# concept of negative feedback circuit

Discussion in 'General Electronics Chat' started by sharanbr, May 22, 2015.

1. ### sharanbr Thread Starter Active Member

Apr 13, 2009
76
1
Hello,

I am pretty new to Analog (IC) design. So, kindly excuse if my questions are basic.

I have several questions with respect to negative feedback circuits,

1) x is the input; y is the output; if K is the gain the forward path; M is the gain in feedback path.

I am assuming that the output would be represented by,

y = K * (x-M*y)

Is this correct?

2) if K = 1 & M = 1 then

y = x-y

What would be the output for such an equation for a) for DC input b) for AC input

For DC input, I see that output goes to zero.

Is this correct?

Can circuit have such values for K & M

3) In case of AC input, what would happen.

Would the output track input with a given gain?

4) I am struggling to clearly understand the need for feedback.

For example, if the aim is to boost output then simple gain in the output path would suffice.
What is the need for negative feedback?

Is the only advantage that if the output drifts for a constant input, the output would automatically adjust?

5) in case of AC input, what would happen if input is changing faster than delay/latency associated with the circuit. This means that input would change before output is propogated back through the feedback path?

2. ### Kermit2 AAC Fanatic!

Feb 5, 2010
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y = x - y is true only when y=0.

3. ### Kermit2 AAC Fanatic!

Feb 5, 2010
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the gain and feedback are in opposition, so output is equal to input times the difference between gain and feedback

Feb 20, 2011
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5. ### crutschow Expert

Mar 14, 2008
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In general, negative feedback provides a correction so that the output more accurately follows the input. In effect the output is compared with the input and a correction is fed back to correct any differences. This correction generally reduces the gain so you trade off gain for accuracy.
An extreme example of this is the typical op amp circuit where the open-loop gain is typically 100,000 or more but the closed-loop gain is usually not more than a couple 100. All this excess gain is used by the negative feedback. This makes the closed-loop gain almost entirely a function of the feedback values and only minutely a function of the op amp open-loop gain.

If the feedback circuit is frequency dependent than that, of course, will be reflected in the output versus frequency.
For example, a series capacitor in the feedback will cause the amp to exhibit a low-pass function at the output. Using frequency dependent feedback networks is a common way to shape the AC response of the amplifier to perform various AC filter or frequency response functions (such as servo or control loop compensation).

6. ### ScottWang Moderator

Aug 23, 2012
5,478
864
If you using an ic or a circuit as the target then the discussion will more practical.

Discussing the general questions, sometimes will be loss the direction as get into the jungle, the direction can be left or right, which way is the right way to get out of the jungle?

7. ### sharanbr Thread Starter Active Member

Apr 13, 2009
76
1
This is where I seem to get a bit lost. In a non-feedback system output = gain*input.
Even in this case, the output does follow the input. Input changes, output changes too.
What is the catch I am missing?

8. ### crutschow Expert

Mar 14, 2008
16,521
4,451
The catch is that for output = gain*input, you are presuming the gain is constant. In real amplifiers the gain is not a constant.
Real amplifiers have gain non-linearities causing distortion, significant gain variations from unit-to-unit, and limited frequency response above which the gain decreases, all of which are improved or minimized by negative feedback.
For example you couldn't achieve the <0.1% distortion, stable gain, and flat frequency response of a modern audio power amplifier without a significant amount of negative feedback.

Last edited: May 23, 2015
9. ### Kermit2 AAC Fanatic!

Feb 5, 2010
4,165
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Not anymore. Maybe I should have said only when x=zero? But, then even that would be wrong due to the sign inversion.

Math class was a long long time ago. I should not post without a full tank of coffee, and even then maybe not.

DerStrom8 likes this.
10. ### studiot AAC Fanatic!

Nov 9, 2007
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519
That hasn't changed with the addition of feedback.

But there is more to feedback than error correction.

Its principal use is to define the output of circuit precisely, regardless of variations in the components themselves.
The feedback allow precise control of circuit gain response and frequency response to the desired level.

There are now two figures for gain.

Open loop gain (without feedback)

Closed loop gain (with feedback)

The closed loop gain may be a specified function of frequency and also a specified function of input so the transfer function may be desired function eg square or square root law.

Finally the feedback may be positive or negative.

Negative feedback is used to control amplifiers and signal processors - those circuits with a signal passing through and an input and an output.

Positive feedback is used to create self oscillating circuits with not input, but an output.

Finally positive feedback can be used to create other regenerative circuits, of more use in the digital world, latches and certain multivibrators.

11. ### tindel Well-Known Member

Sep 16, 2012
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Attached is a little pdf I put together showing the analysis of a typical negative feedback system.

File size:
33.7 KB
Views:
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Feb 17, 2009
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13. ### crutschow Expert

Mar 14, 2008
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How about if x = 2y?

14. ### sharanbr Thread Starter Active Member

Apr 13, 2009
76
1
Thank you all. I am beginning my journey into the the world of Analog IC design.
Even though I don't understand some of the points made here, yet I will find them handy for my reference as I dig deeper into the subject.

I have one more question (more at a conceptual level) which wasn't answered ...

We know that the Amp circuits themselves have a certain amount of latency/delay associated with them.
So, when input changes, this new input would trigger a series of changes in circuit before output is available.
Similarly, the feedback path would also need some more additional time.

So, given this, what happens when input changes such that rate of change at the input is faster than the time taken by the circuit to
evaluate a new set of values. Is this an issue and whether this would result in incorrect output?

15. ### studiot AAC Fanatic!

Nov 9, 2007
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Yes it is called slew rate limiting.

This is really a characteristic of the amplifier circuit, not the feedback circuit.
The amplifier circuit is more complex than the feedback circuit, with longer signal paths in both distance and time so we would normally regard the feedback as instantaneous.
However if there was significant delay for some reason it would affect the output, yes.
This can sometimes be seen in very fast Radio Frequency amps.

Another approach to the problem is called error feed forward, where another (smaller) amplifier is used in the feedback (forward) corcuit to add a compensating signal to the output.

16. ### crutschow Expert

Mar 14, 2008
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4,451
Even if the amp isn't slew-rate limited (which is a large-signal characteristic) it has a frequency response limit which will slow the rise/fall of a step input.
Similarly the frequency characteristics of the feedback network are reflected in the output frequency response/rise time at the output.
The output characteristics can be calculated form the amp and feedback characteristics.

An easy way to experiment with this, and other characteristics of analog circuits is to use a Spice circuit simulator, such as the free LTspice from Linear Technology that a number of us use on these forums.

17. ### tindel Well-Known Member

Sep 16, 2012
593
199

There are several related things going on here: slew rate is one of them... and studiot covered that well.

Another is bandwidth. Each control loop has a bandwidth in which it will work. Typical bandwidth of op-amps these days are anywhere from 100kHz up to about 10MHz. The larger the bandwidth, the faster the response to changes in input. As your input signal starts achieving the maximum bandwidth of the amplifier, the amplifier will have more and more difficulty keeping up and phase lag will start creeping in, and if designed properly, frequencies above the maximum bandwidth will be attenuated before the phase lag hits 180 degrees.

Stability is another item of concern. You are correct that as the input gets faster and faster that the opamp won't keep up. If the control signal is 180 degrees out of phase with the input signal (with the same amplitude) you will experience sustained oscillations - even during normal operation. Another way to think about this - You typically want at least 10dB of attenuation when you hit 180 degree phase shift.

All three of these things work together to produce a stable system and all three must be considered to produce good control loops.