S4-2.5 Wave Propagation

What this is and why it exists

Why does AM radio arrive from another state at night, while your 5G link dies behind one building? Because different frequencies genuinely travel by different physics. This unit is the map from frequency to mechanism — ground wave at the low end, sky wave via the ionosphere at HF, line-of-sight from VHF upward — plus the small set of formulas (critical frequency, MUF, skip distance) that let you design a sky-wave link.

The vocabulary

• Ground wave — propagation hugging the earth's surface, strong at low frequencies, fading with frequency as ground losses rise.
• Tropospheric propagation — bending, reflection and occasional long-range ducting of waves in the lowest atmosphere, where refractive index varies with height.
• Ionosphere — sun-ionised layers of the upper atmosphere that bend and return HF waves; layered, and different by day and night.
• Critical frequency — the highest frequency returned by a layer when fired straight up; set by the layer's peak ionisation.
• MUF (maximum usable frequency) — the highest frequency a slanting path can use between two stations; the critical frequency divided by the cosine of the incidence angle (the secant law).
• Skip distance — the closest ground distance at which a sky wave of a given frequency returns; inside it, sky-wave silence.
• Line-of-sight propagation — travel in nearly straight paths from VHF up; range limited by the horizon, slightly extended by atmospheric refraction.

The mental model

Three floors of one building. Ground floor, up to roughly the MF broadcast band: the wave grips the earth's surface and follows the curve — solid daytime AM coverage — but surface losses grow with frequency, so this floor ends where HF begins. Middle floor, HF (3 to 30 megahertz): the ionosphere is a mirror in the sky, though a refracting mirror — waves bend progressively in the ionised layers and return to earth hundreds or thousands of kilometres away. Top floor, VHF and above: the wave punches through the ionosphere and is gone; links are line-of-sight, horizon-limited, and blocked by buildings — the world of FM, TV, WiFi and 5G.

The middle floor has moving parts. Ionisation follows the sun: the D layer, present by day, mostly absorbs the lower HF bands; the E and F layers do the returning, and at night the D layer disappears while the F layers merge and rise. Distant stations arriving after dark are not a mystery: absorption fell and the mirror moved higher. The engineering handles are exact. Fire straight up and sweep frequency: the highest frequency that still returns is the critical frequency. Tilt the path and geometry helps — the secant law raises the usable ceiling to the MUF for that circuit. Choose a frequency and there is a minimum distance the returning wave can land: the skip distance, inside which that frequency is unreachable by sky wave. Working numericals with the secant law and skip-distance geometry is the exam skill; knowing which floor a given frequency lives on is the career skill.

The troposphere adds a wildcard on the top floor: refractive-index layering bends paths slightly beyond the geometric horizon, and occasionally forms ducts that carry VHF and microwave signals far beyond normal range — welcome on a long link, a nuisance as interference.

What you should now be able to explain or do

Assign any named frequency band to its dominant mechanism. Explain the day-night change in AM and HF reception in terms of the D and F layers. Compute MUF from critical frequency and geometry, and skip distance from frequency and layer height. State what limits line-of-sight range and what ducting does to it.

Check yourself