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I understand that (i) LED's have forward voltage drops (Vf) and (ii) that exceeding the dissipation wattage or max current can damage the device; thus one uses a series resistor to limit the current.

But, I find it strange that there is no maximum rating on any of the data sheet that I can find that might specify when some max input voltage would damage the LED.

While this may not be a valid way to think about it, I'm trying to think of an LED+resistor as a voltage divider, but that implies that the LED's "resistance" varies with voltage because it always (magically) drops the voltage to exactly what it needs. This (possibly incorrect) way of thinking leads me to the following questions:

a) Is it really the case that, even if I provide 500V DC to an LED with an adequate resistor to limit current to prevent exceeding it maximum power dissipation, that it will never crackle and pop, provided that I stay below its maximum current rating and power dissipation?

b) If so, is this because the "ground reference" for the LED is always immediately after the LED's cathode, and so the actual voltage across the device is only ever Vf?

c) And even so, there must be some tiny internal resistance that would become evident (or not?) at higher voltage as across the device, so why do manufacturers not specify a maximum input voltage?

d) Does this behavior hold true for all P-N junction devices?

What is the proper way to think about for forward voltage drops in a current loop containing LEDs or other components that exhibit constant forward voltage drops?

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Thinking of LEDs as a resistance is not correct. They are diodes, not resistors, so they have an I-V curve like a diode:

LED IV curve

Taken from: http://lednique.com/current-voltage-relationships/iv-curves/

So they draw almost no current at all until a threshold voltage and then they switch on and can draw very large current with little further change in voltage.

With that in mind:

a) Is it really the case that, even if I provide 500V DC to an LED with an adequate resistor to limit current to prevent exceeding it maximum power dissipation, that it will never crackle and pop, provided that I stay below its maximum current rating and power dissipation?

The voltage you apply to a diode is set by the current, so you cannot choose them independently. A diode with a forward voltage of 3V at 10mA will always have 3V applied to it when passing 10 mA (ignoring temperature which causes the voltage to shift). Similarly, if 10 mA is passing through, then the voltage across it is 3V.

If you take a 500 V supply and pick a very large resistor to limit current to 10 mA, you'll find that that you still get 3V across that LED and 497V across the (very hot) resistor.

b) If so, is this because the "ground reference" for the LED is always immediately after the LED's cathode, and so the actual voltage across the device is only ever Vf?

Voltage is defined between two points, in this case the two terminals of the LED. The choice of what you define to be ground doesn't matter in this case. If you put it on one side of the diode you have a 3V drop 3V to 0. If you put it on the other you have a 3V drop from 0 to -3V. Either way you still have a 3V drop.

c) And even so, there must be some tiny internal resistance that would become evident (or not?) at higher voltage as across the device, so why do manufacturers not specify a maximum input voltage?

The actual materials and wires of an LED do have some series resistance, so there is a modest internal resistance. This is evident if you look at the I-V curves above, where at higher currents the voltage increases slightly due to the IR drop. This is usually not significant.

d) Does this behavior hold true for all P-N junction devices?

More than that, it applies to all diodes, even Schottky diodes that don't have a P-N junction.

As for your original question about specifying a voltage, the practical reason is that it does not matter. You pick a safe current and a safe temperature. The voltage is therefore automatically safe.

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    \$\begingroup\$ A comment on the plot -- white and blue are typically the same voltage (3.0-3.6V at nominal current), and InGaN green and cyan are the same. AlGaAsP yellow are lower, say 1.8V, and GaP green is 2V. It's perplexing why they thought to draw yellow as the higher curve. \$\endgroup\$ Commented Jul 13 at 3:34

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