Antennas and radio links
For a 30 km link over flat terrain it is not enough for the antennas to see each other: at the midpoint, the Earth rises 13 m and the Fresnel zone has a radius of 14 m. The towers need about 22 m.
01What defines an antenna
An antenna is the transducer between a transmission line and space. The radiation unit covered radiation resistance, the pattern and directivity; to design a link you also need:
| Parameter | What it tells you |
|---|---|
| Gain \( G = e \cdot D \) | The directivity after subtracting the losses of the antenna; given in dBi |
| Beamwidth | The angle between the directions where the power falls to half (−3 dB) |
| Impedance and bandwidth | The range of frequencies where the SWR is acceptable, typically less than 1.5 or 2 |
| Polarization | The orientation of the electric field; the two antennas of the link have to match |
| Front-to-back ratio | How much less it radiates backward than forward |
An antenna works the same for transmitting as for receiving: by reciprocity, the pattern and the gain are the same. In reception, the gain translates into an effective area:
02Antennas in common use
| Antenna | Typical gain | Use |
|---|---|---|
| λ/4 monopole over a ground plane | 5.2 dBi, 36 Ω | AM broadcasting (the tower is the monopole), mobile units, VHF radios |
| Half-wave dipole | 2.15 dBi, 73 Ω | Reference; element of larger antennas |
| Yagi-Uda | 8 to 15 dBi | Television, VHF and UHF links |
| Patch on a board | 6 to 9 dBi | GPS, Wi-Fi, cellular telephony arrays |
| Horn | 10 to 25 dBi | Feed for parabolic dishes, measurement standard |
| Parabolic dish of diameter \( D \) | \( e\,(\pi D/\lambda)^2 \), 30 to 45 dBi | Microwave and satellite links |
The monopole takes advantage of the image formed by the ground plane: it behaves as half a dipole, with half the resistance and twice the directivity, because it radiates only over the upper half-space. The parabolic dish concentrates the energy in a beam of approximate width \( 70°\, \lambda / D \): a 0.6 m dish at 11 GHz has 34 dBi and a 3° beam, and it has to be aimed with that precision.
03The Friis equation
Between two antennas in free space, separated by a distance \( d \) much greater than their size, the received power is:
In decibels, the link is built by adding and subtracting, just like the budget of a line or that of a fiber: transmitter power, minus cables, plus gains, minus path loss. What arrives is compared with the receiver threshold, which starts from thermal noise, −174 dBm per hertz at room temperature, and adds the bandwidth, the noise figure and the signal-to-noise ratio that the modulation requires. The difference is the fade margin, the reserve for rain and for changes in propagation.
04Line of sight and Fresnel zones
A microwave link needs more than just seeing the other antenna: the energy travels through a volume around the direct ray. The first Fresnel zone is the ellipsoid where the indirect path is up to half a wavelength longer than the direct one. Its radius at a point \( d_1 \) and \( d_2 \) from the ends is:
The most common obstacle on a long link is the Earth itself. The refraction of the atmosphere bends the rays downward, and the effect is modeled with an effective Earth radius of 4/3 the real one. Even so, at the center of a 30 km link the ground rises 13 m above the straight line joining the bases of the towers: the antennas have to be about 22 m high to clear 60% of the zone over flat terrain.
Two identical dishes, at the same height over flat terrain. The graph shows the profile (the vertical scale is greatly exaggerated): the bulge of the Earth with an effective radius of 4/3, the line of sight and the first Fresnel zone, with the 60% marked. A 23 dBm radio, 2 dB of cable loss and a receiver with 28 MHz of bandwidth and a 6 dB noise figure that needs a 17 dB signal-to-noise ratio.
05Other propagation mechanisms
| Mechanism | Frequencies | What takes advantage of it |
|---|---|---|
| Ground wave | Long and medium wave | AM radio by day, hundreds of kilometers over moist ground or sea |
| Ionospheric reflection | 3 to 30 MHz | Shortwave with worldwide reach, varying with the time of day and the solar cycle |
| Line of sight | VHF and above | Television, cellular telephony, microwave links |
| Multipath | UHF and microwaves in cities | Reflections off buildings; OFDM and MIMO turn them into an advantage |
| Rain attenuation | Above about 10 GHz | Sets the margin needed on links from 18 to 80 GHz |
06Where it appears in electronics
| System | What decides the link |
|---|---|
| Radio link between base stations | 0.3 to 1.2 m dishes at 6 to 38 GHz, with margin for rain |
| Home Wi-Fi | Antennas of a few dBi, walls and multipath more than distance |
| Satellite television | 60 cm dish at 36,000 km, with a low-noise amplifier at the focus |
| Field telemetry | A Yagi at each end to gain range with low-power transmitters |
Antenna installation and alignment are covered in antennas and in microwave links, in the technician program.
07In the lab
With two identical antennas facing each other at a known distance in the far field, measure the attenuation between them with a generator and an analyzer. Solve for the gain of each from the Friis equation.
Rotate a UHF Yagi on an axis in 10° steps facing a fixed transmitter and plot the pattern. Measure the beamwidth and the front-to-back ratio.
With a terrain profile obtained from an elevation map, design a 5.8 GHz link between two points in the city: tower height, antennas and margin.
08Common mistakes
- Believing that free-space loss depends on frequency by itself. It grows with frequency because the effective area of an antenna of fixed gain shrinks; with antennas of fixed area, the link improves as the frequency goes up.
- Designing with line of sight but without clearing the Fresnel zone. The link works in the test and drops out with changes in refraction.
- Forgetting polarization. Two crossed antennas lose 20 dB or more.
- Leaving no margin. An 18 GHz link with no margin drops out in the first storm.
09Self-assessment
What is the free-space loss over 30 km at 11 GHz?
\( 32.45 + 20\log 11\,000 + 20\log 30 \approx 142.8 \) dB.
What gain does a 0.6 m parabolic dish have at 11 GHz with 55% efficiency?
\( 0.55\,(\pi \cdot 0.6 / 0.0273)^2 \approx 2630 \), that is, 34.2 dBi.
How much does the received power change if the distance is doubled?
It drops 6 dB, to a quarter.
Why does a λ/4 monopole have 36 Ω and not 73 Ω?
Because with its image in the ground plane it forms a half-wave dipole, but only the upper half radiates: the same current delivers half the power.
10Further reading
- Constantine A. Balanis. Antenna Theory: Analysis and Design. 4th ed., Wiley, 2016. The types of antenna one by one, arrays, and the Friis equation with all its assumptions.
- Warren L. Stutzman and Gary A. Thiele. Antenna Theory and Design. 3rd ed., Wiley, 2012. More design-oriented, with good chapters on aperture antennas and parabolic dishes.
- Roger L. Freeman. Radio System Design for Telecommunications. 3rd ed., Wiley, 2007. The design of complete radio links: profiles, Fresnel zones, rain and availability.