Owen wrote:
Tom Donaly wrote:

Owen wrote:

Tom Donaly wrote:

Given a 396 meter length of Radio Shack RG58. At 250 kiloherz TLD says
(after some manipulation) that it has a propagation constant of
689.6 X 10^-9 + j7.933 X 10^-3. Zo is 50 -j4.344. Feed it with a




Doesn't that imply that the the matched line loss at 0.25MHz is
689.6E-9*20*e^1*100 dB/100m?

That is 0.0006dB/100m, it seems too good to be true!

Owen


Hi Owen,
It is too good to be true. (Just consider it came from an unusually
good batch.) The whole exercise is nonsensical, though,
because it results in negative power and a negative SWR. Increase the
loss to a more realistic value and the negative power goes away as
does the negative SWR while the absolute value of the reflection
coefficient is still greater than 1. I was hoping I could get some
kind of nut philosophical justification for negative average power
out of Cecil, but you sprang the trap.
73,
Tom Donaly, KA6RUH


Well, you are right I was fooled by your statement "Given a 396 meter
length of Radio Shack RG58" which seemed to say a real cable.

I suspect the source of "negative power" values stems from the
assumption that Power=Real(Vf*If*-Vf*Ir*), whereas it is my
understanding that the power flow at a point on the line is Real(V*I*)
or Real((Vf+Vr)*(If-Ir)* which expands to Real(Vf*If* - Vf*Ir* + Vr*If*
- VrIr*) so that when Power=Real(Vf*If*-Vf*Ir*) is assumed, two of the
terms (- Vf*Ir* + Vr*If*) are being ignored.

The real part of (-Vf*Ir* + Vr*If*) is zero when Zo is real, so they can
be ignored for calculating real power when Zo is real.

In the case of your example, but using real RG58C/U (and Zo is not
real), it looks to me like Real(Vf*If*-Vf*Ir*) is negative out to about
60m from the load, but Real(V*I*) is always positive and always grows
toward the generator.

A graphic showing the behaviour of the terms is at
http://www.vk1od.net/RG58sol.gif .

Owen

PS: My notation: the * postfix unary operator means complex conjugate,
ie (If-Ir)* means compex congugate of (If-Ir).

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I used the complicated expressions for V and I found
in _Field and Wave Electromagnetics_ by David K. Cheng on page 468,
and then found the power by taking the real part of VI*. If you're
interested in doing it the hard way, you can first find V and I,
then take (V + ZoI)/2Sqrt(ReZo) and call that a. Then take
(V - Zo*I)/2Sqrt(ReZo) and call that b. The power is then just
|a|^2 - |b|^2. This last comes from _Microwave Engineering Using
Microstrips_ by E.F. Fooks and R.A Zakarevicius.
Before doing any of this, though, be sure the propagation constant
is the right one for the Zo of the line. The books give
the propagation constant for a transmission line as sqrt((R + jwL)(G +
jwC)), and Zo as sqrt((R + jwL)/(G + jwL)) so it's reasonable to assume
the two are related. In other words, it doesn't seem as if you can just
pick numbers out of a hat for the two quantities and expect them to mean
anything.
73,
Tom Donaly, KA6RUH