EDIT: I initially asked this about ADCs instead of DACs, but that was a mistake, so I have changed the question accordingly.
Hey everyone!
TL;DR Does a DAC with resolution X mean it can work at a PWM frequency up to X? Or, in other words, is an DAC's precision of PWM voltage output limited by the frequency it is working at?
From my understanding, in the context of having a micro-controller interface with some output device, if you don't have an analog output pin to produce the needed analog voltage, you would use an digital-to-analog convert (DAC) pin, which outputs that same voltage using PWM. PWM has the pin turn on and off (each on or off = a pulse) at a given frequency (PWM frequency). The percentage of pulses that were on is the duty cycle, which in turn determines the voltage output (the on's and off's at certain proportions to each other average out to give some voltage). So if the max. voltage was 5V and the frequency was 50Hz, and you set 40 of the pulses to on, then that's an 80% duty cycle and a 4V output. Correct any of this if I'm wrong.
Now, say the pin that was carrying out this PWM had a resolution that was higher than the frequency. Say the ideal frequency to work with the output device was 50Hz and the analog-to-digital converter's pin's resolution was 64 (6-bit). From my understanding, 64-bit resolution means this ADC can split an analog signal into 64 discrete units. But if it is working at 50Hz, that's just 50 pulses, so only 50 possible discrete values because number of pulses relates to voltage output. Is there any meaning then to having a resolution higher than 50 here (of course 50 isn't an integer power of 2 but that's beside the point)? If not, then is it the case that In micro-controllers, the pulse value of the resolution is mapped using the frequency?
This came up with me because I am currently working with servos that function at 50-60Hz and the resolution of my ADC pins on my micro-controller is 4096, and I'm wondering do I really have that 0.001220703125V precision if the frequency is that?
Would very much appreciate any answer to this.