Electronic – Why is Ib proporional to Ic in a bipolar transistor

bjttransistors

I am really puzzled why the collector current is considered proportional to the base current in a bipolar NPN transitor, ie

$$ I_c = \beta I_b $$

Where I_c is the collector current, I_b the base current and below I_e the emitter current. I can't find any explanation in the books, it seems to be just stated as an empirical result. Is that how I should treat it, just an empirical result?

I know that it can be derived by assuming that the proportion of (conventional) current that enters the emitter from the base is a constant fraction of the collector current, ie

$$ I_c = \alpha I_e $$ and that $$I_b + I_e = I_c $$

but that begs the question why is the fraction of base current entering the emitter stream always assumed to be a fixed proportion?

Best Answer

The collector current is only approximately proportional to the base current. The rate varies with collector current and can vary wildly between individual units of the same type.

It is just that both the collector current and the base current are exponential functions of the base voltage.

See BJT Large signal model