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When we apply pulse-width modulation (PWM) on controlling the brightness of a LED or the speed of a DC motor, is it the lag in our eyes that is responsible for the feeling of a continuous powering or the inertia of the devices?

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Depends on what you are controlling. For DC-motors it is the inertia of the device that acts as a low-pass filter of the PWM modulated signal resulting in a continuous motion. For most LEDs it is the human eyes that do the apparent low-pass filtering.

If the PWM-frequency is not very high you can actually see this by moving your head from left to right while looking at the PWM modulated LED. The light will appear on and off while the LED is moving through your field of vision (this can get very annoying with LED car taillights).

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    $\begingroup$ Re: the last example that you gave above, you can also see this in some cheap clocks and other devices that use 7-segment LED displays. To reduce the number of required components, some designs only use one LED driver that they continuously switch between each of the segments in the display, so there is no point in time where all of the segments are on at exactly the same time. Usually, your visual system lowpass-filters the result so they all look steady, but if you move your head, you can sometimes notice the flicker. $\endgroup$ – Jason R Jul 22 '13 at 13:47
  • $\begingroup$ What happens when you're moving the head that allows the flickering to become observable? $\endgroup$ – TheMeaningfulEngineer Jul 22 '13 at 14:18
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    $\begingroup$ Alan: This is probably more of a biology question so I can just give you half-knowledge in the best case. If your eyes stand still, both the on and off state of the LED land on the same spot of your retina. However, if you quickly move your head or just your eyeballs from left to right, the projection of the LED moves along a line on your retina. Now some parts of it will see the LED when it's on and some parts see it when it's off. Whether or not it works depends on how fast you move your head/eyes, how large the PWM frequency is and probably also on sensitivity towards this effect. $\endgroup$ – jan Jul 22 '13 at 15:15
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For LEDs the filtering can be done by the eye.

For an electric motor there are 2 sources of smoothing. The first is due to a motor being an inductive load. In an inductor the applied voltage is proportional to the rate of change of the current. This means a PWM voltage will result in some sort of triangle wave in the current (which requires a freewheeling diode for when the switch is off). Motor torque is generally proportional to motor current, so you may actually be applying a continuous torque with some ripply. Then the inertia of the motor helps smooth the speed even in the presence of a non-uniform torque.

You can also reduce the actual flicker of an LED by putting an inductor in series with it with a freewheeling diode but this is not usually practical at the frequency one might PWM an LED.

It may also be informative to read about buck converters - particularly in continuous conduction mode. One can think of a DC motor as a speed dependent voltage source, which will allow you to consider it a buck converter that can transfer energy in either direction if it's moving - i.e. regenerative braking.

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