W2EGB
Technical Information

SWR

Applications for Standing Wave Ratio (SWR) are usually in broadcast and other radio frequency applications with antennas and feed lines (so any railfans and others with scanners who may be "listening-in" are hearing something broadcast over an antenna and feed line with some SWR!). For amateurs, SWR is a critical element of good antenna installation.

Conceptually, SWR is the ratio of the amplitude of a wave in an electrical transmission line between its maximum and its (adjacent) minimum. SWR is usually defined as a voltage ratio, called, not unexpectedly, the voltage standing wave ratio, abbreviated VSWR. For example, the VSWR value 1.2:1 denotes a maximum standing wave amplitude that is 1.2 times greater than the minimum standing wave value. An SWR (voltage or otherwise) greater than 1.5:1 typically indicates a serious mismatch in the transmission line.

SWR equals:

EMAX/EMIN
or
IMAX/IMIN
 
where
E = voltage (Electromotive force)
I = current (in amps)

as measured on a line (maximums and minimums); by formula, this can be computed by

1+p/1-p

where p = rho, the voltage reflection coefficient.

Rho is computed in either of the following ways:

a.) p = (PR/PF)1/2
 
where
PR = reflected power
PF = forward power

Under balanced conditions, there should be no reflected power; thus, there would be no be no high voltage or low voltage (or current) points on the line, thus no standing waves.

b.) p = ([(Ra-Zo)+Xa]/[(Ra+Zo)+Xa)1/2
 
where
Ra = output resistance (the load
Xa = output
Zo = the line power

The output resistance and the line impedance should be equal (thus balancing each other out of the numerator) and the output reactance should be as small as possible (thus disappearing from the numerator, making the numerator very small in relation to the denominator). With Ra and Zo equal, the formulas

([Xa]/[2Zo+Xa])1/2
= 0
Lim (Xa)/(2Zo+Xa), Xa -> 0
= 0

This information is courtesy of NC2S.

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