Also known as: harmonic, harmonic distortion, harmonic frequencies
Harmonics are spectral components at integer multiples of a signal’s fundamental frequency f₀ — the second harmonic sits at 2f₀, the third at 3f₀, and so on.1 They arise whenever a device treats a sine wave nonlinearly, and in a transmitter they are a leading source of unwanted spurious emissions that must be suppressed before the signal reaches the antenna.
How it works
Any perfectly linear device passes a pure sine wave through unchanged. Real components — power amplifiers driven near saturation, diodes, and mixers — have a transfer curve that bends. Mathematically, a nonlinear response can be written as a power series y = a₁x + a₂x² + a₃x³ + …, and feeding a sine x = cos(2πf₀t) into the squared and cubed terms generates energy at 2f₀, 3f₀, and higher. The stronger the nonlinearity — the harder an amplifier is driven into compression — the richer the harmonic content.
Two useful facts fall out of this. First, the square-law (even-order) terms create even harmonics while the cubic (odd-order) terms create odd harmonics, so a symmetric, push-pull stage naturally suppresses even harmonics. Second, harmonics always fall above the fundamental at exact integer multiples, which makes them predictable and therefore easy to filter — unlike intermodulation products, which land near the wanted signal.
Total harmonic distortion (THD) quantifies the effect as the ratio of combined harmonic power to the fundamental, usually expressed as a percentage or in dB.2
In practice
Because harmonics land at known frequencies, a transmitter suppresses them with a low-pass or band-pass filter after the final amplifier. A 150 MHz VHF transmitter, for example, uses a low-pass filter that passes 150 MHz but rejects the second harmonic at 300 MHz by tens of dB. Class-C and switching amplifiers are efficient precisely because they run nonlinearly, so they lean hardest on this output filtering; linear classes (A, AB) generate fewer harmonics at the cost of efficiency.
Harmonics matter on the receive side too. A strong local FM broadcast can present a harmonic that lands in a band you are trying to monitor, and the receiver’s own front-end and mixer generate harmonics of the local oscillator that create image and spurious responses. Good RF filtering and avoiding front-end overload keep these in check.
Relevance to SDR
Harmonic suppression is a regulatory requirement: transmitter type-approval rules set hard limits on harmonic radiation, and exceeding them causes interference in unrelated services. For land-mobile trunking systems (P25, DMR, TETRA), base-station and portable transmitters carry cavity and low-pass filters specifically to hold harmonics below the mandated spurious-emission mask.
GopherTrunk is a receive-only decoder and does not transmit, so it produces no harmonics of its own. Harmonics still matter to its users indirectly: cheap SDR front-ends (RTL-SDR dongles and similar) have limited front-end selectivity, so a strong out-of-band signal or its harmonic can overload the tuner and raise the effective noise floor, degrading decode of the wanted control channel. An external band-pass filter ahead of the SDR is the standard cure, and understanding where harmonics fall helps a monitor diagnose a spur that is not actually a real transmission but a harmonic of one.
Sources
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Harmonic — Wikipedia, definition of harmonics as integer multiples of a fundamental frequency. ↩
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Total harmonic distortion — Wikipedia, the metric relating combined harmonic power to the fundamental. ↩