M7-L2 gave you the vocabulary — gain, pattern, half-power beamwidth, polarization, impedance. This lesson spends it. Six antenna families cover almost everything you will meet in practice, from the wire taped inside a doorbell to the 70-metre dish that talks to spacecraft. Each one is a different answer to the same question: how much of the sphere am I willing to give up in exchange for gain? Every antenna here obeys that trade, and the only thing that really changes down the list is how aggressively it takes the deal.
A half-wave dipole is two collinear conductors, each a quarter wavelength long, fed against each other at the centre. That is the whole design. It is the antenna the textbooks solve, the antenna the standards bodies measure against, and the reason you keep meeting the number 2.15 dBi — the gain of a lossless half-wave dipole over the isotropic radiator of M2-L4. The dBd unit exists purely so you can quote gain relative to this antenna instead: 0 dBd = 2.15 dBi.
Its pattern is the figure-of-eight you have already seen: maximum broadside to the wire, a deep null off each end. Spun about the wire axis, that figure-of-eight sweeps out a doughnut — a toroidal pattern, omnidirectional in the plane perpendicular to the conductor. The half-power beamwidth is about 78° in the plane containing the wire, and there is no beamwidth at all in the other plane, because the pattern is flat there. At resonance the feedpoint looks like roughly 73 Ω resistive, which is a happy accident of history: it is close enough to 75 Ω coaxial cable that a dipole can be fed directly, with a match good enough for broadcast reception and no matching network at all.
Do the arithmetic twice and the pattern becomes obvious. At 100 MHz, λ = (3 × 108 m/s) / (100 × 106 Hz) = 3 m, so a half-wave dipole is 3/2 = 1.5 m and a quarter-wave monopole is 3/4 = 0.75 m. At 2.4 GHz, λ = (3 × 108) / (2.4 × 109) = 0.125 m = 12.5 cm, so a half-wave dipole is 6.25 cm and a quarter-wave monopole 3.125 cm. A factor of 24 in frequency is a factor of 24 in size, and that single fact explains why a shortwave antenna is a garden-length wire and a WiFi antenna hides inside a laptop lid.
Cut a dipole in half, throw away the bottom conductor, and stand what is left on a large conducting sheet. The sheet acts as a mirror: by image theory, the currents in the ground plane produce exactly the field that the missing half of the dipole would have produced. Above the sheet, the monopole is indistinguishable from a dipole; below it, there is nothing at all. You have built half an antenna and kept a full pattern — in half the space.
Two consequences follow, and both are arithmetic you should be able to reproduce. First, the same power is now sprayed into a hemisphere rather than a whole sphere, so the power density in the useful directions doubles: +10·log₁₀(2) = +3.01 dB, giving 2.15 + 3 = 5.15 dBi for an ideal quarter-wave monopole over an infinite, perfect ground plane. Second, the feedpoint sees half the voltage across the same current, so the impedance halves: 73/2 ≈ 36 Ω. That is close enough to 50 Ω coax to be workable with a simple match, which is one reason 50 Ω became the industry habit.
The catch is that the ground plane is not optional and is almost never infinite. A quarter-wave monopole is only half of an antenna; the ground plane is the other half, and if it is small, ragged, or the wrong shape, the pattern tilts, the impedance drifts, and the gain falls short of 5.15 dBi. A car roof is a good approximation to an infinite plane at 100 MHz — which is why the classic car radio whip is about 0.75 m — but a handset has no ground plane worth the name. Its “antenna” is a small radiator working against the phone’s own circuit board and metal frame, which is why gripping a phone changes its performance measurably: your hand is part of the antenna.
Why a car whip works and a handset needs cleverness. At 100 MHz a quarter wave is 0.75 m and a car roof is a couple of metres across — several wavelengths of metal to push against, so the mirror is nearly perfect. At 900 MHz a quarter wave is 8.3 cm, and a phone’s ground plane is a board about 7 cm long: comparable to the radiator itself, so the “ground” radiates too. Modern handsets stop pretending and design the chassis as part of the antenna, which is exactly why performance depends on how you hold it.
A patch antenna is a flat rectangle of copper printed on one side of a dielectric board, with a solid ground plane on the other. It radiates from the fringing fields at its two open edges, and the resonant dimension is about half a wavelength in the dielectric, not in air — so the board’s permittivity shrinks it. On common FR-4 (εr ≈ 4.4) the shrink factor is 1/√4.4 ≈ 0.48, so at 2.4 GHz the patch is roughly 12.5 cm / (2 × 2.10) ≈ 3.0 cm on a side rather than 6.25 cm. It is planar, it has a ground plane built in, and it costs nothing beyond the PCB it is already sitting on.
Because a patch radiates only upward from its ground plane, its pattern is a single broad hemispherical lobe — typically about 65° of half-power beamwidth in each principal plane, for 6–9 dBi of gain. The price is bandwidth: a patch is a high-Q resonant cavity, and a plain single-layer patch is usable over only a few percent of its centre frequency. That is fine for a GPS receiver locked to 1575.42 MHz and awkward for anything that must span several bands. Patches are the antennas in phones, in WiFi access points, in GPS pucks and in vehicle telematics modules — and because they are flat, cheap and identical, they are the natural building block for the arrays of M7-L4.
The Yagi-Uda takes a dipole and surrounds it with metal rods that are not connected to anything. Only one element is fed; the rest are parasitic, excited by the driven element’s own field, re-radiating with a phase set by their length and spacing. Get those phases right and the re-radiated fields add in one direction and cancel in the other. The recipe is fixed:
A three-element Yagi — reflector, driven element, one director, on a boom about 0.35 λ long — gives roughly 7–9 dBi with a half-power beamwidth near 55°. Keep adding directors and the gain climbs, slowly and with diminishing returns, to about 15 dBi for a long boom of a dozen or more elements. What you buy alongside gain is a high front-to-back ratio, commonly 15–20 dB, which is why the Yagi is the classic rooftop television antenna: pointed at the transmitter, it not only collects more signal but actively rejects the reflection arriving from behind you. The same shape, at higher frequencies, does fixed point-to-point links on a budget.
Above a few gigahertz a different strategy becomes practical. Instead of shaping the current distribution on wires, you illuminate a large reflector with a small feed antenna and let geometry do the work: a paraboloid turns a spherical wave launched from its focus into a plane wave across its mouth. What matters then is not resonance but aperture — the physical area collecting or launching the wave. This is the family of aperture antennas, and their gain follows one formula:
Take D = 1 m, f = 10 GHz and e = 0.55. First the wavelength: λ = (3 × 108) / (10 × 109) = 0.03 m = 3 cm. Then πD/λ = π × 1 / 0.03 = 104.7, and squaring gives 104.72 = 10 966. Multiply by the efficiency: 0.55 × 10 966 = 6 031. Convert once, in power terms, using the 10·log₁₀ rule of M2-L4:
Now check that figure against the beamwidth, because gain and beamwidth are two views of the same fact (M7-L2). For a circular aperture the half-power beamwidth is approximately 70λ/D in degrees:
Two things fall out of that number. A 2.1° beam means a dish must be aimed to within a fraction of a degree, so mounts must be rigid and wind loading is a real engineering constraint. And because gain is set by geometry rather than resonance, a dish is inherently broadband: change frequency and the gain simply changes with it. Whatever bandwidth limit a dish system has, it comes from the feed antenna, not the reflector. Dishes run from about 30 dBi for a home satellite-television offset to over 60 dBi for deep-space ground stations and radio telescopes.
A horn is a waveguide whose end has been flared open. The flare does two jobs: it grows the aperture, which raises gain, and it eases the transition from the guide’s impedance to free space, which suppresses reflections. There are no resonant elements and nothing to tune, so a horn works across the whole band of the waveguide feeding it — commonly 40% or more of its centre frequency, an order of magnitude more bandwidth than a patch. Typical gains are 10 to 25 dBi; a square aperture about 2.2 λ on a side lands near 15 dBi, with a beamwidth around 30°.
What makes horns special is not the gain but the cleanliness. A well-made horn has very low side lobes, negligible loss, and a pattern that agrees with theory closely enough that its gain can be calculated from its dimensions and trusted. That is why the horn is the standard gain antenna: when a laboratory needs to know an unknown antenna’s gain, it compares it against a calibrated horn. Horns are also the usual feed at the focus of a dish — so the two aperture antennas in this lesson are normally found bolted together, the horn illuminating the reflector that multiplies its gain.
Laid side by side, the six families sort themselves along a single axis of gain against size and bandwidth. Nothing in the table is a ranking; every row is the right answer to some question.
| Type | Typical gain | Bandwidth | Size | Cost | Typical use |
|---|---|---|---|---|---|
| Half-wave dipole | 2.15 dBi | Moderate (~10%) | λ/2 | Very low | FM and TV receive, the reference standard |
| Quarter-wave monopole | 5.15 dBi ideal | Moderate (~10%) | λ/4 + ground plane | Very low | Car radio whips, handsets, walkie-talkies |
| Patch / microstrip | 6–9 dBi | Narrow (1–5%) | ~λ/2 in the dielectric, planar | Very low in volume | Phones, WiFi APs, GPS, array elements |
| Yagi-Uda | 7–9 dBi (3 el.) to ~15 dBi | Narrow (2–5%) | 0.35 λ boom to several λ | Low | Rooftop TV, budget point-to-point links |
| Parabolic dish | 30–60+ dBi | Very wide (set by the feed) | Many λ across | Moderate to high | Satellite links, microwave backhaul, radio astronomy |
| Horn | 10–25 dBi | Very wide (40%+) | A few λ | Moderate (machined) | Calibration standard, dish feed, radar |