# BJT Early Model Analysis

1. Mar 17, 2012

### Trentonx

1. The problem statement, all variables and given/known data
Working with BJT analysis, and varying models for the analysis.
Prove $r_{0}=\frac{V_{a} + V_{CE}}{I_{C}}$, where $r_{0}$ is the resistance for the Early model. I haven't been able to find a circuit or much of anything about this, let alone proving it.

2. Relevant equations

$i_{C} = I_{s}e^{\frac{V_{BE}}{V_{A}}} (1+\frac{V_{CE}}{V_{A}})$
$r_{0} = (\frac{\delta i_{C}}{\delta v_{CE}})$

3. The attempt at a solution
I did the partial derivative (that is what Eq2 mean right?) of $i_C$, and that gives me
$i^{'}_{C}=\frac{I_{s}e^{\frac{V_{BE}}{V_{A}}}}{V_{A}}$, but this doesn't simplify in anyway, and it's $i^{'}_{C}$, not just $i_{C}$. I'm guessing this is the wrong equation, but it's what we've been given.