Antennas: Gain, Aperture, and Why the Ground Plane Is Part of the Radiator

Part of the RF chain series — a page per block. The antenna is at both ends: in front of the filter on receive, and after the coupler on transmit.

The RF chain, block by block —Antenna · Filter · LNA · Mixer · LO · IF & ADC · PA · Isolator · Coupler · Overview

An antenna converts a guided wave into a radiated one. It is also the component least under your control, because its behaviour depends on everything around it — the ground plane, the enclosure, the battery, the user’s hand — and most antenna failures are failures to account for that.

1. The figures of merit

Directivity — how concentrated the radiation is, relative to isotropic. Pure geometry.

Efficiency — how much accepted power actually radiates rather than heating copper, dielectric and nearby lossy material.

Gain = directivity × efficiency, quoted in dBi. This is the number that matters, and the one most often confused with directivity in marketing material.

Impedance bandwidth — where the match is acceptable, usually $|S_{11}| < -10$ dB. Note this is a match specification and says nothing about whether the antenna is radiating: a lossy antenna can have superb return loss precisely because it absorbs rather than reflects. A perfect match is not a working antenna.

Pattern, beamwidth, sidelobes, front-to-back ratio, cross-polarisation — the spatial description, and what a chamber measures.

2. The link budget

$$P_r = P_t\, G_t\, G_r \left(\frac{\lambda}{4\pi R}\right)^{2} \qquad \mathrm{FSPL\ [dB]} = 20\log_{10}\!\left(\frac{4\pi R}{\lambda}\right)$$

Why path loss rises with frequency, and what actually causes it

Space is not lossier at 28 GHz. The $\lambda^2$ in Friis comes from the receiving antenna’s effective aperture:

$$A_e = \frac{G \lambda^{2}}{4\pi}$$

The horn has nearly 18 dB more gain and still catches less than half the power, because aperture scales with $\lambda^2$. That single fact explains millimetre-wave system architecture: you cannot win by making one element better, so you rebuild the aperture out of many elements — and once you have many elements you may as well phase them and steer.

3. Near field and far field

$$R_{\text{ff}} = \frac{2D^{2}}{\lambda} \qquad D = \text{largest antenna dimension}$$

This matters twice. It sets how far away a measurement range or a simulation’s radiation boundary must be. And it means a device characterised at 30 cm may well have been measured in its own near field, where the pattern is not yet formed — so the gain figure does not mean what the datasheet implies.

4. The common types

For reference, the canonical radiators everything else is compared against:

The monopole’s extra 3 dB is not free energy: it radiates into a hemisphere instead of a sphere, so the same power is concentrated into half the solid angle. And “infinite ground plane” is doing real work in that row — see §6.

5. The size limit, which is physics rather than engineering

There is a hard bound on how small an antenna can be for a given bandwidth, and it is worth knowing because it settles arguments before they start. For an antenna that fits inside a sphere of radius $a$, with $k = 2\pi/\lambda$, the Chu–Wheeler limit on radiation $Q$ is:

$$Q_{\min} = \frac{1}{(ka)^{3}} + \frac{1}{ka}$$

and bandwidth follows from $Q$ — for a VSWR-2 definition, $\mathrm{FBW} \approx (S-1)/(Q\sqrt{S}) \approx 0.707/Q$. Run the numbers for real cases:

The 2.4 GHz ISM band is 83.5 MHz wide — 3.4% fractional bandwidth. Read the table: a radiator genuinely confined to a 5 mm sphere cannot cover it, at any efficiency, by any design, ever. A 10 mm sphere can, with margin.

This is the honest explanation of the chip antenna. A 3 × 1 mm ceramic part obviously violates the bound on its own — so it is not the antenna. The board’s ground plane is the radiator, and the chip is a coupling element that excites it. That is why the clearance area, the plane dimensions and the feed position dominate the result, why vendor data is taken on a specified evaluation board, and why a chip antenna on a small board with a small plane is simply a lossy component. The bound has not been beaten; the sphere is bigger than it looks.

Two more consequences worth carrying:

• Efficiency is the escape hatch, and it is a bad one. You can always widen the match by adding loss — a resistor, a lossy ferrite, a deliberately poor conductor — and the return loss will look excellent. The Chu bound constrains the radiating Q, not the total Q. This is the mechanism behind “a perfect match is not a working antenna”, stated in §1 and worth restating here with the reason attached.
• Multiband is harder than wideband at small size, because each band needs its own resonance in the same volume. That is why a small multiband antenna has several arms, and why adding a band late in a project is a redesign rather than a tweak.

6. The thing that ruins PCB antennas

The ground plane is part of the antenna. A monopole or inverted-F does not radiate on its own — it radiates against its ground plane, and the plane’s size and shape set the pattern, the impedance and the efficiency. A chip antenna characterised by its vendor on a 100 × 40 mm evaluation board will behave completely differently on your 25 × 25 mm board, and the datasheet gain will not be reproduced.

The corollaries:

• Keep the ground plane the size the antenna was designed for, or re-tune for yours.
• Keep the clearance region genuinely clear — no copper, no traces, no components, on any layer.
• The enclosure is part of it too. Plastic loads it (shifting frequency down); metal near it detunes or shields it.
• The user is part of it. A hand or a body is lossy dielectric at these frequencies, and hand-loading can cost several dB and shift the tuning.
• The cable is part of it. Feed-line common-mode current radiates, and on a small board the cable can radiate more than the antenna. This is why measurements need a balun or ferrite on the feed, and why a chamber measurement without one measures the cable.

The practical consequence: simulating the antenna alone is nearly meaningless. Simulate it in the assembly — board, components, enclosure — which is a 3D EM problem best handled by a time-domain or MoM solver.

7. Matching, and the two losses people forget to budget

An antenna’s impedance varies across its band, and matching it is a Smith chart exercise. Three practical notes:

Put a pi-network footprint at the feed even if you intend to fit 0 Ω links. Antenna tuning is empirical — it depends on the final mechanical assembly — and having three component sites already laid out turns a re-spin into a component change. Use high-$Q$ parts (wirewound or thin-film inductors, C0G capacitors); a cheap multilayer inductor in a matching network is a resistor with an inductive label, and its loss goes straight into your efficiency.

Match to the antenna in its final environment, measured, not to the simulated or datasheet impedance. The difference is routinely large enough to matter.

Budget the mismatch loss rather than the return loss. They are different numbers and the second one flatters:

VSWR 2 costs half a decibel. That is the number that justifies stopping there on most designs, and it is also the number that says a 3:1 antenna is not a catastrophe if the link has the margin — reflected power is a PA ruggedness problem long before it is a link-budget problem.

And budget the polarisation loss, which is usually bigger. Two linearly polarised antennas tilted by an angle $\theta$ relative to one another lose $-20\log_{10}\cos\theta$:

Circular to linear is a fixed 3.0 dB either way. A handheld device that can be held at any angle has, on average, several decibels of polarisation loss that no amount of antenna efficiency recovers — which is the real argument for circular polarisation on the fixed end of an asymmetric link, and for polarisation diversity where it can be afforded.

8. Measuring one honestly

Efficiency is the measurement most often skipped and the one that catches the real problem. Return loss tells you the power went in; only efficiency tells you it came out as radiation rather than heat.

9. A design method

1. Budget the link. Path loss, required SNR, and therefore the gain needed at each end.
2. Check the size bound from §5 before anything else. If the volume available cannot hold the bandwidth required, no design effort will fix it and the conversation is a mechanical one.
3. Choose a type from the gain, bandwidth and volume available.
4. Fix the ground plane and clearance early — this is a board-layout constraint, not an antenna detail, and it is nearly impossible to add later.
5. Simulate in the assembly, with enclosure and nearby metal.
6. Lay out a tuning network at the feed.
7. Prototype and tune on real hardware, in the real enclosure.
8. Measure pattern, efficiency and OTA, with the feed choked.

10. Example parts, and when to buy rather than print

A printed antenna costs nothing per unit and a great deal in engineering and schedule. A bought antenna costs a few cents to a few dollars and arrives characterised. The crossover is lower than most teams assume — if the volume is under a few hundred thousand units, or the schedule is tight, or nobody on the team has tuned an antenna before, buy it.

Chip and SMD antennas — smallest, most ground-plane dependent, cheapest:

Flexible / FPC antennas with a cable — better efficiency than a chip, and they move the radiator away from the board’s noise:

External and connectorised — where the pattern and efficiency have to be right:

Matching components are part of the antenna choice and deserve the same care: Murata LQW18A wirewound inductors and C0G/NP0 capacitors are the usual choice, because $Q$ in the matching network is efficiency in the antenna.

Always buy a connectorised reference antenna for the band, whatever else you do. When your printed design measures 10 dB down, the only way to know whether the problem is the antenna, the board, the chamber or the radio is to substitute something known-good — and that substitution takes minutes if the part is on the shelf and weeks if it is not.

11. The pitfalls

• Simulating the antenna without its ground plane, enclosure or neighbours.
• Reproducing a chip antenna’s datasheet gain on a smaller ground plane.
• Reading return loss as if it were efficiency.
• Measuring in the near field and quoting the gain as far-field.
• No tuning network footprint, so tuning means a board re-spin.
• A chamber measurement with an unchoked cable — measuring the feed line.
• Components or copper creeping into the keepout on an inner layer.
• Promising a bandwidth the available volume cannot physically support.
• A matching network built from low-$Q$ parts, then blaming the antenna for the efficiency.
• Budgeting return loss and forgetting polarisation, which is usually the larger loss.

Further reading

• Constantine Balanis, Antenna Theory: Analysis and Design. The standard text. Everything in §1 through §4 is here, done properly.
• John Volakis (ed.), Antenna Engineering Handbook. The reference you reach for when you need a specific type rather than the theory.
• Steven Best / Arthur Yaghjian, and the original: L. J. Chu, “Physical limitations of omni-directional antennas”, J. Appl. Phys. 19, 1948 — the bound in §5, from the source.
• Warren Stutzman and Gary Thiele, Antenna Theory and Design. A gentler route into the same material than Balanis.
• Vendor application notes — genuinely. Johanson, Taoglas and Abracon publish ground-plane and clearance guidance for their own parts that is more useful than any textbook for the specific job of making that part work on your board.

The RF chain, block by block —Antenna · Filter · LNA · Mixer · LO · IF & ADC · PA · Isolator · Coupler · Overview

Glossary

Chu–Wheeler limit — The bound on radiation $Q$ for anything inside a sphere of radius $a$: $Q_{\min} = 1/(ka)^3 + 1/(ka)$, and bandwidth follows from it. It settles arguments: a radiator genuinely confined to a 5 mm sphere cannot cover the 2.4 GHz ISM band at any efficiency, by any design.

Counterpoise / ground plane — The other half of a monopole or inverted-F. It is not a reference, it is a radiator, which is why a chip antenna on a small plane behaves nothing like the same part on the vendor’s evaluation board, and why the clearance keepout is a layout constraint rather than a suggestion.

Cross-polarisation — Radiation in the orthogonal polarisation, typically 20–30 dB below the co-polar pattern. It sets the practical floor on polarisation isolation, which is why “infinite rejection at 90°” is a textbook answer rather than a measured one.

Directivity vs gain — Directivity is pure geometry, how concentrated the pattern is. Gain is directivity times radiation efficiency, and it is the number that matters. Marketing material confuses them in one direction only.

Effective aperture — $A_e = G\lambda^2/4\pi$: the collecting area a receiving antenna presents. It carries the $\lambda^2$ in the Friis equation, which is why a 20 dBi horn at 28 GHz catches less power than a 2.15 dBi dipole at 2.45 GHz, and why millimetre-wave systems are built from many elements rather than one better one.

Impedance bandwidth — Where the match is acceptable, usually $|S_{11}| < -10$ dB. A match specification that says nothing about radiation: a lossy antenna can have superb return loss precisely because it absorbs rather than reflects.

$ka$ — Electrical size, $2\pi a/\lambda$. The single parameter the size-bandwidth bound depends on, and the reason “electrically small” ($ka < 1$) is a meaningful category rather than a vague one.

Mismatch loss — $-10\log_{10}(1-|\Gamma|^2)$, the power not delivered because of reflection. Worth budgeting instead of return loss, because the numbers are far less alarming: VSWR 2 is 0.51 dB, which is why chasing a match past about 15 dB of return loss rarely pays.

Near field / far field — The pattern is only formed beyond $R = 2D^2/\lambda$. A part characterised at 30 cm may have been measured inside its own near field, where the gain figure does not mean what the datasheet implies.

PIFA / IFA — Planar and printed inverted-F antennas: the compact, easily printed default for handsets and IoT. Both work against the ground plane, so both inherit everything in the counterpoise entry above.

Polarisation loss — $-20\log_{10}\cos\theta$ for two linear antennas tilted by $\theta$; a fixed 3.0 dB between circular and linear. A handheld device held at any angle averages several decibels of it, which no amount of antenna efficiency recovers.

Radiation efficiency — The fraction of accepted power that leaves as radiation rather than heating copper, dielectric or a nearby hand. Measured in a reverberation chamber or with a Wheeler cap, and the measurement most often skipped — it is the one that separates “matched” from “working”.

Wheeler cap — A conducting shell placed over an antenna so that radiation is suppressed and only loss remains, letting radiation resistance be separated from loss resistance. The cheap way to measure efficiency without a reverberation chamber.

Related

• The RF chain overview
• The filter behind it
• The isolator — which protects the PA from what the antenna reflects
• The directional coupler — how forward and reflected power get measured
• Which solver to use — MoM and time-domain for radiation

Have an antenna that measures nothing like the model, or a link budget that will not close? That’s what we do. Reach us at circuit-design.space.