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Frequency (Hz) and Pulse-Width Modulation (PWM)

Frequency (Hz)​

Frequency describes how often a periodic signal repeats per second. Its unit is the Hertz (Hz): 1 Hz equals one full cycle per second.

The frequency f and the duration of one cycle, the period T, are inverses of each other:

f = 1 / T        (frequency  = 1 / period)
T = 1 / f        (period     = 1 / frequency)

Example: A signal repeats every 1 ms (0.001 s).

f = 1 / 0.001 s = 1000 Hz = 1 kHz

The Problem PWM Solves​

A digital GPIO output can only ever supply two states: HIGH (for example 3.3 V) or LOW (0 V). There is no value in between. Yet many tasks need something in between, such as dimming an LED, running a motor at half speed, or driving a passive buzzer.

Pulse-width modulation (PWM) solves this by switching the output between HIGH and LOW very rapidly. The ratio of HIGH time to the total cycle determines the average power delivered, which the connected device perceives as a value between fully off and fully on.

Duty Cycle​

The duty cycle (in German Puls-Pause-Verhältnis) is the share of one period during which the signal is HIGH:

Duty cycle = (t_on / T) x 100%

t_on = time HIGH within one period
T    = t_on + t_off (full period)
Duty cycleSignalEffect (at 3.3 V)
0 %always LOWfully off
25 %HIGH 1/4 of the timelow power
50 %HIGH half the timehalf power
75 %HIGH 3/4 of the timehigh power
100 %always HIGHfully on

Example: A signal is HIGH for 0.25 ms within a 1 ms period.

Duty cycle = (0.25 ms / 1 ms) x 100% = 25%

Average Output Level​

The average voltage seen by the device scales linearly with the duty cycle:

U_avg = duty cycle x U_max

Example: A 3.3 V output running at a 50 % duty cycle.

U_avg = 0.5 x 3.3 V = 1.65 V
note

PWM does not actually lower the voltage, the output still toggles between 0 V and the full level. The device only behaves as if it received the average, because the switching is faster than it can react.

Calculating the HIGH Time​

Combining the formulas above gives the HIGH time for a chosen frequency and duty cycle:

T = 1 / f
t_on = duty cycle x T

Example: A 1 kHz signal at a 25 % duty cycle.

T = 1 / 1000 Hz = 0.001 s = 1 ms
t_on = 0.25 x 1 ms = 0.25 ms

Typical Applications​

  • Dimming an LED: a higher duty cycle means a brighter LED.
  • Motor and fan speed: at a relatively high frequency the output is toggled between HIGH and LOW; the ratio sets the power, and therefore the speed.
  • Tones on a passive buzzer: the frequency of the PWM signal sets the pitch of the tone.

See Also​