Richard Harrison wrote:
Those are the necessary and sufficient conditions to reverse the
direction of some of the energy in an incident wave on a transmission
line. For a complete reversal, a short or an open is required.

What you say happens at a load is entirely correct. At a
load, there is only one EM wave incident upon the load.
But at an impedance discontinuity in a transmission line
with reflections, there are two EM waves incident upon
the impedance discontinuity, one from each direction.
There's a forward wave coming from the source and a
reflected wave coming from the load.

It might stand to reason that twice as many incident
waves might complicate things beyond what happens at
a load. And things are more complicated as can be
observed from the s-parameter equations. For a single
load, the s-parameter reflected voltage/power equations
reduce to:

b1 = s11*a1 for normalized reflected voltage, and

b1^2 = (s11*a1)^2 for reflected power where s11^2
is the power reflection coefficient

For an impedance discontinuity in the middle of a
transmission line with reflections, the s-parameter
equation for normalized reflected voltage is:

b1 = s11*a1 + s12*a2 for normalized voltage, and

b1^2 = (s11*a1 + s12*a2)^2 for reflected power

It's pretty obvious that the reflected power equation at
the impedance discontinuity is more complicated than the
reflected power equation at the load. In fact, if you
do the squaring of the right hand side of the equation
just above, you get the interference term.

2*s11*s12*a1*a2*cos(phi) where phi is the phase angle
between phasors a1 and a2.

The interference term, in watts, represents the amount
of interference present and affects the magnitude of
the reflected power. Since the amount of interference
affects the total reflected power, it must also affect
the total forward power so as to satisfy the conservation
of energy principle. Since interference affects the
magnitudes of both the reflected power and forward power,
the conclusion is inescapable that interference can also
cause reflections and this is verified by a couple of
technical web pages pertaining to light waves.

www.mellesgriot.com/products/optics/oc_2_1.htm

http://micro.magnet.fsu.edu/primer/j...ons/index.html

Walter Maxwell wrote about such back in the 70's. From
Sec 4.3 of "Reflections" speaking of match points:

"The destructive wave interference between these two
complementary waves ... causes a complete cancellation
of energy flow in the direction toward the generator.
Conversely, the constructive wave interference produces
an energy maximum in the direction toward the load, ..."

In a transmission line with only two directions, when the
energy flow is canceled in one direction, that energy must
necessarily flow in the only other direction available, i.e.
an energy reflection must take place.

So to your list of three things that can cause 100% reflection,
you can add wave cancellation in the form of total destructive
interference between two EM waves traveling in the same direction
in a thansmission line, having equal magnitudes and opposite
phases.
--
73, Cecil, http://www.qsl.net/w5dxp


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