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LEDs can't be connected directly to a source of power - only in series with a current limiting resistor. Which means that when the LED is powered some power is dissipated by that LED and some power is dissipated by the resistor. Which means that some energy is wasted.

Now suppose I need to construct a powerful light source - a house lighting fixture or a car headlight - that uses LEDs as a light source. I will have to connect all LEDs through resistors.

I guess those resistors will waste quite a lot of energy.

How is this problem addressed when using LEDs for lighting?

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LEDs like to be powered with a constant source of current-ie. a fixed current regardless of the voltage it takes to achieve this. In practice for simple applications we assume a fixed forward voltage drop, and use a resistor to achieve the correct current.

However, with changes such as process variation, temperature etc. the forward voltage, and hence the current, will change. For simple applications this is not an issue, but for high power application such as you mention, this does become a problem, and so resistors are not used.

The solution is to include feedback in the circuit. As part of the driver circuitry, the current will be measured and the voltage across the LED controlled to always keep the current at the desired value; as a useful bonus, this also give you the ability to dim the LED by reducing the current.

As you point out, if we turn the excess voltage into heat it ends up being pretty inefficient (this is a form of linear regulator)

The solution is use a switching regulator, which turns the voltage either fully on, or fully off. A capacitor is used to "average" this voltage, and by changing the ratio of the time turned on to the time turned off, we control the average voltage. All with an efficiency of 90%+.

If you're interested, then a commonly used circuit is a buck converter

And if you'd like to get in-depth, then these two videos with Howard Johnson and Bob Pease are extremely good,

Driving High Power LEDs Without Getting Burned - Part 1

Driving High Power LEDs Without Getting Burned - Part 2

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LEDs can be directly connected to a power supply, just that this power supply should be current-regulated instead of the more common voltage-regulated.

Switching power supplies are used to get good efficiency when converting one voltage and current to a different combination of voltage and current. Since voltage times current is power, the voltage x current product out can not exceed the voltage x current product in. In reality, there will be some inefficiency, so the output voltage x current will be a bit less than the input voltage x current. 90% efficiency is quite good. 95% efficiency is exceptionally good. Mainstream off the shelf power supplies are usually in the 80-90% efficiency range.

Whether the power supply regulates voltage or current depends on how the feedback signal is derived. The power supply will attempt to null out the difference between the input reference signal and the feedback signal. If the feedback signal is proportional to output current then it will regulate that current.

For a example of a switching power supply controlling the current thru a string of LEDs, see the schematic of my KnurdLight LED headlamp. The main job of this circuit is to run a roughly constant 20 mA thru a string of 4 white LEDs, which requires around 13V total. The input power is two AA cells which provide about 3V. The main parts of the boost converter are inductor L1, transistor Q2 as the switching, and diode D1. The current to the LEDs goes out connection point P1 and returns at P2. The return current flows thru the current sensing resistor R6. The PIC has a internal 600 mV fixed voltage reference. The voltage from accross R6 is proportional to the LED current, which is compared to the 600 mV reference inside the PIC. The firmware in the PIC uses this one-bit high/low indicator to control the switch Q2.

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