Question

If the open-loop gain decreases due to the frequency or the effects of the system aging, providing that βG is still very large, then the overall system gain ______ (Where G is Open loop voltage gain and β is the feedback fraction)
1. does not change very much
2. increases very much
3. decreases very much
4. fluctuates accordingly inputs

Answer 1

Correct Answer - Option 1 : does not change very much

Concept:

Negative feedback system:

The transfer function of the negative feedback closed-loop control system is given by

TF = G/ (1 + βG)

Where,

G = open-loop gain

β = feedback factor or gain

Explanation:

Given that,

The open-loop gain is decreased due to the frequency or the effects of the system aging.

But the βG is still large

Then,

The overall gain will be

TF = (G↓) / (1 + βG↓)

As βG is still very large we can neglect 1 (1 << βG)

⇒ TF or Overall gain ≈  G / βG ≈ 1\β

Hence, if we neglect 1 in the denominator then there is no change in the gain even though if there is a change in open-loop gain, but if we consider 1 also then there will be a slight change(decreases) in the overall gain not much.