Ground Wave Propagation Questions and Answers

Answer: A

A fourth power law gives a factor of sixteen in power for a doubling of distance:

\[ 10\log_{10} 16 \approx 12 \]

so the signal falls by 12 dB, against six for free space. That much steeper roll off is what limits terrestrial coverage and is one reason cellular systems reuse frequencies at modest distances. Being able to convert quickly between a power law exponent and decibels per octave of range is the most useful arithmetic in coverage planning.

Answer: B

In the fourth power regime the received power is proportional to the product of the squares of the two heights, so doubling either height gains six decibels. That is why base station masts and rooftop antennas are worth their cost. Height matters far beyond simply achieving line of sight, since it also increases the path difference between the two rays. A model that makes a design variable enter as a square identifies immediately where effort is best spent.

Answer: C

Received power varies as the square of the height, so doubling it gives a factor of four:

\[ 10\log_{10} 4 \approx 6 \]

that is 6 dB. The same six decibels would follow from doubling the mobile's height, which is rarely possible. Height gain of this kind is why the first few tens of metres of mast are so valuable and why site acquisition dominates the cost of a cellular network.

Answer: D

The radio horizon is where the straight or refracted ray from the antenna becomes tangent to the earth, and it is slightly further than the optical horizon because of atmospheric refraction. Beyond it, diffraction and tropospheric scatter provide weaker signals rather than none at all. It is a geometric limit rather than an antenna setting or a service boundary. Distinguishing a geometric horizon from an absolute limit of reception prevents overconfident coverage predictions.

Answer: A

Substituting the height directly:

\[ d = 4.12\sqrt{100} = 41.2 \]

kilometres, so about 41 km. The square root means that quadrupling the height only doubles the horizon, which is a strong argument for siting on high ground rather than building a taller mast. Adding the receiving antenna's own horizon gives the total path length available for a line of sight link, which is the calculation actually needed in planning.

Answer: B

Refractive index falls with height in the standard atmosphere, so the ray bends gently downward and follows the curvature a little way, extending the horizon by about fifteen per cent. Representing this by an earth of four thirds the true radius, with straight rays, is the standard simplification. Diffraction extends coverage beyond the horizon but is a separate mechanism, radio and light travel at the same speed, and antenna tilt is a design choice. Curved rays over a real earth are replaced by straight rays over a fictitious one.

Answer: C

Multiplying the earth's radius by four thirds reproduces the effect of standard downward refraction while letting rays be drawn as straight lines on a profile, which makes path planning far easier. Non standard conditions are handled by using a different factor. It has nothing to do with terrain height, the ionosphere or a deliberate margin, though margins are added separately. Replacing a curved ray over a curved earth with a straight ray over a modified earth is a classic engineering simplification.

Answer: D

A strong temperature inversion or a sharp humidity gradient can create a layer in which the wave is refracted back downward repeatedly, so it travels hundreds of kilometres with little loss. It produces both unexpectedly good reception and unexpected interference, particularly over water. Absorption, terrain channelling and conducted propagation are different phenomena. An atmospheric layer behaving as a waveguide is a striking illustration of refraction carried to its extreme.

Answer: A

Because a duct occasionally carries a signal hundreds of kilometres, a frequency assignment that is safe on ordinary days can suffer severe interference for hours at a time, and the statistics of its occurrence must be built into planning criteria. Coverage within the duct is if anything enhanced, polarisation is preserved, and reception is not prevented. A rare but severe condition is harder to plan for than a common mild one, which is why propagation statistics are expressed as percentages of time.

Answer: B

Field strength varies from place to place because of terrain and clutter, so predictions are quoted as a level exceeded at a stated percentage of locations, and often for a stated percentage of time as well. Ninety nine per cent of locations requires a much lower level than fifty per cent. It is a statistical statement about the spatial distribution rather than about the accuracy of the model or the power flow. Coverage is inherently a probability, and treating it as a boundary line is the commonest planning error.