Electronic – Calculating resistor value and power rating for LED driving

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.

While the answers by @Passerby and @MichaelKaras pretty much cover it, there's one more thing to add:

1. Humans perceive light intensity non-linearly: At very low intensities, we are very sensitive to a even slight variation in brightness. On the other hand, at higher intensity, the unassisted human eye is pretty much incapable of discerning differences in intensity.

   This really interesting graph demonstrates this excellently: _^(source)

   Essentially the ability to perceive change in intensity is very high when most of the vision is attributable to the rods of the eye (scotopic vision), and drops very low when the cones are doing the sensing (photopic vision), i.e. at slightly higher luminance.

2. Less critical but good to know: LEDs illuminate somewhat non-linearly versus current, with the graph dropping off the linear as current increases. This is most noticeable with red.

   _^(source)

So, long story short:

The human eye cannot notice even large intensity changes at the higher levels of light that an LED generates at higher currents. Using half or even less than half of nominal rated current (20 mA typical for indicator LEDs, 50mA or more in high power LEDs) will thus work perfectly fine for most indication purposes.

In my designs, 5 mA is my preferred current for all indicator LEDs: Try it, it works great!