Harmonic Frequency

Formula

Description

Any periodic switching waveform generates harmonics at integer multiples of the fundamental switching frequency. In EMC analysis, these harmonics are the primary source of conducted and radiated emissions from switch-mode power supplies, motor drives, and digital clocks. Odd harmonics dominate in symmetric waveforms (50% duty cycle square waves), while even harmonics appear with asymmetric duty cycles. The amplitude of the nth harmonic of an ideal square wave falls off as 1/n, but parasitic ringing can cause certain harmonics to exceed this envelope.

Variables

• f_n — Frequency of the nth harmonic (Hz)
• n — Harmonic number (integer, dimensionless)
• f_sw — Fundamental switching frequency (Hz)

Practical Notes

EMC standards like CISPR 32 and FCC Part 15 specify emission limits from 150 kHz to several GHz. A 100 kHz switching converter has harmonics at 200 kHz, 300 kHz, etc., with significant energy extending to 30-50 MHz depending on edge rates. Spread-spectrum clocking reduces peak harmonic amplitudes by spreading energy across a wider band.