Q.Derive an expression for output impedance of an amplifier with negative feedback.

The output impedance is found by shorting the input, applying a test voltage $V_o$ at the output, and using KVL around the output loop. …

[!TLDR]

$Z_{of} = Z_o/(1+A\beta)$: voltage series negative feedback decreases the output impedance by the factor $(1+A\beta)$.

A low output impedance is desirable so that the amplifier can deliver voltage (or power) to the load without much loss. Voltage series negative feedback achieves this. To find the output impedance we short the input ($V_s = 0$) and apply a hypothetical voltage source $V_o$ at the output, which drives a current $I_o$ (equivalent circuit, Fig. 4.4.3). Here $Z_o$ is the amplifier's internal output impedance and $A V_i$ is the dependent source.

Step 1 — definition.

Step 2 — KVL around the output loop.

Step 3 — input with source shorted. With $V_s = 0$, the net input is just the (opposing) feedback voltage:

Step 4 — substitute into (2).

Collecting the $V_o$ terms, …