Why Unity Feedback is Most Difficult for Stability?

H R Pota

Figure 1 below shows a feedback amplifier. The block A can be an op-amp with a very large value of A. The block f is normally an attenuation network to adjust for the desired closed-loop gain.
fbackSNR.gif
Figure 1: Feedback Amplifier
From Figure 1 we can see that,
So
=
A Se + N
=
 A Si
1 + A f
 -  A N f
1 + A f
 + N
=
 A Si
1 + A f
 +  N
1 + A f
(1)
In the above expression let's substitute N = 0 giving the closed-loop gain as:
 So
Si
 =  A
1 + A f
 .
Amplifiers with varying gains are obtained by adjusting the value of the attenuation of the feedback block f. For a closed-loop gain of 1, f » 1 and this gives an open-loop gain A f = A. But for a closed-loop gain of 10, f = [ 1/10] with the open-loop gain A f = [ A/10]. This means that the open-loop gain for unity closed-loop gain is ten times larger than for a closed-loop gain of 10. The higher the open-loop gain the lower is the gain margin, i.e., the margin against system becoming unstable is ten times lower for a closed-loop unity gain than for a a closed-loop gain of 10.
Please remember that Bode Plot or Nyquist Plot is plotted with open-loop frequency response to predict the closed-loop behaviour. Please also remember that higher the open-loop gain lower are the gain and phase margins.

File translated from TEX by TTH, version 3.40.
On 02 Nov 2004, 14:38.