A half-wavelength wire fed at one end, not the middle. The end of a half-wave wire is a very high impedance, so a transformer at the feed point steps it down to about 50 Ω for coax. The older name for the end-fed half-wave idea is the Zepp, where the wire was fed through a tuned open-wire feeder instead of a transformer.
Why the end is high impedance
Impedance = voltage ÷ current. Current is greatest at the center, voltage at the ends, so the impedance climbs toward the ends.
Feed point impedanceabout 75 Ω
Impedance is voltage divided by current. At the end of the wire the current must be zero and the voltage is at its peak, so the ratio is very high. Drag the feed point toward the end in the diagram above and watch the impedance climb.
The real value depends on wire diameter, height and surroundings, so transformers are built for a typical figure. A 49:1 impedance ratio turns 50 Ω into 49 × 50 = 2450 Ω, and 64:1 into 3200 Ω. Since impedance scales with the square of the turns ratio, 49:1 is 7:1 in turns and 64:1 is 8:1. A real feed point varies from the design value, so the SWR is usable, not perfect.
Harmonics come free
Ideal thin wire in free space; real antennas shift these figures. Current is blue, the feed point is purple.
At every harmonic the end of the wire is still a current null and a voltage peak. The same transformer sees a similarly high impedance on each, so an end-fed half-wave cut for 7.1 MHz is also near resonance at 14.2, 21.3 and 28.4 MHz: the 40, 20, 15 and 10 m bands. Unlike a center-fed dipole, it does not skip the even multiples. Impedances on the different bands are similar, not identical, and the higher bands have multi-lobed patterns.
The return path
Typical values. The transformer turns thousands of ohms into about 50 Ω; the choke keeps the return current off the coax.
A wire fed at one end has only one conductor. The current needs somewhere to return, and the transformer's other terminal connects to the coax shield. Without something to stop it, RF flows on the outside of the coax as well. The result is a feed line that radiates, RF in the shack and SWR that changes when you touch the cable. The fix is a common-mode choke near the feed point and, in many designs, a short counterpoise wire.
Trade-offs
Transformer quality sets loss, bandwidth and heating at power. See Baluns and ununs.
Easy to deploy: one wire, one support, no center insulator, and it can run vertical, sloping or as an inverted V-style shape. It is popular for portable work.
Pattern follows the wire's orientation and height, as for a The half-wave dipole.