Antenna gain and radiation patterns

What gain actually measures, why an antenna cannot amplify, the difference between dBi and dBd, and how to read a radiation pattern.

An antenna cannot amplify anything

This is the first thing to get straight, because the word "gain" invites exactly the wrong mental model. An antenna is a passive lump of metal. It has no power supply. It cannot put out more energy than you feed into it, and a 12 dBi antenna does not turn 100 mW into 1.6 W.

What it does is redistribute. Gain measures how much more power an antenna sends in its best direction compared with a reference antenna radiating the same total power. Every decibel gained in one direction is taken from another. A high-gain antenna is not a louder antenna; it is a narrower one.

The useful consequence is that gain works on receive exactly as it does on transmit. Antennas are reciprocal: the pattern that concentrates your transmitted power into a beam concentrates incoming signal from the same directions. That is why upgrading the antenna at either end of a link helps, and why upgrading both helps twice.

The reference: what "isotropic" means

Gain is meaningless without saying "compared to what". The usual reference is an isotropic radiator — a theoretical point source radiating equally in every direction, its pattern a perfect sphere.

It cannot be built. It is not even physically possible for a real antenna, because any real radiator has structure and therefore direction. It exists purely as a definition, and that is its value: it is an unambiguous yardstick everyone can agree on. Gain against it is writtendBi.

The other common reference is the half-wave dipole, givingdBd. A dipole is a real antenna with real directivity of its own — it already concentrates power towards its broadside — so a gain quoted against it is a smaller number for the same antenna.

dBi = dBd + 2.15

That 2.15 dB is the dipole's own directivity, and it is the single most misquoted figure in antenna specifications. If a datasheet says "3 dB gain" without a suffix, you do not know whether it means 3 dBi or 3 dBd — and those differ by more than a factor of 1.6 in power. Assume nothing; the optimistic reading is usually the one the marketing department intended.

Directivity, efficiency, and why they differ

Two quantities hide inside the word gain, and separating them explains most of the disappointment people have with small antennas.

Directivity is pure geometry: how the radiation is shaped, assuming no losses at all. Efficiency is the fraction of the power you feed in that actually leaves as radiation rather than warming the conductor, the matching components and the surrounding plastic.

Gain = Directivity × Efficiency

A chip antenna a few millimetres across can have perfectly respectable directivity — it is nearly omnidirectional, so its directivity is close to 1 — and still deliver poor gain, because its efficiency might be 40%. Losing 60% of your power as heat costs 4 dB before the signal has gone anywhere. That loss is invisible on a network analyser looking only at match, which is why a well-matched small antenna can still perform badly.

It follows that gain can never exceed directivity, and that any quoted gain figure is really a claim about both. When a very small antenna is quoted with a surprisingly good number, efficiency is where the optimism usually lives.

Reading a radiation pattern

A radiation pattern is a plot of relative field strength against direction, almost always drawn as two slices through the three-dimensional shape:

• The E-plane contains the electric field vector — for a vertical dipole, the vertical slice.
• The H-plane contains the magnetic field, at right angles — the horizontal slice for that same dipole.

A half-wave dipole is often described as omnidirectional, and in the H-plane it is: a circle. In the E-plane it is a figure of eight, with deepnulls off the ends of the element. The full pattern is a doughnut with the antenna through the hole. That matters practically — a vertical whip radiates almost nothing straight up, so a node directly above a gateway can be in a null while one far away on the horizon is fine.

Three numbers summarise most patterns:

• Beamwidth — the angle between the points where power has fallen to half its peak, the −3 dB points. A 12 dBi Yagi might have 30° of beamwidth; a 20 dBi dish only a few degrees.
• Front-to-back ratio — how much less the antenna radiates directly behind it. This decides how well a directional antenna rejects interference from behind, which is often why you fit one.
• Side lobes — the smaller humps either side of the main beam. They are unavoidable, and they are how a "directional" antenna still hears things it is not pointed at.

Watch the scale on any pattern plot. A logarithmic radial scale flatters the antenna by compressing the nulls; a linear one exaggerates the main lobe. The same antenna can look very different on two plots that are both honest.

EIRP: what the regulator actually limits

Transmit power alone is not what the rules cap. What matters is the power radiated in the strongest direction, and that means antenna gain counts.

EIRP (dBm) = P_tx (dBm) + G_tx (dBi) − losses (dB)

So a 14 dBm transmitter into a 6 dBi antenna is 20 dBm EIRP — over the 16 dBm limit that applies in the common EU 868 MHz sub-band, even though the radio itself is well within spec. Fitting a better antenna can put a compliant product out of compliance, which is a genuinely easy mistake to make late in a project. Check the band limitsbefore choosing the antenna, not after.

You may also meet ERP, which is referenced to a dipole rather than an isotropic source. ERP and EIRP differ by the same 2.15 dB as dBd and dBi, and regulations differ over which they specify.

Effective aperture, and why higher frequencies seem to lose more

On receive, it helps to think of an antenna as having an area — the slice of the passing wave it intercepts. That is its effective aperture:

A_e = G · λ² / 4π

The λ² is the important part. For a fixed gain, aperture falls with the square of frequency, so a 2.4 GHz antenna of the same gain as an 868 MHz one physically catches far less of the wave passing it.

This is the honest answer to a question that confuses almost everyone meeting the free-space path lossformula for the first time: why does frequency appear at all, when empty space cannot absorb more at one frequency than another? It does not. Free space is not lossy. The frequency term in FSPL is really the receiving antenna's shrinking aperture, folded into the path by convention.

Computed at build time from A_e = Gλ²/4π with G = 1. The practical reading: identical hardware reaches further at 868 MHz than at 2.45 GHz, by about 9.01 dB of aperture alone.

What a gain figure does not tell you

A single number on a datasheet hides a great deal. It is peak gain, in the best direction, usually measured in an anechoic chamber on a reference ground plane, at one frequency in the middle of the band.

Your antenna will not be in a chamber. It will be near a battery, a metal enclosure, a hand, or a wall — all of which detune it and reshape the pattern. It will be asked to work across a band, not at one spot frequency. And it will often be oriented however the product happens to sit rather than however the measurement was made.

Treat quoted gain as an upper bound obtained under favourable conditions. The realised figure in a product is routinely several decibels worse, and the difference is why link margin exists.

Typical gains, for scale

Realised figures for a decent example of each type, not best-case datasheet numbers. Antenna types covers what each is actually for.