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W5DXP August 14th 03 03:10 AM

Roy Lewallen wrote:

Dr. Slick wrote:
Agreed. Then any mismatch loss from PA to the 50 ohm coax is
never measured at the meter. So we never really measure the reflected
power coming right out of the PA, even if we attach the meter directly
to it's output.


No "reflected power" comes out of a PA.


By definition. I wonder who invented that definition? It seems pretty
obvious that not all PA's are Z0-matched so they will always re-reflect
100% of the incident reflected power. But that is exactly what that
definition implies.
--
73, Cecil http://www.qsl.net/w5dxp



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Reg Edwards August 14th 03 03:40 AM

Dear all, Here's a useful tip -

The loss along any sort of HF transmission line, SWR or not, increases with
line temperature according to just ONE HALF of the resistance-temperature
coefficient of the conductors. Why ? It's something to do with skin
effect.

RTC of copper is near enough 0.4 percent per degree C.

So loss along any line, in dB or nepers, increases by 0.2 percent per degree
C.

Now you may not think this matters very much. But if you consider a seasonal
change in temperature on the ocean bottom of only 2 degree C along a
2000-mile transatlantic cable which has an attenuation at 5 MHz of 1.6 dB
per mile, total attenuation = 3,200 dB, then you will appreciate the
responsibilty laid on the shoulders of the design engineers of the first
oceanic telephone cable systems.

An uncertainty of 0.4 percent of 3,200 dB = 13 dB which is enough to wreck
system operation. Omission of a submerged repeater allows signals to fall
below noise level at the last repeater. Addition of one more repeater
overloads the last repeater causing cross-modulation, cross-talk and noise.
Bear in mind repeaters are both-direction amplifiers and the lowest speech
channels are at 60 KHz where overall attenuation over the same distance is
only about 350 dB.

Repeater power is fedover the the inner cable conductor from constant
current sources at both ends, maximum voltage = 10 KV. +ve from one end, -ve
from the other. During magnetic storms and other disturbances the potential
difference between ground electrodes in N.America and W.Europe can rise to
several thousand volts. Although the last time I measured it on an AVO-8 it
was only 1.3 volts. I did, of course, make use of the safety grounding
stick before using the crocodile clips on the ends of the meter leads.
Depended on the tides and the flow of the Gulf Stream across the Earth's
magnetic line of force.

It always struck me as being highly incongruous, even absurd, that in normal
operation, cables of the highest possible quality materials, manufactured by
automatically controlled, specially-designed precision machinery, laid at
great expense by an 8000-ton, specially-design ship over thousands of miles,
should end up by being terminated with a foot or so of soldered, screwed-up,
cotton-covered 22-gauge wire rescued from the terminal-station scrap bin.
This is true. I have seen both ends with my own eyes. On one occasion I even
did the soldering after completing overall tests! But I was careful to use
a fairly straight length of wire with sufficient sag to eliminate any
possible tension beyond that due to its own weight.

Dear readers, believe me, there's no time to worry about SWR when loss in
revenue amounts to $100,000 per hour + repair-ship expenses every time a
flatfish trawler scoops up a cable in its net, cuts it free with an axe, and
the skipper sneaks away at top speed without telling anybody in case he has
to pay for the damage.

Coax cable Zo = 43 ohms. Diameter over polyethylene = 1 inch. Inner
conductor = longitudinal overlapping crimped copper tape, laid over the
cable's principal strength-member of a number of high-tensile steel wires,
overall inner diameter about 1/3 inch. Outer conductor = 6, touching,
longitudinal aluminium tapes with a small spiral lay. Sheath = 0.1-inch
thick extrusion of black polyethylene if I remember correctly. For shallow
water and continental shelves there was a number of protective heavy iron
wires laid on a bed of tarred hessian as had been used for 100 years on the
first of the Atlantic telegraph cables.

I sometimes think of (the later) Lord Kelvin who followed his calculations
with the recommendation to investors "Go ahead, make and lay the bloody
stuff". But it was Heaviside, a generation later, a genius who died of
neglect, who eventually described how the "bloody stuff" and radio
propagation really worked.

Folks, just a little light-hearted digression, a respite from so-called SWR
meters. Please continue with your discussion. ;o)
----
Reg, G4FGQ



JDer8745 August 14th 03 03:41 PM

Someone sed:

"The SWR is based on the ratio of the forward to the reflected power."

But this isn't the *definition* of SWR.

Trivia question: What is the definition of SWR?

73 de Jack, K9CUN

Tom Bruhns August 14th 03 04:13 PM

(Tom Bruhns) wrote in message om...
....
The resistance of the copper in the transmission line changes with
temperature. If ambient is 20C and you put in enough power to heat up
the line (center conductor) to 70C, that's a 50C change, and will
result in about an 18% increase in resistance. So if you had a line
which had 3dB loss at 20C, it would increase to about 3.5dB at 70C.
If the load end has a 2:1 SWR, then the sending end will have about
1.40:1 SWR at 20C and about 1.35:1 at 70C. It's not a _big_ change,
but it should be observable on an SWR meter that is accurate over a
wide range of powers.


Correction... First, thanks to Reg for his posting on the same
general topic. He pointed out that the RF resistances changes as the
square root of the DC resistance, and though I know that perfectly
well, had not put that into the above statements. With that
correction, I believe the result will be more like a change of 8% in
RF resistance, a loss change from 3.00dB to 3.26dB, and a change from
about 1.40 to 1.37 SWR. The point is the same; it would be observable
on a good SWR meter, though not distinguishable from other effects on
a typical cheap one.

Cheers,
Tom

Dave Shrader August 14th 03 05:20 PM

There is NO definition of SWR!!

There is a definition for VSWR!

There is a definition of ISWR!

But, unfortunately, there is NO definition for SWR!! Why don't you
offer one?

Deacon Dave, W1MCE

JDer8745 wrote:
Someone sed:

"The SWR is based on the ratio of the forward to the reflected power."

But this isn't the *definition* of SWR.

Trivia question: What is the definition of SWR?

73 de Jack, K9CUN



Roy Lewallen August 14th 03 07:17 PM

You must not have seen my posting yesterday on this thread, where I gave
the definition. Do I need to post it again?

Roy Lewallen, W7EL

JDer8745 wrote:
Someone sed:

"The SWR is based on the ratio of the forward to the reflected power."

But this isn't the *definition* of SWR.

Trivia question: What is the definition of SWR?

73 de Jack, K9CUN



Richard Clark August 14th 03 07:28 PM

On Thu, 14 Aug 2003 08:30:20 +0100, "Ian White, G3SEK"
wrote:


The subject is why SWR meters might read differently with different
lengths of coax. Your statements about mismatch uncertainty are true,
but not relevant.


Hi Ian,

Look at the subject line above. Everything reported by me responds
directly to it. I notice you have nothing relevant to add in that
regard.

To this point NO ONE has responded to the data, nor to the
authoritative citations. It would be more useful for you folks to
point out error rather than simply arm-chair your way through this
with denial. To this point NO ONE has offered any synopsis of my
error in method. Such close examination appears to be confined to
re-evaluations of the CFA which lack both, and thus make a more
amusing target that does not test anyone's skill beyond debate. In
the words of Ho Chi Minh: "Paper Tigers."

Also to this point, the only "critics" have been those with a voiced
interest in not assigning a value to Source Z, but again demonstrating
a more than ample capacity to arm-chair their way through byzantine
explanations of what it is "not." Bench work seems to be anathema,
however I do enjoy the zen-cartwheels being performed, thanks.

If I were to offer this with the infinite regress of Cecil's logic,
hide my data, and embellish my method, you would all be compounding
this thread to 600 entries. I don't play that game, sorry to
disappoint you fellows, but I don't write to entertain (even if I can
do it better than you without really trying - sometimes, like now,
opportunity begs). The repetition of data, like denial, is not
debate, so I am satisfied to post real bench work once, and pull paper
tails until that goes stale.

I am particularly amused by protestations that examination of data is
not worth anyone's time, but offering editorialization is. :-)
Clearly most of you should take more pleasure in your amusing
recreations.

You guys worry this out of all proportion, you act like this is
especially important and it certainly seems to set your teeth on edge.
As many would point out, this is only a hobby; it's not like your job
is on the line, or that you have to meet a customer's expectation. :-)

73's
Richard Clark, KB7QHC

W5DXP August 14th 03 07:49 PM

Richard Clark wrote:
I am particularly amused by protestations that examination of data is
not worth anyone's time, but offering editorialization is. :-)


For those of us who missed the data, what date and title does
that posting possess?
--
73, Cecil, W5DXP


Richard Clark August 14th 03 08:08 PM

On 14 Aug 2003 08:30:53 -0700, (Tom Bruhns) wrote:

"Ian White, G3SEK" wrote in message ...
...
The subject is why SWR meters might read differently with different
lengths of coax. Your statements about mismatch uncertainty are true,
but not relevant.


Somewhere in all this mess, I believe RC posted that the OP's
originally posted observations supported his claim (that source
impedance affects line SWR), but yet when I go back and read the OP's
observations, they are that the POWER delivered to the load changes
significantly with line length and the measured line SWR DOES NOT
change noticably.

It seems to me that the OP's observations directly support that the
line SWR does not change with changes in source impedance: if the
transmitter output impedance is not equal to the line impedance, the
additional line can be though of as lumped with the transmitter and
where it connects to the original length would be the point where the
source impedance would be measured...and it would have changed
significantly with added line, while the SWR did not.

Cheers,
Tom


Hi Tom,

Thanks for actually looking. You are indeed correct in your statement
about the "small" variation of SWR:
SWR DOES NOT change noticably.

This, too, is consistent with the data I have offered. Casual
benchwork is as likely to reveal that as not. This is to say that no
real examination was originally performed, it was discovered by
accident (the portents of the variation of Power were more
distracting) and the readings were discarded as, perhaps, simple
statistical fluctuation. If through the sheer chance of opportunistic
luck in drawing different line lengths into the original posting,
those values may have been far more significant. If I had trimmed my
data to a very short interval, it would have matched his. The
variation follows a sine curve shape (if anyone had actually viewed
the data, this would be obvious) and you can take several readings
along the slope with alarm, or several along the crest to
indifference. This simply reveals that the original posting lacked
many essential details, but contained many confirmatory ones.

This does not change the fact that as a subset of my data, that it
lacks supporting my results simply because it does not go to the
breadth nor depth of my study. I in fact offered three significant
quotes of his original observations made that are classic indicators
of Mismatch Uncertainty. The simple point of that issue is that you
cannot measure Power with any promise of accuracy when placed between
two discontinuities. Unless you can describe all paths. This is a
staple of simple wave interference. It necessarily follows that if
you cannot determine Power due to this indeterminacy, you have no
chance of determining SWR (you can certainly offer a reading and go on
about life blithely unaware).

Simply put, I don't see anyone here willing to put their "faith" to
the test; and I am the only one here with my skin in the game. I am
far more likely to accept error through honest effort equal to mine
that demonstrates it. But critics to this point have not only refused
to step up to the bench, but they have also denied the argument
through aggressively ignoring my methods and their results. I observe
far more reading of my comments here, than with that one posting. As
such, it is more than obvious that entertainment is the driving force
for this criticism, not technical review.

73's
Richard Clark, KB7QHC

Tom Bruhns August 14th 03 09:07 PM

(JDer8745) wrote in message ...

Trivia question: What is the definition of SWR?


Oh, Jack, that's not a _trivia_ question, that's a _TRICK_ question! :-)

Cheers,
Tom

W5DXP August 14th 03 09:13 PM

Richard Clark wrote:
How curious of you to have missed this pæan to your style:


Not curious at all, Richard. My Mother is in the hospital
with terminal leukemia.
--
73, Cecil, W5DXP


Tom Bruhns August 14th 03 09:17 PM

Richard,

Thank you very much for posting that reference to John Juroshek's
article. It happens to cover a topic very near and dear to my heart,
and I called John and we had a nice chat about it. In addition, I
told him where I saw the reference, and asked him if he would say that
the SWR on a line, in steady state excitation, with a source at one
end and a load at the other, depended on the source's source
impedance. He said it of course does not, and cannot understand how
you would have interpreted it that way.

Should I check with any of the other authors?

Cheers,
Tom

Richard Clark wrote in message . ..
On Tue, 12 Aug 2003 02:48:49 -0700, Roy Lewallen
wrote:

Almost correct.

The transmitter output impedance has no effect whatsoever on the line's SWR.

Roy Lewallen, W7EL


Hi Roy,

Entirely incorrect.

Transmitter output impedance that does not conform to transmission
line Z, when presented with a mismatched load through that line, adds
mismatch uncertainty in the form of an indeterminate SWR and
indeterminate Power to the load.

This has already been demonstrated twice. This has long been
documented with NBS/NIST references going back 4 decades. There is
nothing mysterious about it at all, and it conforms to the rather
simple principles of wave interference so poorly presented by Cecil in
months past.

The authoritative site:
http://www.boulder.nist.gov/div813/index.html

Direct reference:
"Juroshek, J. R.; A Direct Calibration Method for Measuring
Equivalent Source Mismatch; Microwave J., pp. 106-118;
October 1997

Obscure references:
http://www.boulder.nist.gov/div813/r...00S_n2nNet.pdf
"With vector measurements of the generator and meter reflection
coefficients Ãg and Ãm, respectively, the power of the incident
signal am can be related to the power of the source."

http://www.boulder.nist.gov/div813/r...FRad_ARFTG.pdf
which describes radiometer calibration (perhaps too exotic for this
group)
"tests are based on two assumptions. First, the network responds
linearly to our signal ( no power compression), and second, the
radiometer is sufficiently isolated from the source impedance."
...
"One of the assumptions made in deriving eq. (2) was that the
output from the radiometer is not dependent on the source
impedance. In the construction of the radiometer, two isolators
are inserted at the input of the radiometer to isolate the
radiometer from the source."
...
"The mismatch uncertainty depends strongly on the poorly known
correlation between uncertainties in the measurements of different
reflection coefficients, and so we use the maximum of the
uncertainties obtained by assuming either complete correlation or
no correlation whatsoever."

"Forthcoming Paper: Influence of Impedance Mismatch Effects on
Measurements of Unloaded Q Factors of Transmission Mode Dielectric
Resonators"
IEEE Transaction on Applied Superconductivity

"Analysis of Interconnection Network and Mismatch in the
Nose-to-Nose Calibration
Automatic RF Techniques Group , June 15-16, 2000 , Boston, MA -
June 01, 2000
"We analyze the input networks of the samplers used in the
nose-to-nose calibration method. Our model demonstrates that the
required input network conditions are satisfied in this method and
shows the interconnection errors are limited to measurement
uncertainties of input reflection coefficients and adapter
S-parameters utilized during the calibration procedure. Further,
the input network model fully includes the effects of mismatch
reflections, and we use the model to reconcile nose-to-nose
waveform correction methods with traditional signal power
measurement techniques."

As I mentioned, obscure references. However, given the impetus of
their discussion is long known (and that I have already provided the
original references they rely on), NIST presumes the investigators
already have that basis of knowledge.

73's
Richard Clark, KB7QHC


Richard Clark August 14th 03 09:55 PM

On 14 Aug 2003 13:17:40 -0700, (Tom Bruhns) wrote:

Richard,

Thank you very much for posting that reference to John Juroshek's
article. It happens to cover a topic very near and dear to my heart,
and I called John and we had a nice chat about it. In addition, I
told him where I saw the reference, and asked him if he would say that
the SWR on a line, in steady state excitation, with a source at one
end and a load at the other, depended on the source's source
impedance. He said it of course does not, and cannot understand how
you would have interpreted it that way.

Should I check with any of the other authors?

Cheers,
Tom


Hi Tom,

Feel free to do that. I cannot imagine I hold sway over that anyway.
Do you really need more proof, or is your question an honest enquiry
suggesting you accept the possibility that someone else may actually
stand with me?

You among the many have done more in less time. I can accept
negative, informed response. Can he explain my posting? That is the
more telling as it is MY statement, not your summary of it.

I am not looking to shift the goal posts during the game, the posting
contains the beginning and end of it. It stands alone, or it falls
because of its own errors, not those appended, removed, remodeled,
explained, or fancified through specious "debate." I find more
entertainment in bearding the complacency it meets.

I have seen my results dismissed. I hardly find it surprising, but
with repetition it seems those in chant mode are insecure with their
mantra. After all what purpose is there in saying it twice in a round
of three postings? (or 3 of 5, or 5 of 7....).

73's
Richard Clark, KB7QHC

Richard Clark August 14th 03 10:02 PM

On 14 Aug 2003 13:17:40 -0700, (Tom Bruhns) wrote:

Thank you very much for posting that reference to John Juroshek's
article. It happens to cover a topic very near and dear to my heart,
and I called John and we had a nice chat about it.


Hi Tom,

As an after thought, but not secondary in my mind (tho' certainly in
the heat of response). You are welcome. I am glad that even the
obscure references elicit a positive outcome regardless of how it
suits my thesis. THIS is the point of my writing (the rest is simply
the struggle of titanic ego).

73's
Richard Clark, KB7QHC

Richard Clark August 14th 03 11:25 PM

On Thu, 14 Aug 2003 14:56:27 -0700, W5DXP
wrote:

Richard Clark wrote:
You among the many have done more in less time. I can accept
negative, informed response. Can he explain my posting? That is the
more telling as it is MY statement, not your summary of it.


A couple of questions about your data. What kind of coax and
connectors are used for the BVT?


hardline of RG-58 dimension;
only two connectors, the gozinta, and the comesoutta (never changed
throughout any variation nor calibration).

What kind of wattmeter was
used for the readings?


Bird.


The load seems to be 50/3 = 16.67 ohms. I would like to see
the same data for a load of 50 ohms.


That is already discussed in the report.

Seems you are getting
the same resulting effect that I do (on purpose) when I vary
the length of my ladder-line while watching the 50 ohm SWR.
Your results may repeat every 1/2WL. What if you had gone
out to 20 feet instead of stopping at 15 feet?


I have no reason to think it would offer any change in a periodic
variation already in evidence.


One last thought. Did you consider common-mode current
possibilities?


Yes.

73's
Richard Clark, KB7QHC

Dr. Slick August 15th 03 02:08 AM

W5DXP wrote in message ...

By definition. I wonder who invented that definition? It seems pretty
obvious that not all PA's are Z0-matched so they will always re-reflect
100% of the incident reflected power. But that is exactly what that
definition implies.



Your vocabulary is very confusing here, Cecil. "Incident"
usually refers to the forward power, so when you say "incident
reflected" it's extremely confusing.


Slick

Dr. Slick August 15th 03 02:13 AM

Roy Lewallen wrote in message ...
Dr. Slick wrote:

Agreed. Then any mismatch loss from PA to the 50 ohm coax is
never measured at the meter. So we never really measure the reflected
power coming right out of the PA, even if we attach the meter directly
to it's output.


No "reflected power" comes out of a PA.

Roy Lewallen, W7EL


Maybe that why you can't measure it.


Slick

Dr. Slick August 15th 03 02:40 AM

Roy Lewallen wrote in message ...

The observation that changing line length changes the measured SWR is
regularly reported in this newsgroup, and the explanation is as
regularly provided.

There are at least three ways this can happen.

1. The SWR meter is designed for an SWR that's different from the line
impedance. It's easy to show that this will result in different readings
for different line lengths. I've measured RG-58 at over 60 ohms
characteristic impedance, so this can happen even with a perfect 50 ohm
SWR meter and "50 ohm" line. In this case, changing line length isn't
really changing the line's SWR, just the meter reading.


But a 60 ohm transmission line transformation from a non-50 ohm
load will certainly change the SWR, as it won't be on the constant
VSWR circle anymore.



2. There's significant loss in the cable. In that case, the longer the
distance between the meter and the load, the better the SWR.


That's the obvious one.


3. There's current on the outside of the coax. This means that the
outside of the transmission line is actually part of the antenna. When
you change its length, it changes the effective length of the antenna,
which really does change the SWR. Current on the outside of the cable
can also get into a poorly shielded SWR meter and modify its reading.

And this is all in agreement with established theory. So you see, theory
does say you can change the SWR reading, and in some cases, the actual
SWR, by changing the coax length. But only under very specific
circumstances. When observations don't match theory, chances are
overwhelming high that either the observation is erroneous or
misinterpreted, or theory is being misapplied.

Roy Lewallen, W7EL




I believe the source of confusion is he


PA----+----50 ohm line----+SWR meter+----50 ohm line----+50 ohm dummy
load
1 2 3



The "+" are connector points. You folks are saying that as you
change the PA (source) impedance, that the SWR you read will remain
the same, even if the incident power changes due to the change in
reflected power at point 1.

This i can agree with, as no matter how much incident power makes
it past the impedance discontinuity at point 1, the system after this
point will theoretically always reflect the same ratio of reflected
power to incident.
But, if you place an SWR meter of the same impedance as the output
of the PA at point 1, you will definitely see a change in SWR at point
1 as you change the PA impedance, as you are changing the reference
impedance (center of Smith re-normalized). This is what i thought you
meant when you said "change the source impedance", but you meant to
say "change the source, but keep the reference impedance the same".

Understood, assuming this is what you guys mean.


Slick

Dr. Slick August 15th 03 02:46 AM

Roy Lewallen wrote in message ...
If you ever do see an equation which shows transmission line SWR as a
function of source impedance, please let me know where you see it. I'll
add it to my list of untrustworthy sources.

A simple experiment could be set up to disprove it.

Roy Lewallen, W7EL




I believe we are both right, and there is simply a misunderstanding
here.

I believe the source of confusion is he


PA----+----50 ohm line----+SWR meter+----50 ohm line----+50 ohm dummy
load
1 2 3



The "+" are connector points. You folks are saying that as you
change the PA (source) impedance, that the SWR you read will remain
the same, even if the incident power changes due to the change in
reflected power at point 1.

This i can agree with, as no matter how much incident power makes
it past the impedance discontinuity at point 1, the system after this
point will theoretically always reflect the same ratio of reflected
power to incident.
But, if you place an SWR meter of the SAME IMPEDANCE AS THE OUTPUT
of the PA at point 1, you will definitely see a change in SWR at point
1 as you change the PA impedance, as you are changing the reference
impedance (center of Smith re-normalized). This is what i thought you
meant when you said "change the source impedance", but you meant to
say "change the source, but keep the reference impedance the same".

Understood, assuming this is what you guys mean.


Slick

Dr. Slick August 15th 03 02:53 AM

W5DXP wrote in message ...


I was thinking about how you changed the impedance of your SWR
meter, and I doubt that simply changing the terminating resistors to
ground on both directional couplers is all you have to do.

I believe this because the SWR/power meter needs to be a Zo ohm
Thru, with a microstrip line of a certain dielectric thickness, and
particular width and spacing from the couplers. And you cannot change
these very easily.

Do you have a schematic for us to see?


Slick

JDer8745 August 15th 03 03:16 AM


You must not have seen my posting yesterday on this thread, where I gave
the definition. Do I need to post it again?

Roy Lewallen, W7EL

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

No I saw it right *after* I posted. DUH

Jack K9CUN

Richard Clark August 15th 03 04:05 AM

On 14 Aug 2003 18:46:56 -0700, (Dr. Slick) wrote:

PA----+----50 ohm line----+SWR meter+----50 ohm line----+50 ohm dummy
load
1 2 3
The "+" are connector points. You folks are saying that as you
change the PA (source) impedance, that the SWR you read will remain
the same, even if the incident power changes due to the change in
reflected power at point 1.


Reading a SWR at this point 1 (or 2 or 3), as specified above, would
simply be zero deflection confirming the remainder of the circuit has
no return.

This i can agree with, as no matter how much incident power makes
it past the impedance discontinuity at point 1, the system after this
point will theoretically always reflect the same ratio of reflected
power to incident.


It will reflect nothing, by specification of the circuit above.

But, if you place an SWR meter of the SAME IMPEDANCE AS THE OUTPUT


But? What has departed will not turn around after the fact of
changing something as immaterial as this presumed meter Z (which is no
more than the minutia of the scale unless circuit gross dimensions
exceed wavelength considerations). If this were significant, the
meter circuit itself would be the point of discontinuity and thus
reflective, but this would be wholly unobserved because
1. The meter pick-up (as it were) follows the discontinuity
2. The power flowing from the meter encounters no other discontinuity
as specified by the circuit above.

Given 2., it follows that zero deflection will still resolve to zero
deflection irrespective of the meter's guts.

To force a reading would require reflection from the output of the
meter's bridge/coupler which simply casts the issue back to a lousy
meter design (but one with apparent high sensitivity - in other words,
it is sucking out a huge amount of power to do the same chore others
do better with less). One can certainly conspire to screw up by
simply ignoring circuit dimension and wavelength - or taking a chance
with selecting an anonymous instrument from the bottom of the drawer
(which is the same thing). Any reading other than zero deflection
from the circuit above would indeed indicate a system failure (the
instrument being part of the system). Take care that failure here is
measured by degree - any reading forces other tests and in and of it
self is not conclusive of anything.

of the PA at point 1, you will definitely see a change in SWR at point
1 as you change the PA impedance, as you are changing the reference
impedance (center of Smith re-normalized). This is what i thought you
meant when you said "change the source impedance", but you meant to
say "change the source, but keep the reference impedance the same".

Understood, assuming this is what you guys mean.


Slick


Serious SWR measurement at high frequency is far more simply achieved
with greater precision, accuracy, and less impact on the system
employing the rather more creaky methods of a slotted line. With this
approach you can at least relate to the serious considerations of
characteristic Z and wavelength specific issues (and often answered
with simple plumbing components hand crafted once to last decades).
Calibration is as simple as replacing the ruler if it falls off (if
you first confirm that the connections are not reflective, but then we
return to the discussion above).

Once again, it is a chicken and egg problem. You need a better method
of SWR determination to validate a poorer one. There is no such thing
as self validating this particular instrument above HF. A poor Bird
Wattmeter is especially prone to reflective connections (notorious in
fact) and given those connections do this before the reading, many
users are quite satisfied in their state of ignorance. But again,
this hardly amounts to much, unless you wish to achieve an accurate
Power determination. Often the system reflections will eclipse those
of the connectors and still be perfectly useful in an industrial
setting. The user of the Bird in that community doesn't really care
about absolute Power, only relative Power with mediocre absolute
accuracy. Quite often they are simply tasked to confirm levels within
2 or 3dB; the instrument's slop of 1dB is often accounted for within
the methods of measuring those specified levels. The universality of
the Bird is due only to robustness.

Your circuit above is simply the first step in
selecting/calibrating/verifying an instrument. Throw a mismatch into
the game and lights will begin to flash.

73's
Richard Clark, KB7QHC

Roy Lewallen August 15th 03 04:30 AM

Dr. Slick wrote:
Roy Lewallen wrote in message ...

The observation that changing line length changes the measured SWR is
regularly reported in this newsgroup, and the explanation is as
regularly provided.

There are at least three ways this can happen.

1. The SWR meter is designed for an SWR that's different from the line
impedance. It's easy to show that this will result in different readings
for different line lengths. I've measured RG-58 at over 60 ohms
characteristic impedance, so this can happen even with a perfect 50 ohm
SWR meter and "50 ohm" line. In this case, changing line length isn't
really changing the line's SWR, just the meter reading.



But a 60 ohm transmission line transformation from a non-50 ohm
load will certainly change the SWR, as it won't be on the constant
VSWR circle anymore.


Once again, you're confusing the SWR meter reading with the SWR on the
line. When the line and SWR impedances are different, the two are *not*
the same. When I speak of the SWR on the line, I mean the SWR on the
line, not the meter reading.

Now look at the sentence you wrote. It's not very clear to me, but it
would certainly make more sense if you replaced "the SWR" with "the SWR
meter reading". Do *not* confuse the two.




2. There's significant loss in the cable. In that case, the longer the
distance between the meter and the load, the better the SWR.



That's the obvious one.



3. There's current on the outside of the coax. This means that the
outside of the transmission line is actually part of the antenna. When
you change its length, it changes the effective length of the antenna,
which really does change the SWR. Current on the outside of the cable
can also get into a poorly shielded SWR meter and modify its reading.

And this is all in agreement with established theory. So you see, theory
does say you can change the SWR reading, and in some cases, the actual
SWR, by changing the coax length. But only under very specific
circumstances. When observations don't match theory, chances are
overwhelming high that either the observation is erroneous or
misinterpreted, or theory is being misapplied.

Roy Lewallen, W7EL





I believe the source of confusion is he


PA----+----50 ohm line----+SWR meter+----50 ohm line----+50 ohm dummy
load
1 2 3



The "+" are connector points. You folks are saying that as you
change the PA (source) impedance, that the SWR you read will remain
the same, even if the incident power changes due to the change in
reflected power at point 1.


I'm saying that the line SWR doesn't change when you change the source
impedance. I didn't say anything about incident or reflected power
anywhere. And I won't. Cecil probably said something about the incident
and reflected power, but explanations in those terms are strictly up to him.

If you were to change the impedance of the left hand line (the one
between the PA and meter), then the SWR on the left hand line would
change, but the SWR on the right hand line wouldn't, and the SWR meter
reading would remain the same. For that matter, you can do anything you
want between the SWR meter and the PA -- add an impedance of any kind in
series or parallel, change the left hand transmission line length and/or
Z0, change the power, whatever you want, and it won't change either the
meter's indicated SWR or the actual SWR on the right hand line. The rule
is that whatever you change, it won't affect the SWR on any line that's
"downstream" (toward the load) from the change you made.

This i can agree with, as no matter how much incident power makes
it past the impedance discontinuity at point 1, the system after this
point will theoretically always reflect the same ratio of reflected
power to incident.


Be really, really careful when you start talking about forward and
reflected power. It can very easily lead you to wrong conclusions about
what's going on. Just check the postings on this group for the past few
months for evidence. All the phenomena you can observe and measure can
be fully explained by looking at forward and reverse voltage and current
waves, and it's a whole lot less hazardous.

One of the several problems with thinking in terms of forward and
reflected power is that it's universally meant to refer to average
power. So you've lost all time and phase information, making it
impossible to clearly see how the traveling waves interact. If you must
deal with "forward power" and "reverse power", do your thinking and
calculations with voltage and current waves, then calculate the power
when you're all done.

As I said before, the ratio of forward to reflected voltage or current
is independent of the source impedance. That ratio, when measured at the
load, is simply the reflection coefficient at that point.

But, if you place an SWR meter of the same impedance as the output
of the PA at point 1, you will definitely see a change in SWR at point
1 as you change the PA impedance, as you are changing the reference
impedance (center of Smith re-normalized).


No, you won't see a change in the SWR at point 1 as you change the PA
impedance. All the fiddling you do with your Smith chart just won't make
it happen. Sorry.

The SWR, voltage, current, impedance, power, reflection coefficient,
waves, or anything else don't change in response to your Smith chart
exercises.

This is what i thought you
meant when you said "change the source impedance", but you meant to
say "change the source, but keep the reference impedance the same".


No. When I said change the source impedance, I meant change the source
impedance. Surely we don't need a discussion about what "impedance"
means? When you get out your grease pencil and change the reference
value of your Smith chart, it doesn't magically change the waves on the
line on your workbench.


Understood, assuming this is what you guys mean.


It's time for me to leave this discussion. I've tried to make my
statement as clearly and simply as I know how, but somehow people have
decided that I really meant something else, or that there's this
condition or that condition that cause exceptions to it, or that it all
depends on what you scribble on your Smith chart with a grease pencil.
It bears a striking resemblance to a political science (what an
oxymoron!) course I took, in which we could make up any definition for
anything, or any interpretation of anything anyone said or wrote (and
were encouraged to do so), and all were equally valid. I've spent too
much time interacting with engineers and not nearly enough with
politicians and philosophers to know how to deal well with this
fuzziness. Anyone who really cares can look up the equations in a couple
of minutes. I'm sure they're on the web, if you have an aversion to
paper media.

Look up the equations, study them, understand them. If you don't believe
them, make up your own equations. Then set up a couple of simple
experiments to test them, and see which are right. That's how science
and engineering are done.

Roy Lewallen, W7EL


W5DXP August 15th 03 03:11 PM

Dr. Slick wrote:
Your vocabulary is very confusing here, Cecil. "Incident"
usually refers to the forward power, so when you say "incident
reflected" it's extremely confusing.


"Forward power incident upon the load" or "Reflected power
incident upon the source" makes sense to me. Given the
definition of "incident", the reflected power has to
be incident upon something. Simply replace "incident upon"
with "arriving at".
--
73, Cecil, W5DXP


W5DXP August 15th 03 06:53 PM

Dr. Slick wrote:

W5DXP wrote:
It seems pretty
obvious that not all PA's are Z0-matched so they will always re-reflect
100% of the incident reflected power. But that is exactly what that
definition implies.


Your vocabulary is very confusing here, Cecil. "Incident"
usually refers to the forward power, so when you say "incident
reflected" it's extremely confusing.


The point was not to confuse. So allow me to re-word it.

Some say there is zero power reflected from a PA. For that to
be true, all PA's must exhibit an impedance of Z0, i.e. all PA's
must be Z0-matched. Doesn't that seem a little far-fetched?

Some say that 100% of the reflected power is re-reflected by
the PA. For that to be true, all PA's must exhibit an open,
short, or pure reactance to the reflected waves. Doesn't that
seem a little far-fetched?

The problem lies in the definition of "generated power" which
is forward power minus reflected power. A mental exercise will
illustrate.

XMTR---one second long feedline-----mismatched load

For the first two seconds, a directional wattmeter at the
XMTR reads 100W forward, zero watts reflected.

During steady-state, the directional wattmeter reads 100W
forward, 25 watts reflected.

If the XMTR is a 100W signal generator equipped with a circulator
and load resistor, we have no problem deciding that the signal
generator is generating a continuous 100W and dissipating whatever
reflected energy arrives.

If the XMTR is a ham transmitter, we say it generates 100W for
two seconds, and after that, it generates 75 watts, by definition.
This seems to me to be just a useful shortcut that avoids opening
Pandora's Box (in which the source is located). :-)

If a transmitter only generates (forward power minus reflected
power), it follows that the transmitter always re-reflects 100%
of the reflected power arriving at its terminals. Does that
sound reasonable?

Or, if reflected energy is never re-reflected from a PA, then
the PA must be dissipating the reflected power, which it previously
generated, just like a signal generator with circulator load does.
Does that sound reasonable?

Or, if there is a circulator load, the reflected waves contain
energy, but if there's not a circulator load, the reflected waves
don't contain any energy. Does that sound reasonable?

What sounds reasonable to me is that the reflected waves arriving
back at the source obey the rules of the wave reflection model
as described by Ramo and Whinnery. But since the impedance presented
to the reflected waves by the transmitter is usually unknown, we
are again up that proverbial creek without a paddle.

So, by all means, use the shortcuts, but recognize that they are
definitional shortcuts which may or may not represent reality.
--
73, Cecil, W5DXP



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Dr. Slick August 15th 03 08:00 PM

W5DXP wrote in message ...
Dr. Slick wrote:
Your vocabulary is very confusing here, Cecil. "Incident"
usually refers to the forward power, so when you say "incident
reflected" it's extremely confusing.


"Forward power incident upon the load" or "Reflected power
incident upon the source" makes sense to me. Given the
definition of "incident", the reflected power has to
be incident upon something. Simply replace "incident upon"
with "arriving at".



"Forward Incident" a bit redundant in my opinion. "Incident"
usually refers to the power moving towards the load, away from the
generator.

And your previous quote was: "It seems pretty
obvious that not all PA's are Z0-matched so they will always
re-reflect
100% of the incident reflected power."

So here, you don't say where it is "incident" upon, of where it
is arriving at, athough I assume you mean simply the reflected power.

I'm just trying to make your vocabulary less confusing.


Slick

W5DXP August 15th 03 08:20 PM

Dr. Slick wrote:
"Forward Incident" a bit redundant in my opinion. "Incident"
usually refers to the power moving towards the load, away from the
generator.


I don't think that is true. The HP ap note, AN 95-1, refers to
"the voltage wave incident on port 1" and "the voltage wave
incident on port 2". Those two waves are moving in opposite
directions, one toward the load and one toward the source.
--
73, Cecil, W5DXP



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Richard Clark August 15th 03 08:47 PM

On Fri, 15 Aug 2003 11:39:51 -0700, W5DXP
wrote:

You can't measure phase or magnitude?


I simply cannot differentiate what part of the forward wave has been
reflected back from the source Vs what part is actually generated
by the source. That's the crux of the problem.


Hi Cecil,

But since the impedance presented
to the reflected waves by the transmitter is usually unknown

You have a forward part from the transmitter,
a reverse part from the reflection.

What more do you need unless you are discarding phase? If so, recover
it (if this is all about a SWR meter, then take out the diodes and use
a comparator).

73's
Richard Clark, KB7QHC

W5DXP August 15th 03 09:01 PM

Richard Clark wrote:
You have a forward part from the transmitter,
a reverse part from the reflection.


We are talking about re-reflection FROM THE SOURCE!
The forward part and re-reflected part from the source
are coherent and traveling in the same direction so they
cannot be separated for measurement purposes. That's
why Bruene tried to determine the source impedance by
bouncing another separate signal off the source.
--
73, Cecil, W5DXP



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Roy Lewallen August 15th 03 09:31 PM

Dr. Slick wrote:
Roy Lewallen wrote in message ...

This is typical of you, Roy, for you to back out of a discussion
when you don't want to admit that maybe someone else has a logical
point. I've agreed with you on many things (antennas as transducers
and such), but like many intelligent but close-minded people, you
cannot accept someone elses points.

I guess you think other people can't teach you anything, eh?

NO ONE knows it all, even about a specific topic as impedance
matching.


Slick


Let me explain why I leave these discussions.

I certainly don't know everything, and am constantly learning. But not
from threads like this one. I can change the SWR on a transmission line
by renormalizing my Smith chart? Is that a "logical point" I'm running
away from?

The reason I post in the first place isn't to try and convince the party
I'm directing my posting to. Nor is it an ego trip. What I hope to
accomplish is to provide a counterpoint to what I see as incorrect
information. This group is read by a very large number of "lurkers" who
seldom or never post. I know this for a fact, because many of them
introduce themselves to me at Dayton and other places I appear publicly.
When someone posts misinformation on this group, I try to present what I
consider to be correct.

There are people, some of whom post here, who won't be convinced
regardless of the evidence. It's as much a total waste of time to argue
with those people as it is to try and convince someone his religion is
wrong. When I encounter a person like that, I'll post my point of view,
present what evidence I can, then withdraw. I have much better things to
do than continue flogging a dead horse. I feel that the lurkers, who are
really the people I'm addressing, should be able to make up their minds
on the basis of what's been presented.

There's more than ample evidence to back up what I've said that's easily
available to anyone with a real interest in learning. Anyone who really
cares and is willing to invest even a modicum of effort can search out
the information and reach a conclusion. You've chosen not to go to that
effort(*), but rather interpret what I say in a way that suits your
preconception. Sorry, I just won't waste more of my time trying to talk
you out of it. If lurkers are convinced by your arguments and find them
more compelling than the ones I've made, then so be it. I've done what I
can. To continue posting over and over again the same thing isn't my
choice of a way to use my time.

There are people who feel that the person who posts the last message
"wins", and so anyone who withdraws has "lost". You can see the result
of this philosophy in the threads that have run to literally hundreds of
postings without ever resolving the issue. It's simply not a game I play.

Roy Lewallen, W7EL

(*) For example, have you ever looked up the equations for calculation
of SWR? Noticed that there's no term for the source impedance? And no
term for your Smith chart normalization factor?


W5DXP August 15th 03 09:58 PM

Richard Clark wrote:
W5DXP wrote:
The forward part and re-reflected part from the source
are coherent and traveling in the same direction so they
cannot be separated for measurement purposes.


That separation is unnecessary as it represents a sufficiently fixed
value for every moment beyond the first millisecond for usual
applications.


So what part of the generated signal is actually generated and
what part is merely re-reflected energy?
--
73, Cecil http://www.qsl.net/w5dxp



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Richard Clark August 15th 03 11:17 PM

On Fri, 15 Aug 2003 15:58:08 -0500, W5DXP
wrote:

Richard Clark wrote:
W5DXP wrote:
The forward part and re-reflected part from the source
are coherent and traveling in the same direction so they
cannot be separated for measurement purposes.


That separation is unnecessary as it represents a sufficiently fixed
value for every moment beyond the first millisecond for usual
applications.


So what part of the generated signal is actually generated and
what part is merely re-reflected energy?


Hi Cecil,

Separation is unnecessary after the first millisecond. Impedance from
that time on is sufficiently fixed to measure. You can answer your
own question from the resultant, but it is of no particular interest
in the determination.

73's
Richard Clark, KB7QHC

W5DXP August 16th 03 02:14 AM

Richard Clark wrote:
Separation is unnecessary after the first millisecond. Impedance from
that time on is sufficiently fixed to measure. You can answer your
own question from the resultant, but it is of no particular interest
in the determination.


I don't have a question, Richard, I am trying to answer yours. What
difference can it make in the SWR if "separation is unnecessary"?
--
73, Cecil http://www.qsl.net/w5dxp



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W5DXP August 16th 03 02:31 AM

Tarmo Tammaru wrote:
Try this out. You have an amplifier of unknown source impedance connected
through a directional meter to a 1/4 wavelength line that is shorted at the
far end. Without knowing about SWR, you know (because you are a ham radio
operator) that the amp is driving an infinite impedance, and delivering 0
power. Now if you adjust the amp so the meter reads 100W in both directions,
the amp is still delivering 0 power, and 100% of the reflected wave is
rereflected. Where did the 100W come from? the amp delivered it during the
first 1/2 cycle after it was turned on. It didn't "know" the line was
shorted until the first reflection came back.


How do you know that the amplifier is not "delivering" 100W of forward power
and dissipating 100W of reflected power (as it would with a circulator+load)?
How do you prove that the impedance looking back into the amp is zero, infinity,
or purely reactive? Doesn't it have everything to do with the arbitrary
definition of "delivered" which doesn't necessarily match reality?
--
73, Cecil http://www.qsl.net/w5dxp



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Tarmo Tammaru August 16th 03 03:09 AM


"W5DXP" wrote in message
...
How do you know that the amplifier is not "delivering" 100W of forward

power
and dissipating 100W of reflected power (as it would with a

circulator+load)?

Aha, I will give you special dispensation. You are allowed to bias the amp
for true class B, and measure the DC drain current. No way is the drain
current going to be different from the case of a plain open circuit. Power
(RF) can not be more than Power (DC)

How do you prove that the impedance looking back into the amp is zero,

infinity,
or purely reactive?


Use any RF impedance meter you want.

Doesn't it have everything to do with the arbitrary
definition of "delivered" which doesn't necessarily match reality?


I think the only alternative in un nice; namely that there is no reflection
in steady state

Tam/WB2TT
--
73, Cecil http://www.qsl.net/w5dxp



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W5DXP August 16th 03 03:19 AM

Richard Clark wrote:
In the scope of Z determination, I am wholly unconcerned with what
precedes the first millisecond. Perhaps you should phrase your
question along other lines.


You theorized uncertainty because of reflections from all directions.
You seem now to be "unconcerned" about that uncertainty.
--
73, Cecil http://www.qsl.net/w5dxp



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W5DXP August 16th 03 03:23 AM

Tarmo Tammaru wrote:
I think the only alternative in un nice; namely that there is no reflection
in steady state


There are an infinite number of possibilities between the rails of 100%
re-reflection and zero re-reflection. I suspect a PA obeys the rules of
the wave reflection model set forth in Ramo & Whinnery.
--
73, Cecil http://www.qsl.net/w5dxp



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Richard Clark August 16th 03 03:35 AM

On Fri, 15 Aug 2003 21:19:19 -0500, W5DXP
wrote:

Richard Clark wrote:
In the scope of Z determination, I am wholly unconcerned with what
precedes the first millisecond. Perhaps you should phrase your
question along other lines.


You theorized uncertainty because of reflections from all directions.
You seem now to be "unconcerned" about that uncertainty.


Hi Cecil,

In the first millisecond, yes. Do you have a question about it
following that point in time?

73's
Richard Clark, KB7QHC

W5DXP August 16th 03 05:37 AM

Dr. Slick wrote:
Well, this is clearer than what you wrote earlier, as they have
included the "on port 1" part, whereas you stated just "incident
reflected", which told us nothing.


I stated: If ..., PA's will always re-reflect 100% of the incident
reflected power. That's obviously reflected power incident upon
the PA.
--
73, Cecil http://www.qsl.net/w5dxp



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Roy Lewallen August 16th 03 08:25 AM

Ok, I'll try once more.

Look again at what I wrote earlier:

No, you won't see a change in the SWR at point 1 as you change the PA
impedance. All the fiddling you do with your Smith chart just won't

make
it happen. Sorry.

The SWR, voltage, current, impedance, power, reflection coefficient,
waves, or anything else don't change in response to your Smith chart
exercises.


To which you replied:

Absolutely incorrect. Time for you to review your Smith Chart
again.


Here's an experiment for you to try.

On your workbench, measure the characteristic impedance of a cable, or
connect it to a source or load and measure the SWR on it. Now go over to
your desk, take out your grease pencil, and change the reference
impedance of your Smith chart. Go back to the bench, check the SWR and
the cable Z0. Has it changed?

If the answer is yes, I'll admit having a serious shortcoming in my
knowledge of the power of the Smith chart.

If *you'll* review the Smith chart again, you'll find that *if* you set
the reference impedance to the Z0 of the transmission line you're
analyzing, then the SWR, impedances, and so forth that your read from
the Smith chart are correct. If you set the reference impedance to some
other value, an SWR read from the chart certainly isn't the SWR on the
transmission line.

Z0 in the equation you quote refers to the characteristic impedance of a
transmission line. If you change the impedance of the transmission line,
given the same load impedance Zl, you change the SWR, as the equation
indicates. (Changing the reflection coefficient changes the SWR on the
line.) But changing the reference value on your Smith chart doesn't
change the characteristic impedance of the cable.

Now let's see what you wrote this time:

Dr. Slick wrote:
. . .
When you change Zo, you change the normalized center of the
Smith, and therefore the Ref. Coeff. and SWR, looking into the same
load.


Yes. When you change the line's Z0, you should change the normalization
of the Smith chart. But changing the normalization of the Smith chart
doesn't magically change the cable dimensions to give it a
correspondingly new Z0. (Or does it? Something I'm missing here?)

The Smith Chart is an extremely powerful graphical RF tool, which
has become part of the basis for communicating in the RF world, as
well as a standard for displaying impedance on most RF measuring
devices.

You need to read up on this if you want to understand me.


Thank you, although I'm not an expert at using the Smith chart, I know
my way around the circle. But perhaps more study would reveal the
mechanism by which changing the chart reference causes spontaneous
redimensioning of the cable.

Even when the other person is correct too? I think it IS an ego
trip if you can't admit someone has a point, and are too scared to
discuss it further for fear of looking weak or exposing a lack of
knowledge about something.


All right, I was scared to admit that you have a point, that all you
have to do to change a line's SWR is to go over to the desk and change
your Smith chart. But I've overcome my fear now, and am exposing my
ignorance, or weakness as you say, for all to see.

I'd like to learn more about the mechanism, though. When you renormalize
your Smith chart, is the line's Z0 changed by a spontaneous change in
inner conductor diameter, outer conductor diameter, dielectric
permittivity, or some combination? Is it some sort of telekinesis, or
perhaps something to do with Chi? I never could quite get the hang of
Feng Shui, so maybe that's it. I can't find any reference to the
phenomenon you're claiming in my engineering texts -- perhaps an occult
or New Age bookstore would be more fruitful?

From Pozar's Microwave Engineering:

Reflection Coefficient = (Zl-Zo)/(Zl+Zo)

Where Zl is a purely real load impedance, and Zo is the
purely real characteristic impedance reference.

When you change Zo, you change the normalized center of the
Smith, and therefore the Ref. Coeff. and SWR, looking into the same
load.


Almost right, but a misplaced "therefore". The reflection coefficient
and SWR don't change because you change the Smith chart normalization.
They change because you've changed the cable's Z0. If you know how to
use a Smith chart correctly, you can then go and renormalize your Smith
chart to the new Z0 (as you've said), and from it you can read what the
new reflection coefficient and SWR are. Or you can forget the Smith
chart altogether and measure them, or calculate them from an equation.
But if you normalize your Smith chart to some value other than the
cable's Z0, you're no longer reading the transmission line impedances
and SWR from it.

It sure looks to me like you're confusing reality with what you read
from your arbitrarily normalized Smith chart. They're not the same. Just
like the reading on an SWR meter isn't the same as the SWR on a
transmission line of a different impedance. And actually for exactly the
same reason. Hm, maybe that provides even one more way to say it. Set up
your source, cable, and SWR meter like you have it in your earlier
posting. Replace the 50 ohm SWR meter with a 75 ohm SWR meter.
Renormalize your Smith chart for 75 ohms. Presto! The SWR meter reads
the same as the Smith chart! But y'know what? YOU DIDN'T CHANGE THE SWR
ON THE TRANSMISSION LINE. Put the 50 ohm SWR meter back in just on the
load side of the 75 ohm one. It reads just the same as it did before,
and it's reading the actual SWR on the 50 ohm line between it and the load.

Again, changing the Smith chart's normalization does not change a
cable's Z0 or SWR. Feng Shui and voodoo notwithstanding.

A Smith chart is simply (not to disparage in any way its ingeniousness
or utility) a polar plot of reflection coefficient on a special scale.
(The trick is, of course, generating the scale, an exercise in conformal
mapping I recall doing in fields class.) Check it out -- measure the
length of the vector from the center to any impedance point (with the
chart radius equalling one), and the angle from the main axis (zero ohms
being the positive direction), and you'll see you have the reflection
coefficient.

I can't figure out any more ways to say this.

I am always interested in learning. I don't use a Smith chart a great
deal, but I know Tom Bruhns, a regular poster here, does. I'll gladly
defer to him on issues of Smith chart use, and hope he'll feel free to
correct me on any errors I've made in the above discussion -- as he has
a number of times in the past, and which I've greatly appreciated. Walt
Maxwell, an occasional poster, is truly a Smith chart expert, and I'd
also welcome any corrections or amplifications he'd care to make. Or any
other knowledgeable Smith chart user.

Roy Lewallen, W7EL



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