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218 Chapter 12. Ampliﬁers and Oscillators

xs + xi =xs-xf Amplifier xo =Axi
_ A
xf =βxo

Feedback
circuit
β

Figure 12.21: Block diagram illustrating the principle of feedback

Thus the actual input to the ampliﬁer becomes
x i = x s − x f = x s − βx ◦ in case of negative feedback and
x i = x s + x f = x s + βx ◦ in case of positive feedback.
Consider a negative feedback case. The actual input to the ampli-
ﬁer,
x i = x s − βx ◦ (12.12)
We have ampliﬁer gain,

x ◦
A = (12.13)
x i

(12.14)
Ax i = x o
Substituting equation 12.12 in equation 12.14, we get,

A(x s − βx o ) = x o (12.15)
Rearranging,
(1 + Aβ)x o = Ax s (12.16)

Or
x ◦ A
= (12.17)
x s 1 + Aβ
x ◦ /x s is the gain of the ampliﬁer with feedback which is usually
given the symbol G. Therefore the gain with negative feedback is ex-
pressed as,

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