What Is Harmonic Distortion?
A nonlinear RF amplifier produces output not only at the fundamental frequency f₀ but also at integer multiples (harmonics): 2f₀, 3f₀, 4f₀, etc. These harmonics must be filtered before transmission to meet regulatory emission requirements.
Harmonic Level Approximation
For a weakly nonlinear amplifier, harmonic levels relative to fundamental: 2nd harmonic: H₂ = OIP2 − P_out + constant [approximately] 3rd harmonic: H₃ ≈ 3·P_in − 2·OIP3 − P_out [from Taylor series model] Typical harmonic levels for a PA at P1dB (Class AB): 2nd harmonic: −15 to −25 dBc below fundamental 3rd harmonic: −25 to −40 dBc below fundamental At +33 dBm TX power with H₂ = −20 dBc: 2nd harmonic level = 33 − 20 = +13 dBm at 2×f₀
Regulatory Harmonic Emission Limits
| Regulation | Limit | Frequency |
|---|---|---|
| FCC Part 15 (802.11 WiFi) | −41.3 dBm EIRP | Spurious emissions, all harmonics |
| 3GPP TS 36.101 (LTE UE) | −30 dBm | 30 MHz – 1 GHz out-of-band |
| ETSI EN 300 328 (WiFi EU) | −30 dBm | 1–12.75 GHz spurious |
Required Filter Rejection for Harmonics
At 2.4 GHz WiFi, +20 dBm TX, H₂ = −20 dBc (raw PA): H₂ raw power = 20 − 20 = 0 dBm at 4.8 GHz FCC limit at 4.8 GHz: −41.3 dBm EIRP (assuming 0 dBi antenna, EIRP = conducted) Required rejection at 4.8 GHz: 0 − (−41.3) = 41.3 dB Filter spec: BPF must provide >42 dB rejection at 2×2.4 GHz = 4.8 GHz Load filter .s2p in RF View → marker at 4.8 GHz → verify >42 dB rejection
RF View Harmonic Analysis: Load TX filter .s2p, extend frequency range to 2× or 3× operating frequency, use single marker at harmonic frequencies to measure rejection. Verify compliance margin. Free on Android.