PWM

The idea

A MOSFET is either fully on or fully off. To give a motor some of the power, switch it on for part of each cycle, thousands of times a second. The motor is far too slow to notice the flicker, so it responds to the average voltage. This is pulse width modulation (PWM).

The definitions

Symbol	Meaning
$T$	Period: the time for one on-plus-off cycle, $T=t_{on}+t_{off}$
$F$	Frequency: cycles per second, $F=1/T$
$D$	Duty cycle: fraction of the time it’s on, $D=t_{on}/T$, from 0 to 1

$\boxed{V_{avg}=D\times V_{DD}}$

Why: for a fraction $D$ of the time the motor sees $V_{DD}$, and for the rest it sees 0 V. The average is $D\times V_{DD}+(1-D)\times 0$.

Worked example

A 24 V battery drives a motor with PWM at 20 kHz and 30% duty. Find $T$, $t_{on}$ and the average voltage.

Answer

$T=1/20000=50$ µs. $t_{on}=0.3\times 50=15$ µs, so $t_{off}=35$ µs. $V_{avg}=0.3\times 24=7.2$ V.

Why the frequency matters

• Too low (under ~1 kHz) and you can hear the motor whine, and the current ripples a lot.
• Higher frequencies give smoother current and smaller converter parts, but every switch costs energy, so switching loss rises with frequency.

Check yourself

1. What duty cycle gives 9 V from a 12 V supply?

$D=9/12=0.75$, so 75%.