
Maxim shows how to build a 112 watt DC-DC boost driver for long strings of LEDs. The driver is current controlled,with adjustable output from 0 to 1.5Amps.
This reference design is for a high-voltage boost current source for very long strings of LEDs. Applications that use long LED strings include, but are not limited to, streetlights and parking garage lights. Long LED strings can be a very cost-effective way to drive LEDs. Also, since the LEDs will have exactly the same current, brightness variations are nicely controlled. This design has a 24V input, up to a 75V LED output, and drives 1.5A through the LED string (or strings, if paralleled). The measured input power is 115.49W and the output power is 111.6W for an efficiency of about 96.6%.

This is so cool. I wonder how small you could get it if you only wanted to drive regular 20 to 40 ma leds.
There’s a ton of stuff out there. Here’s a 3mm x 3mm QFN part that will do what you want:
TPS61042
There’s even an evaluation board with LEDs on it:
TPS61042 EVM
Only $49 and they include a BOM, schematic, etc.
Yeah, as andrew said, there are quite a bit of solutions out there for small size led drivers for such a small load. Most MCU’s can output a little of current, and if you stick a resistor on there to current limit it then you have a super simple led driver! Kind of. :P
Anyways, the biggest items here are the inductor, capacitors, and the copper pads for the switching fets. Inductor is large because of the large power demand. As inductance increases, more of the wire is looped around a core, which increases the coil resistance, which then increases temperature rise under load. If you want lower resistance then the wire used for the coil gets thicker, which means the coil of wire itself uses more space, in turn making the whole inductor larger, but less power wasted. Though, if you increase the switching frequency then you can use a smaller inductive inductor, which in turn decreases the size since you need less wire to make the inductor coil.
Capacitors are kind of large in this case because the switching frequency is only 200 KHz, and such a large power draw, so to prevent a big voltage ripple, you stick more capacitors on it.
The copper pads for the switching fets are large because they act as (I suppose) heat sinks for the fets, and also as a low resistance path from the fets to the inductor, to the capacitors, and then to output.
The TPS61042 has integrated switching fets so you don’t need to use board space for your own. The fets are internal in this one because the load is very small, and voltage is mostly low, which means that not much of the die is used for the switching fets, making TI happy and keeping the price down of the ic.
If you want, you can get rid of the brightness control by just holding the Brightness control pin high, saving you a resistor or two. The capacitor needs to be only 100 nF apparently with this driver, and if your output voltage is low, you can probably find a very small capacitor for such a value. If you stack each required passive next to each other, then you will probably find it to be much smaller than the evaluation board.
Sometimes they put a example design with the essential circuitry in the data sheet to show you optimum layout, but here they did not. Though, if you look at the evaluation board, you will probably use up far more space for the LED’s then the entire layout for the led driver itself. Of course, if you are willing to pay more, you can probably find exotic passives that are very tine yet satisfy requirements such as inductance and capacitance.
Apologies if you know this already, I am hoping that others may read this and get a better idea for why LED drivers, or switching power supplies, are sized the way they are.
I’m currently designing a board based on this little chip to drive a cheap chinese made led panel, I’ll let you know how it goes :)