On Thu, 01 Mar 2007 21:04:36 GMT, Owen Duffy wrote:

I am not sure of what you mean by the "right circumstances".

Hi Owen,

It should be under "all circumstances." However, to reveal it
requires the "right circumstances." This again returns us to the
discussion of source resistance/impedance. A matching source driving
a mismatched load through a line of indeterminate length can exhibit
this variation, but it will require considerable skill to see it. If
you force the problem by mismatching the source as well (this then
means that the line is mismatched at both ends, much like your
halfwave model); then you can observe a variation in power readings
along its length that vary sinusoidally.

If you use an instrument that is calibrated for an impedance other than
the line under test,

That is not the case, although there are occasions where power has to
be determined in a heavily mismatched situation - this is done with
considerable error if the line lengths are unknown. If they are, then
corrections can be made.

your measurement does not indicate VSWR on the line

I have restricted myself to the cyclic display of powers.

under test, and the instrument readings will be different than I outlined
in the previous paragraph. Fig 3 in my article at
http://www.vk1od.net/VSWR/VSWRMeter.htm shows a line labelled "VSWR(50)"
that indicates the values that would be indicated / calculated using a 50
ohm instrument in a 75 ohm cable with a 1.5:1 VSWR.

Well, at a quick glance and noting no tabular form of data, what is
presented wouldn't reveal cyclic variation anyway for two reasons:
1. It lacks resolution (not enough places);
2. It lacks sufficient mismatch.
This is not a complaint, merely an observation because the evidence
for your example is hidden deep in the decimal places.

The solution is simple conceptually and mathematically. Reference any
discussion of Two Beam Interference as treated in Optics. For the
special case the math devolves to:
I = 2 · I1 · (1 + cos(theta2 - theta1 - delta))

Conceptually, it is only the combination of phase and amplitude from
two sources (each reflecting interface on the ends of the line).

73's
Richard Clark, KB7QHC

Richard Clark wrote in
:

I have restricted myself to the cyclic display of powers.
....
Well, at a quick glance and noting no tabular form of data, what is
presented wouldn't reveal cyclic variation anyway for two reasons:
1. It lacks resolution (not enough places);
2. It lacks sufficient mismatch.
This is not a complaint, merely an observation because the evidence
for your example is hidden deep in the decimal places.

The graph at http://www.vk1od.net/lost/RG58sol.gif has not been labelled
for presentation, so you will need to make some allowance in reading it.

The case that is plotted is an extreme mismatch, ou you might argue
impractical, but it is extreme enought to show the effects clearly on a
graph. The x axis is displacement from the load (-ve towards the
generator).

The red line is the so called "forward power" (Real(Vf^2/Zo)) that would
be indicated by a correctly calibrated sampler like a Bird 43, but
correctly calibrated means for the actual Zo, not the nominal 50+j0.

The dashed purple line is the so called "reflected power" (Real(Vr^2/Zo))
under the same conditions.

The power at a point is shown by the cyan line.

The dashed olive line is Real(Vf^2/Zo))-Real(Vf^2/Zo) (so called forward
power - reflected power). It is not the same as as the power because it
ignores two terms of the power expansion. A Bird 43 callibrated for the
actual Zo would lead you to this line.

This is a very detailed RLGC model, and it reveals from the P(x) line
that attenuation per unit length is not constant, a result of the loss
being higher in the region of a current maximum. Nevertheless, a sampler
that responds to Vf or Vr will not expose the true power curve (due to
the two missing terms).

I have thought at times of writing an article that explains the effects
on a true practical transmission line, and what practical instruments
calibrated for 50+j0 would indicate. I doubt that it would have appeal,
people like the "reflected power is dissipated in the transmitter and may
overheat it" explanation... it is easier to swallow.

Owen

Owen Duffy wrote in
:


Hmmm, replying to my own postings again!

This is a very detailed RLGC model, and it reveals from the P(x) line
that attenuation per unit length is not constant, a result of the loss
being higher in the region of a current maximum. Nevertheless, a
sampler that responds to Vf or Vr will not expose the true power curve
(due to the two missing terms).

The two "missing" terms are the second and third lines in the legend, the
crossproducts in the power equation expansion. In the case where Zo is
purely real, these terms are equal and opposite in phase and cancel out.

Owen

Owen Duffy wrote:
people like the "reflected power is dissipated in the transmitter and may
overheat it" explanation... it is easier to swallow.

If the forward current and reflected current are in phase
at the source, it may indeed become overheated due to an
over-current condition.

But just as likely (with random feedline lengths) is that
the forward voltage and reflected voltage may be in phase
at the source and blow out the finals due to over-voltage
conditions.

The two above events never occur at the same time. Over-
current conditions occur at low voltages. Over-voltage
conditions occur at low currents.
--
73, Cecil http://www.w5dxp.com

On Fri, 02 Mar 2007 00:18:02 GMT, Owen Duffy wrote:

The case that is plotted is an extreme mismatch, ou you might argue
impractical, but it is extreme enought to show the effects clearly on a
graph. The x axis is displacement from the load (-ve towards the
generator).

Hi Owen,

Chipman shows much the same work in Chapter 8. If you got a copy you
might find it an useful resource as his math and discussion goes well
beyond the usual coverage.

73's
Richard Clark, KB7QHC

Richard Clark wrote in
:

On Fri, 02 Mar 2007 00:18:02 GMT, Owen Duffy wrote:

The case that is plotted is an extreme mismatch, ou you might argue
impractical, but it is extreme enought to show the effects clearly on a
graph. The x axis is displacement from the load (-ve towards the
generator).

Hi Owen,

Chipman shows much the same work in Chapter 8. If you got a copy you
might find it an useful resource as his math and discussion goes well
beyond the usual coverage.

Re Chipman, no I don't have Chipman on the shelf. It sounds like I am
poorer for that, but there you go. Allmost all of what I have stated here
is based on just two things:
- that V/I=Zo for a travelling wave in a transmission line, and that
(Vf+Vr)/(If-Ir) at the load end of the line must equal Zload;
- that the voltage or current decays as e^(gamma*x).
Both are explained in probably any transmission line text, but the graphs
I created show a picture that, IMHO, is worth the proverbial thousand
words. Exploring the shape of the lines is revealing.

For example, you will remember Dr Ace (IIRC) asserting that rho cannot be
greater than 1, and supporting that with the challenge to demonstrate
rho1 with a Bird 43. Of course the Bird 43 cannot demonstrate rho1, it
is calibrated for Zo=50+j0 and rho1 is only possible if Zo has
sufficient -ve reactance to create an observable rho1 on a suitably
inductive load. So, at the risk of exciting another debate, rho can be
greater than one, but the maths that supports that proposition also
explains why you wont observe it on a Bird 43.

Owen

Owen Duffy wrote:
- that V/I=Zo for a travelling wave in a transmission line, and that
(Vf+Vr)/(If-Ir) at the load end of the line must equal Zload;

It seems that we can draw some conclusions from these
assumptions.

Vf*If*cos(0) = forward joules/sec

Vr*Ir*cos(0) = reflected joules/sec

The forward and reflected energy waves actually exist
and are the building blocks of the standing wave.

Vf and Vr are phasors and therefore subject to
superposition and interference.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote in news:AmWFh.2314$tv6.372
@newssvr19.news.prodigy.net:

Owen Duffy wrote:
- that V/I=Zo for a travelling wave in a transmission line, and that
(Vf+Vr)/(If-Ir) at the load end of the line must equal Zload;

It seems that we can draw some conclusions from these
assumptions.

Vf*If*cos(0) = forward joules/sec

What is this "we" business? That is your conclusion

What is the cos(0) term for Cecil? Are you implying that the phase angle of
Zo is 0? That isn't true in the general case, it is true ONLY for lossless
or distortionless lines.

Owen

Owen Duffy wrote:
What is this "we" business? That is your conclusion

Hams have a habit of saying "we", Owen. Are you a ham?
We have an IC-756PRO. We are a Texas Aggie. We drive a
GMC pickup. We are not married.

What is the cos(0) term for Cecil? Are you implying that the phase angle of
Zo is 0? That isn't true in the general case, it is true ONLY for lossless
or distortionless lines.

We sometimes assume lossless lines for the sake of discussion
which is often a close enough approximation to real-world
lines. We don't have our books with us but seems we remember
that the Z0 phase angle for common Z0 lines is about 1-2
degrees.
--
73, Cecil http://www.w5dxp.com