The previous lesson established how an antenna turns a current into a wave and back again. This one is about the spec sheet. Every antenna ever sold is described by the same short list of numbers — gain, beamwidth, polarization, impedance, efficiency — and once you can read those seven quantities you can compare a $3 whip to a $30,000 dish without ever seeing either one. You already have the decibel from M2-L4, including what the “i” in dBi refers to, so this lesson spends its effort on what the numbers mean rather than on how to take a logarithm.
An antenna radiates unevenly — more power this way, less that way. Directivity D measures that unevenness and nothing else: it is the power density in the antenna’s best direction divided by the power density an isotropic radiator would produce with the same radiated power. Directivity is pure geometry. A perfectly lossless antenna and a badly corroded one of identical shape have identical directivity.
Gain G asks the more useful question: how much power density do I get in the best direction for each watt I fed in? Some of what you feed in never leaves — it warms the conductors and the plastic. The fraction that does leave is the radiation efficiency erad, and it is the only difference between the two quantities:
In decibels the multiplication becomes a subtraction, which is why efficiency is often quoted as a loss. An antenna with 38.3 dBi of directivity and 60% radiation efficiency has a gain of 38.3 + 10·log₁₀(0.6) = 38.3 − 2.22 = 36.1 dBi. At 90% efficiency the penalty is only 10·log₁₀(0.9) = −0.46 dB; at 50% it is exactly −3.01 dB. Datasheets almost always quote gain, because that is what a link actually gets — but simulation tools happily print directivity, and confusing the two is a common way to lose a couple of decibels on paper that you never had in hardware.
A gain figure is meaningless without saying what it is a gain over. Two references are in circulation. dBi compares against the isotropic radiator — the imaginary antenna that spreads power perfectly evenly, which cannot be built and is therefore an unimpeachable yardstick. dBd compares against a real half-wave dipole. M2-L4 already pinned that dipole down: its directivity is 1.641, and 10·log₁₀(1.641) = 2.15 dBi. So the dipole is 2.15 dB better than isotropic, and converting between the two references is a single addition:
The practical consequence is commercial. dBd numbers are 2.15 lower than dBi numbers for the same hardware, so marketing departments quote dBi and cautious engineering departments quote dBd. When two antennas look 2 dB apart on paper, check the units before you believe the difference is real.
A single peak gain figure throws away almost everything. The full description is the radiation pattern: relative radiated power as a function of direction, normalised so the peak reads 0 dB and plotted on a polar grid. Patterns are drawn in decibels rather than in linear power because the interesting features — the small lobes that will pick up your neighbour’s interference — are 20 to 40 dB down and simply vanish on a linear plot.
A pattern is three-dimensional, so it is published as two orthogonal two-dimensional cuts. The E-plane cut contains the electric-field vector — for a vertical dipole, a vertical slice. The H-plane cut contains the magnetic field and is perpendicular to it — for the same dipole, the horizontal slice, which is a perfect circle. The two cuts need not look remotely alike: a base-station panel might be 65° wide in one plane and 7° in the other, which is exactly how it covers a street without wasting power on the sky.
The half-power beamwidth (HPBW), also written as the −3 dB beamwidth, is the angle between the two directions either side of the peak where radiated power has fallen to half. Half the power is 10·log₁₀(0.5) = −3.01 dB, which is where the second name comes from. A half-wave dipole measures about 78° in its E-plane. For an aperture antenna — a dish, a horn, a patch array — the beamwidth follows from the aperture size in wavelengths:
Take a 1 m dish at 10 GHz. First the wavelength, from M3-L1: λ = c/f = (3 × 10⁸)/(10 × 10⁹) = 0.03 m, or 3 cm. Then HPBW ≈ 70 × 0.03 / 1 = 2.1°. That is a beam narrower than the width of your thumb at arm’s length, which tells you immediately that this antenna needs a mount, not a bracket. Beamwidth and gain are two views of the same fact, and for a pencil beam they are linked directly:
Check it against the dish. With both beamwidths at 2.1°, G ≈ 30000/(2.1 × 2.1) = 30000/4.41 = 6803, and 10·log₁₀(6803) = 38.3 dBi. An entirely independent route is the aperture formula G = ea(πDa/λ)², which for the same dish at a typical 60% aperture efficiency gives 0.6 × (π × 1/0.03)² = 0.6 × 104.72² = 0.6 × 10966 = 6580, or 38.2 dBi. Two different rules of thumb, one tenth of a decibel apart — which is about as much agreement as antenna engineering ever offers, and a good sign that both are worth remembering.
Polarization describes the orientation of the electric field as the wave goes by. If the field stays along one axis the wave is linearly polarized — vertical for the whip on a taxi, horizontal for old rooftop television aerials, and slanted at ±45° for the cross-polarized pairs in cellular base stations. A linear antenna radiates and receives that one orientation, and a receiver tilted relative to the transmitter recovers only the projection of the field onto its own axis.
Feed two crossed elements with signals a quarter-cycle apart in phase and the resulting field rotates once per RF cycle. That is circular polarization, and it comes in two senses that do not talk to each other: RHCP (right-hand circular, rotating clockwise as seen from behind, along the direction of travel) and LHCP. A circular wave carries no preferred axis, so a linear receiver of any tilt sees the same thing — half the power.
| Transmit | Receive | Loss | Why |
|---|---|---|---|
| Vertical | Vertical | 0 dB | Matched |
| Vertical | Tilted 45° | 3 dB | cos²(45°) = 0.5 |
| Vertical | Horizontal | Infinite in theory, 20–30 dB in practice | Real antennas leak into the cross-polarization |
| Linear | Circular (either sense) | 3 dB | Only half the rotating field aligns |
| RHCP | LHCP | Infinite in theory, 20–30 dB in practice | Opposite senses are orthogonal |
That 3 dB penalty for mixing linear and circular is exactly why satellite systems pay it happily. A satellite has no idea how your handset is being held, and the ionosphere rotates linear polarization unpredictably on its way through — so a linear downlink would fade between full signal and nothing. GPS transmits RHCP, which any orientation of receiver picks up with a fixed, predictable 3 dB loss instead of an unpredictable one. Satellite television and most space links use circular for the same reason, and the RHCP/LHCP pair doubles as a way to send two independent signals on one frequency.
To the transmitter, an antenna is a load, and radio hardware has settled on a 50 Ω convention for that load — a historical compromise between the cable geometry that minimises loss and the one that handles the most power. Cable television is the notable exception at 75 Ω. If the antenna’s input impedance is not 50 Ω, part of the wave travelling up the feed line hits the discontinuity and comes back. The reflection coefficient Γ measures that, and the standing wave the forward and reflected waves create together is what a VSWR meter reads:
Work the standard case. A VSWR of 2:1 means Γ = (2 − 1)/(2 + 1) = 0.333, so |Γ|² = 0.111: 11.1% of the power comes back and 88.9% goes into the antenna. As a loss that is 10·log₁₀(0.889) = −0.51 dB. Return loss is −20·log₁₀(0.333) = 9.5 dB. Half a decibel is nothing; this is why 2:1 is the usual pass/fail line on a datasheet, and why chasing a perfect match is rarely worth the effort.
| VSWR | |Γ| | Power reflected | Mismatch loss | Return loss |
|---|---|---|---|---|
| 1.0:1 | 0 | 0% | 0 dB | ∞ |
| 1.5:1 | 0.200 | 4.0% | 0.18 dB | 14.0 dB |
| 2.0:1 | 0.333 | 11.1% | 0.51 dB | 9.5 dB |
| 3.0:1 | 0.500 | 25.0% | 1.25 dB | 6.0 dB |
| 5.0:1 | 0.667 | 44.4% | 2.55 dB | 3.5 dB |
Two cautions. First, mismatch is frequency-dependent: an antenna is matched over a band, and the band edges are usually defined as wherever VSWR crosses 2:1. Second, reflected power does not disappear — at high transmit powers it goes back into the power amplifier, which is why a transmitter with a disconnected antenna can destroy itself.
Radiation efficiency collects everything that turns input power into heat instead of radiation. Ohmic loss is resistance in the conductors, worsened at high frequency by the skin effect crowding current into a thin surface layer. Dielectric loss is energy absorbed by the insulators and substrates the fields pass through — the reason a cheap circuit-board material makes a poor patch antenna. Loss in the matching network and in the feed cable is bookkept separately but costs you the same watts. A well-built resonant antenna reaches 90–95%; a printed antenna crammed into a phone may be at 40–50%, and that is before a hand covers it.
The dominant cause of poor efficiency is the one M7-L1 already set up: a physically small antenna is an inefficient antenna. Shrink an antenna well below the resonant fraction of a wavelength and its radiation resistance collapses toward zero while its ohmic resistance does not, so an ever larger share of the current merely heats the metal. It also becomes highly reactive and narrowband, so the matching network needed to fix the impedance adds losses of its own. This is the hard physical floor under every “why is the antenna in this device so bad” complaint, and it is why an AM broadcast receiver at 1 MHz — where a wavelength is 300 m — uses a ferrite loop that is astonishingly inefficient and works anyway, because the transmitter is enormous.
Where these numbers get used. M7-L3 takes each parameter here and shows what the common antenna types — dipole, monopole, patch, Yagi, dish, horn — actually achieve. M7-L4 shows how to build a pattern deliberately by combining elements into an array, and how to steer that pattern electronically. M8-L1 is where gain finally earns its keep, feeding the path-loss and link-budget calculation that decides whether a link closes at all — the arithmetic M2-L4 previewed in decibels.