[TowerTalk] Re: coax as balanced line

[Jim Reid]

At 04:30 PM 8/1/97 -0400, Ronald D Rossi wrote:

>>>>Jim Reid said:
>> Eveidedntly the cables do act as parallel resistances, so
>> the R that causes loss is cut in half,  so down goes the
>> loss.
>
>Parallel resistance would imply that the Z would be 1/2 rather than
double. In 
>my opinion W0UN has it right with his analogy 1/2 the power down each line
at 
>the same loss per line as a single run. If the signal were not making a
round 
>trip so-to-speak (balanced) the loss would be 1/2, but so would the
impedance.
>

But Ronald,  the R in R+/-jX in the coax cable's characteristic impedance
is what is 50 ohms,  not the loss resistance of the wire!  The R which
is 50 ohms in the characteristic impedance statement is the "effective"
R which would be calculated form the "apparent" resistance resulting
from the necessity of the line appearing to the RF signal as a series
of inductors,  each of which has a shunt capacitor across to the other
conductor of the line.  The series inductor limits the rate at which
the shunt capacitor can charge;  this sets up a particular voltage
and current relation of the line which is entirely controlled by
the line geometry;  in this way the line has an "apparent" resistance,
which is called the characteristic impedance ( in the old days,
it was called the surge impedance reflecting the idea of the limitation
to the line capacitance charging time).

This R of the line impedance that the RF sees when the reactance terms
are equal and opposite (that is the antenna system is "tuned") is NOT 
the resistance that causes RF signal loss.  The R that causes loss is 
approximately the resistance measured with a DC ohm meter.  
This is the R that is reduced with parallel shielded lines.  
Forget that one is using a piece of coax
as an easy way to get a shielded line; it is not wired up as,  and
does not behave as coax cable does,  that is the entire point of
using four pieces of coax in a parallel/parallel configuration to
realize a very low loss transmission line.

Were the R that causes signal loss in a 50 ohm characteristic
impedance transmission line really 50 ohms,  a 1.5kW signal 
travelling down the line would try to dissipate the entire
1500 watt signal in the line;  nothing would reach the antenna.
Note: 50 ohm coax line fed from and delivering to matched 50
ohm source and load impedances will have an rms voltage on the
line of 274 volts and an rms current flow of about 5.5 amps,  so
5.5 amps squared X 50 ohms = 1500 watts.  Obviously this is
not the way the transmission line operates!


And, BTW,  the signal does not make a round trip when traversing
parallel shielded lines,  it does travel through loss resistances
which are equal,  and in parallel,  so the loss is cut in half
using two lines, and to 1/4th using four lines.

73,  Jim, KH7M


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