A Real Antenna Is Five Per Cent Shorter Than the Textbook Says

Cut long and trim, never the reverse

The velocity factor is not a constant of nature: it depends on the conductor's diameter relative to the wavelength, on the insulation around it, and on what the antenna is mounted near. Values from 0.94 to 0.98 are all defensible for a thin wire in open air, and the difference across that range is several centimetres at 100 MHz. Since a wire can always be shortened and never lengthened, the working practice is to cut a few per cent long, measure the resonance, and trim towards it in small steps — and to do the trimming with the antenna in its final position, because moving it near a wall or a mast changes the answer again.

Why low frequencies are so awkward

The table's first row is the whole story of long-wave broadcasting: a resonant quarter-wave at 100 kHz is 712 metres, taller than any structure ever built for the purpose, so transmitters use masts a fraction of that height and compensate electrically for the shortfall. The compensation costs efficiency, which is why long-wave stations run enormous power for coverage that a hand-sized aerial achieves at gigahertz frequencies. The trade runs the other way too: at 2.4 GHz the quarter-wave is under three centimetres, small enough to print on a circuit board, which is precisely why that band is where wireless gadgets ended up.

Frequently asked questions

Why a quarter wave and not a half?

Because a conducting ground plane supplies the missing half by reflection. A quarter-wave whip standing on a car roof, a metal chassis or a set of radial wires behaves electrically like a half-wave dipole whose lower element is the mirror image of the upper one, which halves the physical size for the same resonance. The catch is that the ground plane has to be there and has to be adequate: a whip on a plastic enclosure with no counterpoise is not a quarter-wave antenna, it is a mismatched piece of wire, and it will radiate a fraction of what it should.

Does an antenna have to be resonant to work?

No, but a non-resonant one is harder to feed. Resonance means the antenna looks like a pure resistance to the transmitter, so power flows into it instead of being reflected back down the cable; away from resonance it looks partly reactive, and a matching network has to make up the difference. Broadband antennas do exactly that by design, trading some efficiency for a wide usable range. The practical consequence for anyone cutting wire is that a slightly wrong length is a nuisance rather than a disaster — the standing wave ratio rises, some power comes back, and everything still works a little worse.