Cecil More wrote:
wrote:
Cecil Moore wrote:
power = volts * amps
= (Vfwd + Vref) * (Ifwd + Iref)
= Vf*If + Vf*Ir + Vr*If + Vr*Ir
Seems you've lost a couple of terms in there.
As with any other math model, the negligible secondary terms
are dropped. If the phase angle above is close to 90 degrees,
two terms drop out. A Bird wattmeter assumes that two of the
phase angles are close to 90 degrees. If they are not, you are
using the wrong instrument for your measurements, a common problem.
So again, it works in the specific, but not in the general case.
Does this mean that forward and reverse waves only have power in
the special case of low-loss feedlines?
It means that if you use a 50 ohm Bird wattmeter in any environment
except a 50 ohm one, you are using the wrong instrument.
The answer appears orthogonal to the question.
With my model, incident and reflected VOLTAGE waves and CURRENT waves
do exist. This is in common, I think, with most authors on the subject.
And this all works fine since superposition holds for voltage
and current.
It certainly doesn't work with your assertion that reflections don't
exist.
Go back 3 sentences and re-read "reflected VOLTAGE waves and CURRENT
waves
do exist". I think you were quoting from something I wrote.
Your math model would have us believe that a power source pumps energy
into voltage and current waves only to have that energy disappear from
the universe for a time that is convenient for your math model. Of course,
that very energy is magically created once again at the load. We've heard
this bad magician's trick before. "Close your eyes while I make this
elephant disappear."
I am unsure how you extrapolate this from my writings.
To recap. Everything with the incident and reflected wave model
works as long as you stick to voltage and current waves. It is only
when extended to include power (as done by Bird and others), that
the model starts to deteriorate.
For a resistive 50 ohm environment, the model does not deteriorate.
The Bird is designed for such an environment. There doesn't exist
any real-world instrument that will measure anything and everything.
Every real-world measuring instrument has limitations. If you attempt
to use a Bird in a 100-j100 ohm environment, that is your problem,
not Bird's.
So you are agreed: The reflected POWER model does not work in general.
So to get the right answers in the general case (using my definition
of general), compute your forward and reverse voltages and currents.
Use superposition to derive the resultant voltages and currents at
any point on the line and then use p(t) = v(t) * i(t) to compute
the power, which you may then average if you desire.
We've already been down this road but here it is, once again. Consider
a one second long lossless feedline with an SWR of 5.83:1 and a Z0-matched
source of 100 watts. After steady-state is reached, the feedline contains
300 joules of energy which cannot stand still. A Bird wattmeter reads 200w
forward and 100w reflected. Your power calculation gives 100 watts everywhere
implying that there are only 100 joules in transit in the feedline.
No. You have made an incorrect implication. 100 watts flowing says
nothing about how much energy is stored.
What
happened to the other 200 joules pumped into the system by the source during
the transient state? Hint: there is 100 joules in the reflected waves and 100
joules in the re-reflected waves. The Bird is correct.
Your experiment appears to be incompletely or incorrectly specified.
If the source is Z0 matched to the transmission line, how did you
get a re-reflected wave at the source?
....Keith