Derive the expression for the gain of an amplifier with negative feedb

1.	Derive the expression for the gain of an amplifier with negative feedback.
Answer» The open loop gain of an amplifier is β = \(\frac{V_f}{V_o}\), V_f = βV_o V_i = V_s - V_f V_i = V_s - βV_o V_i= V_s - β.AV_i V_i + β AV_i = V_s V_i(1 + Aβ) = V_s A_f = \(\frac{V_o}{V_s}\) = \(\frac{V_o}{V_i(1+A\beta)}\) A_f = \(\frac{A}{1+A\beta}\)

Derive the expression for the gain of an amplifier with negative feedback.

Answer»

The open loop gain of an amplifier is

β = \(\frac{V_f}{V_o}\), V_f = βV_o

V_i = V_s - V_f

V_i = V_s - βV_o

V_i= V_s - β.AV_i

V_i + β AV_i = V_s

V_i(1 + Aβ) = V_s

A_f = \(\frac{V_o}{V_s}\)

= \(\frac{V_o}{V_i(1+A\beta)}\)

A_f = \(\frac{A}{1+A\beta}\)