Antennas, wireless links and propagation environments

Gain describes direction and a reference

An antenna couples a circuit to a radiated electromagnetic field. Its radiation pattern describes directional behaviour. Gain relative to an isotropic reference describes concentration together with the efficiency convention used; an antenna does not create energy merely by having gain. Directional gain can improve one direction while reducing coverage elsewhere.

Receive effective aperture relates arriving power density to available received power under matching and polarization conditions. For the corresponding antenna, Ae=Gλ²/(4π). This is an effective collecting area, which need not equal its visible physical area. Polarization describes the field’s orientation and evolution; incompatible transmit and receive polarization can reduce coupling.

Know what the free-space model assumes

For matched, polarization-aligned antennas in one another’s far field with an unobstructed free-space path, Pr=PtGtGr(λ/(4πR))². Powers use consistent linear units and gains are linear ratios in this expression. R is separation and λ wavelength. Gains must correspond to the actual directions and frequency.

The far-field assumption concerns antenna dimensions as well as wavelength and separation. An apparent line of sight does not automatically establish every model condition. Free-space spreading is not energy absorption: it describes how much of the outgoing field the specified receiving antenna collects. A path through weather, terrain or structures adds other effects.

Add physical mechanisms deliberately

Reflected paths can arrive with different delays and phases, causing constructive or destructive combination. Motion can change those phases and produce fading. Obstacles can introduce diffraction or blockage; materials can absorb or scatter energy. Antenna misalignment and installation surroundings can alter the actual pattern compared with an isolated component specification.

A gain increase can narrow useful pointing tolerance. Diversity may help when its paths fail differently, but two closely related observations can share the same blockage. Evaluate the environment and service over time rather than equating a single power reading with reliable coverage. Frequency and power selections also require the applicable operational context; these numerical examples authorize no transmission.

A conditional far-field calculation

Assume Pt=.05 W, Gt=4, Gr=2, λ=.15 m and R=100 m, with all stated ideal conditions supplied. Pr=.05×4×2(.15/(4π100))²=5.699×10⁻⁹W, or about−52.442 dBm. Here dBm means 10 log₁₀ of power relative to 1 mW.

At 200 m with unchanged antenna gains and wavelength, power is one-quarter, 6.021 dB lower. This is about−58.462 dBm. The graph omits fading, feeder loss and receiver noise. It is a conditional range curve rather than a site survey, an equipment rating or proof of a specific data rate.

Try the reasoning

1. Does doubling distance halve received power in this model?

   Show the answer and reasoning

   No. The inverse-square relationship makes it one-quarter when other quantities remain fixed.

2. Can an antenna gain be inserted as 6 into the linear equation because it is 6 dBi?

   Show the answer and reasoning

   No. A gain of 6 dBi corresponds to a linear ratio 10^(6/10)≈3.981. Decibels and linear ratios must not be mixed.

3. A transmitter is visible but the link fades with movement. Is that impossible?

   Show the answer and reasoning

   No. Multipath and pattern/polarization changes can vary received signal despite a visible direct path.

What to carry forward

Antenna and channel assumptions determine the scope of every wireless prediction.