Electronic – How to determine forward voltage for overdriven LEDs

No, it's not correct, if only because neither the LED nor the power supply are 3.3V. The power supply may be 3.28V, and the LED voltage 3.32V, and then the simple calculation for the series resistor doesn't hold anymore.

The model of a LED is not just a constant voltage drop, but rather a constant voltage in series with a resistor, the internal resistance. Since I don't have the data for your LED let's look at this characteristic for another LED, the Kingbright KP-2012EC LED:

For currents higher than 10mA the curve is straight, and the slope is the inverse of the internal resistance. At 20mA the forward voltage is 2V, at 10mA this is 1.95V. Then the internal resistance is

\$R_{INT} = \dfrac{V_1 - V_2}{I_1 - I_2} = \dfrac{2V - 1.95V}{20mA - 10mA} = 5\Omega\$.

The intrinsic voltage is

\$V_{INT} = V_1 - I_1 \times R_{INT} = 2V - 20mA \times 5\Omega = 1.9V.\$

Suppose we have a power supply of 2V, then the problem looks a bit like the original, where we had 3.3V for both supply and LED. If we would connect the LED through a 0\$\Omega\$ resistor (both voltages are equal after all!) we get a LED current of 20mA. If the power supply voltage would change to 2.05V, just a 50mV rise, then the LED current would be

\$ I_{LED} = \dfrac{2.05V - 1.9V}{5\Omega} = 30mA.\$

So a small change in voltage will result in a large change in current. This shows in the steepness of the graph, and the low internal resistance. That's why you need an external resistance which is much higher, so that we have the current better under control. Of course, a voltage drop of 10mV over, say, 100\$\Omega\$ gives only 100\$\mu\$A, which will be hardly visible. Therefore also a higher voltage difference is required.

You always need a sufficiently large voltage drop over the resistor to have a more or less constant LED current.

You seem to have some basic misconceptions.

First, the voltage spec of LEDs doesn't tell you the fixed voltage you should run them at. It tells you the voltage range you will get when running the LED at some current. LEDs are diodes, so at the normal operating point the voltage varies little as a function of current. Flip this around and you see that the current will vary a lot with a small change in voltage. LEDs are so sensitive to voltage variations, and the exact voltage to achieve full brightness can vary enough, so that you can't usefully drive a LED with a fixed voltage because the current will be too unpredictable. Think of these devices as being driven with specified current, and the voltage just comes along for the ride. The voltage spec is there only to give you some idea what that voltage will be.

Second, when you exceed maximum specs on any device, it is grossly unfair to blame its resulting failure on bad manufacturing. The point of a spec is to tell you what you can do to the device so that it will continue to meet its other specs and not fail.

You left out the all-important information of what size and type of LEDs these are and the actual voltage and current you are driving them with. If they are losing brightness and changing color from only 24 hours of use, then you are overdriving them. That is exactly the kind of failures to be expected from moderate overdriving.

If you have typical T1-3/4 LEDs, then assume they are rated for 20 mA. Most discrete LEDs are rated for 20 mA, some more. Some very small suface mount LEDs are rated for less. The voltage at full rated current is usually a bit over 3 V for blue, about 2.1 V for green, and around 1.8 V for red. Again, that is not a spec to drive the LED at, but what you are likely to end up at when driven properly at full brightness.

LEDs intended for lighting are a different matter. These come in more expensive packages designed to allow for heat removal. As a result, they can be driven harder for the same size. There are many proprietary packages, and units that look similar can actually be quite different. Some can take 100s of mA or more if kept at the right temperature, but you really need a datasheet to know how to use them effectively but still not damage them. These kind of high performance LEDs are tuned closer to the edge with less wiggle room past the specs.