# Is it possible to calculate a diode's V-I curve?

the other day I was confused because I din't get how an led has different voltage drop's depending on the resistance of a resistor and the voltage supplied by the battery. But then someone answered my question and told me that an led has a resistance as well. And that, that resistance changes depending on the heat generated by the LED and that creates a non linear curve.

So I was wondering... Is there a way to calculate this non-linear curve. And If there isn't then how does an app like "Every Circuit" calculates it?

Here are some screenshots I took too show y'all what I'm talking about.

And here is how that curve would look on a graph:

• You can model a diode characteristic with an exponential curve, and use that in your simulation. The simplest 'exponential curve' model requires you to specify the reverse saturation current: look at the Shockley diode equation here: en.wikipedia.org/wiki/Diode . (Oh, and BTW, a 'load line' is another thing). – Sredni Vashtar Sep 9 '16 at 2:22
• Thanks Sredni Vashtar :P.. wasn't you the one that answered my other question too lol... I would +1 ur answer but i dont have enough reputation lol... thx anyways! ill go look at it rn – CosnotraLF Sep 9 '16 at 2:28
• @SredniVashtar Go ahead and make that an answer? – user2943160 Sep 9 '16 at 2:43
• This older post deals with the process of mathematically modelling a LED and includes a procedure for generating a model. I'll post it for "related reading". electronics.stackexchange.com/a/9543/638 – W5VO Sep 9 '16 at 4:01

LEDs and light bulbs have an essentially different dependance on temperature.

In light bulbs the non-linearity of the V-I char is essentially due to the operating temperature: the hotter the filament, the harder it is for electrons to travel through madly-hot atoms, the higher the resistivity. The key point here is that the temperature rises because current is passing through the filament: you cannot have a functioning light bulb at ambient temperature, because if you somehow manage to cool it down, it won't emit visible light.

In LEDs, even though the temperature does have a primary role (because it affects the tail of the electron population distribution that will have enough energy to cross the band gap), you can cool the device at the temperature you like and it will still work as intended (actually better).

The corresponding resistance of a LED is better seen as the (local, i.e. in a neighbor of your operating point) slope of the V-I characteristic supplied to you by the manufacturer.

You can model a diode characteristic with an exponential curve, and use that in your simulation. The simplest 'exponential curve' model requires you to specify the reverse saturation current for the device.

Look at the Shockley diode equation here: en.wikipedia.org/wiki/Diode.

$I=I_{\mathrm {S} }\left(e^{\frac {V_{\text{D}}}{nV_{\text{T}}}}-1\right)$

(Here $V_T$ is the thermal voltage that depends on temperature; its value at ambient temperature - about 300 K - is around 25-26 mV; $n$ is just a factor that will help you tune your curve to make it more similar to the actual device's.)

The curve is just an exponential translated downward by an amount corresponding to the inverse saturation current

Image taken from here.

Note that the Shockley equation does not model the breakdown behavior, that is that other exponential runoff that happens for big negative voltages. More elaborate models (such as those used by SPICE) can do that and much more, but this is beyond the scope of this answer. You can read more on this page from Wikipedia.

• Wow 😶 U are so smart bro 😂😂... Keep up the good work! – CosnotraLF Sep 9 '16 at 4:10
• Lol I'm sorry... But I have another question for u... How do u calculate Is(Saturation current) and Vt? – CosnotraLF Sep 9 '16 at 20:22
• Vt is just kT / q and, as stated above, is about 26 mV at room temperature. For Is, well... you need some solid state physics: en.wikipedia.org/wiki/Shockley_diode_equation . You can consider that a parameter given by the manufacturer. – Sredni Vashtar Sep 9 '16 at 20:29
• Oh so on the datasheet im looking at it right now and says as follows... Ir(reverse current) is 10uA(micro-amps) When Vr = 5... is that the saturation current...? – CosnotraLF Sep 9 '16 at 21:16