Electrical – How to calculate current(I) when I don’t know voltage drop

All LEDs can be modelled as zener diodes with a colour/substrate specific forward voltage Vf and a series resistive Rs, where they combine both to give the Vf at rated current. Rs tends to be small so you can neglect it for approximations of adding current limiting series resistors. (see below)

Therefore the current is non-linear and proportional to the voltage difference between the supply and the Vf drop at desired current.

Batteries with low voltage variation are ideal such as Lithium primary cells. Most White flashlights using 3V per LED use these without series resistors as the Li cell is also 3V. However they may be specify a sorted bin of LED's to achieve this.

My Rule of Thumb is to string arrays of LED's such that the voltage difference is ~1V for the current limiting Resistor for a fixed regulator. If the supply range has a wide range, e.g. 10 ~15V then a constant current sink circuit is best.

Additional Info

For more accuracy over a wider range of currents, you can determine the Rs value from the specsheets for a given temperature. The Vf forward voltage also is a function of temperature which affects the results slightly. THe Rs of LED's is much lower than the dynamic Rs of Zeners using silicon junctions.

• 20mA HB devices are <20 ohms.
• 300mA HB devices are < 2 ohms.
• 1Amp power modules are ~ 0.3 ohm.
• Rs for LED arrays , add in series, and divide in parallel.
• Old technology LEDs were much higher Rs values.
• Rs will reduce as the current increases but you can approximate it at the 10% of rated current value and extrapolate if the device stays at constant temp.
• Because of the Shockley effect with voltage variationmyou can actually calculate the junction temperature from the voltage drop of a calibrated LED.

You really can't accurately predict the current in this sort of application. If you use the datasheet curves, you can guesstimate what it should be (roughly) but slight changes in supply voltage, in driver drop and changes in temperature (as well as part-to-part variations) will cause large changes in the current.

As you didn't grace us with a link to the part datasheet (assuming that a decent one even exists), I'll pull one at random (an Rohm SMLP36RGB2W3) off the interwebs and refer to it:

With this particular set of RGB LEDs, you can see that the RED LED is going to be easy. With a nominal 3V Vdd we can put zero ohms in series (leaving nothing for the driver) and the blue LED will conduct about 5mA. The green LED with zero ohms in series will typically only conduct about 2mA.

However if the supply voltage (with zero ohms in series) is increased or decreased, the blue LED will go from 1.5mA to more than the 10mA maximum. The green LED will go from way under 1mA (basically off) to more than 7mA. In this case, the green LED has a higher Vf than the blue, because its high-efficiency InGaN construction rather than the cheaper GaP.

If the green was GaP, it would probably be workable (over moderate temperature range and with a tightly regulated Vdd) but you're really in guessing (or at least empirical testing) territory rather than engineering territory. You certainly will not be able to get a stable "white" by combining RGB since the color balance will change radically with supply voltage and temperature.