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Quarter-wave transformer calculator

How it works

A line exactly λ/4 long inverts impedance: what is at one end becomes Z₀²/Z at the other. Take a line of impedance √(Z1·Z2) and two different impedances are matched. Simpler than any tuner, but only at one frequency.

Z1 50 ΩZt = √(Z1·Z2)Z2 112 Ωλg/4the length is worked out with the velocity factor of the cable
A length of line of impedance Zt = √(Z1·Z2) and λ/4 long matches two different impedances
Frequency (MHz)
Source impedance Z1 (Ω)
Load impedance Z2 (Ω)
Transformer cable
Insulation material
ε of the insulation
Result
Transformer characteristic impedance
Transformer length (λg/4)
Wavelength in the line (λg)
Bandwidth at SWR ≤ 2

📐 The formulas​

Characteristic impedance of the transformer:

Z_t = √(Z1 × Z2)

Section length:

λg/4 = 299792.458 / (f × √ε) / 4    [mm]

Bandwidth at SWR ≤ 2 (Γm = 1/3):

x  = 2 × Γm × Z_t / |Z1 − Z2| / √(1 − Γm²)
BW = 2 − 4 × arccos(x) / π      (a fraction of f, if x < 1)

Symbols:​

  • Z1 — source impedance (usually 50 Ω)
  • Z2 — load impedance (the antenna feedpoint)
  • ε — permittivity of the transformer's dielectric
Where this calculator stops:
  • The transformer matches resistances only; reactance has to be cancelled first
  • It works at one frequency — outside the calculated bandwidth the SWR climbs quickly
  • Cable of the required impedance does not always exist: people usually take the nearest standard type
  • The greater the difference between Z1 and Z2, the narrower the bandwidth

🎯 In practice​

  • Matching a folded dipole (280 Ω) to 50 Ω cable.
  • Feeding a quad or a delta loop with an impedance of 100–120 Ω.
  • Making up non-standard impedances: two 100 Ω sections in parallel give 50, two of 75 give 37.5.
Practical advice:
  1. Work out the length with the velocity factor of the very cable you are making the transformer from.
  2. Matching 50 to 100 Ω calls for 70.7 Ω — in practice people use ordinary 75 Ω cable.
  3. A two-stage transformer gives a wider bandwidth: two λ/4 sections with an intermediate impedance.

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

How to cite this calculator
UR3PKI. «Quarter-wave transformer calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/quarter_wave (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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