How a trap dipole works
A trap is a parallel inductor and capacitor that resonates on the higher band. At resonance it has a very high impedance, so it cuts the wire off, and the inner sections work as an ordinary half-wave dipole on the higher band. On the lower band the trap is below resonance, where it behaves as an inductor. That inductance electrically lengthens the antenna, so the outer sections can be shorter than they'd need to be for a full-size dipole on the lower band.
Trap reactance on the lower band: X = 2πfL ÷ (1 − (f ÷ ftrap)²)
The outer length comes from the standard loading-coil formula for a dipole, as used in the ARRL Antenna Book. It treats each half as a transmission line with a characteristic impedance set by the wire's length and diameter:
Z0 = 60 × (ln(4h ÷ d) − 1)
A is the electrical length of the inner section and B the outer section, both at the lower band, h is the length of one half and d the wire diameter. With the classic W3DZZ 80m and 40m design (60 pF and 8.2 µH traps), the calculator gives inner sections of about 9.9 m and outer sections of about 6.9 m (32.6 ft and 22.8 ft), close to the published 33 ft and 22 ft.
Building the traps
Use a high-voltage capacitor, since the trap sees high RF voltage. A 5 kV ceramic capacitor or a length of coax used as a capacitor works well at 100 W. Wind the coil on PVC tube, then measure the trap's resonant frequency with a NanoVNA or dip meter before fitting it, and adjust the turns to get it right. A trap that resonates slightly low makes the inner section look longer on the higher band, so it's worth getting this right. Traps lose a little power, and the antenna's bandwidth on the lower band is narrower than a full-size dipole's.
How a fan dipole works
A fan dipole is several dipoles joined at one feedpoint. Each element is resonant on its own band, where it has a low impedance, while the others are far from resonance and draw little current. Spread the element ends apart by 15 to 30 cm, with spacers or by running them in different directions.
The elements interact, so tune them in order from the longest to the shortest, and expect the shorter ones to need slight lengthening. The calculator adds 4% spare to each leg for this. You often don't need a separate element for a harmonically related band. A 40m element is close to 3/2 wavelengths on 15m, so it usually works there too.
Questions
What are the W3DZZ trap dipole dimensions?
Inner sections of about 10.1 m (33 ft) each side to the traps, then about 6.7 m (22 ft) of wire beyond each trap. The traps are about 8.2 µH and 60 pF, resonant near 7.2 MHz.
How far apart should fan dipole elements be?
Spread the ends by 15 to 30 cm or more. Closer spacing increases interaction, so the shorter elements need more lengthening.
Do I need a 15m element on a 40m fan dipole?
Usually not. A 40m dipole is about 3/2 wavelengths on 15m, so it resonates there too, though the pattern has more lobes.
Is a trap dipole shorter than a normal dipole?
Yes. The traps' inductance loads the outer sections, so a trap dipole for 80m and 40m is around 34 m long instead of about 38 m.