How an Aerial Radiates

A 10-watt handheld on a good rooftop aerial will out-perform a 50-watt transceiver on a bad one, every evening of the week. The aerial is the only part of the station that touches the outside world, and the part a beginner can build for the price of a few metres of wire. The examiner knows it: Section A asks the length of a dipole, where the current is largest, what the feedpoint impedance is and what polarisation belongs to — and every one of those can be reasoned out rather than memorised.

What an aerial actually does

Inside the feeder, radio-frequency energy is guided: trapped between two conductors, going where they go. Out in the open the same energy travels as a free-space wave needing no conductor at all, and the aerial is the structure that lets it cross from one condition to the other. An aerial converts guided electromagnetic waves into free-space electromagnetic waves, and the reverse on receive. That sentence, almost word for word, is the answer to the first question on the paper.

The crossing is not automatic, because the two sides do not look alike electrically. Free space has a characteristic impedance of about 377 Ω — the ratio of the electric field to the magnetic field in a travelling wave, and a real physical property of empty space. Your feeder is 50 Ω, and 50 Ω joined straight to 377 Ω throws nearly all the power back at you. The aerial is what reconciles the two, which is why the examiner asks what an aerial is analogous to and expects the answer a transformer: it matches the impedance of the feeder to the impedance of free space.

The process is also reciprocal: the same structure works identically in reverse, with the same pattern and the same gain. There is no fundamental difference between a transmitting and a receiving aerial apart from how much power it must survive.

How a current in a wire radiates

Take a two-wire feeder with the far end open. Current sloshes back and forth along it, but the two conductors sit close together carrying equal currents in opposite directions, so their fields cancel and nothing escapes — which is exactly what a feeder is for. Now fold the last quarter wavelength of each conductor outwards until the two are in line, pointing away from each other. The currents no longer cancel: they flow the same way in space at any instant, along a wire a useful fraction of a wavelength long. Every change in that current changes the magnetic field around the wire, a changing magnetic field creates an electric field, which creates a magnetic field in turn, and the pair detach and walk off into space at 300 000 km per second, self-sustaining. That opened-out feeder is a dipole, and it is why current is what radiates: where the current is largest, that part of the wire radiates hardest.

Resonance, and why half a wavelength is the natural unit

A wire with open ends behaves like the tuned circuits in the resonance lesson, except that its inductance and capacitance are spread along the wire rather than lumped into components, so it has a natural frequency at which it accepts energy readily and stores almost none as reactance.

That happens when the wire is half a wavelength long. A wave sent from the centre travels a quarter wavelength to an open end, reflects and comes back another quarter — half a wavelength in all, so it arrives exactly in step with the next wave leaving. The wire supports a standing wave that fits it perfectly, and at that length it looks like a pure resistance to the feeder: no reactance to cancel, nothing thrown back. That is why the half wave is the natural unit, and the reference case the exam is built on.

The half-wave dipole, and the two constants

A half-wave dipole is two equal legs of wire, fed at the centre, with a total length of half a wavelength. Start with the wavelength itself:

Half of that is the free-space half wavelength, 150 ÷ f. A real wire does not resonate at exactly that length: two effects, both pulling the same way, make it resonate a little short.

• The wave travels slightly slower along a conductor of finite thickness than it does in free space — a velocity factor a shade below 1.
• The ends of the wire, the end insulators and everything near them add capacitance, so the aerial behaves as though it were electrically longer than it measures. This is the end effect.

Together they come to about five per cent, a velocity factor of roughly 0.95. Do the arithmetic on the constant itself:

Round it down and you have the practical constant every amateur uses:

The same rule in feet is 468 ÷ f, which is what older American handbooks print — it is not a different rule, only different units.

Worked example 1 — a 40 metre dipole

What is the approximate length of a half-wave dipole resonant at 7100 kHz?

First convert: 7100 kHz = 7.1 MHz.

Length = 142 ÷ 7.1 = 20 metres, so each leg is 10 m.

Worked example 2 — a 2 metre dipole

For the middle of the Indian 2 m band, 145 MHz:

142 ÷ 145 = 0.98 m total, so each leg is 49 cm — which is also the length of a quarter-wave whip for 2 m, and why the rubber duck on a handheld, a fraction of that length, cannot be an efficient aerial.

Cut one yourself

Type a frequency into the cutter below, or press a band button, and it gives the wavelength, the dipole and its legs, the quarter-wave radiator and the five-eighths figure with the division that produced each. Work the examples above on paper first, then check yourself here; for a full cutting list use the antenna calculator.

Current and voltage along the wire

The standing wave on a resonant dipole is not the same everywhere along it. The ends are open circuits — no current can flow off the end of a wire — so the current there is zero and largest in the middle, while the voltage does the opposite: smallest at the centre, swinging hardest at the ends.

Three practical conclusions follow from that one picture. Feed it in the middle: impedance is voltage divided by current, so the centre — high current, low voltage — is a low-impedance point a 50 or 75 Ω feeder can drive directly, while the ends run to several thousand ohms and cannot be. The middle does most of the radiating, because that is where the current is, so a loading coil near the centre beats one at the base. And the ends are dangerous: kilovolts appear there at legal power, so use good end insulators and keep the ends out of reach on the terrace.

Feedpoint impedance

A resonant half-wave dipole in free space presents about 73 Ω at its centre, purely resistive. That is the number the exam wants. Above real ground the figure moves with height, roughly 50 to 90 Ω, which is why ordinary 50 Ω coax feeds a dipole at a perfectly workable 1.5:1 with no matching at all.

Stand half a dipole upright over a conducting ground and the ground supplies the mirror image of the missing half. It radiates the same way but into half the space, so it develops the same current for half the voltage: a quarter-wave ground plane presents about 36 Ω, a poor match for 50 Ω coax. Bending the radials downwards to roughly 45 degrees raises it to about 50 Ω — which, rather than tidiness, is why the radials on a commercial ground plane droop.

Radiation resistance is not loss resistance

Power leaves a transmitting aerial as a wave: nothing gets hot, yet the transmitter sees a load drawing power. It is convenient to account for that as though the radiated power were dissipated in a resistor:

Radiation resistance is that fictitious resistance: the value which, substituted for the aerial, would consume exactly as much power as the aerial radiates. No such resistor exists. Loss resistance is real and unwelcome — the resistance of the wire and of any loading coil, and losses in insulators and poor earth connections. Power that goes into loss resistance becomes heat and never leaves the roof. Efficiency is the split between the two:

This is why short aerials disappoint. A full-size 40 m dipole has a radiation resistance near 73 Ω, so 1 Ω of loss hardly matters; a heavily shortened whip for the same band may show 2 Ω, and that same 1 Ω then throws away a third of your power as heat.

The isotropic radiator, gain, dBi and dBd

To say an aerial has “gain” you need something to compare it with. The reference is the isotropic radiator: a point source radiating equally in every direction, its pattern a perfect sphere. It cannot be built; it exists so that everyone's gain figures mean the same thing. An aerial generates no power, so gain always means concentration — energy taken from directions you do not want and added to the one you do. A half-wave dipole, by refusing to radiate off its ends, already concentrates 1.64 times as much power broadside as an isotropic source would:

So the dipole itself has 2.15 dB of gain over isotropic. Gain quoted against isotropic is written dBi; gain quoted against a half-wave dipole is dBd. The two scales differ by that fixed step:

Worked example 3 — reading an advertisement

An aerial is advertised at 12.15 dBi. What is its gain over a dipole?

12.15 − 2.15 = 10 dBd

Manufacturers quote dBi because it is the larger number. Adding instead of subtracting gives 14.3, the distractor the paper offers.

ERP and EIRP

Gain and power combine into one figure when a regulator wants to know how loud you actually are in your best direction. ERP, effective radiated power, is transmitter power less feeder and connector losses, multiplied by the gain over a half-wave dipole. EIRP, equivalent isotropically radiated power, is the same sum referred to an isotropic radiator instead, so EIRP = ERP + 2.15 dB and EIRP is always the larger number for the same station. The Indian rules use EIRP where it matters: amateur-satellite operation, open to General grade only, is capped at 30 dBW e.i.r.p.

Polarisation belongs to the aerial

A radio wave has an electric field and a magnetic field at right angles to each other and to the direction of travel. By convention, polarisation is the direction of the electric (E) field, and the E field lies along the radiating conductor: a horizontal dipole radiates a horizontally polarised wave, a vertical whip a vertical one. So polarisation is a property of the aerial. The transmitter and receiver behind it neither know nor care how it is mounted; turn the aerial on its side and the polarisation turns with it.

Get the two ends wrong and you pay for it: a vertical aerial hears a horizontally polarised signal about 20 dB down on a line-of-sight VHF path, which turns a comfortable contact into nothing at all. Hence the conventions, which are worth following exactly:

The pattern of a dipole

A dipole radiates best at right angles to its own axis and hardly at all off its ends, giving the familiar figure of eight broadside to the wire — each short length of wire radiates sideways and not along its own direction, and the whole wire adds up the same way. The nulls off the ends are useful: choosing which way to run a wire across the roof can drop an interfering station a long way while leaving the wanted one untouched. The next lesson plots this pattern against five others on the same grid.

Height above ground and the take-off angle

No aerial on a roof is in free space. The ground beneath acts as an imperfect mirror: the direct ray and the ground-reflected ray add where they are in step and cancel where they are not, and the height decides at which angles that happens. Height therefore sets the angle of radiation, or take-off angle, more than any other single factor.

So raising a horizontal dipole from a quarter wavelength to half a wavelength lowers its angle of radiation, which favours DX. On 20 m half a wavelength is about 10 m of height, which a normal terrace can manage; on 40 m it is 20 m, which it usually cannot. That is exactly why a rooftop 40 m dipole is superb for working Chennai from Pune and mediocre for working Europe. Why a low angle reaches further is a propagation question, worked through in the propagation lesson.