Owen wrote:

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 .


I meant to also mention the response of a typical reflectometer.

The type of reflectometer that samples the voltage at a point, and the
current at the same point to create a voltage proportional to that
current, (such that the magnitude and phase of the voltage due to the
current sample is equal to and opposite to the voltage sample when the
line is terminated in its characteristic impedance,) then adds the two
voltages algebraicly and measures the magnitude of the resultant
responds to Vr, or if it is turned around, to Vf. Such an instrument
does not respond to the two cross product terms terms discussed in the
quote.

So even if you adjusted such a reflectometer so that it nulled on the
true Zo of the cable by adjusting the phase and amplitude of the voltage
same wrt current sample, it would respond to Vf and Vr and could not be
scaled to read forward and reverse power (since it doesn't respond to
the cross product terms).

So, in Tom's case (though with real RG58), a reflectometer of that type,
properly nulled and scaled in Watts would indicate more reflected power
than forward close to the load. The instrument is correctly responding
to the magnitude of the reflection coefficient, but scaling in Watts can
only be valid for Zo real.

Owen


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

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