What causes harmonics in RF systems?

Any device with a nonlinear transfer function generates harmonics. When a pure sine wave at frequency f passes through a nonlinear element, the output contains the fundamental plus harmonics at 2f, 3f, 4f, etc. Symmetric nonlinearity (like a push-pull amplifier clipping equally on both halves of the waveform) produces only odd harmonics (3f, 5f, 7f). Asymmetric nonlinearity (like a single-ended amplifier with different clipping on positive and negative peaks) produces both even and odd harmonics. Class-AB power amplifiers are a primary source: as the output approaches compression, even-order harmonics (2f) appear at levels 20 to 30 dBc below the fundamental, while odd-order harmonics (3f) appear at 30 to 40 dBc.

What are the FCC limits for harmonic emissions?

FCC Part 97 (amateur radio) requires harmonics to be suppressed to 43 dB below the carrier for transmitters above 25 watts, and 40 dB below for lower power levels. FCC Part 15 (unlicensed devices) limits all spurious emissions including harmonics to minus 41.2 dBm at 3 meters above 960 MHz. For cellular base stations (Part 22/24/27), out-of-band emissions at harmonic frequencies must be below minus 13 dBm per MHz. Meeting these limits requires a harmonic filter (lowpass or bandpass) between the PA and the antenna, typically providing 40 to 60 dB of attenuation at the second harmonic and 50 to 70 dB at the third.

How do push-pull amplifiers cancel even harmonics?

A push-pull amplifier uses two transistors driven 180 degrees out of phase. The fundamental outputs add in phase at the output combiner. The second harmonic outputs, being at 2f, are 360 degrees apart (equivalent to in phase) at the individual transistors but are inverted by the push-pull combiner and cancel. The third harmonic outputs are 540 degrees apart (equivalent to 180 degrees) at the transistors and add constructively at the output. In practice, device matching limits second harmonic cancellation to 15 to 25 dB, not infinite suppression. This is still valuable: a push-pull GaN PA might achieve minus 30 dBc second harmonic versus minus 15 dBc for a single-ended design, reducing the harmonic filter requirements significantly.

Signal Processing

Harmonic

A transmitter at 900 MHz does not just emit at 900 MHz. Its power amplifier, driven into compression for efficiency, also radiates at 1.8 GHz (second harmonic), 2.7 GHz (third harmonic), and every integer multiple of the fundamental. The second harmonic of a 900 MHz GSM transmitter falls directly on the 1800 MHz DCS band. Without a harmonic filter, the transmitter would jam an entirely different cellular network. Harmonics are an unavoidable consequence of nonlinearity: any device that clips, saturates, or compresses a signal creates energy at integer multiples of the input frequency. Controlling them is not optional; regulatory limits (FCC, ETSI) require suppression of 40 to 70 dB below the carrier.

Category: Signal Processing

Frequencies: 2f, 3f, 4f, ...

Suppression: 40 to 70 dBc required

Where Harmonics Come From and How to Kill Them

PA Class	HD2 (2f)	HD3 (3f)	HD4 (4f)	Filter Needed	Architecture Notes
Class A	−30 to −40 dBc	−40 to −50 dBc	−50+ dBc	2-pole LPF	Low distortion, low efficiency
Class AB (single-ended)	−15 to −25 dBc	−25 to −35 dBc	−35 to −45 dBc	3 to 5-pole LPF	Most common PA class
Class AB (push-pull)	−30 to −40 dBc	−25 to −35 dBc	−45 to −55 dBc	2 to 3-pole LPF	Even harmonics cancelled
Class C	−10 to −15 dBc	−15 to −25 dBc	−20 to −30 dBc	5 to 7-pole LPF	High efficiency, high harmonics
Class E/F	−10 to −20 dBc	−15 to −25 dBc	−25 to −35 dBc	5+ pole LPF	Switching mode, rich harmonics

Total harmonic distortion:
THD = √(P_2f + P_3f + P_4f + ...) / P_f × 100%

Individual harmonic level:
HD_n = P_nf / P_f (in dBc: 10·log(P_nf/P_f))

FCC Part 97 (amateur): ≤−43 dBc (>25 W)
FCC Part 15 (unlicensed): ≤−41.2 dBm at 3m
A 50 W (47 dBm) amateur transmitter needs harmonics below +4 dBm, requiring ~43 dB of combined PA + filter suppression at 2f.

Common Questions

Frequently Asked Questions

What causes harmonics?

Any nonlinear transfer function. Symmetric clipping (push-pull) creates odd harmonics only. Asymmetric clipping (single-ended) creates both even and odd. Class AB PAs near compression: HD2 at −20 dBc, HD3 at −30 dBc typically.

FCC harmonic limits?

Part 97 (amateur): −43 dBc above 25 W. Part 15 (unlicensed): −41.2 dBm at 3m. Cellular BS: −13 dBm/MHz. Meeting these requires 40 to 60 dB harmonic filter attenuation at 2f, 50 to 70 dB at 3f.

How does push-pull cancel even harmonics?

Two transistors driven 180° out of phase: fundamentals add, 2f signals cancel at the combiner. Practical cancellation: 15 to 25 dB (limited by device matching). Reduces harmonic filter complexity significantly.

Related Terms

← HPBW Harmonic Balance →

Compliance

Harmonic Filter Design Tool

Specify fundamental frequency, PA harmonic levels, and regulatory limit. Generate the lowpass filter order, cutoff frequency, and component values needed for compliance.

Design Filter