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Re: How to set up a diff equation for circuit with a diode?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62815] Re: How to set up a diff equation for circuit with a diode?
*From*: "siliconmike" <siliconmike at yahoo.com>
*Date*: Tue, 6 Dec 2005 00:03:11 -0500 (EST)
*References*: <dn0v2m$8g2$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
I figured out this. Please comment:
During forward bias, voltage across diode = 0.026 ln [10^12 I + 1] <-
from diode equation
During reverse bias, diode can be modelled as a large resistor, eg
10^12 ohms. voltage = I * R_Large
So the differential equation looks like:
V = IR + LI' + 0.026 ln[ 10^12 Abs[I] + 1] * U[I] + I * R_Large U[-I]
where U is the Unit Step function (can be modelled as a continuous
function using tanh).
L and R are inductance and resistance in series with a source V(t)
I modelled U as U[I] = (1+ Tanh[IB])/2 where B is a very large number,
eg 10^12
Works great in mathematica using NDSolve.
Mike
siliconmike wrote:
> I'm kind of curious how to set up a nonlinear differential equation and
> then solve it using NDSolve in case of the following setup:
>
> Battery V in series with a diode, R and L.
>
> To simplify, we may assume that diode is a pure conducting device in
> forward direction and pure blocking device in the reverse direction.
>
> Now how to set up a differential equation for the current I(t), that is
> solvable using NDSolve?
>
> Thanks
> Mike
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