I'm confused.
In different sources sometimes I find the equation
\$ I_C = I_S\cdot\left(e^{\frac{U_{BE}}{U_T}}-1\right) \$
or like wikipedia
\$ I_C = I_S\cdot e^{\frac{U_{BE}}{U_T}} \$
Can someone explain which equation is used in which case? Or is it just a simplification?
Thank you
Kind regards Thomas
Under FORWARD bias case, since the exponential term dominates, you take \$I_C=I_S\cdot e^{\frac{U_{BE}}{U_T}}\$ neglecting reverse current.
However at lower values of UB, its better to take the first expression as both are comparable to some extent.
Under reverse bias you can even approximate the first equation to :
\$I_C = -I_S\$ since the exponential term is negligible(example: \$e^{\frac{-5}{0.026}} \approx 0\$.
In short,
\$I_C=I_S\cdot \left(e^{\frac{U_{BE}}{U_T}}-1\right)\$ (lower positive/negative values of UB) .
\$I_C=I_S\cdot e^{\frac{U_{BE}}{U_T}}\$ (high positive values of UB).
\$I_C=I_S\cdot (−1)\$ (high negative values of UB).
