Cecil Moore wrote:

For that statement, the length of the feedline is unknown
and the load is unknown.

I was commenting on this, the subject of our conversation:

"Consider the following:

Source---50 ohm feedline---+---1/2WL 150 ohm---50 ohm load"

As I was saying, for the two boundaries as a network, and we call rho at
the first boundary r12 and rho at the second boundary r23 then
rho(network) = (r12 + r23)/(1 + r12*r23) = 0. Note that if we use your
value for r12, the network generates a reflection. I note the utility
of negative rho in this example.

Seems to me, rho
cannot both cause a voltage and be caused by a (voltage divided
by a current) which is an impedance upon which rho is dependent.

Voltages on a transmission line do not determine reflection
coefficients.
Reflection coefficients are determined by characteristic impedances, not
virtual ones.

73, Jim AC6XG

Jim Kelley wrote:
. . .
Voltages on a transmission line do not determine reflection
coefficients.
Reflection coefficients are determined by characteristic impedances, not
virtual ones.

73, Jim AC6XG

I disagree with this. When applied to transmission lines, the (voltage)
reflection coefficient is, as far as I can tell, universally defined as
the ratio of reflected to forward voltage to reverse voltage at a point.
So a reflection coefficient can be, and often is, calculated for every
point along a line, not just at discontinuities or points of actual
reflection. This can be done with nothing more than the knowledge of the
values of forward and reflected voltages at the point of calculation.

As it turns out, the value of the reflection coefficient at any point
will be equal to (Z - Z0) / (Z + Z0), where Z is the impedance seen
looking down the line toward the load at the point of calculation. I'm
very leery of the use of "virtual" anything, since it often adds an
unnecessary level of confusion. But if I were to calculate a reflection
coefficient at some point along a continuous line, I could replace the
remainder of the line and the load with a lumped load of impedance Z,
and maintain exactly the same reflection coefficient and forward and
reverse traveling waves in the remaining line. I wouldn't object, then,
if someone would say that there was a "virtual impedance" of Z at that
point when the line was intact, since all properties prior to that point
are unchanged if a lumped Z of that value is substituted for the
remainder. (I personally wouldn't call it "virtual" -- I'd just call it
the Z at that point, since it's the ratio of V to I there.) The point is
that the reflection coefficient was the same before and after the
substitution of the remaining line with a real lumped Z. Before the
substitution, reflection was occurring at the load. After, the
reflection is occurring at the new, substituted Z load. Yet the
reflection coefficient and traveling waves remain the same on the
remaining line.

A reflection coefficient isn't the cause of anything. It's simply a
calculated quantity used for computational and conceptual convenience.
Only an impedance discontinuity causes reflections, but we can calculate
a reflection coefficient at any point we choose, with its value being
well defined and unambiguous.

Roy Lewallen, W7EL

Jim Kelley wrote:


Cecil Moore wrote:
For that statement, the length of the feedline is unknown
and the load is unknown.

I was commenting on this, the subject of our conversation:

My statement that you objected to didn't have anything to
do with the following.

"Consider the following:

Source---50 ohm feedline---+---1/2WL 150 ohm---50 ohm load"

Reflection coefficients are determined by characteristic impedances, not
virtual ones.

On the contrary, the reflection coefficient, rho, at '+' in
the example above, is NOT determined by the characteristic
impedances. Above, rho (looking at '+' from the left) is determined
by taking the square root of (Pref/Pfwd) = 0. (150-50)/(150+50) is
NOT rho. I was mistaken to call that quantity "rho" in my article.
That quantity that I called "rho" is actually 's11' and I need to
update my article.
--
73, Cecil, W5DXP

Roy Lewallen wrote:

Jim Kelley wrote:
. . .
Voltages on a transmission line do not determine reflection
coefficients.
Reflection coefficients are determined by characteristic impedances, not
virtual ones.

73, Jim AC6XG

I disagree with this. When applied to transmission lines, the (voltage)
reflection coefficient is, as far as I can tell, universally defined as
the ratio of reflected to forward voltage to reverse voltage at a point.

That rho is equivalent to that ratio of voltages is not in dispute. I
might dispute that it's 'defined' by that ratio. We agree the
reflection is caused by an impedance discontinuity. It is the
relationship of those impedances that determines how much of an incident
voltage will be reflected. From my perspective, one builds a network of
impedances in order to achieve the desired voltage relationships. But
one cannot build voltage relationships in order to obtain a network of
impedances.

Maybe it's another chicken and egg argument.

Only an impedance discontinuity causes reflections, but we can calculate
a reflection coefficient at any point we choose, with its value being
well defined and unambiguous.

Wouldn't the most well defined and unabiguous be at a point of
reflection? ;-)

73, Jim AC6XG

Cecil Moore wrote:

Jim Kelley wrote:
Reflection coefficients are determined by characteristic impedances, not
virtual ones.

On the contrary, the reflection coefficient, rho, at '+' in
the example above, is NOT determined by the characteristic
impedances.

I just showed you how characteristic impedances are used to calculate
the reflection coefficient at '+'. But you can wish it into the
cornfield if you like, Anthony. :-)

(150-50)/(150+50) is
NOT rho.

Is it the reflection coefficient for a 50 ohm to 150 ohm impedance
discontinuity?

I was mistaken to call that quantity "rho" in my article.
That quantity that I called "rho" is actually 's11' and I need to
update my article.

Since S-parameters were never even mentioned in your article, updating
it seems an understatement.

73, Jim AC6XG

On Thu, 02 Oct 2003 14:00:26 -0700, Jim Kelley
wrote:
updating it seems an understatement.
:-)

Jim Kelley wrote:
Roy Lewallen wrote:

Jim Kelley wrote:
. . .
Voltages on a transmission line do not determine reflection
coefficients.
Reflection coefficients are determined by characteristic impedances, not
virtual ones.

73, Jim AC6XG

I disagree with this. When applied to transmission lines, the (voltage)
reflection coefficient is, as far as I can tell, universally defined as
the ratio of reflected to forward voltage to reverse voltage at a point.


That rho is equivalent to that ratio of voltages is not in dispute. I
might dispute that it's 'defined' by that ratio.

I stand corrected on that point. I did a quick scan of ten
electromagnetics references. Seven quite clearly defined it that way.
One (Magnusson) was vague, and one (Jordan & Balmain) gave pretty equal
weight to both V and Z ratios as a definition. Holt, whom I consider one
my best references, clearly defines reflection coefficient in terms of
impedances. Regardless of definition, virtually all give both the V and
Z relationships which are, of course, mathematically equivalent.

We agree the
reflection is caused by an impedance discontinuity. It is the
relationship of those impedances that determines how much of an incident
voltage will be reflected. From my perspective, one builds a network of
impedances in order to achieve the desired voltage relationships. But
one cannot build voltage relationships in order to obtain a network of
impedances.

Maybe it's another chicken and egg argument.

I think so. One sees different impedances, i.e., V/I ratios, along a
transmission line, so it could be argued that impedances have been
created from voltages and currents. But I'll leave the arguing to those
people more interested in philosophy than engineering. As long as the
principles are understood and communicated, the point of view is largely
a matter of taste.


Only an impedance discontinuity causes reflections, but we can calculate
a reflection coefficient at any point we choose, with its value being
well defined and unambiguous.


Wouldn't the most well defined and unabiguous be at a point of
reflection? ;-)


I don't think so. It's completely well defined and unambiguous at any
point along the line. At any point, there's only one value of Vf and Vr,
and only one value of Z and Z0, so there can only be one value of
reflection coefficient. Knowing the reflection coefficient and Z0, for
example, one knows for sure what the value of Z is at that point. I find
that a number of the text authors freely use the concept of reflection
coefficient at any point along a line, not necessarily a point of
reflection. I don't have any problem with it, either. I see requiring a
reflection in order to have a reflection coefficient as sort of like
requiring dissipation in order to have a resistance. It's not really
necessary, and the calculated value can still have meaning.

Please don't let this detract from the ongoing discussion. It's really a
minor point.

Roy Lewallen, W7EL

I disagree with this. When applied to transmission lines, the (voltage)
reflection coefficient is, as far as I can tell, universally defined as
the ratio of reflected to forward voltage to reverse voltage at a point.
So a reflection coefficient can be, and often is, calculated for every
point along a line, not just at discontinuities or points of actual
reflection.

This can be done with nothing more than the knowledge of the
values of forward and reflected voltages at the point of calculation.

=============================

Sorry! Just to continue and further confuse the haggling, the forward
voltages are unknown because one does not know, in the case of amateur
systems, what is the internal voltage and internal impedance of the
transmitter.

It is this unknown voltage and internal impedance which the so-called SWR
(Rho) meter merely ASSUMES.

Are you disagreeing with something I said, or just adding a note? If
disagreeing, what again was it that you disagree with?

The source voltage and internal impedance have nothing to do with the
reflection coefficient at any point. The forward and reverse voltages
are indeed known if one knows, for example, the line Z0 and the load
impedance and the load power, voltage, or current. It's not necessary to
know the source impedance to find these values, the forward and reverse
voltages, or the reflection coefficient.

Roy Lewallen, W7EL

Reg Edwards wrote:
I disagree with this. When applied to transmission lines, the (voltage)
reflection coefficient is, as far as I can tell, universally defined as
the ratio of reflected to forward voltage to reverse voltage at a point.
So a reflection coefficient can be, and often is, calculated for every
point along a line, not just at discontinuities or points of actual
reflection.


This can be done with nothing more than the knowledge of the
values of forward and reflected voltages at the point of calculation.


=============================

Sorry! Just to continue and further confuse the haggling, the forward
voltages are unknown because one does not know, in the case of amateur
systems, what is the internal voltage and internal impedance of the
transmitter.

It is this unknown voltage and internal impedance which the so-called SWR
(Rho) meter merely ASSUMES.

Jim Kelley wrote:
I just showed you how characteristic impedances are used to calculate
the reflection coefficient at '+'. But you can wish it into the
cornfield if you like, Anthony. :-)

Absolutely no chance that you are simply wrong?

(150-50)/(150+50) is NOT rho.

Is it the reflection coefficient for a 50 ohm to 150 ohm impedance
discontinuity?

It is the 's11' reflection coefficient for that impedance discontinuity.
It is NOT the 'rho' at '+' unless the signals are orthogonal to each
other at '+'. Chances are they are not orthogonal.

I was mistaken to call that quantity "rho" in my article.
That quantity that I called "rho" is actually 's11' and I need to
update my article.

Since S-parameters were never even mentioned in your article, updating
it seems an understatement.

In my article, I called (Z1-Z0)/(Z1+Z0) the RHO(fv) and said it was
equal to S11. I should just have called it 'S11'. And I just checked
my web page. S11 is definitely mentioned in my article.
--
73, Cecil http://www.qsl.net/w5dxp



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