W2EGB
Technical Information

Applications for 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.

SWR equals:

E_MAX/E_MIN

or

I_MAX/I_MIN

 

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 = (P_R/P_F)^1/2

 

where

P_R = reflected power

P_F = 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 = ([(R_a-Z_o)²+X_a²]/[(R_a+Z_o)²+X_a)^1/2

 

where

R_a = output resistance (the load

X_a = output

Z_o = 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

([X_a²]/[2Z_o²+X_a²])^1/2

= 0

Lim (X_a²)/(2Z_o²+X_a²), X_a -> 0

= 0

This information is courtesy of NC2S Electronics Information.