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I want to create a circuit to drive 5050 SMD RGB LEDs in my motorcycle which has power supply of 12V from sealed Lead-acid battery.

Spec for 5050 RGB LED is:

5050 SMD LED Forward voltage limits

Maximum allowed forward current per LED is 20mA.

I want it be able to drive at least 3 LEDs in series, so essentially 3 branches since there are 3 LEDs to light up to get required color. Planning to allow to drop maximum 3.5V per Green/Blue LEDs and 2.3V for Red LEDs.

So, I assume my circuit should be able to deliver at least 10.5V (3 x 3.5V)

Since the power supply is Lead-acid battery. It may come down at safe level 11.8V. I thought about using LM317 and LM7812 but found they have high drop out voltage thus will not be giving enough voltage if battery is at 11.8V.

Are there better voltage regulators with low drop out voltage?

Or will it be possible build one with discrete components with not that bad in terms of efficiency?

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Indeed there is too little voltage "headroom" for a linear voltage regulator.

I see several solutions:

1) The simplest solution is to just use a series resistor and give the resistor such a value that the current will be maximum (20 mA) at the highest battery voltage (let's say 14.5 V). So for three 3.5 V LEDs in series that would result in: 14.5 V - (3x3.5) = 4 V, 4 V / 20 mA = 200 ohms. When the battery voltage is lower, the current will be less than 20 mA so the LEDs will be less bright. It depends on the LEDs how noticeable this is.

2) Same as 1 but instead of 3 LEDs in series, use 2 LEDs in series. That way more voltage will drop across the resistor and that will mean that the current will vary less over battery voltage. It will still vary but less. Note that this is of course less efficient as the total current will be larger as you will need more LED series circuits. But since the LED current is only 20 mA per circuit you're hardly loading the battery at all.

3) If you must have a fixed current, use a DCDC boost converter to boost the voltage up to for example 25 V, then you can even connect 6 LEDs in series, with a resistor of course. That Boost converter will regulate the output voltage to 25 V (or whatever you set it to but must be higher than highest battery voltage!) independent of the battery voltage.

Personally I would recommend option 1) as it is the simplest and will very likely be good enough.

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All you need is the appropriate resistor for 14V operation. What you want to do is EXACTLY how simple/dumb led strips work. 3 leds in series, or for rgb 5050 3 parallel strings of 3 led in series, each with its own resistor. 16 to 18V at "12V", and 20mA at 14V.

For a simple circuit like this, you cannot get better, simple, cheap efficiency like a single resistor. 18mA * 1V across the resistor = 0.018 Watts, out of 0.217 Watts. That's 90% efficiency.

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