Henry Kolesnik wrote:

The previous thread got too big and convoluted for me so I started another
if for no other reason than my own clarity and convenience. It's still the
same question "I know that any power not dissipated by an antenna is
reflected back to the
transmitter. Then the transmitter "reflects" this reflection back to
antenna, ad nauseum until its all gone. I also know that a short or an open
is required to reflect power and I'm searching for which it is, an open or a
short. I'm inclined to think it's a virtual open but I'm at a loss to
understand that and I wonder if someone has a good explanation or analogy
and some math wouldn't hurt".

Hank, Here's what happens at the match point in an amateur radio antenna
system. Walter Maxwell himself references J. C. Slater's book.

From _Microwave_Transmission_, by J. C. Slater: "We can get a better
understanding of (matching) devices by considering reflections at
discontinuities. This method is useful in considering any impedance-
matching device, and we shall think of it first in connection with the
ordinary quarter-wave transformer. The object of this transformer is
to eliminate the reflection that would be present if the impedance
Z1 were connected directly to Zt."

The diagram is: Z1----1/4WL Z0----Zt where Z0 is a 1/4WL transformer
section that matches Z1 to Zt.

"The method of eliminating reflections is based on the interference
between waves. Two waves half a wavelength apart are in opposite
phases, and the sum of them, if their amplitudes are numerically
equal, is zero. The fundamental principle behind the elimination of
reflections is then to have each reflected wave canceled by another
wave of equal amplitude and opposite phase. In order that this second
wave may have traveled half a wavelength farther than the first, it is
obvious that it must have gone a quarter wavelength farther up the line,
and correspondingly a quarter of a wavelength back, before it meets the
original reflected wave. In other words, two discontinuities in characteristic
impedance, of such magnitude as to give equal amplitudes of reflected waves
and spaced a quarter of a wavelength apart, will give no net reflection
and hence will not introduce reflections into the line."

Here's how to perform an experiment to answer your questions. The source
(SGCL) is a Signal Generator equipped with a Circulator and Load. It puts
out a constant 100 watts. All reflected power is dissipated in the circulator
load.
very short
100W SGCL---50 ohm line---tuner----------450 ohm line------------Load

Initially, the system is tuned for a match so there are no reflections
on the 50 ohm line. Then the load is changed to 450 ohms. Assuming the
load was not 450 ohms to start with, this will cause reflections to
appear on the 50 ohm line. We can use an oscilloscope to measure the
magnitude and phase of the voltage across the 50 ohm circulator load
resistor. That's the reflected voltage. We can calculate the reflected
current through the 50 ohm circulator load resistor. So now we have the
component voltage and current reflected from the input to the tuner.
We can reference the phase of the reflected voltage and current to
the phase of the source voltage. Let's say the source voltage has a
reference phase of zero degrees.

Assume we measured a reflected voltage of 30 volts at 10 degrees and
calculated a reflected current of 0.6 amps at 190 degrees. (Note that
the reflected current is always 180 degrees out of phase with the
reflected voltage.)

Now switch the load from 450 ohms back to the original load. What
happens at the tuner input to achieve a match is the superposition
of two reflected waves. We know what the first one looks like so
we deduce what the second one looks like.

The first reflected wave, reflected from match point at the
tuner input is:

30 volts at 10 degrees and 0.6 amps at 190 degrees

The second reflected wave, returning from the load and reaching
the match point at the tuner input is:

30 volts at 190 degrees and 0.6 amps at 10 degrees

Adding those two voltages yields zero volts. Adding those two
currents yields zero amps. Thus the match is accomplished.

What the tuner does is shift the magnitude and phase of the voltage
and current reflected from the load to cancel the reflection of the
source wave that occurs at the input of the tuner.

The reflected voltage flowing toward the source is canceled to zero
through superposition of the two reflected voltage waves.

The reflected current flowing toward the source is canceled to zero
through superposition of the two reflected current waves.

That's how all matching devices work according to J. C. Slater.
--
73, Cecil http://www.qsl.net/w5dxp





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