On Sun, 15 Apr 2007 19:23:56 +1000, Alan Peake wrote:



Walter Maxwell wrote:
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We have thus proved that the virtual short circuit established at the stub point is actually performing as a
real short circuit.
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Walt, W2DU

It is interesting to look at a single short pulse propagating along the
TL. At the stub point, the pulse must encounter a discontinuity in
impedance and therefore there will be a reflection. This can been seen
on a TDR. So there is a real reflection from a stub regardless of
whether or not it is a virtual short.
Alan
VK2ADB

I thank you for that, Alan, because, to continue, when the pulse is replaced with a sine wave, there is also a
reflection from the stub. And when going still further, since the stub presents a susceptance equal to the
line susceptance of the opposite sign at the stub point, some of the sine wave continues along the line and
reaches the mismatched termination, which also produces a real reflection. When the stub is placed at the
proper place on the line relative to the SWR (mismatch), the phase of the waves (voltage and current)
reflected from the load are opposite, respectively, to those of the waves reflected from the stub. The sum of
the voltage waves then yield a resultant reflection coefficient of 180° and the sum of the current waves yield
a resultant of 0°, establishing a short circuit to both sets of reflected waves, but an open circuit to the
source waves.

For people who understand that fields (voltage and current) radiating from two vertical radiators that are of
the same magnitude and of opposite sign result in a null in their radiation pattern in a particular direction
must also understand that for the null to be established there must also be interaction, or interference, or
summing between the fields to cause the travel to cease in the null direction. These people also understand
that energy that was traveling in the null direction has been re-directed in another direction, raising the
level of the energy in that direction from the original level.

IMHO, these people can't have it both ways. If the fields interact, or interfere in space, such as in those
radiated from two radiators, then coherent fields traveling in a transmission line must also interact,
interfere, or sum. This is the concept on which I'm basing my impedance matching analogy using the summation
of reflection coefficients.

Walt