On Apr 17, 11:55 am, Jim Kelley wrote:
On Apr 16, 9:20 pm, Cecil Moore wrote:



Do you believe Jim's argument that two coherent EM
waves of equal magnitudes and opposite phases traveling
collinearly in the same direction in a transmission line
can never be canceled?

I asked you to show me the two waves of equal magnitude and opposite
phase travelling in the same direction in a transmission line. Show
me the waves, Cecil.

May I offer an example for Cecil.

Two signal generators, each with an output (source) impedance of 50
Ohms,
each connected to 0.25 wavelength of 50 Ohm line. Let us call them
North and
South with their output lines heading towards each other.

The two output lines are connected in parallel to a 3rd 50 Ohm line
heading
east that is 0.5 wavelengths long terminated in 50 Ohms.

The generators are constructed in the Thevenin style with a very low
impedance
voltage source connected in series with a 50 Ohm resistor.

Turn on the voltage source in the North generator. The wave leaves
the
generator, arriving at the joint 0.25 cycles later. Some of this wave
is
reflected and for the wave that goes through, half of it goes east
towards the load and reaches the load 0.5 cycles later, while the
other half
continues south towards the South generator which it reaches 0.25
cycles after
reaching the joint.

Since everything is terminated in 50 Ohms, there are no reflections
and the
system is in steady state 0.75 cycles after the North voltage source
is turned
on.

Turn on the South voltage source which, for interest, is 180 degrees
out of
phase with the North. Heading towards the joint is a new wave which,
when
it reaches the joint, some is reflected and the rest goes through
splitting
between north and east. The east wave is 180 degrees out of phase
with
the pre-existing wave from the North generator and cancels completely
on
the East line. The other half of the wave from the South generator
heads
north where it reaches the North generator after 0.25 cycles.

Again, since all lines are terminated in 50 Ohms, there are no
reflections.

0.75 cycles after the South source is turned on there is no energy
left in
the East line. Where did it go? Drained by load, it was.

0.5 cycles after the South source is turned on, the North generator
stops
supplying energy to the line because the voltage wave from the South
is in
phase with output from the North and no current flows.

0.5 cycles after the South source is turned on, it stops supplying
energy
to the line since the orignal wave from the north plus the reflection
from
the joint is always equal to the source voltage so no current flows.

0.75 cycles after the South source is turned on, the system is in
steady
state. The last thing that happens is that energy finishes draining
from
the East line.

So it appears that two waves in the line going east are 180 degrees
out
of phase and cancelling. Call this Explanation A.

Let us do the experiment in a slightly different order...

Connect only the lines going north and south, leave the line going
east disconnected.

Turn on the two sources and let the system stabilize. At the joint
between north and south will be voltage null where the voltage
is always 0. Now connect the east line to this voltage null.
Since there is 0 voltage here, there will be no waves sent down
the line so there can not be any cancellation. Call this Explanation
B.