Question

Q 9. The open-loop gain of an amplifier is A = 65 , and the feedback factor is B = 0.5 . If the open-loop gain A changes by -18% and the feedback factor B changes by +17%, determine the closed-loop gain Af (25 points)

Answer 1

If the closed loop gain is Af, open loop gain is given by A and the feedback factor is $\beta$

Then the expression for closed loop gain is

Af 1+ BA

Given open loop gain is A=65 and feedback factor $\beta$ = 0.5, we can calculate closed loop gain as:

$A_{f } = \frac{65}{1+65*0.5}=1.9402$

Now,

Open loop gain changes by -18%

New open loop gain is

$A' = A-\frac{18A}{100} = 0.82A$

A = 53.3

Feedback factor changes by a factor of +17%

New feedback factor is

$\beta ' = \beta +\frac{17\beta }{100} = 1.17\beta$

$\beta ' = 0.585$

Therefore, new value of closed loop gain is

$A_{f }' = \frac{A'}{1+\beta' A'}$

$A_{f } = \frac{53.3}{1+53.3*0.585}=1.6562$