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Stub matching calculator

Matching with no components at all

A stub is a length of the same line connected in parallel at a calculated distance from the load. No coils, no capacitors: the geometry does all the work. On VHF and above it is the most dependable way to match, because there is nothing in it to break down and nothing to age.

Z₀ 50 ΩZLshortedld
The stub goes at the calculated distance d from the load
Frequency (MHz)
Line characteristic impedance Z₀ (Ω)
Load R (Ω)
Load X (Ω)
Cable / velocity factor
Stub type

📐 The formulas​

Distance from the load (two solutions, both valid):

if RL ≠ Z₀:
    t = [ XL ± √( RL·((Z₀ − RL)² + XL²) / Z₀ ) ] / (RL − Z₀)
if RL = Z₀:
    t = −XL / (2·Z₀)

d/λ = arctan(t) / 2π          (if negative, add 0.5)

The susceptance the stub must provide:

B = [ RL²·t − (Z₀ − XL·t)(XL + Z₀·t) ] / ( Z₀·(RL² + (XL + Z₀·t)²) )

Stub length:

open:     l/λ = −arctan(B·Z₀) / 2π
shorted:  l/λ =  arctan(1/(B·Z₀)) / 2π

Physical length = (l/λ) × λ × vf

Where this calculator stops:
  • The calculation is for a shunt stub; a series stub works out differently
  • The stub must be the same cable as the line — a different velocity factor wrecks the calculation
  • Line losses are not accounted for: on long runs and at high frequencies they shift the result
  • The match is exact only at the design frequency, and the worse the original mismatch, the narrower the bandwidth

🎯 In practice​

  • Matching a VHF antenna whose impedance you have measured.
  • Matching with no components where a capacitor would break down and a coil would get hot.
  • Checking someone else's design: is the stub really where it should be.
Practical advice:
  1. Measure ZL with an analyser at the point of connection — guesswork does not work here.
  2. Of the two solutions take whichever is easier to build; the difference in bandwidth is small.
  3. A shorted stub is mechanically sounder: it has no open end for water to get into.
  4. Cut long and trim to the analyser — you cannot add length back.

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

How to cite this calculator
UR3PKI. «Stub matching calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/lines/stub_match (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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