An antenna is the doorway between a wire and open space: it turns a current into a traveling wave, and a passing wave back into a current. Its size, shape and spacing decide how well it does that, at which frequency, and in which direction.
Common mix-up: an antenna doesn't add power, and a bigger one isn't automatically "stronger." Gain means taking power away from some directions and sending it to others. The right size is set by the wavelength, not by how much signal you want.
In How a wave is born we saw that any accelerating charge radiates: wiggle an electron and a kink runs off through its field at the speed of light. Every radio transmitter on Earth is built on that one fact. An antenna is simply the piece of metal where the wiggling happens on purpose, and efficiently.
Any wire carrying alternating current radiates a little. Your house wiring does, at 60 hertz, and it's almost useless at it: a 60 Hz wave is about 5,000 km long, and a wire a few meters long is so tiny next to that that almost nothing gets out. Good antennas are a sizeable fraction of a wavelength long, so the charge has room to build up a big, coordinated swing.
The picture to keep in mind: the transmitter pushes charge up the antenna, then down, then up again, millions or billions of times a second. Close to the metal, most of the field just stores energy and hands it back each cycle; that's the near field. About a wavelength out, the field lines pinch off into closed loops that no longer need the antenna at all. That's the far field, and it carries energy away for good.
Run the film backwards and you have a receiver. A passing wave's electric field pushes on the free electrons in the metal and drives a tiny current into the radio. This symmetry is called reciprocity: an antenna's resonant frequency, pattern, gain and impedance are identical whether it transmits or receives. Your router listens with the same sticks it talks with, and a satellite TV dish would make an equally good transmitter if you bolted a transmitter to its feed.
For a short dipole of length L with a realistic, tapering current, Rrad ≈ 20π²(L/λ)². Make it 1/50 of a wavelength long and Rrad ≈ 0.08 Ω. The copper and any matching coil easily have a few ohms of loss, so nearly all the power becomes heat instead of radio.
A car's 80 cm AM whip at 1 MHz (λ ≈ 300 m) is a short monopole, Rrad ≈ 40π²(0.8/300)² ≈ 0.003 Ω. As a transmitter it would be a disaster. As a receiver it's fine, because at AM frequencies the natural and man-made noise the antenna picks up is far stronger than the receiver's own noise. Wasting most of the signal also wastes most of the noise, so the ratio between them survives.
Another way to see an antenna: it's an impedance transformer between a feedline (usually 50 Ω) and free space, whose wave impedance is √(μ₀/ε₀) ≈ 376.7 Ω.
Feed a straight wire in the middle. Current rushes out toward the tips, where it has nowhere to go, so it reflects and comes back. At the open tips the current must be zero; at the feed it can be large. The shortest wire where a standing wave fits that rule, zero at both ends and a peak in the middle, is half a wavelength long. That's the half-wave dipole, the reference antenna of the whole field.
At that length the reflected wave arrives back at the feed in step with the transmitter's next push, like pushing a swing at exactly the right moment. The antenna then looks to the transmitter like a plain resistor: no energy sloshing uselessly back into the cable, just power going out. For a thin half-wave dipole that resistance is about 73 Ω.
The numbers follow straight from λ = c/f. At 2.4 GHz, λ = 12.49 cm, so λ/2 = 6.25 cm. For FM radio at 100 MHz, λ = 3.00 m and λ/2 = 1.50 m, which is why the old "rabbit ears" pulled out to about a meter and a half end to end. At 1 MHz, AM radio, half a wavelength is 150 m, so nobody builds AM dipoles; they build towers (next section).
Real dipoles are cut about 5% short. Two reasons, really the same one: the tips have extra capacitance from fringing fields, which makes the wire act electrically longer than it is, and a wire of exactly λ/2 still shows a little leftover reactance (about +42 Ω) at the feed. Trimming it to roughly 0.47–0.48 λ cancels that. So a practical 2.4 GHz dipole is about 5.9 cm tip to tip, and an FM dipole about 1.42 m. Fatter elements need a little more trimming and work over a wider band of frequencies.
Then the cable. Most radio gear uses 50 Ω coax. For air-filled coax, loss is lowest near 77 Ω and power handling is highest near 30 Ω; 50 Ω became the standard compromise. Cable TV uses 75 Ω because a receiver cares about loss, not power. Plugging a 73 Ω dipole into 50 Ω coax reflects only about 3.5% of the power, a loss of 0.15 dB, which is why nobody loses sleep over it. Fold the dipole into a long thin loop and its resistance rises about fourfold, to roughly 290 Ω: that's why old TV antennas used 300 Ω flat twin-lead.
Assume the current on the dipole is a sine-shaped standing wave, I(z) = I₀ cos(2πz/λ). Work out the far field it creates, integrate the power over a sphere, and divide by ½I₀². The answer is Rrad = 30 · Cin(2π) ≈ 73.1 Ω, where Cin is a standard cosine integral (Cin(2π) ≈ 2.438).
A load Z on a line of impedance Z₀ reflects a fraction Γ = (Z − Z₀)/(Z + Z₀) of the voltage. For 73 Ω on 50 Ω: Γ = 23/123 ≈ 0.187, so Γ² ≈ 3.5% of the power bounces back. The standing-wave ratio is (1+Γ)/(1−Γ) ≈ 1.46 and the mismatch loss is −10·log₁₀(1 − Γ²) ≈ 0.15 dB.
A dipole is balanced (two symmetric arms); coax is unbalanced (a center wire inside a shield). Joined directly, current leaks onto the outside of the shield and the cable starts radiating too. A balun (balanced-to-unbalanced transformer) at the feed stops that.
Cut a dipole in half and stand the top half on a big sheet of metal. The sheet acts like a mirror: currents in it create exactly the field the missing bottom half would have made. This is called image theory, and it means a quarter-wave rod over a ground plane behaves like a half-wave dipole, with half the feed resistance (about 36.5 Ω).
Because all the energy goes into the half-space above the ground, the pattern is half a doughnut and the peak is twice as strong: an ideal monopole on an infinite perfect ground has 5.15 dBi of directivity. Real ground planes are finite, so real numbers are lower and the beam tilts upward a little.
Examples are everywhere. A car's FM whip is about 75 cm, a quarter of 3 m, with the car body as its mirror. AM broadcast towers are monopoles too, often around a quarter wave tall: 75 m at 1 MHz. The ground under them isn't a good enough mirror, so stations bury a ring of copper radials, traditionally 120 of them, each about a quarter wave long.
Phones are the extreme case. A quarter wave at 700 MHz is 10.7 cm, wider than the phone. So phone antennas use the whole chassis: a small feed strip, or a segment of the metal frame (those thin plastic lines on the sides of many phones), drives current through the entire circuit board, which acts as the other half of the antenna. That's also why your hand changes the signal: it's a lossy lump of salt water pressed against the radiator.
36.5 Ω on 50 Ω coax gives Γ ≈ 0.16, which is tolerable but not great. The classic fix on a "ground-plane" antenna is to replace the solid sheet with three or four quarter-wave radials and droop them downward at about 45°. That raises the feed resistance toward 50 Ω and lowers the beam toward the horizon.
Electrically shortened antennas (the stubby "rubber duck" on a walkie-talkie, the helix in a GPS puck) coil the wire so a quarter wave fits in less space. The price is a narrower usable band and lower efficiency.
No real antenna radiates equally in all directions. A dipole throws its energy out sideways, in a doughnut around the wire, and sends nothing straight off its ends. By reciprocity it's also deaf off its ends. That's one reason a laptop directly above a router with upright antennas can get a weaker signal than one across the room. The width of the doughnut's main lobe, measured between the half-power points, is 78°.
To compare antennas, engineers use an imaginary isotropic antenna that radiates the same in every direction. Directivity is how much stronger an antenna's best direction is than that isotropic average. Gain is directivity times efficiency, so it also charges for losses. Both are quoted in dBi, decibels over isotropic. A half-wave dipole is 1.64×, or 2.15 dBi. Gain is never free power: squeezing energy into one direction steals it from others.
What regulators actually limit is EIRP, the transmitter power plus antenna gain: the power an isotropic antenna would need to match the beam. A Wi-Fi radio at 20 dBm (100 mW) on a 2.15 dBi dipole has an EIRP of about 22 dBm. In the US, 2.4 GHz point-to-multipoint gear may reach 36 dBm EIRP (1 W into a 6 dBi antenna).
The Yagi-Uda antenna, published by Hidetsugu Yagi and Shintaro Uda in 1926, gets gain by adding rods that aren't wired to anything. A slightly longer reflector sits behind the powered element; shorter directors sit in front, spaced a fraction of a wavelength apart. Each rod picks up the field and re-radiates it with a phase shift, so the waves add in front and cancel behind. Three elements give roughly 7 dBi; a long rooftop TV Yagi with a dozen directors reaches 12–15 dBi.
Polarization is the direction the electric field points. A vertical antenna transmits vertically polarized waves and is blind to horizontal ones. Tilt the receiving antenna by an angle ψ and the received power falls by cos²ψ: 45° costs 3 dB, and 90° is in theory total loss (in practice 20–30 dB). Satellites often use circular polarization, where the field rotates as it travels; GPS uses right-hand circular at 1575.42 MHz so the receiver's orientation doesn't matter. Indoors, reflections scramble polarization, which softens the penalty for a phone held at odd angles.
For a half-wave dipole, the far field at angle ψ from the wire is proportional to cos(½π cos ψ) / sin ψ. It's 1 broadside (ψ = 90°) and falls to 0 along the axis. Power goes as the square. The half-power points are at ψ ≈ 51° and 129°, which is where the 78° beamwidth comes from.
Directivity is D = 4π Umax / Prad, where U is the power per unit solid angle. For the dipole pattern above, D ≈ 1.64. For a tiny "Hertzian" dipole with a sin ψ pattern, D = 1.5 (1.76 dBi). Lengthening the dipole to λ/2 narrows the doughnut only slightly.
You'll also see dBd, gain over a dipole. dBi = dBd + 2.15. Marketing sheets sometimes quote whichever number looks bigger.
A parabola has one magic property: every ray arriving parallel to its axis reflects through the same point, the focus, and all those paths are exactly the same length. So a wave collected over the whole face of a dish arrives at the feed perfectly in step. In transmit, the feed's spreading wave leaves the dish as a nearly parallel beam.
The bigger the dish compared with the wavelength, the narrower the beam and the higher the gain. Take a 60 cm satellite TV dish at 12 GHz. λ = 2.50 cm, so πD/λ ≈ 75.5. Square it: about 5,690. Real dishes catch 55–70% of the ideal (some feed energy misses the rim, and the illumination isn't uniform); with 65% that's about 3,700, or 35.7 dBi. The beam is about 2.9° wide, which is why the installer has to aim it carefully at a satellite 35,786 km away. At that distance the beam is still about 1,800 km across, so one satellite covers a whole country.
Gain grows with diameter squared and frequency squared. NASA's Deep Space Network uses 70 m dishes at 8.4 GHz: about 74 dBi and a beam 0.036° wide, enough to hear Voyager 1 from more than 24 billion kilometers away.
The useful concept here is effective aperture: the area of passing wave an antenna actually captures. For a dish it's roughly its physical area times its efficiency. For a simple dipole it's tiny and depends only on the wavelength. That idea is the key to the next chapter's biggest misconception about frequency and range.
Any antenna's gain and effective aperture are tied by G = 4π Ae / λ². For a dish, Ae = η · πD²/4, and substituting gives G = η π² D² / λ², the formula above.
Run it the other way: a lossless half-wave dipole (G = 1.64) at 2.4 GHz has Ae = 1.64 × λ²/4π ≈ 20 cm², about the size of a matchbox, even though the wire itself is a thin 6 cm stick. An antenna catches energy from an area much wider than the metal.
Most home satellite dishes are offset dishes: a slice cut from one side of a large parabola, so the feed hangs below the beam instead of shadowing it. That's why they seem to point at the ground.
Line up N identical antennas a distance d apart and feed them the same signal. Straight ahead (broadside), their waves travel equal distances and add up in step. Off to the side, each wave has a slightly different path and they partly cancel. The result is a beam that gets narrower as the row gets longer. Eight elements half a wavelength apart give a beam about 13° wide.
Now delay each element's signal a little more than its neighbor's. The direction where everything adds in step moves sideways: the beam steers, with no moving parts. That is a phased array. Keep the spacing at or below half a wavelength, or extra full-strength beams called grating lobes appear in directions you didn't ask for. The instrument below shows exactly when.
Real examples: 5G millimeter-wave phones work near 28 GHz, where λ = 10.7 mm and half-wave spacing is just 5.4 mm, so a row of four elements is about 2 cm long. Phones carry several such modules on different edges because a hand easily blocks one. A Starlink user terminal is a flat panel of many hundreds of small elements working near 11–12 GHz; it tracks satellites that cross the sky in a few minutes, re-aiming electronically far faster than any motor could.
MIMO (multiple-input, multiple-output) uses several antennas differently. Indoors, a signal reaches the receiver by many reflected paths, and antennas half a wavelength or more apart see different mixes of them. With M transmit and N receive antennas, a radio can send up to the smaller of M and N separate data streams on the same frequency at the same time and untangle them mathematically. A 2×2 Wi-Fi link roughly doubles the peak rate of a 1×1 link. How signals travel shows the multipath that makes this possible.
Which is why a modern phone carries ten or more antennas. No single piece of metal can be resonant at 600 MHz cellular, 1.5 GHz GPS, 2.4, 5 and 6 GHz Wi-Fi, 3.5 GHz 5G, ultra-wideband near 6.5–8 GHz and 28 GHz millimeter wave. Most bands also get two or four antennas for MIMO and for switching away from whichever one your hand is covering. NFC at 13.56 MHz uses a coil instead: its wavelength is 22 m, so it works by magnetic coupling over a few centimeters rather than by radiating a wave.
The total pattern is the element pattern times the array factor. For N equal elements with spacing d and phase step Δφ, AF(θ) = sin(Nψ/2) / (N sin(ψ/2)), with ψ = (2πd/λ) sin θ − Δφ. The main beam sits where ψ = 0.
ψ = 0 is not the only place the sum peaks: it peaks again whenever ψ = ±2π. Those are the grating lobes. They stay out of the real directions (|sin θ| ≤ 1) only if d < λ / (1 + |sin θ₀|). At broadside that's d < λ; to steer all the way to the side you need d ≤ λ/2.
The broadside half-power beamwidth is about 0.886 λ/(N d) radians: 0.22 rad, or 12.7°, for 8 elements at λ/2. Steer the beam by θ₀ and the array looks shorter from that direction, so the beam widens by about 1/cos θ₀ and the gain drops. That's why flat arrays rarely steer beyond about 60° from straight ahead.
Set the number of elements, their spacing and the phase step; the polar plot is the real array pattern, in decibels. Drag on the plot to aim the beam: the phase step follows.
Slide the frequency or pick a service. The dipole and the quarter-wave whip are drawn to the same scale as the everyday object above them.
Change the dish size, frequency and efficiency. The wedge is the real half-power beam angle; the bar below puts the gain next to other antennas.
| Antenna | Typical gain | Pattern | Size | Where you've seen it |
|---|---|---|---|---|
| Isotropic | 0 dBi | Equal everywhere | A point (imaginary) | Nowhere: it's the yardstick |
| Half-wave dipole | 2.15 dBi | Doughnut, nulls off the ends | λ/2 | Router sticks, FM rabbit ears |
| Quarter-wave monopole | 2–5 dBi (5.15 on ideal ground) | Half doughnut above ground | λ/4 plus a ground plane | Car whips, AM towers, walkie-talkies |
| Patch | ≈ 6–8 dBi | One broad lobe | ≈ λ/2 square on a board | GPS pucks, Wi-Fi panels, array elements |
| Yagi-Uda | 7–15 dBi | Forward beam | One to several λ long | Rooftop TV, ham radio |
| Parabolic dish | 25–75 dBi | Pencil beam | Many λ across | Satellite TV, deep-space links |
| Phased array | Element + 10 log₁₀ N | Steerable beam | N elements ≈ λ/2 apart | Starlink, 5G mmWave, radar |