantic rhetoric and the rest.
I'll shut up now.
GoatGuy
- Status
- This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.