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 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.
εA = +20 * log (1 + |ΓA
* ΓB|) [dB]
-20 * log (1 - |ΓA
* ΓB|) [dB]
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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 |
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VSWRMAX = SA * SB VSWRMIN = SA
/ SB
where
| SA = larger of the two VSWRs SB = 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
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