I'm working on a project involving driving LEDs at a 20kHz PWM frequency with 1024 bit resolution. I've calculated that the minimum pulse time, (1/frequency)/resolution, would result in a minimum pulse time of ~50ns, which means I need rise and fall times of <25ns of all of the components I'm using to turn the LEDs on and off. While there are components that meet this specification, it's pretty demanding and I'd like to use some cheaper, more widely available ICs.
My thought is that while 1024 resolution is useful in adjusting the output of the LEDs in fine increments in my use case, I don't actually need a minimum brightness of 1/1024, but could probably get away with a minimum of 1% of the total brightness, or 1024 x 0.01, which is roughly 10x the minimum pulse width or about 500ns. This results in rise and falls times of 250ns, which greater increases the number of available components.
Is my understanding of the PWM frequency, resolution and duty cycle relationship correct here?