On 10/8/2015 4:09 AM, Jeff wrote:

His statement does not imply his results and analysis will apply to a
long line. He is talking about analyzing a short line and comparing to
the results obtained with the other analysis method for a short line.

You obviously have not fully understood the article. The whole thrust of
it is comparing the v short analysis with statements from Maxwell's book
that are specific to a long line, as are the references from the ARRL
handbook etc.. He even quotes Maxwell: "Of course, the attenuation is
greater when there is a load mismatch, because in addition to the
attenuation of the forward power, the reflected power is also attenuated
during its return to the transmatch"; which is obviously talking about
the 'normal' set-up of Tx, ATU , feeder, then antenna.

Yes, the article is probably more or less correct for a very short line,
BUT ONLY FOR A VERY SHORT LINE, taking the analysis and assumptions
further, as the author does from 'REFLECTIONS II' onwards, is NOT CORRECT.

Let me pose you a question, take an infinitely long lossy transmission
line and load it with Zo/3 as in the article; what is the impedance seem
by the Tx, and what is the loss 1000m along the line?

If the 'simple linear solution' is to be believed the impedance seen at
the Tx depends on the load, but wait the wave has not got to the load
yet, a real measurement would show the impedance to be that of the line
Zo, and the loss whatever the loss/unit length of the feeder X1000
happens to be.

Zo of a transmission line is also known as the Surge Impedance, and that
is the impedance seen before any reflections come into play due to
mismatches etc.

If the circuit in question handles low-frequencies, such short time
delays are introduced by a transmission line between when the AC source
outputs a voltage peak and when the source “sees” that peak loaded by
the terminating impedance (round-trip time for the incident wave to
reach the line’s end and reflect back to the source) are of little
consequence. The actual phase difference between start-of-line and
end-of-line signals is negligible, because line-length propagations
occur within a very small fraction of the AC waveform’s period. For all
practical purposes, we can say that voltage along all respective points
on a low-frequency, two-conductor line are equal and in-phase with each
other at any given point in time.

This of course lead us back to the articles simple analysis only being
correct when the line is short cf a wavelength.

By contrast, an electrically long line where the propagation time is a
significant fraction or even a multiple of the signal period the
reflected signals phase is different enough to be of concern.

When a source is connected to a load via a 'long' transmission line, the
line’s own characteristic impedance dominates over load impedance in
determining circuit behaviour. In other words a long line acts as the
principal component in the circuit, its own characteristics
overshadowing the load’s. With a source connected to one end of the
cable and a load to the other, current drawn from the source is a
function primarily of the line and not the load.

This is increasingly true the longer the transmission line is. Consider
the infinite length cable above, no matter what kind of load we connect
to one end of this line, the source (connected to the other end) will
only see Zo, because the line’s infinite length prevents the signal from
ever reaching the end where the load is connected. In this scenario,
line impedance exclusively defines circuit behaviour, rendering the load
completely irrelevant.

I would also question the articles use of some formulas, for example, I
think that in the limit the equation for the impedance of a parallel
line breaks down and is not accurate. Also as an aside I find the
constant use of the wording "Maxwell's Equations" annoying and
misleading as they have nothing to do with the 'real' Maxwell's Equations!!

Anyway all of the article can be blown out of the water by some practice
measurement of a real life situation, which will show that a 3:1
mismatch will produce the same loss regardless of whether it is Zo*3 or
Z0/3 when you are talking about feeding an antenna.

Jeff

Great, Jeff! I would support your suggestion to make measurements. All
you need to do is set up his scenario and collect some data. Please use
his identical set-up to confirm or refute his results.