# LED modeling with Shockley diode equation

I'm working on a project where I need to model the voltage/current relationship of various LEDs. I'm wondering what values I would need to use for the saturation current in the Shockley diode equation for various colors - I know the proper thing to do would be to take the LEDs in question and measure the forward voltage at various currents and fit a curve, but at the moment for my rough calculations I don't need that level of accuracy. Anyone have any "ballpark figures"?

• Related Question: electronics.stackexchange.com/q/9510/638 – W5VO May 10 '11 at 21:36
• Thanks - I didn't know about the "emission coefficient." edit: I think perhaps what I'll do is find a generic LED spice model of a particular color and use the values I find there as a first approximation for my calculations. – Bitrex May 10 '11 at 21:45

There's a few things that you can do:

1. Find a SPICE model for your particular LED. SPICE uses the Shockley diode model, so you can just pull Is and N from the model card.
2. Find a datasheet for the LED in question (with a graph indicating a voltage-current relationship) and model only Is and N, which is actually not very difficult. See my answer on "How to model a LED" for most of what you need to get started. Only solving for Is and N will work well until you start trying to use the equation for peak currents (high current, low duty cycle).
3. Take the forward threshold voltage of the diode, and solve the diode equation for Is. Guess about 1.8-2.0 for N and just be satisfied with the result. It won't track reality very well, but it will behave like a diode.
4. Take the values for this red LED and hope that they mostly work for your LED.

IS=1a RS=3.3 N=1.8

Keep in mind that different color LEDs have different forward voltage drops, and that even diodes with the same color can have different voltages. Also, the diode equation neglects series resistance, which can have a significant effect at high currents. It is up to you to understand your accuracy requirements, and to know the limitations of your calculations.