Propagation characteristics of radio waves
Radio waves are classed by frequency band, and each band travels in its own favourite way.
- Ground wave (LF and MF, below about 2 MHz): follows the curve of the ground. The ground takes away energy, more at higher frequencies, so range is about 100 to 1000 km (sea water is better than dry land). Used for AM broadcast and marine MF.
- Sky wave (HF, about 2 to 30 MHz): the ionosphere is a region 60 to 400 km up where sunlight splits air into charged particles. It has layers D (absorbs, only by day), E and F (reflect). A wave sent upward at a slant is bent back down. The landing point may be thousands of km away, and a second hop can follow.
- Space wave (VHF, UHF, microwave, above about 30 MHz): travels in a straight line, partly direct and partly reflected from the ground. The range is the radio horizon: d ≈ 4.12 (√h1 + √h2) km, h in metres. Tall towers see further. Used for FM, TV, mobile and microwave links.
Very high frequencies pass through the ionosphere, so satellites use them. Critical frequency fc is the highest frequency reflected from straight up; fc ≈ 9 √N (N = electrons per m³, fc in Hz). For a slanted beam the highest frequency that still comes back is the maximum usable frequency, MUF = fc / cos θ, where θ is the angle of incidence. The skip distance is the shortest distance where the sky wave lands; between the ground-wave range and the skip distance is the skip zone with no signal.
Propagation phenomena
On its journey a wave can do many things:
- Reflection: bounces from the ionosphere, the sea, a building. The wave gets a second path to the receiver.
- Refraction: bends when the speed changes, like the bending in the ionosphere. Bent back to Earth, this is how sky waves return.
- Diffraction: bends round a sharp edge or a hill. Long waves bend more than short ones, so AM goes round hills but UHF does not.
- Absorption: energy is lost to ground, rain or the D layer. Microwaves are weakened by heavy rain.
- Scattering: rough patches and rain send energy in many directions, which can carry a signal past the horizon a little.
- Multipath and fading: the same signal arrives by two paths. If they add, the signal is strong; if they cancel, it fades. The ionosphere moves, so HF fading is slow and deep; walking with a mobile phone also causes fast fading.
- Ducting: on warm still days a layer of air can trap VHF waves and carry them far beyond the horizon.
- Ionospheric storms from the Sun can black out HF radio for hours.
Key formulas and definitions
- Wavelength: λ = c / f, c = 3 × 10⁸ m/s
- Radio horizon: d ≈ 4.12 (√h1 + √h2) km, h in metres
- Critical frequency: fc ≈ 9 √N (N in electrons per m³, fc in Hz)
- Maximum usable frequency: MUF = fc / cos θ (θ = angle of incidence)
- Bands: ground wave < 2 MHz; sky wave 2–30 MHz; space wave > 30 MHz
Worked examples
1. A TV tower is 100 m high and the receiving antenna is 4 m high. What is the radio horizon distance?
d = 4.12 × (√100 + √4) = 4.12 × (10 + 2) = 4.12 × 12 ≈ 49.4 km.
2. The F layer has N = 10¹² electrons per m³. Find the critical frequency.
fc = 9 √N = 9 × √(10¹²) = 9 × 10⁶ Hz = 9 MHz. Waves above 9 MHz sent straight up go through.
3. The critical frequency is 8 MHz. A wave hits the layer at an angle of incidence of 60°. Find the MUF.
cos 60° = 0.5. MUF = 8 / 0.5 = 16 MHz. A 20 MHz wave at this angle would not come back.
4. A wave arrives by two paths. One path is 300 m longer than the other. What is the time difference?
Δt = 300 / (3 × 10⁸) = 10⁻⁶ s = 1 µs. This delay is what makes the two paths add or cancel, and cause multipath fading.
Common mistakes
- Saying every radio wave goes round the Earth. Only low frequencies hug the ground; VHF and above go straight.
- Thinking the ionosphere reflects every frequency. Above the MUF the wave goes through, which is why satellites work.
- Confusing skip distance with skip zone. Skip distance is the first landing point; the skip zone is the silent area before it.
- Forgetting that radio horizon uses antenna heights in metres and gives km, with the factor 4.12 (not 3.57 for the plain visual horizon).