Feedback, or how to be late and be on time the same time, all the time.

# Feedback, or how to be late and be on time the same time, all the time.

Posted 3rd November 2010 at 05:19 AM by jan.didden
Updated 3rd November 2010 at 10:20 AM by jan.didden

Just a couple of days ago I posted something to try to debunk that tired old myth that 'feedback always comes too late and therefor can't work'. Apart from the fact that obviously it does work, which makes the first statement pretty stupid to begin with, here's my take on it.

The myth may result from an often repeated misconception that feedback comes 'after the fact' and therefore always comes too late.
This has been shown to not be the case over and over again but if you have no engineering background it may be difficult to grasp the concept. Let me try to help.

Obviously, there is a signal delay in an amp from input to output and back to the input through the feedback loop. Since the feedback loop is generally a pair of resistors, the bulk of the delay is in the amp. That is the case both in non-feedback as well as in feedback amps. Such delays are very small, often fractions of a microsecond, and in this context can be ignored.

What is often confused with delay is the phaseshift of the signal while traversing the amp (again, phaseshift through the feedback network can safely be ignored in all but pathological cases). Now if you put a sine wave signal and its phase-shifted version on a scope, it appears that the lagging signal is delayed with respect to the other signal. But it is important to note that it is not strictly the case. Take the case of a sinusoidal current into a cap. The voltage that appears on the cap as a result of the current looks like that current and lags the current by 90 degrees. But, and this is important, any change in that current will have an immediate effect on the voltage! It is not that a chance in current makes the voltage chance some time later, no, the voltage on the cap immedately starts to chance when the currrent starts to change. In hindsignt, it is obvious: the current and voltage are phase-shifted with respect to each other but there is never a 'dead band' where the voltage 'waits' for the current to change. OK, so we have that out of the way.

So, the signal fed back to the input immediately changes if the input signal (or the output signal) changes; feedback does not 'come too late'. But because of phase shift in the amp, the fed back signal is phase shifted (and generally lags) the input signal. But the change in input signal immediately leads to a change in output voltage as well as feedback voltage. I know, it doesn't sound intuitive, but is it basic circuit theory nevertheless.

There are two effects from that phaseshift through the loop.
1 - The feedback mechanism depends on cancellation of (a fraction of) the output signal with the input signal, leaving only the difference, the distortion. That distortion (in opposite phase), is amplified and cancels the distortion in the output, making the amp more linear. With increasing frequency, the phaseshift between the (fraction of) the output and the input increases. Therefor, that cancellation gets less and less complete, making the feedback work less and less well with rising frequency. That is the reason that almost all amps show rising distortion with frequency: the feedback gets less effective.

2 - Another effect of increasing phase shift with frequency concerns stability. If you go so high in freq that the phaseshift approaches 180 degrees, your nfb turns into pfb. That means that the amp sort of generates it's own input signal that gets send around and around, much like howling in a system where the mike picks up the speaker signal, sends it back through the amp etc. If that happens, AND you still have gain in your circuit, you have an oscillator.

The difference between the actual phase shift and the dreaded 180 degrees, at the point where your gain drops down to one (so it can't oscillate), is called the phase margin. Now, even with some phase margin (less than 180 degrees phase shift and still gain > 1) you start to see ringing on fast signals.

But, it is very straight forward engineering to design your circuit to any stability point you want. Sometimes engineers accept some ringing at say supersonic frequencies because a) there will never be any signal in that region except on the test bench and b) it allows just a bit more nfb in the lower freqs to make the circuit a bit more linear or transparent.

jan didden
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