Consider an amplifier, shown in Fig.1, whose input-output relationship under small signal conditions given by,

(1)

Substituting in Eq.(1.1),

(2)

To solve for , represent the transfer function of the feedback amplifier by power series as,

(3)

and evaluate for , , ,

From Eq.(1.3),

(4)

Partially differentiation of Eq.(1.2) w.r.t gives,

(5)

From Eq.(1.3), if .

(6)

Differentiate Eq.(1.4) w.r.t and solving for yields,

(7)

Similarly solving for ,

(8)

Amplifier without Feedback

For an amplifier without feedback defined by Eq.[1], the output due to input is given by,

(9)

So the second and third order harmonic distortions for small signals for an amplifier without feedback are given by

(10)

(11)

Amplifier with Feedback

(12)

(13)