how do you get a nominal 2 amps across the LED's when everything is going through a small

Small resistor = That resistance is about the same as two feet of wire. It is almost zero. No problem for the current to flow.
That resistance is about like the resistance of our amp meter. If you inserted a meter in the flow of current to the LEDs, it is about the same thing.
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About the resistor and current. In the data sheet 0.1 ohm = 1A, 0.05 ohm=2A. I would pick the resistor for the max you want. Say 2A (or what ever you want maybe 1.5A). Maybe at power up the first couple of cycles might get to 3A but very soon the current will be right, set by the resistor. The first cycles will go into the output capacitors that need charged up. No LED current. As the voltage gets near Vf the current will flow in the LEDs and not in the capacitors.

 

Small resistor = That resistance is about the same as two feet of wire. It is almost zero. No problem for the current to flow.
That resistance is about like the resistance of our amp meter. If you inserted a meter in the flow of current to the LEDs, it is about the same thing.
-----edited-----
About the resistor and current. In the data sheet 0.1 ohm = 1A, 0.05 ohm=2A. I would pick the resistor for the max you want. Say 2A (or what ever you want maybe 1.5A). Maybe at power up the first couple of cycles might get to 3A but very soon the current will be right, set by the resistor. The first cycles will go into the output capacitors that need charged up. No LED current. As the voltage gets near Vf the current will flow in the LEDs and not in the capacitors.

Thanks. I forget that the 1/8w rating is what the resistor dissipates to heat, not what passes through it.

I think you're right about setting the value to 2a as well. I thought it would be fun to have the ability over drive the LED's in the PIC chip software, but in reality it wouldn't be very useful. It's smart to stay within spec.

 

ability over drive the LED's in the PIC chip software

There is a Vset pin. If the pin is pulled below 0.3V the PWM shuts off. If you leave the pin not connected thing work. You can set a pin to low and then switch the pin from out or input. If input the pin is the same as not pulling on the PWM. But if the pin is (low and output) the PWM is off. If you turn set this pin at about 500hz and 50% duty cycle it will be half power. Your eye can not see 500hz. or even 100hz. You can reduce the power by setting the duty cycle. (not the same as the duty cycle the PWM is making)

Why PWM the LED at high current when you could just reduce the current. Your eye sees 50% as half power so that is fine. White LEDs change color some at low current. If you ran the LED at 10% you likely can see the color change. If you run the LED at 1.5A and 10% of the time the eye will see the right color and 1/10 as bright.

 

There is a Vset pin. If the pin is pulled below 0.3V the PWM shuts off. If you leave the pin not connected thing work. You can set a pin to low and then switch the pin from out or input. If input the pin is the same as not pulling on the PWM. But if the pin is (low and output) the PWM is off. If you turn set this pin at about 500hz and 50% duty cycle it will be half power. Your eye can not see 500hz. or even 100hz. You can reduce the power by setting the duty cycle. (not the same as the duty cycle the PWM is making)

Why PWM the LED at high current when you could just reduce the current. Your eye sees 50% as half power so that is fine. White LEDs change color some at low current. If you ran the LED at 10% you likely can see the color change. If you run the LED at 1.5A and 10% of the time the eye will see the right color and 1/10 as bright.

That makes a lot of sense.

I wasn't clear enough. I am using the Pic chip to PWM dim the LED's on demand. I want to control the brightness with the push of a button. I am also using this Pic chip to control battery charging (switch off battery when mains connected, so the battery can charge without a load interfering with it).

I am also going to use the Pic chip to set output profiles based on what power adapter is plugged into it. It's going to have a "sense" input pin, based on voltage, so it will know what power source is connected. If it has a low wattage source, like an automotive power socket adapter, it will only go so bright so it doesn't over amp the power source. If it has an a/c adapter, it will output full brightness.

Understanding this better though, I may want to use another Pic pin to actually adjust the current sense resistor, and then keep the PWM profile the same.