# VSWR Mismatch Errors

Both amplitude and phase errors are introduced when mismatched impedances are present at an electrical interface. When an ideal match is not encountered by the incident (forward) wave, part of it is coupled to the load and part is reflected back to the source. Upon arriving back at the source, part of the reflected wave is coupled back to the source and the rest is reflected back again to the load. The process iterates until the amplitude of the wave is attenuated to an insignificant level due to the loss of the interface (cable, connector, waveguide, etc.). Each time a reverse and forward reflection occurs, the amplitude and phase of all the signal components traversing the path between the source and the load add vectorially. The result is ripple across the frequency band (since the VSWR of each interface typically varies with frequency), as well as a portion of the incident power being reflected back to the source. What begins as a pure sinewave can look like a real mess when viewed on an oscilloscope.

Amplitude Error

Note: Only enter values in the yellow cells or risk overwriting formulas!

εA = +20 * log (1 + |ΓA * ΓB|)  [dB]

-20 * log (1 - |ΓA * ΓB|)  [dB]

Phase Error

εΦ = ±(180 / π) *| ΓA| * |ΓB|  [°]

Note: This formula has also been seen
written as

εΦ= ±(180 / π) * sin-1 (|ΓA| * |ΓB|)  [°]

but for small angles, the difference
is negligible.

See a derivation of this equation as provided by Haris Tabakovic

Resultant MIN and MAX

VSWRMAX = SA * SB
VSWRMIN = SA / SB

where

 SA = larger of the two VSWRsSB = smaller of the two VSWRs

Example

VSWRA = 2.5:1  -->  SA = 2.5
VSWRB = 2.0:1  -->  SB = 2.0
VSWRMAX = 2.5 * 2.0 = 5.0  = 5.0:1
VSWRMIN = 2.5 / 2.0 = 1.25  = 1.25:1

Here is a JavaScript calculator for VSWR / Return Loss / Reflection Coefficient / Mismatch Error / Improvement