Frequency and wavelength
From Wikiham, the ham radio free encyclopedia
Frequency is the number of cycles per second, measured in hertz (Hz). Wavelength is the distance occupied by one cycle of a travelling wave. Their relationship helps explain band names, antenna dimensions and electrical lengths.
Basic relationship
λ = v / f λ ≈ 300 / f_MHz (metres, free-space estimate)
λ is wavelength in metres, v is propagation speed in metres per second and f is frequency in hertz. In vacuum, v equals the speed of light, 299,792,458 m/s. Air is close enough to vacuum for many initial antenna estimates.
| Frequency | Approximate free-space wavelength | Quarter wavelength |
|---|---|---|
| 7 MHz | 42.8 m | 10.7 m |
| 14 MHz | 21.4 m | 5.35 m |
| 27 MHz | 11.1 m | 2.78 m |
| 144 MHz | 2.08 m | 0.520 m |
The 27 MHz CB band is called 11 metres because of its approximate wavelength. A band name is a convenient label; it is not an exact wavelength at every frequency in that band.
Electrical length
An antenna with a quarter-wave electrical length is not necessarily a wire exactly one quarter of a free-space wavelength long. Geometry, conductor thickness, insulation, loading and nearby objects affect its behaviour.
Waves also travel more slowly in a transmission line than in free space. With a cable velocity factor VF:
Cable wavelength = VF c / f
At 27 MHz, a cable with VF = 0.66 has a wavelength of about 7.33 m. Its quarter-wave electrical length is therefore about 1.83 m. This is a cable example, not a prescription for the length of a radiating antenna.