There is an amplifier of 60dB voltage gain and output impedance $Z_o$=12k$\Omega$. It is required to modify its output impedance to 600$\Omega$ by applying negative feedback. Calculate the value of the feedback factor. Also find the percentage change in the overall gain, for 10% change in the gain of the internal amplifier.

There is an amplifier of 60dB voltage gain and output impedance $Zo$=12k$Ω$. It is required to modify its

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Z_o

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[!TLDR]

To bring $Z_o=12$ kΩ down to 600 Ω needs $\beta=0.019$ (1.9%), and then a 10% internal gain change appears as only 0.5% at the output.

Convert the gain: $60\text{ dB}\Rightarrow A=1000$ . Voltage-series negative feedback reduces output impedance by $(1+A\beta)$ :

Z_{of} = \dfrac{Z_o}{1+A\beta} \;\Rightarrow\; 1+A\beta = \dfrac{Z_o}{Z_{of}} = \dfrac{12000}{600} = 20

Hence $A\beta = 19$ and, with $A=1000$ ,

$\beta = \dfrac{19}{1000} = 0.019 = 1.9\%$ …