Engineering Thevenin equivalent of an LED circuit

[Marshillboy]

Homework Statement

How would I go about determining the Thevenin equivalent of a simple circuit involving a battery and an LED? I suppose there could be a series resistor to prevent excess draw and burning out of the diode.

This question seems very odd since LEDs by definition don't involve a linear relationship between voltage and current.

Homework Equations

Thevenin's theorem

The Attempt at a Solution

Not sure how to go about starting this.

 

[rude man]

Homework Statement

How would I go about determining the Thevenin equivalent of a simple circuit involving a battery and an LED? I suppose there could be a series resistor to prevent excess draw and burning out of the diode.

This question seems very odd since LEDs by definition don't involve a linear relationship between voltage and current.

Homework Equations

Thevenin's theorem

The Attempt at a Solution

Not sure how to go about starting this.

The LED is a nonlinear component, as you say. There is no such thing as a Thevenin equivalent for a component or network including a nonlinear component.

However, if you consider the LED in its ON state, then you can model it as a resistor for small current variations. If the LED is modeled as a standard diode (which I'm not sure is an entirely valid thing to do), then

i = i₀e^qV/kT
so the variational impedance is R_var= 1/(∂i/∂V) and so
(∂i/∂V) = qi/kT or R_var = kT/qi
where
q = electronic charge
k = Boltzmann's constant
T = Kelvin temoperature.
At room temperature, kT/q ~ 26mV.