Recirculation Current in an Inductor

[EigenFunctions]

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:

Vdiode=Vinductor+Vresistor

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?

Thanks,
EigenFunctions

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.

 

[marcusl]

Solve numerically the way Spice would. Also check your signs. Shouldn't all terms in your ODE be positive?

 

[EigenFunctions]

Inductor is energy source re: Recirculation Current in an Inductor

Solve numerically the way Spice would. Also check your signs. Shouldn't all terms in your ODE be positive?

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.

Thanks,
EigenFunctions