Cecil Moore wrote:
wrote:
May I suggest that if you had read the posting to which I
responded and the rest of my response you would have found
exactly the example you are looking for: the forward
voltage and current on a transmission line when a standing
wave is present (and the reflected as well).
How did the standing wave get there in the first place? *POWER*
from the generator. You simply cannot have standing waves without
a power source, a forward wave, and a reflected wave.
You are asking us to completely ignore the cause of standing waves.
It is not obvious to me how you extrapolate my postings to these
outrageous assertions.
For sure there is power from the generator. It is needed to charge
the line and to provide whatever power is consumed in the load
and line losses.
When a standing wave is present, for sure there is a forward
and reflected voltage and current wave. After all it is called
a voltage standing wave.
But these voltage and current forward and reflected waves do not
have power. They are exactly the same as the voltages computed
using superposition in circuit analysis, they are superposed in
exactly the same way to find the resultant voltage, and it is
illegal, except in special cases, to assume that these constituent
voltage terms represent power.
May I suggest, for clearer understanding, that just for a few
moments (say 30 minutes), you set aside RF and consider how
a line is charged by a step function. Do the voltage and
current reflection diagrams. And then consider the energy
flow just in front and just following the voltage step
as it propagates down the line and back and down and back...
Take the time to do this for the following cases...
- matched generator
- line terminated in Z0
- line open
- line shorted
After the line has charged consider what happens when
the generator voltage is set back to 0.
Do it all again for a mismatched generator.
Then for a charged open termination line, consider what
happens when a load of Z0 is applied. And then when the
load is removed.
For each of these cases determine how the voltage fronts
propagate, the energy flow in front of and following the
step, the resulting energy distribution on the line and
whether this energy is stored in the capacitance or
inductance or H field or E field.
Because of the step function excitation, none of these
computations are difficult.
With this example it is easy to see when energy is flowing
and when it is not, and contrast this to the energy flows
computed using the forward and reflected voltages.
Well maybe the above is more than 30 minutes, but there
is much to be learned from a thorough understanding of
the behaviour with this simple excitation.
Now replace step excitation with sinusoidal; the principles
are the same, but the computations are more complex and
the resulting voltage and energy distributions on the line
are more interesting. But the fundamentals are the same.
The above thought experiment was the one that made clear
to me the fallacy of assigning power to the forward and
reflected voltage waves.
So there is some risk for you doing this thought experiment;
the results may conflict with some of your deeply held
beliefs. It is a risk worth taking.
....Keith