I even don't know how this form can be induced. I know that I have to study more but I really want to know about this form please help (please ignore the actual value. I just want to know about formula)
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You can derive this from the Shockley equation:
*Vbe = Vt(ln(Ic/Is)) so at two different currents Ic and Ic0 we have
\$V_{BE} - V_{BE0} \$ = \$V_T (\ln(I_C/I_S) - \ln(I_{C0}/I_S))\$ = \$V_T \cdot \ln (I_C/I_{C0})\$
At room temperature Vt = kT/q is about 25mV.
By using two currents, the saturation current Is cancels out, so you can predict the behavior independent of the device parameters.
* We can ignore the factor of 1 in the Shockley equation at reasonable currents >> Is.

Spehro Pefhany
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