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Recirculation Current in an Inductor

  1. Dec 6, 2006 #1
    I am trying to derive an equation for a simple inductive circuit which is the serial connection of an inductor (L), a resistor (R) and a Diode (D). The initial condition is a current flowing (Izero). Using Kirchhoff's law, the basic equation is:


    The inductor is L*di/dt, the resistor is i*R and a simple model for a diode is n*VT*ln(i/Is+1) where n, VT and Is are constants. So the differential equation becomes:

    L*di/dt + i*R = n*VT*ln(i/Is+1)

    Putting it in standard form:

    di/dt + [i*R/L - (n*VT/L)*ln((i/Is)+1)] = 0

    I don't know how to deal with the expression in the square brackets.

    Any suggestions?


    PS - the diode function comes from Idiode(v) = Is*(exp(v/(n*VT)-1) as used in spice. Later, I will sum in an additional term for a diodes ohmic resistance.

    Attached Files:

  2. jcsd
  3. Dec 6, 2006 #2


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    Solve numerically the way Spice would. Also check your signs. Shouldn't all terms in your ODE be positive?
  4. Dec 6, 2006 #3
    Inductor is energy source re: Recirculation Current in an Inductor

    You are correct, since the energy is stored in the inductor, it should be (see the updated attachment):

    Vinductor = Vdiode + Vresistor

    It seems like there should be a way to solve it, maybe with a Taylor series or something like that.


    Attached Files:

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