KCC's quizzes AQQ235 about a bipolar common emitter amplifier - a kind proposal from our colleague Martin Walker

First let's assume by "gain" you mean small signal voltage gain. In that case for the common emitter configuration without an emitter degeneration resistor the gain Av is gm * Rc (a dimensionless ratio) . For a BJT device we know that gm = Ic/Vt (where Vt is the thermal voltage which is about 26 mV at room temperature). We are also given that half of Vcc or 3 V is dropped across Rc so Ic = 3/Rc. Using these equations and solving for Av we get 3V/26mV or about 115. It turns out that the absolute value of Rc drops out in the calculation and all we need to know is that Rb1 and Rb2 are such that the voltage at the collector is as stated in the problem statement.

-DM

Thanks Doug! Yes, the "gain" mentioned here is of course related to the small signal gain! Your reasoning conducting to the gain estimation is brillant! We will see later how other will describe this circuit! May be some comment from the original author...

That circuit / question is a classic New College candidate interview question going back to when I interviewed 46 years ago here in Wilmington. It gets to the heart of if the student was paying attention in Electronics I class. They always get bogged down in large signal vs small signal models and they insist that the resistor values must be known and what's beta (as other respondents here seem to have) etc. Beta (and the base current) has nothing to do with small signal analysis. Yes, the small signal gain varies with DC operating point Ic and of course temperature due to Vt = kT/q.

That circuit / question is a classic New College candidate interview question going back to when I interviewed 46 years ago here in Wilmington. It gets to the heart of if the student was paying attention in Electronics I class. They always get bogged down in large signal vs small signal models and they insist that the resistor values must be known and what's beta (as other respondents here seem to have) etc. Beta (and the base current) has nothing to do with small signal analysis. Yes, the small signal gain varies with DC operating point Ic and of course temperature due to Vt = kT/q.