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Hairpin match calculator

The point, which is easy to get backwards

A Yagi driven element sits at 20–30 Ω, half what the feedline wants. The hairpin brings it up to 50, but only if the element is deliberately made shorter than resonance. That is why “tuning the driven element to resonance” here means ruining the match: the hairpin is left with nothing to cancel.

lS 50 mm50 Ω feeder
The driven element is deliberately short of resonance — the hairpin cancels its capacitive reactance
Frequency (MHz)
Driven element resistance (Ω)
Feedline impedance (Ω)
Hairpin conductor spacing (mm)
Hairpin conductor diameter (mm)
What the driven element has to do
Driven element reactance (shorten to)
Matching Q
Hairpin
Required hairpin reactance
Equivalent inductance
Hairpin characteristic impedance
Hairpin length

📐 The formulas​

Q  = √( Z₀ / Ra − 1 )
Xs = −Q × Ra        ← shorten the element until it shows this reactance
Xp = Z₀ / Q         ← this is the reactance the hairpin must provide
L  = Xp / (2πf)

The hairpin as a shorted two-wire line:

Z₀_hp = 276 × log10( 2S / d )
l = (λ / 2π) × arctan( Xp / Z₀_hp )

Symbols:​

  • Ra — the resistive part at the driven element feed point (20…30 Ω for a Yagi)
  • S — centre-to-centre spacing of the hairpin conductors, d — their diameter
Where this calculator stops:
  • A hairpin works only when Ra < Z₀. For Ra > 50 Ω you need a gamma or T match — the calculator says so
  • Ra is something you enter, not something it works out: take it from modelling or from a measurement
  • The two-wire Z₀ formula holds for S > 2d; closer than that it overstates the impedance
  • The boom and the mounting hardware are not accounted for, and they add capacitance at the feed point

🎯 In practice​

  • A VHF Yagi — the classic use, and the commonest.
  • Matching any antenna with a low resistive part — a two-element beam, for instance.
  • Replacing a gamma match where you want symmetry and would rather not have a capacitor.
Practical advice:
  1. Shorten the driven element until its reactance reaches the calculated figure — that is the whole adjustment.
  2. A lumped coil of the same inductance will do instead of the hairpin; the line is simply more stable mechanically.
  3. A sliding shorting bar makes the hairpin length easy to trim without unsoldering anything.
  4. The feed point is balanced, so a choke on the feedline is not optional.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Hairpin match calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/antennas/hairpin (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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