S4-2.3 Antenna Arrays

What this is and why it exists

One antenna's pattern is fixed by its shape. Several antennas fed together make a pattern you can design — and steer electronically, with no moving parts. That idea, the array, is how radar sweeps the sky and how a 5G base station points a private beam at your phone. The unit's one great abstraction is the array factor, and everything else is choices about spacing, phase and amplitude.

The vocabulary

• Array factor — the pattern the array geometry and feeding alone would produce with ideal point sources; multiply by the element's own pattern for the total.
• Uniform array — equal amplitudes, equal spacing, a constant phase step from element to element.
• Broadside array — elements fed in phase; the beam fires at right angles to the line of the array.
• End-fire array — the phase step matches the spacing delay; the beam fires along the line of the array.
• Binomial array — amplitudes follow binomial coefficients: no side lobes at all, at the cost of a wide main beam.
• Tschebyscheff array — amplitudes chosen so every side lobe sits at one designed level; the sharpest beam possible for that level.
• Phased array — an array whose per-element phases are electronically adjustable, steering the beam without motion.

The mental model

Stones dropped in a pond. Two stones dropped together make ripples that reinforce along the centre line and cancel along seams — that interference figure is the array factor of a two-element array. Feed both elements in phase and the reinforcement is at right angles to the pair: broadside. Delay one element by exactly the time the wave needs to travel between them and the reinforcement follows the line of the pair: end-fire. Every array behaviour is that picture with more stones.

The total pattern obeys one clean law — pattern multiplication: element pattern times array factor. The array factor is where design happens, because it alone depends on the three knobs of number, spacing and phase. More elements sharpen the beam and raise directivity; a uniform N-element array's directivity grows in proportion to N. But uniform feeding has a signature flaw: side lobes, the strongest only about 13 decibels below the main beam, leaking power into — and receiving interference from — unintended directions.

Amplitude tapering is the trade for that. Binomial weighting removes side lobes entirely and pays with a broad main beam; Tschebyscheff weighting is the exact optimum in between, pinning all side lobes at one chosen level while keeping the narrowest beam that level permits. Beamwidth against side-lobe level is THE array design decision, and it has no free option.

The phased array makes the phase knob live: shift the inter-element phase electronically and the beam swings in microseconds. One aperture then serves many users in turn — which is precisely what massive MIMO in 5G does with dozens of elements.

What you should now be able to explain or do

Derive the two-element array factor from path difference and phase difference. State the feeding conditions for broadside and end-fire operation and sketch both beams. Explain the uniform array's side-lobe level and what binomial and Tschebyscheff weightings do about it. Describe how a phased array steers, in two sentences.

Check yourself