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Smith Chart Calculator (Z to S11, VSWR, Return Loss)

Convert between complex load impedance, reflection coefficient (S11), VSWR, return loss, and mismatch loss for a given system Z0. Pure-ohm inputs, no length or frequency.

Smith Chart / Z to S11 Calculator

Convert between complex load impedance, reflection coefficient (S11), VSWR, return loss, and mismatch loss for a given system Z0.

Inputs

Ω
Ω
Ω
Γ = |Γ| = 0.248inductive (+jX)capacitive (-jX)openshortZ0 = 50 Ω
Z to S11 to VSWR
|S11|
0.2477
angle -46.8 deg
VSWR
1.659

More

Return loss12.12 dB
Mismatch loss0.275 dB
Γ (real)0.1697
Γ (imag)-0.1805

Analytical calculation

Every step the calculator runs, with the formula, your numbers plugged in, and the result.

Reflection coefficient
Load impedance Z_L = R + jX referenced to Z0.
VSWR
Voltage standing wave ratio follows directly from |Gamma|.
Return loss
How many dB down the reflected wave is.
Mismatch loss
Fraction of forward power lost to the reflection.

Frequently asked

What VSWR is "good"?

VSWR < 1.5 (RL > 14 dB) is acceptable for most antenna systems; VSWR < 1.2 (RL > 21 dB) is great. Below 1.05 you're in the noise floor of most VNAs.

Why is mismatch loss small even at VSWR 2?

VSWR 2 only loses about 0.5 dB to reflection; the bigger problem is that the reflected energy can mess with your PA, mixer, or oscillator.

References

  • PrimaryPozar, D. M. Microwave Engineering, 4th ed., Wiley 2011, Sec. 2.3 (terminated lossless line: reflection coefficient, VSWR, return loss, mismatch loss) and Sec. 2.4 (Smith chart construction).
  • OriginalSmith, P. H. "Transmission Line Calculator," Electronics, vol. 12, January 1939, pp. 29-31.
  • ConceptSmith chart (overview)

Closed-form is just the start.

These calculators hand you the analytical starting point. RayRF takes you the rest of the way: antennas, filters, feedlines, and more, simulated on your real stackup with copper losses, dielectric loss, and finite ground. Roughly a second per iteration.

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