I have a 5 V embedded circuit where a 10 kΩ pot controls the duty cycle of an LED. I noticed that when the duty cycle is only 0.39% (or 1/255 bits), the LED is still perceptibly bright. I'm looking at the PWM signal on an oscilloscope and can see that the +5V fraction takes up only 65 us of a 16.4 ms period.
What is the expected brightness of a conventional LED at duty cycles less than 1%? Feels like it should be completely off.
Can anyone derive the equation relating brightness to duty cycle in this case?
Also checkout this article which gets close to the answer: https://codeinsecurity.wordpress.com/2023/07/17/the-problem-with-driving-leds-with-pwm/
"However, if you linearly sweep the duty cycle from 0-100%, you won’t see a smooth linear increase in brightness. This is because our eyes are far more sensitive to changes in brightness in the dark than in bright light; the evolutionary reasons for this are fairly obvious. If you graph the PWM duty cycle versus the normalized perceptual brightness, you’ll get a curve that looks something like this [logarithmic curve, no equation given]. At just 5% duty cycle, the perceptual brightness of the LED already exceeds 20% of the maximum."
(this leads to a gamma correction technique)
EDIT: This is a 5 V circuit, typical breadboard LED in series with a 1 kΩ resistor. The 5 V is PWM at variable duty cycle. What happens to the LED over over the full range of an 8 bit duty cycle? At what point is the LED perceptibly off? Apparently not unless the duty cycle is exactly zero.