Transmitters ideally generate a single radio-frequency carrier. In reality, non-linear devices (amplifiers, mixers, oscillators) generate harmonics — unwanted frequencies that occur at integer multiples of the fundamental operating frequency.
Managing harmonic emissions is essential in amateur radio to:
- Meet FCC spectral-purity requirements
- Prevent interference to other services
- Ensure amplifier and antenna efficiency
- Maintain good operating practice
This article explains how harmonics are calculated and provides a full multi-band table of harmonic frequencies across the HF, VHF, and UHF amateur spectrum.
Where the Harmonic Formulas Come From
Harmonics arise from non-linear system behavior, which can be modeled as a polynomial expansion:x(t)=a1cos(2πft)+a2cos2(2πft)+a3cos3(2πft)+…
Expanding the powers using trigonometric identities produces components at:f,2f,3f,4f,…
These are the 1st, 2nd, 3rd, and 4th-order harmonics.
Harmonic Frequency Formula (from Fourier theory of nonlinear systems):fn=n⋅f1
Where:
- f1 = fundamental (operating) frequency
- n = harmonic number (1, 2, 3, 4 …)
- fn = frequency of the nth harmonic
This formula is derived directly from the mathematics of Fourier series and trigonometric power expansions, as found in:
- The ARRL Handbook for Radio Communications
- A. Oppenheim & A. Willsky, Signals and Systems
- David M. Pozar, Microwave Engineering
Step-by-Step Example Calculation
Suppose you are transmitting on 40 meters (7.100 MHz).
1st harmonic (fundamental):
f1=1⋅7.100=7.100 MHz
2nd harmonic:
f2=2⋅7.100=14.200 MHz
3rd harmonic:
f3=3⋅7.100=21.300 MHz
4th harmonic:
f4=4⋅7.100=28.400 MHz
Notice how the harmonics fall inside other amateur bands, which is why filtering is critical.
Harmonics of Every Amateur Radio Band (1st–4th Order)
Notes
- Frequencies use the approximate band centers commonly referenced for calculation.
- Units are MHz for HF/VHF/UHF except 70 cm where GHz is more conventional.
Master Harmonic Table
| Amateur Band | Fundamental (1st) | 2nd Harmonic | 3rd Harmonic | 4th Harmonic |
|---|---|---|---|---|
| 160 m (1.85 MHz) | 1.85 | 3.70 | 5.55 | 7.40 |
| 80 m (3.65 MHz) | 3.65 | 7.30 | 10.95 | 14.60 |
| 40 m (7.10 MHz) | 7.10 | 14.20 | 21.30 | 28.40 |
| 30 m (10.15 MHz) | 10.15 | 20.30 | 30.45 | 40.60 |
| 20 m (14.20 MHz) | 14.20 | 28.40 | 42.60 | 56.80 |
| 17 m (18.10 MHz) | 18.10 | 36.20 | 54.30 | 72.40 |
| 15 m (21.25 MHz) | 21.25 | 42.50 | 63.75 | 85.00 |
| 12 m (24.95 MHz) | 24.95 | 49.90 | 74.85 | 99.80 |
| 10 m (28.50 MHz) | 28.50 | 57.00 | 85.50 | 114.00 |
| 6 m (50.25 MHz) | 50.25 | 100.50 | 150.75 | 201.00 |
| 2 m (146.00 MHz) | 146.0 | 292.0 | 438.0 | 584.0 |
| 70 cm (440 MHz) | 0.440 GHz | 0.880 GHz | 1.320 GHz | 1.760 GHz |
Why Harmonics Matter When Operating HF/VHF/UHF
1. Harmonics fall into other amateur bands
Example:
40 m → 2nd harmonic lands directly in 20 m.
15 m → 2nd harmonic lands exactly on 10 m.
2. Harmonics can interfere with non-amateur services
UHF harmonics may encroach on:
- Aviation bands
- Satellite downlinks
- LTE cellular blocks
- Public safety channels
3. Antennas may unintentionally radiate harmonics
Some antennas have gain peaks at harmonic frequencies.
4. Power amplifiers strongly magnify harmonic distortion
Class AB and C PA stages will produce nonlinear outputs unless low-pass filters are used.
How to Reduce Harmonic Emissions
✔ Use proper low-pass filters (LPF)
Especially after power amplifiers.
✔ Ensure clean drive levels
Overdriving creates nonlinearity → more harmonics.
✔ Use well-designed antennas
High SWR and poor matching increases spurious radiation.
✔ Verify with a spectrum analyzer or SDR
A TinySA, RTL-SDR, or Siglent SA can easily visualize harmonic content.
Conclusion
Harmonics in amateur radio occur at exact multiples of the fundamental frequency. The calculation is simple:fn=nf1
—but the operational implications are serious. Understanding where your 2nd, 3rd, and 4th-order harmonics fall helps ensure compliance, reduce interference, and maintain clean, efficient transmissions.