I'm confused
- but as we know, that ain't difficult.
Are we doing 2 topics in one here?
1. How to smooth the power to reduce/prevent strobe effect.
2. Choosing a PWM frequency to get the most duty steps/resolution.
I realise they can be related; after all (going to extremes) a 10MHz PWM would probably mean no perceivable strobe on your bike wheels so smoothing not required.
If you want to go the smoothing route then your design will depend on the LED power required.
I would be tempted to have a bench-test before going OTT with PWM resolution. When I was playing with a design I had 100 steps for each RGB channel and that was well OTT as duties of 50,50,49 and 50,50,48 (R,G,B) were no different to my eyes.And that was BEFORE I went to the pub!
BTW; PICMultiCalc: Although it's aimed at PIC programmers it does give good information wrt accuracy and duty steps for a given clock and chosen PWM. PIC derives it's values using a sequence of dividers so (generally) as you get to the higher end of the frequencies the accuracy and resolution decrease. You may select 50 or 51% but there is no difference.
So, whilst it's not aimed specifically at PICAXE programming it does provide a useful reference as to the 'goings on' in PIC.