How do you calculate the analogWrite bit for a given freqency?

[drakejest]

I would like to know what is the highest number of bits for the analogWriteRes() i can do for a given frequency? Specifically 90kHz PWM frequency. What is the formula?

[earlephilhower]

arduino-pico/cores/rp2040/wiring_analog.cpp

Lines 87 to 103 in 07781e9

	if (!scaleInitted) {
	// For low frequencies, we need to scale the output max value up to achieve lower periods
	analogWritePseudoScale = 1;
	while (((clock_get_hz(clk_sys) / ((float)analogScale * analogFreq)) > 255.0) && (analogScale < 32678)) {
	analogWritePseudoScale++;
	analogScale *= 2;
	DEBUGCORE("Adjusting analogWrite values PS=%d, scale=%lu\n", analogWritePseudoScale, analogScale);
	}
	// For high frequencies, we need to scale the output max value down to actually hit the frequency target
	analogWriteSlowScale = 1;
	while (((clock_get_hz(clk_sys) / ((float)analogScale * analogFreq)) < 1.0) && (analogScale >= 6)) {
	analogWriteSlowScale++;
	analogScale /= 2;
	DEBUGCORE("Adjusting analogWrite values SS=%d, scale=%lu\n", analogWriteSlowScale, analogScale);
	}
	scaleInitted = true;
	}

. We obey the frequency first, then derate the bits so it can happen w/o needing a bit clock > fSYS.

Enable core debug and debug Serial output and it'll dump the calculated values.