Convert between frequency and wavelength for RF design, antennas, and electromagnetic waves.
Wavelength changes with medium; frequency remains constant
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| Band | Frequency | Wavelength | Applications |
|---|---|---|---|
| ELF | 3-30 Hz | 100,000-10,000 km | Submarine comms |
| LF | 30-300 kHz | 10-1 km | AM radio, navigation |
| MF | 300 kHz-3 MHz | 1000-100 m | AM broadcast |
| HF | 3-30 MHz | 100-10 m | Shortwave, amateur |
| VHF | 30-300 MHz | 10-1 m | FM radio, TV |
| UHF | 300 MHz-3 GHz | 1 m-10 cm | WiFi, cellular, GPS |
| SHF | 3-30 GHz | 10-1 cm | Radar, satellite |
| EHF | 30-300 GHz | 10-1 mm | 5G mmWave, imaging |
| Infrared | 300 GHz-430 THz | 1 mm-700 nm | Thermal, fiber optic |
Where λ is wavelength, c is speed of light (299,792,458 m/s in vacuum), v is wave velocity in medium, and f is frequency. In a medium with refractive index n: v = c/n
Frequency and wavelength are inversely related through the wave equation. When an electromagnetic wave travels through different media, its frequency stays constant but wavelength changes based on the medium's properties.
The speed of light c is constant. Higher frequency = shorter wavelength.
Wavelength shrinks by factor n (refractive index). Frequency unchanged.
Antennas are typically λ/4 (quarter wave) or λ/2 (half wave) in length. For 2.4 GHz WiFi: λ = 12.5 cm, so a quarter wave antenna is ~3.1 cm.
Trace lengths matter when approaching λ/10 of the signal frequency. At 1 GHz, λ = 30 cm, so traces >3 cm need transmission line treatment.
Ground plane via stitching should be spaced <λ/20 to prevent resonance. At 5 GHz, keep via spacing under 3 mm.
Distributed element filters use quarter-wave stubs. Physical length depends on effective dielectric constant of PCB material.
Cables and traces can act as antennas at their resonant frequencies. Keep lengths well below λ/4 to minimize radiation.
Common wavelengths: 850 nm (multimode), 1310 nm and 1550 nm (single-mode). Frequency is in the hundreds of THz.
| Application | Frequency | Wavelength (air) | λ/4 Antenna |
|---|---|---|---|
| FM Radio | 88-108 MHz | ~3 m | ~75 cm |
| 433 MHz ISM | 433.92 MHz | 69 cm | 17.3 cm |
| LoRa (EU) | 868 MHz | 34.5 cm | 8.6 cm |
| LoRa (US) | 915 MHz | 32.8 cm | 8.2 cm |
| GPS L1 | 1575.42 MHz | 19 cm | 4.8 cm |
| WiFi 2.4 GHz | 2400-2483 MHz | 12.5 cm | 3.1 cm |
| WiFi 5 GHz | 5150-5850 MHz | ~5.5 cm | ~1.4 cm |
| 5G Sub-6 | 3.5 GHz | 8.6 cm | 2.1 cm |
| 5G mmWave | 28 GHz | 10.7 mm | 2.7 mm |