The Phased Array

One Flat Panel, Any Direction in the Sky

This panel carries 32 × 32 = 1,024 small gold squares, each one an antenna. Together they send the same wave, which adds up above the panel into a narrow beam.

Where the beam points is set not by turning the panel but by when each element sends. Change a set of numbers and the beam points elsewhere; nothing has to swing round in between.

With 32 elements in a row half a wavelength apart, the beam is about 3.2° wide. Panels like this can usually lean their beam 50° to 60° either side.

32 × 32 elements · spacing λ/2 · beam about 3.2° wide

Many Small Waves Make One Beam

On its own, each small antenna sends a wave that spreads every way: weak, with no direction.

Put many in a row and let them send together, and their waves meet and add. Straight ahead, the crests from every element arrive together and pile up: the wave is strongest there, the main beam. At a slant the paths differ, and crests meet troughs and cancel.

The tank on the right shows the same thing with a row of fine pins tapping the water. The bright lines are crests.

All in step: the beam is square to the row

Each a Little Later, and the Wavefront Tilts

Let each element send a little later than its left-hand neighbour, by a fixed phase step Δφ.

The later waves have not gone as far as the earlier ones, so the wavefront joining them leans. A wave always travels square to its front, so the beam turns.

The angle follows sin θ = Δφ·λ / (2π d), with d the spacing and λ the wavelength. A larger Δφ leans it further; its sign picks the side.

sin θ = Δφ · λ / (2π d)

Half a Wavelength Apart

The elements cannot be too far apart. Once the spacing passes λ / (1 + |sin θ|), a second beam as strong as the main one appears in another direction: a grating lobe.

The reason is that phase comes round in a circle: in that direction, neighbouring elements differ by exactly one whole wavelength, so they line up too.

With about half a wavelength between elements, no grating lobe appears at any angle. That is why a 28 GHz array has its elements about 5.4 mm apart.

No grating lobe: d < λ / (1 + |sin θ|)

More Elements, a Narrower Beam

The longer the row, the narrower the beam: about 0.886·λ / (N·d) radians wide. Twice the elements, half the width. Steered away from straight ahead, the beam widens by about 1/cos θ.

Either side of the main beam are rings of weak side lobes. With every element equally strong, the highest is about 13 dB below the main beam.

Making the middle elements stronger and the edges weaker (a taper) pushes the side lobes lower, at the cost of a slightly wider beam.

Width ≈ 0.886 λ / (N d) · uniform: first side lobe about −13 dB

The Panel, Cut Open

One corner of the panel is cut away to show its layers. On top is the white radome, which the radio waves pass through.

Below it: the gold patch antennas on green solder mask, the dielectric and the copper ground plane, the feed-network board, the beamforming chips, and an aluminium plate with fins to carry the heat away.

A patch is a little under half a wavelength long in the dielectric, so the higher the frequency, the smaller and denser the patches.

Layer by Layer

The layers move apart along the panel’s normal. Rest the pointer on one and it is lifted out on its own and named.

The gold traces on the feed board split in two, then in four, and so on, carrying the signal to every chip; each chip passes it on to its own patches.

Where Each Element’s Phase Comes From

In the beamforming chips, every element has its own phase shifter and amplifier. Here each chip serves 4 × 4 = 16 elements.

With “Show phases” on, each patch is coloured by its phase: along a row the colour turns step by step. That step is Δφ.

Digital beamforming instead sets each element’s phase in the digital signal, and can form several beams at once.

Phase of element n: −n · Δφ

Where They Are Used

5G millimetre wave: band n257 runs from 26.5 to 29.5 GHz, and at 28 GHz the wavelength is about 10.7 mm. A phone’s millimetre-wave antenna module is itself a small phased array, and a phone can hold up to four. One experimental 28 GHz array drives 64 antennas from 4 chips and steers its beams over ±50° in 1.4° steps.

Satellite terminals: Starlink’s user terminal is an electronic phased-array panel with a 110° field of view. It receives at 10.7 to 12.7 GHz and sends at 14.0 to 14.5 GHz (Ku band). The satellite crosses the sky; the panel stays still and its beam follows.

Radar: in an active electronically scanned array (AESA) every element has its own transmit-receive module, and the beam can point somewhere new between one pulse and the next. The US National Severe Storms Laboratory’s experimental phased-array weather radar has 4,864 elements and scans the whole sky in under a minute; today’s turning radars take four to six.

The first demonstration was in 1905: Braun’s assistants set three antennas in a triangle and let one send a quarter cycle late, and the waves leaned to one side. Swapping the antennas’ roles turned the direction.

Light can be steered the same way: an optical phased array does it for a lidar, with elements spaced on the scale of the light’s wavelength; most are still at the research stage.

λ = c / f · 28 GHz → 10.7 mm · 12 GHz → 25 mm

Receiving Works the Same Way

An antenna’s pattern is the same for sending and receiving (reciprocity). A wave arriving from one direction reaches the elements one after another; shift them by the same phase steps and add, and only signals from that direction pile up, while the rest cancel.

In an active array, sending and receiving go through different amplifiers, so reciprocity does not apply directly; but on receive each element is given its phase in the same way, and the pattern follows the same array factor.

So the same panel that points its beam at a satellite also listens only in that direction. Here the waves run backwards, converging on the panel.