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Old February 8th 08, 02:56 AM 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 6, 8:02*am, Cecil Moore wrote:
Keith Dysart wrote:
Cecil Moore wrote:


* * * * * * Rs * * * Vg * Pfor--25w * * * * Vl
* * * *+----/\/\/-----+----------------------+
* * * *| * *50 ohm * * * ~23w--Pref * * * * |
* * * *| * *0.04w * * * * * * * * * * * * * */ *1.92w
* * * Vs * * * * * * * * 90 degrees * * * * *\ * Rl
* *100 cos(wt) 1.96w * * 50 ohm line * * * * / *1 ohm
* * * *| * * * * * * * * * * * * * * * * * * \ *load
* * * *| * * * * * * * * * * * * * * * * * * |
* * * *+--------------+----------------------+
* * * gnd

When you find (as you will), that Pfor and Vfor
do not change when the reflected wave returns,
it should be difficult to assert that the
reflected wave is re-reflected at Vg.


Not difficult at all. I've added the powers to the
diagram above. The reflected power is ~23 watts.
The power dissipated in the source resistor is
~0.04 watts. The reflected power is obviously *NOT*
being dissipated in the source resistor so where
is it going instead? The answer is destructive
interference at the source resistor is redistributing
the reflected energy back toward the load as an
equal magnitude of constructive interference.
I call that a reflection.


When we analyze this circuit we find that there is
no voltage re-reflection when the wave gets back
to the generator. This is clear because Vf does not
change, which it would have to do if any of Vr was
re-reflected.

And yet it appears that you are claiming that power
is reflected at the generator. How can power be
reflected if voltage is not?

You may find the Excel spreadsheet on this page
http://keith.dysart.googlepages.com/...oad,reflection
interesting.

It computes the various results for the circuit we
have been discussing. Input Vs, Rs, Rl and line length
and it will compute the various voltages, currents and
powers.

After entering the circuit parameters, click "First".
The circuit conditions at the end of the first round
trip will be computed. Click "Next" to have any
re-reflection included into the forward conditions
for the next round trip.

When Rs is 50 ohms (i.e. it matches the line impedance),
the circuit conditions settle to their final state
immediately, as would be expected when there is no
reflection at the generator. Change Rs to a value other
than 50 and it takes many clicks of "Next" before the
conditions settle. At each click, Vf changes as some of
Vr is re-reflected and added to Vf.

...Keith