bjt gain help

Discussion in 'Homework Help' started by MHillis, Nov 1, 2014.

  1. MHillis

    Thread Starter New Member

    Oct 25, 2014
    6
    0
    So this circuit is supposed to model a bipolar junction transistor. I am a bit stuck with solving for the ratio listed because V0 tends to go away in my attempts.
    1. I start by writing the current through the diode depending entirely on the voltage supplied by Vs.
    2. With IE in terms of Vs I can multiply with alpha and RL to get the voltage across the resistor.
    3.Then I write Vs and VL in terms of their DC and AC components. Then I get that because V0 << VT I can treat that exp(VoCos(wt)/VT)=1 and it drops away.

    What I would expect for this circuit is for the ratio between V0 and V2 to be equal to the ratio between vB and v1. The intent of the circuit I imagine would be to provide a gain to a small signal (here that is the AC term) while the DC term maintains the diode's forward bias. Is there a better way to approach this problem?
    Screenshot (2).png
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,715
    4,788
    You are making too much of an approximation. You are assuming the exponential term is a constant. What you need to do is keep the constant and the linear term.
     
  3. blah2222

    Well-Known Member

    May 3, 2010
    553
    33
    By telling you that V0 << Vt (thermal voltage ~= 26mVdc @ room temp.), this ends up being a simple small-signal theory problem.

    The input signal contains what looks like a DC term Vb and a small-signal V0cos(wt). You can approximate a linear relationship between the current/voltage through/across the diode by assuming that V0 is a very small AC signal wiggling around a DC signal Vb.

    Given the equation of the diode, you can differentiate to find the slope, to determine how much the current will fluctuate as a result of the voltage perturbation.

    You can drop the '-1' term for the differentiation to simplify the result as it is insignificant.
     
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