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:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Recirculation Current in an Inductor

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