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Old February 9th 08, 02:06 AM posted to rec.radio.amateur.antenna
Cecil Moore[_2_] Cecil Moore[_2_] is offline
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First recorded activity by RadioBanter: Mar 2007
Posts: 3,521
Default Derivation of Reflection Coefficient vs SWR

Keith Dysart wrote:
Are you sure? I thought a reflection was something that
occurred at an impedance discontinuity and the magnitude
of the voltage reflection was defined by

Vr = Vincident * ReflectionCoefficient
= Vincident * (Z2-Z1)/(Z2+Z1)


That's true for normal reflections which involve only
one wave. Wave cancellation is a different kind of
energy reflection involving two waves. The energy flow is
canceled in one direction and therefore flows in the
other direction. In optics, it is known as a redistribution
of energy in directions that allow constructive interference.
In a transmission line, there are only two possible directions
so any redistribution of energy due to destructive interference
can be considered to be a reflection in the opposite direction,
the only direction available to constructive interference.

and that the reflected voltage then added to any wave
already travelling in that direction.


True for a single wave reflection. For two interacting
waves, the voltage in one of the waves can simply replace
the voltage in the other wave. In our example, the reflected
voltage simply replaces the source voltage component.

But you are claiming that power can be reflected when
voltage is not. I have never encountered this claim before.


When the reflected wave arrives, it cancels most of the
existing forward wave from the source. The reflected
voltage exactly equals the canceled source voltage in
our example because the source resistance is the same
as the Z0 of the line.

Are you sure?


It is obvious that reflected energy never flows in the
source resistor so it must go in the only other direction
possible. Yes, I am sure. The conservation of energy
principle will allow nothing else.
--
73, Cecil http://www.w5dxp.com