Re: Analyzing Stub Matching with Reflection Coefficients

On Apr 17, 11:55 am, Jim Kelley <jwkel...@xxxxxxx> wrote:
On Apr 16, 9:20 pm, Cecil Moore <nos...@xxxxxxxxx> 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.

It is important to note that the end state of the two experiments is
exactly the same, and yet Explanation A has cancelling waves, while
Explanation B does not.

So which explanation is CORRECT?

--------

It is valuable to study the final state regardless of the explanation
used.

In this steady state, the voltage at the joint is always 0.
This means that no energy is flowing across the joint in any
direction.
(Remember energy flow is power which is volts times amps; no volts, no
power).

There is no energy entering the East line. How can there be when the
voltage
at the entrance is always 0.

There is no energy flowing from North to South or South to North
across the
joint. (Remember P=VI and V is always 0).

There is no energy flowing out of either generator since their output
currents are zero. (Remember P=VI).

There is no dissipation in either source resistor since the current
through them is zero. (Remember P=VI).

Neither source is adding any energy to the system since the current
from each source is zero. (Remember P=VI).

The voltage on the East line is 0 at all points.

There is a standing wave on the North-South line with a voltage null
at the joint and a current null at each end.

-----

But some will argue that there are two energy containing travelling
waves going north and south despite it being clear that with a voltage
of 0 in the middle of the line, no energy can be crossing this point.

Some will argue that there are two energetic waves in the east line
which are cancelling despite it being clear that this depends on the
order in which the connections are made.

The paradoxes. The paradoxes.

--------

It is noted that this experiment does not use Icom transmitters, but
it is believed that any wave behaviours holds for equipment other than
Icom and so the experiment is still valid.

Some may argue that a perfect generator can not be constructed, but
really that is a matter of cash; with enough cash one can construct
a generator that is arbitrarily close to perfect. Of course the
same holds for the ideal transmission lines and the terminators.
The lack of absolute perfection does not obviate the value
of the thought experiment for furthering understanding.

Note that the generators are fully specified so any cautions about
using Thevenin or Norton equivalents do not apply since we are not
dealing with equivalents.

....Keith

.

Relevant Pages

  • Re: what happens to reflected energy ?
    ... passed there is no power flowing in the line. ... Choose an arbitrary point on the line and observe the voltage. ... The energy flowing at this point on the line will ... a forward wave defined by Vf=If*Z0, ...
    (rec.radio.amateur.antenna)
  • Re: Derivation of Reflection Coefficient vs SWR
    ... is reflected when a wave encounters a discontinuity. ... After two seconds it reaches the generator. ... energy is stored on a transmission line. ... Here is a link to a web site discussing reflections and more. ...
    (rec.radio.amateur.antenna)
  • Re: Current across the antenna loading coil - from scratch
    ... A standing wave voltage passes exactly as much current through a capacitance as a traveling wave voltage does. ... But a standing wave still represents storage of energy in the line, as with any resonant structure, and that stored energy shows up as magnetic fields and electric fields along the line. ...
    (rec.radio.amateur.antenna)
  • Re: Standing-Wave Current vs Traveling-Wave Current
    ... how is energy stored in the stub? ... If they reflect, the voltage of each component will add on itself, and the individual currents will reverse on themselves and therefore subtract. ... The stub is 1/4 wavelength long physically, but it is 1/2 wavelength long electrically, so that if we have energy present in the time-distance shape of a sine wave, we would have an entire 1/2 wave's worth of energy present on the stub at all times. ...
    (rec.radio.amateur.antenna)
  • Re: what happens to reflected energy ?
    ... this is AFTER you disconnected the load resistor. ... reflected on a line with constant DC voltage and 0 current. ... We can also compute the average energy flow over some ... a forward wave defined by Vf=If*Z0, ...
    (rec.radio.amateur.antenna)