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3.5.4: Common Emitter Models

  • Page ID
    89964
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    From terminal B, a current I_B flows into the anode end of a diode that is oriented with its cathode end pointing down. The vertical wire leading out of its cathode connects to a horizontal wire with both ends as terminals labeled E. A current I_C flows in through a terminal C, and passes through a downwards-facing current source of beta I_B that also leads to the wire EE.
    Figure \(\PageIndex{1}\): Discrete model for the common emitter configuration

    For the base, however, only a small fraction of the current that goes through this "diode" actually goes in through the base, the rest is coming in through the collector. Thus we have to make a couple of changes. \[\begin{array}{l} I_{C} &= \alpha I_{E} \\ &= \alpha I_{\text{sat}} \left( e^{\frac{q V_{\text{BE}}}{kT}} - 1 \right) \end{array} \nonumber \]

    \[\begin{array}{l} I_{B} &= \frac{I_{C}}{\beta} \\ &= \frac{\alpha I_{\text{sat}}}{\beta} \left( e^{\frac{q V_{\text{BE}}}{kT}} - 1 \right) \end{array} \nonumber \]

    So the operational equation for the diode in the base circuit still is the usual exponential function of \(V_{\text{BE}}\), except that it now has a saturation current of \(\frac{\alpha I_{\text{sat}}}{\beta}\) instead of just \(I_{\text{sat}}\).

    In principle you could put this model into a circuit, and analyze it to find all of the necessary voltages and currents. However, this would not be very convenient. The base-emitter junction is connected by a diode, which as we know, has a very nonlinear \(I \text{-} V\) relationship. It would be nice if we could come up with a linear model which, at least over some limited range of inputs, we could use with confidence.


    This page titled 3.5.4: Common Emitter Models is shared under a CC BY-NC-SA 1.0 license and was authored, remixed, and/or curated by Bill Wilson via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.