How far a signal reaches is a sum: power in, minus the loss on the way, plus what the antennas add. This topic turns that sentence into numbers, and shows what antennas actually do.
1. DefinitionHow a signal travels, and what an antenna does
- Free-space loss. A signal spreads out as it travels, so the power through a given area falls with distance, even in empty space and with nothing absorbing it.
- Reflection. A wave bounces off large smooth surfaces such as walls, floors, metal and glass. This creates the echoes (multipath) from the Foundations topic on waves.
- Absorption. Materials turn some of the energy into heat. Water, concrete and people absorb more than plasterboard and air.
- Diffraction and scattering. Waves bend around edges and scatter off small objects, which is how a signal reaches places with no straight line to the antenna.
- An antenna converts between the electrical signal in a cable and a radio wave in space. It does not make power; it chooses where the power goes. Its gain (in dBi) says how much stronger it is in its best direction than an ideal all-direction antenna.
- A link budget adds up every gain and subtracts every loss between the transmitter and the receiver.
2. PurposeWhy engineers calculate it
- Planning. Before any equipment is bought, a link budget tells you roughly how far a signal will reach and what it takes to cover a space.
- Troubleshooting. A weak signal is either too much loss, too little power or a poor antenna arrangement. The budget shows which.
- Compliance. Regulators limit radiated power (EIRP), so you must know what the antenna adds.
3. MechanismBuild a link budget
The model uses the free-space loss at 1 m plus a path-loss exponent n for the building and a loss for each wall. Drag the transmit power, the walls and the level the receiver needs, and compare how the three bands reach with the same settings.
Try this. (1) Choose free space (n = 2) and note the range, then choose cluttered (n = 4). (2) Add two walls. (3) Switch from 2.4 to 6 GHz with everything else equal. The higher band loses range because free-space loss rises with frequency, and each extra wall costs the same number of decibels whatever the distance.
4. VisualAntenna patterns and the Fresnel zone
An antenna’s pattern shows where its power goes. A dipole radiates in a doughnut shape; a directional antenna squeezes the same power into a narrow beam, so it is stronger on boresight and weaker elsewhere.
A line-of-sight link also needs room around the line. The first Fresnel zone is the ellipsoid in which reflected waves arrive less than half a wavelength late; anything that cuts into it costs signal even when the straight line is clear.
5. MathematicsThe formulas, with numbers
Free-space path loss is FSPL = 20 log10(d) + 20 log10(f) – 27.55 dB, with d in metres and f in MHz (ITU-R P.525). Every doubling of distance adds 20 log10(2) = 6 dB. Every doubling of frequency adds the same 6 dB.
| Free-space loss at | 1 m | 10 m | 100 m |
|---|---|---|---|
| 2.4 GHz (2437 MHz) | 40.2 dB | 60.2 dB | 80.2 dB |
| 5 GHz (5500 MHz) | 47.3 dB | 67.3 dB | 87.3 dB |
| 6 GHz (6135 MHz) | 48.2 dB | 68.2 dB | 88.2 dB |
Indoors the loss grows faster than free space. A common model is PL(d) = PL(1 m) + 10 n log10(d) + wall losses, where n is about 2 in free space and larger in cluttered buildings (ITU-R P.1238 gives measured values for offices and homes). Treat n and wall losses as numbers to measure, not constants.
Link budget. Received power = EIRP – path loss + receive antenna gain. Worked example: 20 dBm EIRP in 5 GHz, a client that needs -67 dBm, n = 3 and one 5 dB wall. The most path loss you can afford is 20 – (-67) = 87 dB. Take off 47.3 dB (free space at 1 m) and 5 dB (wall): 34.7 dB is left for 30 log10(d), so d = 1034.7 / 30 = 14.4 m.
First Fresnel zone radius at the middle of a link of length d is 0.5 × sqrt(λ d). For d = 100 m, that is 1.75 m at 2437 MHz and 1.17 m at 5500 MHz, so the zone is narrower at higher frequencies. Keeping about 60% of that radius clear is a common rule of thumb.
Antenna gain and beamwidth. Gain is not free: a gain of G dBi means the power is concentrated into roughly a solid angle of 4π / 10G/10 steradians. A half-wave dipole has 2.15 dBi, so dBd = dBi – 2.15.
6. Real-world behaviourWhat the textbook leaves out
- Materials differ widely. Plasterboard, brick, concrete, glass with metal coating, lifts and water tanks each cost a different amount, and the cost depends on the angle and the frequency. That is why an on-site survey beats a rule of thumb.
- Antenna orientation matters. A vertical dipole radiates little along its length, and a client whose antenna is tilted may see a weaker signal than one that is upright. Polarisation mismatch costs signal too.
- The link is two-way. A loud access point and a quiet phone give a link that is good in one direction and poor in the other; the client’s power and antennas set the return path.
- Gain moves coverage, it does not add it. A high-gain antenna stretches the beam in one direction at the expense of others, and regulators limit the EIRP it produces.
Practical validationProve it in a capture and on a spectrum analyser
Reading about a band is one thing; seeing it in your own evidence is the skill. These checks work with any monitor-mode capture:
- Stand next to an access point and record the signal strength at 1, 2, 4 and 8 m along a clear line. Each doubling of distance should cost roughly 6 dB in free space and more in a cluttered room. The slope gives you the exponent: n = (signal at 1 m – signal at d) / (10 log10 d).
- Rotate a phone or laptop by 90 degrees at the same spot and see how much the signal changes.
- Question to answer: with the same transmit power, how much shorter is the range at 6 GHz than at 2.4 GHz in free space? (Answer: free-space loss is 20 log10(6135 / 2437) = 8.0 dB higher, so the range is 108.0/20 = 2.5 times shorter.)
Check your understandingQuick quiz
ReferencesSources and further reading
- ITU-R P.525: Calculation of free-space attenuation
- ITU-R P.1238: Propagation data and prediction methods for indoor radiocommunication systems
- Ofcom: UK Interface Requirement 2030 (IR 2030), current edition
Free-space loss is defined by ITU-R P.525 and indoor models by ITU-R P.1238. Antenna patterns in the models are idealised teaching shapes, and the exponent and wall losses are inputs to explore, not measured values. The EIRP limits are from Ofcom IR 2030 for the UK; other regions set their own.