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Tool 07 · Available

VSWR, Return Loss & Reflection

Convert among reflection coefficient, return loss, mismatch loss, VSWR, and impedance.

Typical inputs
Γ magnitude/angle, VSWR, positive return loss, S11 dB, reflected power, or complex load and real Z0.
Calculated output
Complex Γ, magnitude/phase, VSWR, return loss, mismatch loss, reflected power, and load impedance.
Model status
Release B · documented and numerically tested
Engineering question

How much of the incident power is reflected by this mismatch?

Reflection conversion workbench

Select one primary representation. Scalar inputs do not invent phase; they use 0° and say so. Return loss is positive while S11 magnitude in dB is normally negative.

Reflection coefficient0.100000 ∠ 0.000°Γ = 0.100000 + j0.000000
VSWR
1.222222 : 1
Positive return loss
20.000000 dB
S11 magnitude
-20.000000 dB
Reflected power
1.000000%
Accepted power
99.000000%
not antenna radiation efficiency
Mismatch loss
0.043648 dB
Equivalent load Z
61.11111 + j0.00000 Ω
Normalized impedance z
1.22222 + j0.00000

Calculation path

  1. VSWR=1+∣Γ∣1−∣Γ∣\mathrm{VSWR} = \frac{1+|\Gamma|}{1-|\Gamma|}
  2. RL=−20log⁡10∣Γ∣S11[dB]=−RL\mathrm{RL} = -20\log _{10}|\Gamma|\qquad S_{11}[\mathrm{dB}] = -\mathrm{RL}
  3. PreflectedPincident=∣Γ∣2PacceptedPincident=1−∣Γ∣2\frac{P_{\mathrm{reflected}}}{P_{\mathrm{incident}}} = |\Gamma|^{2}\qquad \frac{P_{\mathrm{accepted}}}{P_{\mathrm{incident}}} = 1-|\Gamma|^{2}
  4. Input match does not state radiation efficiency or realized antenna performance.
Model

What this calculator is doing

All views transform the same reflection coefficient. The passive boundary |Γ| ≤ 1 is enforced and matched and total-reflection limits are represented explicitly.

Decision

How to read the result

Use return or mismatch loss for power accounting; use complex Γ or impedance for correction. Phase matters even when two loads have equal VSWR.

Equations & conventions

  • Γ=ZL−Z0ZL+Z0\Gamma=\frac{Z_{\mathrm L}-Z_0}{Z_{\mathrm L}+Z_0}
  • VSWR=1+∣Γ∣1−∣Γ∣\mathrm{VSWR} = \frac{1+|\Gamma|}{1-|\Gamma|}
  • RL=−20log⁡10∣Γ∣\mathrm{RL} = -20 \log _{10}|\Gamma|
  • Γ is the complex voltage-wave reflection coefficient at the stated plane.
  • VSWR is (1+|Γ|)/(1−|Γ|).
  • Return loss is the positive quantity −20 log10|Γ|.

Independently checked example

Checked example: ZL = 100 Ω on Z0 = 50 Ω gives Γ = 1/3, VSWR = 2, return loss = 9.542425 dB, and 11.1111% reflected power.

Common mistakes

  • Calling negative S11 dB a negative return loss.
  • Assuming equal VSWR means equal complex impedance.

Assumptions, validity & omissions

  • Z₀ is positive and real.
  • Passive reflection inputs require |Γ| ≤ 1.
  • Return loss is displayed as a positive loss quantity.

Sources & model provenance

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