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[TowerTalk] SWR question

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Subject: [TowerTalk] SWR question
From: (Chuck Counselman)
Date: Fri Feb 28 10:49:27 2003
In most discussions about the consequences of high SWR, and perhaps 
in this one, forward power is confused with _net_ forward power.  By 
_net_ forward power I mean forward power minus reverse power.

E-M waves, carrying power, travel in both directions on a 
transmission line.  A directional coupler/bridge whose characteristic 
impedance Zo matches that of the line distinguishes between and can 
measure each of these two, forward and reverse, waves separately. 
 From the amplitudes (in volts or amps) of the two waves and Zo, a 
typical "SWR" meter derives (by some analog or digital process of 
calculation) the power carried by each of the forward and reverse 
waves, the percentage of "reflected" (i.e., the ratio of reverse to 
forward) power, and/or the VSWR.

E.g., a VSWR equal to 3 corresponds to a forward-wave amplitude (in 
volts) equal to two times the reverse-wave amplitude (in volts); 
maximum voltage on the line occurs where the amplitudes of the two 
waves are in-phase (2+1=3); minimum voltage on the line occurs where 
the amplitudes of the two waves have opposite phases (2-1=1); and 
reflected-power ratio equals 25%.

Assuming for simplicity that the line is lossless and that a 100-watt 
transmitter is matched to the line by a lossless "antenna tuner" or 
matching network, then:

(1) A meter between the transmitter and the tuner will indicate
     Forward power =  100 watts;
     Reverse power =    0 watts;
     % refl. power =    0 %;
     VSWR          =  1:1; and
     the _net_ forward power is 100 - 0 = 100 watts.

(2) A meter between the tuner and the antenna will indicate
     Forward power =  133.33 watts;
     Reverse power =   33.33 watts;
     % refl. power =   25 %;
     VSWR          =  3:1; and
     the _net_ forward power is 133.33 - 33.33 = 100 watts.
     Note that the forward power exceeds the power output
     from the transmitter because the 33.33 watts of reverse
     power returning to the tuner is reflected from the tuner
     back toward the antenna.

All of the 100 watts put out by the transmitter is delivered to the 
load, i.e., the antenna, because we have assumed no losses.  If the 
antenna itself has no loss, and if nothing in the near field of the 
antenna (e.g., the earth) dissipates power, then all of the 100 watts 
put out by the transmitter is actually radiated.

In the real world, both the line and the tuner have losses, and the 
story is different in several respects:  First, some of transmitter's 
output power is dissipated in the tuner.  Second, some of the reverse 
power returning to the tuner is dissipated in the tuner and not 
reflected back toward the antenna.  Third, some of the forward power, 
and some of the reverse power, flowing in the line between the tuner 
and the antenna, are dissipated in the line.  The arithmetic is 
somewhat complicated, but it's easy with a computer.  Various 
computer programs are available, some from the ARRL, and some from 
the web (e.g., see <>).

An interesting question for you armchair lawyers out there: Does the 
FCC's peak-transmitted-power limit of 1500 watts refer to the forward 
power somewhere, or to the _net_ forward power?

IMO, the FCC regulation _must_ refer to _net_ forward power because 
forward power can be almost anything, depending on where you measure 
it, for a given transmitter power, for a given radiated power, or for 
a given power delivered to the antenna.

73 de Chuck, W1HIS

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