Hello there,
I have a project and I don't know how to continue. Maybe anyone can help me. I search for a 20w DC DC step up converter where you can control the current via PWM. Or maybe you have another idea for the problem: I have a 35V led with 600mA current and a 11,1V battery. I want to dim the LED indirectly with the an arduino. Unfortunately I cannot find a DC DC step up converter fitting my specifications...
Thank you and have a great day 
Try a step up converter and a MOSFET controlled by PWM. Add the current limiting resistor to the LED strip. Add a big capacitor to the controller to reduce PWM switching effects.
Also check whether your LED assembly can be dimmed at all. Data sheet?
And you really do "need" a special constant-current driver for high-power LEDs. This is NOT easy to build yourself!
LEDs are non-linear (like all diodes) so their resistance changes with voltage. When you feed the correct current with a constant-current power supply, the voltage "falls into place".
If you feed it a fixed voltage from a regular power supply the current is hard to control.
With "regular little" LEDs we use a series resistor to control/limit the current, but this is inefficient with larger LEDs and you need a higher-power resistor.
With a normal fixed-voltage power supply the voltage depends on load. With nothing connected no current flows but the voltage remains constant.
If nothing is connected to a constant-current supply the voltage jumps-up to however high the power supply can go as it tries to push current through infinite resistance.
P.S.
In case you don't know this, high-power LEDs also need a heatsink.
So, what are you recommending instead?
You may suggest a constant-current circuit using a FET,
But that is exactly as inefficient in general. 
Then you need a high power transistor instead of a high power resistor.
But actually we don't know at all whether and how dimming can be achieved with that LED thingy.
I have successfully dimmed high power LEDs that are fed from a mains powered current source by putting an N channel MOSFET in the negative supply and driving the MOSFET with PWM. No guarantee this will work with all LED drivers of course, but it certainly works with the ones I have.
My point precisely. 
The problem with that is that if it is actually a current driver, then it will drive whatever its load is as DVDdoug points out in #4 up to whatever voltage is necessary to maintain that constant current.
Now if it has - and it almost always will - a capacitor at its output to stabilise the switchmode converter, then that constant current will be the average and the capacitor voltage will rise until that average is reached (or is limited by the supply voltage) and the current during the "on" part of the PWM cycle will proportionately increase - if the PWM is 50%, then the "on" current will double.
This is anything but desirable.
Not to mention that in almost all "mains powered current sources", the negative output is derived from a bridge rectifier connected to the mains.
Hey! It works just fine!
I accept that I might be lucky with the particular LED drivers I have and it might not be any good with different ones.
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