Multiple hop and atmospheric ducts

Multiple hop

Multiple-hop (multi-hop) propagation is sky-wave transmission in which the wave is reflected by the ionosphere, comes down, is reflected by the earth's surface, goes up again, and so on, several times before reaching a distant receiver.

  ~~~~~~/\~~~~~~~~/\~~~~~~~~/\~~~~~~ F2 layer
       /  \      /  \      /  \
      /    \    /    \    /    \
  ===Tx=====\==/======\==/======Rx===
           earth      earth
   hop 1      hop 2      hop 3

• Single-hop range is limited by earth curvature: about 2000 km via E layer and about 4000 km via F2.
• Longer distances (round the world) need multiple hops.
• Each hop adds loss (ground reflection loss, D-layer absorption twice per hop), so the signal weakens and fades more; sea surface is a better reflector than land.
• Multiple paths with different hop counts can arrive together, causing multipath fading and echo.

Use of atmospheric ducts for microwave propagation

An atmospheric duct is a layer of the lower atmosphere in which the refractive index decreases so rapidly with height (dM/dh < 0, where M = (n − 1 + h/R) × 10⁶) that rays bend down more strongly than the earth curves. The duct traps the wave between its boundaries (or between the upper boundary and the ground), guiding it like a waveguide.

   ~~~~~~~~~~~ top of duct ~~~~~~~~~~~~
    /\     /\     /\     /\     /\
   /  \   /  \   /  \   /  \   /  \
  Tx===\=/====\=/====\=/====\=/====Rx
       ground / sea surface

Causes: temperature inversion (warm, dry air above cool, moist air), especially over sea and on calm evenings; sharp fall of humidity with height.

How it helps microwaves:

1. Microwave antennas placed inside (or near) the duct and aimed at low angles launch rays that are repeatedly bent back, so they follow the earth's curvature.
2. The duct acts like a waveguide; only wavelengths small compared with duct thickness are trapped (λ_max ≈ 2.5 d √(ΔM × 10⁻⁶)), which suits VHF high end, UHF and microwaves (thickness from a few m to some hundred m).
3. Ranges of several hundred to over 1000 km beyond the normal radio horizon become possible with low loss.

Limitations: ducts depend on weather and are not permanent, so they cannot be relied on for regular links. They often cause unwanted long-range interference and radar false echoes ("anomalous propagation"). Planned microwave links use them only opportunistically, mostly over sea.