I was wondering if anyone could tell me the use of the inductor in the follow circuit? I get that it is a common emitter with feedback resistor (R2) which reduces the effect of a different transistor gain and temperature, etc, but I am not sure about the inductor.
A inductor can be used as a load impedance in high frequency circuits to provide a high stage gain since its impedance can be much higher at the signal frequency than a collector resistor for a given transistor bias current.
You just make the inductance high enough for the inductive impedance at the signal frequency to get the gain you desire.
The gain limit is generally determined by the load impedance connected to the transistor collector, so the limits effectively how high you can go.
Thus you make the inductance no higher than the limit imposed by the load to minimize the size of the inductor.