Antenna tables modelled in NEC2

The 468/f rule against the model

* Outside the IARU Region 1 band edges.

Why they differ. 468 / f(MHz) feet (= 142.65 / f metres) is 0.952 × λ/2. In the model, a bare 2 mm wire in free space resonates at 0.964–0.976 × λ/2, so the modelled length is 1.3–2.5 % longer than the rule, and a wire cut to the rule resonates about that much higher (on 20 m: 14.446 MHz in free space instead of 14.175 MHz). How much shorter than λ/2 a dipole is depends on how thick the conductor is compared with the wavelength (table below). Height matters too: in the model, at 10 m the dipole is shorter than in free space on 160 m, 80 m, 60 m, 40 m, 17 m, 15 m, 12 m, 6 m and longer on 30 m, 20 m, 10 m; the effect of the ground swings with the height in wavelengths. Real antennas add things this model leaves out: insulation on the wire, end insulators and the wire looped through them, sag or an inverted-V shape, and nearby objects. These usually make the resonant length shorter, towards 468/f. NEC2 cannot model wire insulation.

Trimming. Resonance moves about inversely with length: 1 % shorter raises the resonant frequency by about 1 % (on 40 m, 1 % of 20.31 m is 20 cm, or 10 cm per leg, for about 71 kHz). Start a little long, measure where the SWR is lowest, and shorten both legs equally.

Quarter-wave vertical with 4 radials (ground plane)

The length is the vertical radiator and each of the 4 radials (all the same length), fed at the base between the radiator and the radials. The radials are straight and horizontal at 90° to each other. With horizontal radials the feed-point resistance is low (about 23.1 Ω in free space), so on 50 Ω coax the SWR is about 2:1 without a matching network (see the SWR column). On the low bands the nearby lossy ground raises R; part of that is loss, not radiation. Radials lying on or buried in the ground behave differently and are not covered here: NEC2 cannot model wires on or in the ground. 234 / f(MHz) feet (= 71.32 / f metres) is half of 468/f, 0.952 × λ/4; with 4 horizontal radials the model resonates close to a full λ/4, so the rule comes out about 5 % short here.

Wire thickness: 20 m dipole in free space at 14.175 MHz

A thicker conductor resonates shorter. The 2.0 mm wire used in the tables above gives k = 0.970 on 20 m; the 468/f rule (k = 0.952) matches only a conductor about 25 mm thick (k = 0.954) on this band. The effect depends on λ / d, so a given wire is relatively thicker, and shorter, on the higher bands. Gauge: nearest AWG from the wire gauge calculator.

Method and assumptions

• Engine: NEC2 (Numerical Electromagnetics Code, a method-of-moments wire-antenna solver) through PyNEC 2.3.4, the Python interface to the necpp library. For each row the length is changed until the reactance at the feed point is below 0.01 Ω at the band centre.
• Wire: round, bare copper, 2.0 mm diameter, conductivity 5.8 × 10⁷ S/m on every segment (NEC load type 5, which includes skin effect). No insulation.
• Segments: dipole 51, fed in the centre segment; vertical 25 on the radiator and on each radial, fed in the bottom segment of the radiator. Doubling the number of segments changed no length in the tables by more than 0.02 %.
• Ground: "average" ground, relative permittivity 13 and conductivity 0.005 S/m, with the Sommerfeld-Norton method (NEC2 GN 2), which stays accurate for wires close to the ground. Real soil varies a lot; poorer soil changes the low-band values most. Free space means no ground at all.
• Heights: dipole horizontal at 10 m; vertical with its base and radials at 3 m.
• Frequencies: the middle of each band in the IARU Region 1 band plan: 160 m 1.905, 80 m 3.650, 60 m 5.359, 40 m 7.100, 30 m 10.125, 20 m 14.175, 17 m 18.118, 15 m 21.225, 12 m 24.940, 10 m 28.850, 6 m 52.000 MHz. 6 m is 50–54 MHz in the Region 1 plan; many countries allow only part of it. For another frequency, scale the length by the frequency ratio (a few kHz make little difference).
• Not modelled: insulation, insulators and wire loops at the ends, sag, inverted-V or sloping wires, the feed line and balun, current on the outside of the coax, trees, buildings, masts and other antennas.