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BJT Early Model Analysis

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Working with BJT analysis, and varying models for the analysis.
    Prove [itex]r_{0}=\frac{V_{a} + V_{CE}}{I_{C}}[/itex], where [itex]r_{0}[/itex] 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

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

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