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 [tex]\alpha[/tex], where [tex]\alpha = \frac{\beta}{\beta+1}[/tex]. 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 [tex]I_c = \frac{\beta}{\beta+1}I_e[/tex] (Ie is the emitter current) I have:(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Common base amplifier current gain

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