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The open loop gain (Gd) of an amplifier is normally very large. In case there ar

ID: 1845784 • Letter: T

Question

The open loop gain (Gd) of an amplifier is normally very large. In case there are modifying inputs, this open loop gain can change significantly. On the other hand, the feedback component consumes less power and it is less subjected to the interference from the modifying inputs. Let's start by assuming open loop gain Gd= 104, feedback factor Hf= 0.1. Calculate the close loop gain A = y/xd in Fig. 2. Now if Gd is reduced by 10%, what is the corresponding decrease in A? More formally, desensitivity factor is defined as: find function f explicitly.

Explanation / Answer

Close loop Gain

= Gd/(1 + Gd*Hf)

= 10000/(1 + 1000)

= 9.99

If Gd is reduced by 10%, Gd = 0.9(Actual Gd)

Thus, New A = 9000/(1 + 900) = 9.988

Now, A = G/(1 + GH)

dA/dG = 1/(1+GH)^2

Desensitivity

= dA/dG * G/A

= 1/(1+GH)^2 * (1+GH)/

= 1/(1+GH)

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