Common base amplifier current gain

[bitrex]

Hi folks - I'm trying to follow along in a textbook the derivation of the common-base current gain equation, and I'm having a bit of trouble. The common base current gain is supposed to be approximately $$\alpha$$, where $$\alpha = \frac{\beta}{\beta+1}$$. Doing a nodal analysis with the signal applied to the emitter through the intrinsic emitter resistance, the base grounded, and the collector current equal to $$I_c = \frac{\beta}{\beta+1}I_e$$ (Ie is the emitter current) I have:

$$\frac{I_i}{I_o} = \frac{\frac{V_in}{r_e}} {\frac{\beta}{\beta+1}{\frac{V_in}{r_e}}}} = \frac{\beta+1}{\beta}$$. Unfortunately the correct answer is obviously $$\alpha = \frac{\beta}{\beta+1}$$, which the equation I have doesn't evaluate to. Can anyone see where I went wrong?

 

[bitrex]

Nevermind, I see it now that I typed it up! It should of course be $$\frac{I_o}{I_i}$$, not the other way around.

 

[Bob S]

The real advantage in common base bipolar transistor RF amplifiers is the high voltage gain from a low impedance source.