Question 8.12: The input and output voltages of an amplifier are 2 mV and 2...

The input and output voltages of an amplifier are 2 mV and 2V, respectively. The input and output impedances of the amplifier without feedback is 5 KΩ and 100 Ω, respectively. The closed-loop gain of the amplifier with negative feedback is 100. Calculate the input and output impedances with feedback.

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Z_{in} = 5 KΩ
Z_{0}= 100 Ω
A_{f} = 100

A=\frac{V_{0}}{V_{i}}=\frac{2}{2×10^{-3}}=1,000

We know,

A_{f}=\frac{A}{1+βA}

Substituting values,

100=\frac{1,000}{1+β×1,000}

or,                                1+1,000 β= 10

or,                                β=\frac{9}{1,000}=0.009

Z_{in} with feedback = (1+βA) Z_{in} = (1+0.009 ×1,000) ×5 KΩ
= 50 KΩ

Z_{0} with feedback =\frac{Z_{0} }{1+βA}=\frac{100}{(1+0.09 ×1,000)}=10  Ω.

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