They say for Common-Base Amplifier, the short circuit current gain is found by using T-Model for High Frequencies and is given by :

$\Large \color{green}{|A_{ib}| = \frac{\alpha}{\sqrt{1 + (\frac{f}{f_{\alpha}})^2}}}$

How can I derive it?

Question

They say for Common-Base Amplifier, the short circuit current gain is found by using T-Model for High Frequencies and is given by :

$\Large \color{green}{|A_{ib}| = \frac{\alpha}{\sqrt{1 + (\frac{f}{f_{\alpha}})^2}}}$

How can I derive it?

kenljw · Answer

First the low frequency current gain from emitter to collector is
alpha = beta/(beta + 1)
f sub alpha is the 3 dB point current gain frequency, giving a complex number with 6 dB roll off per octave
The denominator given adjust the magnitude to current gain vs frequency, you can also derive a phase shift equation

anonymous · Answer

I want to derive the said equation buddy..

kenljw · Answer

for fa at gain 3db down low frequency. f is frequency
gain proportions to fa/(fa + jf)   note at f=fa is 3dB point 1/squart(2)
magnitude of gain is sqrt{fa^2/(fa^2 + f^2) = (1/sqrt[1 + (f/fa)^2}

anonymous · Answer

@KenLJW , I appreciate you that you are replying and helping me, but I need to know more on this, so I hope we can talk when we both will be online.. I am not getting you properly.

Any link or site you want to give, that is also appreciated.. :)

kenljw · Answer

I assume you haven't been introduced to Bode plots which gives and an approximation of Gain vs frequency.  Generally all gains have a low frequency value and as frequency increases a breaking point, 3 dB point, at which the magnitude of gain changes by factor 1/sqrt[2}.  At this point the gain begins to show a complex nature, due to phase shift in device, and subsequent magnitude of gain with changes in frequency is proportional to the magnitude of the complex Gain.

anonymous · Answer

Is there any way to prove what you are saying with some nice derivation?? Using High Frequency T-Model for Common Base Transistor??

kenljw · Answer

Generally I'm use common emitter configuration in which the low frequency model has no capacitance.  For the high frequency model there's two added capacitances,  Cpi the capacitance between base and emitter, and Cmu the capacitance between collector and base.  It's these two capacitance that cause the 6 dB/octave roll off of the gain between emitter and collector.  I suspect you can add these capacitances to your supposed T model to get the result your looking for.