Antenna length calculator

How a linked dipole works

One dipole per band, built into one wire. Each leg is cut into sections joined by links (connectors you can open or close). “Band changing is accomplished by simply connecting different sections of the dipole together,” giving “a full-sized efficient dipole on each band.”^[1]

Links open = highest band. With every link open, only the inner sections are connected: that’s the highest band. Close the first link on both legs to add the next sections and drop to the next band, and so on.

Tune from the middle out. One builder’s method:^[2]

1. Cut every section a little long (it’s easier to shorten than lengthen). “Start with the highest frequency (top sections closest to the centre)” with all links open.
2. Raise it to its normal height and check SWR at the bottom, middle and top of the band.
3. Trim both sides by the same amount — “Always trim both sides equally, otherwise you’ll end up with an unbalanced dipole.” Take small bites; it’s easier to shorten than lengthen.
4. When that band is right, close the first links and tune the next band by trimming the next sections. Repeat outward.
5. “Finally, re-check all 3 bands again (don’t forget to unlink/link the segments as you do your measurements).”

1. SOTABEAMS, “What is a Linked Dipole?”
2. VK5PAS, “Making Your Own Linked Dipole Antenna” (40/15/10m build; tuning section)

Why only these bands?

The end of a half-wave wire is a high-impedance point. Current drops to zero at the end of the wire and voltage peaks there. High voltage and low current means high impedance — roughly 1,800 to 5,000 Ω.^[1] A 49:1 or 64:1 transformer steps that down to about 50 Ω for your coax.

Higher bands fit whole half-waves. Double the frequency and the same wire holds two half-waves; triple it and it holds three. The end is still a zero-current, high-impedance point, so the same transformer still matches. ARRL’s EFHW kit article puts it this way: 66 ft of wire is “a half wavelength for the 40-meter band, but also a full wave for the 20-meter band, a double full wave for the 10-meter band, and three half-wavelengths for the 15-meter band.”^[2]

Lower bands don’t fit. Below the band you cut for, the wire is shorter than a half-wave. Current is still flowing at the feed end, the impedance is much lower, and the transformer can’t match it. The same article notes that 33 ft is a half-wave on 20m and two half-waves on 10m^[2] — on 40m it’s only a quarter-wave. Want 40m? Cut the wire for 40m. You’ll get 20, 15 and 10m too.

Harmonics land a little high. End effect matters less on higher bands, so “a radiator for 7.2 MHz has to be somewhat longer than twice the length of a radiator for 3.6 MHz.”^[3] So the upper bands can land a little above exact multiples. ARRL’s kit adds a 100 pF capacitor across the radio side of the transformer, and Dörenberg uses 100–150 pF there to counteract the transformer’s inductance on 15–10m.^{[2] [3]}

Commercial example. MFJ’s 132 ft 80m EFHW (MFJ-1982) lists 80, 40, 30, 20, 17, 15, 12 and 10m, and notes it “resonates slightly above the 30-meter band, so a tuner is normally needed” there. It has a 6-turn coil wound into the wire about 6 ft from the matching unit; the manual calls it a compensating coil but doesn’t say what it does.^[8] A coil in the same spot on our DudeTenna kit is what gets 15m and part of 10m to resonate (next paragraph).

The small coil near the feed. Our own DudeTenna 40m EFHW kit uses the same idea: a coil of 10–12 turns in the wire just past 6 ft from the transformer, with “the exact number of turns … found during the tuning process.” The build guide says it “isn’t critical if you only plan on using the 40m and 20m bands,” but is important if you want the antenna “to resonate on the 15m and in part of the 10m band.”^[9] This is a different coil from the large loading coil used to shorten an 80m or 160m EFHW.

1. Steve Yates, AA5TB, “The End Fed Half Wave Antenna”
2. Frank Bontenbal, PA2DKW, “End-Fed Half-Wave Antenna Kit,” ARRL
3. F. Dörenberg, “Multi-band end-fed”
4. ARRL, “EFHW Antenna 80m Extension Kit” (~110 µH, 170 turns of 0.5 mm wire, after the ~66 ft radiator)
5. VU3DXR, “Shortened EFHW Antenna for 80m to 10m” (67 ft + 110 µH + ~8 ft; the coil “acts as an RF choke on higher frequencies”)
6. ON7EQ, “EFHW Antenna” (110 µH coil: ~20 kHz under 3:1 on 80m; light-duty coil burned at high power)
7. 73QRZ NEC-2 check (nec2c): 66 ft + 110 µH + 7 ft tail resonates near 3.67 MHz; 132 ft + 220 µH + 14 ft near 1.84 MHz. Coil turns use the same Wheeler formula as our coil calculator.
8. MFJ, MFJ-1982/1984 manual: 132 ft covers 80, 40, 30, 20, 17, 15, 12 and 10m; 30m needs a tuner; a small 6-turn compensating coil sits about 6 ft from the matching unit.
9. HRD Industries (Ham Radio Dude), “DudeTenna 100+ Watt EFHW Kit Build Instructions,” section “Add the Dudecoil” (our own product); tuning video: tuning video linked in the guide
10. Wikipedia, “Impedance matching”: impedance is reflected through a transformer “by the square of the turns ratio.”
11. JYR8010 retail listing: “8 Band 10m 12m 15m 17m 20m 30m 40m 80m Long Wire Antenna, 1:64 Balun” (example listing)

Before you cut metal

Where the numbers come from. Reflector, director lengths, spacing, gain and front-to-back are from NBS Technical Note 688 (Viezbicke, 1976), Table 1.^[1] Its gains are measured against a dipole: “If referenced to an isotropic source, the values must be increased by 2.16 dB.” TN 688 doesn’t give a driven-element length (“The driven element consisted of a λ/2 folded dipole”), so *the driven element uses W1JR’s 0.473λ, quoted by N1TA^[2] — a secondary source. Trim or match it for resonance.

Element thickness changes the lengths. TN 688 used elements 0.0085λ thick. “The larger diameter elements yielded maximum gain at shorter lengths,” and a metal boom needs its own correction (TN 688 Figs. 9 and 10).^[1] ARRL: lengths “will vary slightly in actual practice with the element diameter and the method of supporting the elements.”^[3] K6STI: “conductive mounting brackets, and through-the-boom mounting shorten effective element length.”^[4]

Model it first. For a real build, check the design in an antenna modeling program with your actual element sizes and boom before cutting. K6STI’s published 6m Yagi, for example, was optimized with MININEC and checked in NEC.^[4]

1. P. P. Viezbicke, “Yagi Antenna Design,” NBS Technical Note 688, 1976 (measured at 400 MHz)
2. N1TA, “W1JR optimized proportions” (driven element 0.473λ)
3. ARRL, The Radio Amateur’s Handbook, 1981, ch. 20
4. K6STI, “Optimised Six-Metre Yagi”

Why does a 5/8 wave need a coil?

A 1/4-wave vertical matches on its own. Its base is about 36 Ω,^[1] close enough to 50 Ω coax.

A 5/8 wave is taller for a reason. At 5/8λ a vertical “radiates a maximum amount of its power in horizontal directions”^[1] — toward the horizon, where distant stations are. In our model it puts about 2.8 dB more signal at the horizon than a 1/4 wave over perfect ground. We haven’t modeled real ground, so the real-world gain difference may differ.^[2] The model also shows a small lobe going up at about 60°.^[2]

But its base isn't 50 Ω. At this length the base looks like --: more resistance than your coax wants, plus a lot of capacitance (the −j part).^[2] Feed it straight with coax and the SWR is far too high.

The coil fixes both. A coil from the base of the radiator to ground cancels the capacitance. Tapping the coax a few turns up from the ground end turns the coil into a step-down transformer, so the radio sees about 50 Ω. Bonus: the coil DC-grounds the radiator, which bleeds off static.^[3]

Why not a plain series coil? A coil in series with the coax can cancel the capacitance too (--), but it leaves the resistance alone, so SWR stays around --. That's why most builds use the tapped coil.

How to tune it. Wind the coil, put the tap where shown, then check SWR. Move the tap in small steps for the lowest SWR, and trim the radiator to move the dip in frequency. Coil size, wire and nearby metal all shift the numbers, so treat them as a starting point.

1. Wikipedia, “Monopole antenna” (1/4-wave = 36.5 Ω; 5/8-wave and Ballantine, 1924)
2. 73QRZ NEC-2 model (nec2c): vertical over perfect ground, length 585/f, radius λ/1400 (whip/tubing) or λ/20000 (thin wire). Results: 93 − j323 Ω and 131 − j571 Ω; 7.96 dBi vs 5.15 dBi at the horizon for a 234/f quarter-wave.
3. Dr Jonathan P. Hare, “5/8 wave vertical for 2m band using 3D printed parts,” Creative Science Centre