Double-Stub Tuner
A double-stub tuner matches a load using two shunt stubs at a fixed spacing — the arrangement used in adjustable lab tuners, where the stub positions can't move but their lengths can. This tool finds both solutions for the two stub lengths, flags the "forbidden region" (loads whose conductance is too high to match at the chosen spacing), and confirms the design by transforming the load through the network to an input VSWR of 1. The first stub sits at the load; the second is one spacing away.
Equations & Parameters ▸
\(t=\tan\beta d,\quad B_1=-B_L+\dfrac{Y_0\pm\sqrt{(1+t^2)G_L Y_0-G_L^2 t^2}}{t}\)
\(B_2=\dfrac{\pm Y_0\sqrt{(1+t^2)G_L Y_0-G_L^2 t^2}+G_L Y_0}{G_L\,t}\)
solutions exist only if \(G_L\le Y_0\,\dfrac{1+t^2}{t^2}=\dfrac{Y_0}{\sin^2\beta d}\)
\(B_2=\dfrac{\pm Y_0\sqrt{(1+t^2)G_L Y_0-G_L^2 t^2}+G_L Y_0}{G_L\,t}\)
solutions exist only if \(G_L\le Y_0\,\dfrac{1+t^2}{t^2}=\dfrac{Y_0}{\sin^2\beta d}\)
| RL, XL | Load resistance and reactance (Ω). |
| Z0 | Line / stub characteristic impedance (Ω). |
| d | Stub spacing (λ). Common values: 0.125 (λ/8) or 0.375 (3λ/8). |
| Stub | Open- or short-circuited shunt stubs. |
Reference: D. M. Pozar, Microwave Engineering, 4th ed., §5.3 (double-stub tuning).
Inputs
Ω
Real partΩ
Imag partΩ
Referenceλ
FixedShunt stubs
Results
Solution 1
Stub 1 length ℓ₁—
Stub 2 length ℓ₂—
Resulting VSWR—
Solution 2
Stub 1 length ℓ₁—
Stub 2 length ℓ₂—
Resulting VSWR—
Matchability
Load conductance GL—
Max GL at this spacing—
Diagram