Transmission Line + Shunt Stub Calculator

Calculate impedance transformation on a lossy transmission line and the effect of a shunt stub. The stub may be open, shorted, or terminated in an arbitrary complex impedance.

Main transmission line

Characteristic impedance Z₀ (Ω)

Frequency (MHz)

Main line length (m)

Velocity factor

Loss (dB / 100 m)

Load

Load resistance R (Ω)

Load reactance X (Ω)

Measurement / tap position

The tap position is controlled by the slider next to the main Smith chart. The numeric value below can still be used for direct entry.

Distance from load (m)

Distance from generator (m)

The blue spiral answers: "What impedance do I see looking toward the load from this position?" The complete physical line remains present. A stub connected at the tap is then combined in parallel with that impedance.

Shunt stub

Stub characteristic impedance Z₀ (Ω)

Stub length (m)

Stub velocity factor

Stub loss (dB / 100 m)

Termination

Stub load R (Ω)

Stub load X (Ω)

Results

Load impedance

Impedance toward load at tap

Stub impedance at tap

Combined tap impedance

Complete-line input impedance

Tap VSWR, looking toward load

Tap |Γ|

Tap return loss

Main electrical length

Stub electrical length

Main one-way loss

Stub one-way loss

Physical arrangement

Main-line Smith chart

Tap position

2.00 m from load

Stub length

1.00 m

Stub load X

+50 Ω

The sliders update the Smith chart and calculations immediately. The Stub load X slider is shown only when Complex load is selected. When hoovering the mouse pointer over a slider, the slider can be fine tuned with the mouse wheel. Use shift+mouse wheel for less fine tune steps. With the mouse pointer inside the chart, the chart can be zoomed in/out with the mouse wheel. Double click left mouse button to restore full view, left+drag pans the chart

Chart: drag to pan • mouse wheel to zoom • double-click to reset view

Load Impedance toward load Selected tap Complete-line input

The blue spiral starts at the load (0 m) and follows the impedance toward the load as the observation point moves toward the generator. Labels on the spiral are physical distance from the load.

Stub Smith chart

This chart uses the stub's own characteristic impedance as its normalization. The orange curve is the transformation from the stub termination to the tap.

Tap admittance calculation

Main-line admittance

Stub admittance

Total tap admittance

Total tap impedance

Y_tap = Y_main + Y_stub
Z_tap = 1 / Y_tap

Main-line impedance versus distance from load

Distance	Electrical length	R (Ω)	X (Ω)	\|Γ\|	VSWR

Equations

Z(d) = Z0 [ ZL + Z0 tanh(γd) ] / [ Z0 + ZL tanh(γd) ]

γ = α + jβ. The same equation is used for the stub, using the stub's own Z₀, velocity factor and loss.

Ytap = 1 / Zmain(tap) + 1 / Zstub(tap)