The smallest resistance for current splitting sort of thing ?

This is a theoretical question so I am going to try to put this in general terms.

Say one has a constant current source of 50mA connected to two LED string connected in parallel. To ensure that one string does not hog all the current we put an 'identical' resistor on each string.

What determines the smallest resistance that can be used?

Again I do not have an application for this. It is just a question that has been rolling around upstairs.

3v0 said:

Say one has a constant current source of 50mA connected to two LED string connected in parallel. To ensure that one string does not hog all the current we put an 'identical' resistor on each string.

What determines the smallest resistance that can be used?

Click to expand...

The difference in the forward voltage of the LEDs and the amount of different current (resulting in different brightness) between the two strings of LEDs.

It may be that the needed resistors are larger than one would need with a constant voltage supply so it would be a bad idea.

Generally, you would split the 50 mA in half and use Vf to calculate the resistors . R= Vf/25mA each.

Vf varies in general, but bigger Vf variations are by color. Then there are eye sensitivities etc. This is to just say that if the colors of the LED's are different, you have other issues to worry about.

I have one white LED with a forward voltage of 3.14V and another white LED with a forward voltage of 3.21V. Separately or in parallel they both produce the same brightness.

AG. Agreed.

But take different colors and the world changes. See: https://wolfcrow.com/blog/notes-by-dr-optoglass-the-human-eye-part-iii/

Obviously a large R makes them insensitive to variations in ESR. The question is how small can you make it to avoid Thermal runaway.
The answer depends on how well matched they are to begin with and the solution is to add a small fixed R slightly greater than this variation in ESR.

I have used this theorem for many years successfully. It works. The thermal-resistive sensitivity or Thermal Resistance must be lower than the electrical resistive sensitivity or ESR, the ratio must be < 1. This is to say there is a direct relationship between the units of Degrees (C) per Watt and ESR Ohms with Watts per Amp

Understand that ESR occurs with any Diode that saturates and gets lower with higher power diodes.
The product of ESR * Pd turns out to be fairly constant for each chemistry of diodes ( Si, Ge, AlGaAs etc)

Also understand that Vf vs Current,If is predictable at 25'C but Tj junction temp. always rises due to Rja, Thermal resistance, which results in a drop in voltage. As the Diode gets hot, Vf may drop a few hundred mV due to this thermometer effect adding a smaller fixed R in series balances the LEDs or makes them more matched.

This applies to both a CC source and a CV source not exceeding the total parallel rated current of all devices.

Let me try to explain.
There is a passive loop gain of positive feedback which if it exceeds 1 results in Thermal Runaway and destructive current hogging of one device in parallel with others. The runaway effect occurs when the temperature sensitive voltage drops as it draws more power which results in a lower voltage until it takes all of the current in the parallel load. To prevent this requires the improved thermal sensitivity or reduced electrical sensitivity by having a larger fixed ESR in series than the other devices. This limits the current enough to prevent thermal runaway.

Without the long proof, I have found the optimal resistance to put add a series R = ESR of the LED. This exceeds the min ESR and increases the forward voltage slightly but reduces the variation in Vf by 50% for voltage vs current.

The sensitivity of power to voltage is called the Shockly Effect and is a negative tempearture coefficient based on the size of the device or Thermal Resistance which results in delta V/T sensitivity or gain. Larger LEDs have lower Thermal Resistance and ESR so this ratio is controlled by adding a small series resistance. Actually the minimum amount is closer to the 3 sigma variation of ESR of all devices used, which normally is quite tight from the same supplier and same batch can be near 1% rather than typical 50~150% variation of ESR at a fixed current.

I have also found that single LED's with a power rating of Pd have an ESR ~= 1 Watt-Ohm/Pd so that a 3W LED is approx 0.33 Ohm ESR and Vf can be predicted at various power levels and a 100mW LED is 10 Ohms. This is an industry average and better wafer suppliers will have lower ESR to make better LED's. I have also noted high efficacy LED's will also tend to have the relatively low ESR, by comparison.

The eye has a poor memory for brightness as it constant adapts to intensity and glare so unless it is modulated, one cannot remember a variation difference of < 50%

Tony,

Is it possible to determine the ESR of a given LED by measurement, say at two values of If?

Yes of course. Preferably those 2 levels of current are near the expected operating levels ,
but it is still possible to measure threshold voltage Vth at < 1% If(max) and then measure Vf at If (max) to make an approximation of ESR if one does it quickly, then estimate thermal rise and Shockley effect of drop in drop in voltage for steady state.


ESR follows Ohm's Law for small changes in current when saturated, meaning that as power dissipation does not change drastically, it is fairly accurate.
There are many ways to do it, including reading the VI curves on the product specs.

There are many methods. Since tolerance is high, use good estimates from measurements.

Be sure that when changing the current, it does not change voltage due to thermal shift, so the measurement of must be relatively quick.

ESR=delta V/delta I

Below is a new high power Cree array of 4 LEDs either 6 or 12V option, 130 lumen / W
Note the slope is ESR
so as slope with current rises, ESR drops a bit


They often spec Vf at @If @25'C as the test is done in milliseconds with a pulse.

I have a very cheap Chinese flashlight (torch for Brits) with 24 white LEDs in parallel. There is NO current-limiting resistor, its current is limited by its three AAA battery cells in series. All the LEDs appear to have the same brightness and none have burned out yet. Did somebody in the factory measure and sort the LEDs so their forward voltages are all the same?

They dont sort LED's in China by hand.

Every device is 100% tested and sorted into bins by machine.

There may be hundreds of factory bins and only a dozens available to the customer including color, voltage and intensity variations.

Devices from the same batch will often have a maximum deviation of a couple millivolts @20mA for all working devices from the same wafer.

This means no external series resistor is needed by supplier selection as the wire bond resistance is adequate.
But when you get to higher power > 0.1W with significant junction rise, then Shockley effects become significant as do voltage variations from ESR from different batches.