Antenna Radiation Patterns: Lobes, Arrays and Beam Steering

The polar plot: gain as a function of direction

An antenna does not radiate power equally in all directions — even the most idealised omnidirectional source, the isotropic radiator, is a mathematical fiction used only as a 0 dBi reference. Every real antenna concentrates energy preferentially into some directions at the expense of others, and the radiation pattern is the plot of relative field strength (or power) against angle that shows exactly how. Plotted in polar form, distance from the origin at angle θ equals the gain in that direction; the resulting lobes — a dominant main lobe and smaller side lobes — are an antenna's fingerprint.

A short dipole has a doughnut-shaped pattern in 3D — maximum broadside, zero along its own axis — because it is a single oscillating current whose radiated field from every point along the wire adds constructively broadside and cancels along the axis. Its classic normalised power pattern is

U(θ) ∝ ( cos(π/2 · cosθ) / sinθ )²      — half-wave dipole
U(θ) ∝ sin²θ                              — infinitesimal (Hertzian) dipole

A quarter-wave monopole over a ground plane radiates only the upper half of that same doughnut — image theory says the ground plane behaves as a mirror, doubling the field in the upper hemisphere and eliminating the lower one, which is why a monopole has roughly 3 dB more gain than a dipole for the same input power despite using half the physical element.

Arrays: many elements, one steerable beam

A Yagi-Uda antenna gets directivity from a single driven dipole flanked by passive elements: a slightly longer reflector behind it and one or more slightly shorter directors in front. Each passive element re-radiates the field it intercepts with a phase set by its own length and spacing, and those re-radiated waves interfere constructively toward the directors and destructively toward the reflector — no extra feed power, no extra electronics, just geometry choosing which way the interference pattern adds up.

A phased array does the same trick electronically. Feed N identical elements with the same signal but a progressive phase shift Δφ between adjacent elements, and the far-field pattern is the single-element pattern multiplied by an array factor — this is the pattern multiplication theorem, the single most useful idea in array design:

AF(θ) = Σ_{n=0}^{N-1} exp[ j·n·(kd·sinθ + Δφ) ]        k = 2π/λ, d = element spacing
total pattern(θ) = element pattern(θ) × |AF(θ)|²

The array factor's main beam points where every term adds in phase, at kd·sinθ + Δφ = 0. Because Δφ is set electronically per element (a phase shifter or, digitally, a complex weight in software), the beam can be steered in microseconds with no moving parts — this is exactly how 5G massive-MIMO base stations and military and weather radar steer their beams, and how a patch antenna array on a phone forms a directional beam toward a cell tower to save power and reduce interference.

Reading the numbers: gain, beamwidth, side lobes, front-to-back

Four numbers summarise a pattern. Directivity/gain (dBi) is how much more power density the main lobe delivers compared to an isotropic radiator with the same total input power — a narrower main lobe necessarily means higher peak gain, because total radiated power is conserved and squeezing it into a smaller solid angle raises the peak. Half-power beamwidth (HPBW) is the angular width of the main lobe between its −3 dB points, the practical measure of how 'tight' the beam is. Side-lobe level (dB below the main lobe peak) matters enormously for radar and cellular systems, since energy in the side lobes is wasted at best and a source of unwanted interference or false detections at worst. Front-to-back ratio measures how well a directional antenna rejects signals from behind it — critical for a Yagi pointed at one transmitter in a room full of others.

Why the array factor changes with array size and spacing

Adding more elements narrows the main lobe of the array factor (more terms means sharper constructive/destructive interference, exactly like adding slits to a diffraction grating narrows its bright fringes) but does not by itself change the total power — the same energy is squeezed into a tighter cone, raising peak gain roughly proportionally to N. Element spacing matters just as much: spacing beyond half a wavelength lets the array factor develop extra, undesired grating lobes — full-strength copies of the main beam pointing in spurious directions — which is why practical phased arrays almost always keep d ≤ λ/2.

Frequently asked questions

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