## Class-D PWM Harmonics

Features to note in this plot of the PWM harmonic content versus the duty cycle:

• At idle (D=0.5) only odd harmonics are present, as expected from a square wave
• Away from idle (D<0.5 or D>0.5) even harmonics added, as expected from PWM
• Magnitudes are equal at duty cycle extremes, as expected from an impulse function

If the class-D amplifier is a hysteresis modulator with a passive 2nd order output filter:

Features to note in this new plot of the PWM harmonic content versus the duty cycle:

• The harmonics increase abruptly as clipping is approached, consistent with observation
• At idle the output is dominated by the fundamental (i.e. a low level sine wave at $f_{s}$)
• Designs with more stable switching frequency at duty cycle extremes are easier to filter

Switching frequency versus duty cycle relationship for a hysteresis modulator:

$f_{s}=4D\left ( 1-D \right )f_{0}$

$f_{s}$ is the switching frequency at $D$
$f_{0}$ is the switching frequency at $D=0.5$
$D$ is the duty cycle $0\leq D\leq 1$