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Old February 5th 08, 04:38 PM posted to rec.radio.amateur.antenna
Keith Dysart[_2_] Keith Dysart[_2_] is offline
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First recorded activity by RadioBanter: May 2007
Posts: 492
Default Derivation of Reflection Coefficient vs SWR

On Feb 5, 7:40*am, Cecil Moore wrote:
Keith Dysart wrote:
The power provided by the source is equal
to the power dissipated in the source resistor and the
power dissipated in the load resistor.


49.999 = 31.249 + 18.75


So all the energy is accounted for, as expected.


I'm surprised you don't see your own contradiction.

If, as you say, the reflected wave is not reflected by
the source, then the reflected wave flows through the
source resistor to ground and is dissipated.

If the reflected wave is dissipated in the source
resistor, it cannot join the forward wave.

The forward wave is 25 joules/sec. The source is
supplying 18.75 joules/sec. If the reflected wave
is dissipated in the source, where is the other
6.25 joules/sec coming from? Is it mere coincidence
that the reflected wave is 6.25 joules/sec????

Hint: You cannot eat your reflected wave and have it too.

If the forward power is greater than the source power,
the reflected wave is joining the forward wave, i.e.
being reflected by the source.


I wondered if this bit of numerology would lead to
confusion, and apparently it has.

Consider what happens when the source is first turned on.
Immediately
Pf.avg = 25 W

Sometime later the forward wave reaches the load and a
reflected wave is returned
Pr.avg = 6.25 W

Later, this wave arrives back at the generator.

How does this reflected wave of 6.25 W affect the already
present forward wave of 25 W when it arrives back at the
generator. It affects it not one iota. The forward power
remains the same, the forward voltage remains the same
and the forward current remains the same. This is the
meaning of no reflection.

The one thing that changes is the net average power which
decreases to 18.75 W.

I would suggest that you start with the circuit I proposed
and analyze it with the technique of your choice.
What is the final Vf, Vr, Pf.avg, Pr.avg, Pg.avg and Pl.avg?
Are your answers different than mine?
If so, we can explore which approach is in error.
What happens at the generator when the first reflection
arrives back at the generator?
Does Vf and Pf.avg change? Or remain the same?

When Pf.avg remains the same, how can it be claimed that
the reflected wave is re-reflected?

...Keith