All NewsGroup readers appear to agree that rho is the reflection
coefficient.

Beyond that it seems that there are dissenters...

Here's some thoughts which will cause readers to pause... er... delay, when
it comes
to complex Zo and complex rho.

rho is the ratio of the reflected voltage wave "b" to the incident voltage
wave "a".

rho = b/a = (ZL - Zo)/(ZL + Zo)

rho is then in general a complex function of angular frequency w = 2*pi*f
where f
is "cyclic" frequency in Hz simply because both ZL and Zo can themselves be
complex.

rho may of course be considered to be a"transfer function" which yeilds the
reflected
voltage "b" or voltage echo, sometimes known as the "talker echo", which
results from
the application of the incident voltage "a".

rho(jw) = [(ZL(jw) - Zo(jw))/(ZL(jw) + Zo(jw))] = |rho(w)|*exp[j*phie(w)]

Where phie(w) is widely known in the literature as the "echo phase" and
|rho(w)| is
the magitude of the reflection coefficient.

Following the literature and taking natural logarithm's of the inverse of
rho one finds that:

ln[1/rho(jw)] = -ln|rho(w)| - j*phie(w) = Ae(w) - j*phie(w)

Where Ae(w):

Ae(w) = -ln|rho(jw)| "Echo Attenuation or Return Loss"

Measures the echo attenuation in Nepers and is the so-called "Echo
Attenuation" or "Return Loss", in Nepers (Np).

Ae(w) measures how much the talker echo or reflected voltage echo "b" is
attenuated below the incident voltage wave "a".

Aside: Europeans seem to prefer the term Echo Attenuation and the symbol
Ae(w) and Np units [which is also my personal preference] however North
American authors seem to prefer the term "Return Loss" and symbol RL and
prefer to use dB units rather that Np units. For those who need to convert
from Np to dB that conversion is simply dB = 20 log(e) = 8.686 Np.

Of more interest to those fans of complex Zo is phie(w), the so-called
"Echo Phase" or "Return Phase" measured in radians. The Echo Phase
measures the phase lag of the voltage echo as compared to the phase
angle of the incident voltage.

Now for some stuff that should really interest Cecil.

:-)

Differentiating the echo phase phie(w) with respect to w, one obtains the
well-known "Echo Group Delay", this echo group delay or, as it is sometimes
called, the "Return Delay", is always a real function and is given by.

taugre(w) = d[phie(w)]/dw

and has units of seconds.

taugre(w) measures the group delay of the returned voltage echo as a
function of frequency. In a differential bandwidth dw the value of
taugre(w) measures the average delay of a "packet" of energy launched by the
incident wave "a" in that differential frequency band dw and returned to the
source in the voltage echo.

Wow, sort of like transmission line radar. Question for Time Domain
Reflectometer
fans:

Is this taugre(w) the delay that would be measured by a TDR?

An even more interesting quantity is the echo group velocity or vge(w) which
is simply the reciprocal of taugre(w)

vge(w) = 1/taugre(w)

which has units of inverse seconds.

The vge(w) may never be faster than the speed of light in the Zo media.
In general the velocity of frequency groups is not constant with frequency!

vge(w) gives the actual group velocity of packets or groups of frequencies
in the echo as it passes from the source back around to the source again.
It is a function of frequency and illustrates that in transmission lines
with
complex Zo not all frequencies in the echo travel with the same velocity and
some frequencies actually arrive back at the source before the others.

Should designers of echo cancellers for complex Zo lines care about this?

Of course no such thing occurs with real Zo lines!

Real Zo lines are sooooo dull and unintersting!

Another interesting quantity which I am sure Cecil will enjoy is the
so-called echo phase delay or tauphe(w)

tauphe(w) = phie(w)/w

The echo phase delay is an interesting function and I will leave it to the
reader to work out its' physical significance. This quantity leads to the
very curious echo phase velocity or vpe(w)

vpe(w) = 1/tauphe(w)

It is interesting to note that vpe(w) can actually exceed the speed of light
in the Zo media. In a transmission system with a real Zo of course
vpe = vge. But in the widely deployed complex Zo telephone twisted
pair plant it is not.

Things are really dull and uninteresting when Zo is real, huh?

Finally the arcane "echo signal front delay" tausfe(w), when it exists
equals the limit.

tausfe(w) = limit as w - infinity of the ration phie(w)/w

And of course the reciprocal of the echo signal front delay gives the echo
signal front velocity vsfe(w) when it exists, thus:

vsfe(w) = 1/tausfe(w) when it exists.

It is left as an exercise for the reader to find out under what physical
circumstances this exotic velocity exists and just what it's physical
meaning might be...

A quantity of great great interest to Cecil will be the value of the echo
group delay evaluated at the origin (DC)!

taugre(w) evaluated at w = 0 [DC] gives the first "time moment" of the echo!

taugre(0) = T*area of voltage echo = Integral from 0 to infinity of
t*b(t)*dt

taugre(0) when divided by the area under the echo voltage gives the average
time delay T by which the energy in the echo is delayed.

T = taugre(0)/area under b(t).

It turns out that this is an extremely useful value to know if one is
interested in designing or operating an effective and feasible analog or
digital talker echo canceller to suppress echos on the line and allow the
receiver to receive remotely generated signals in the face of extremely
strong incident signals.

Circuitry or algorithms that can make fast real time estimates of T are
highly desirable and are held as trade secrets by certain companies.

The design and operation of talker echo cancellers for transmission systems
with complex Zo is quite a complicated and challenging task.

That's enough titilating information for fans of complex Zo.

And so... until the next time...

I'd like some thoughts and comments these arcane and exotic functions and
about
comparisons between such functions for transmission systems with real Zo and
those with complex Zo.

Thoughts, comments?

--
Peter K1PO
Indialantic By-the-Sea, FL.

On Tue, 09 Sep 2003 13:51:33 GMT, "Peter O. Brackett"
wrote:
....

It turns out that this is an extremely useful value to know if one is
interested in designing or operating an effective and feasible analog or
digital talker echo canceller to suppress echos on the line and allow the
receiver to receive remotely generated signals in the face of extremely
strong incident signals.
....

I'd like some thoughts and comments these arcane and exotic functions and
about
comparisons between such functions for transmission systems with real Zo and
those with complex Zo.

Thoughts, comments?

Hi Peter,

Well, if we scrapped all the antennas, killed the RF and
interconnected a million miles of transmission line - this might be
interesting. We could call it telephony. The next wave would be gold
plated 00 wire gauge lines connected to dusty rock band amplifiers
(new-age linears) that had been sitting dormant in the garage since
adolescence. Cecil could then argue the use of the Wah-Wah pedal to
conjugate the group velocity.

The topics discussed would be rec. but not radio. maybe amateur.
(amateur telephony?) and certainly not antenna. There ya' go! Design
a telephony antenna to eliminate all these transmission line problems.
Do it from first principles too. ;-)

73's
Richard Clark, KB7QHC

Bill:

[snip]
Are you really serious? Do you really want folks
to grind through all of this and propose
counter-arguments, questions, etc?

I suggest most respectfully "enough is enough".

A carefully written QEX article by you on this
entire subject would be a good idea and a
permanent part of the literature.

Bill W0IYH
[snip]

Hi Bill...

Well a lot of this material is already a permanent part of the professional
literature, in both IEEE Publications and Standards Organizations
contributions. Not very accessible to amateurs. And so it seems that
others
outside the xDSL industry are not aware of all the work that has gone on
with
broadband data transmission over complex Zo transmission lines.

I personally believe that the full duplex transmission of broad band
multi-megabit data over several thousand foot multi-pair twisted
pair complex Zo cables is one of the most challenging transmission
line problems ever tackled by man and solved by modern science
and engineering. The several extant solutions to that problem developed
by the digital subscriber loop [xDSL] industry certainly makes clear
a lot of the transmission issues that are sometimes subjected to fuzzy
thinking and discussed loosely on this NewsGroup from time to time.

A few months ago, I posted on here a few items of interest from the
detailed measurement and characterization work done world wide
by ETSI, ITU and ANSI and documented in ANSI T1E1.4
contributions on the details of the Zo of complex Zo transmission lines,
but there seemed to be little interest in such data from the NewsGroup
participants who seem to concentrate only upon short lossless,
distortionless
50 Ohm lines.

Perhaps the amateur radio community is simply not interested in
leading edge advances in communications technologies outside of
the conventional amateur communications techniques.

:-)

I would be willing to write such an article for QEX, however...
not without an invitation to do so. An unsolicted contribution would
be a lot of work on the part of anyone who undertook
such a project and it might all be for naught.

Personally I wouldn't do so without a clear indication from the
editor that such an article could be published. This is simply because
time is valuable and the fear that an unsolicited manuscript might be
be rejected simply because, although interesting, it would be of
little interest to the amateur radio community.

I can however provide professional technical references to anyone
who might have a sincere interest in learning about such things.

--
Peter K1PO
Indialantic By-the-Sea, FL.

Peter O. Brackett wrote:


A few months ago, I posted on here a few items of interest from the
detailed measurement and characterization work done world wide
by ETSI, ITU and ANSI and documented in ANSI T1E1.4
contributions on the details of the Zo of complex Zo transmission lines,
but there seemed to be little interest in such data from the NewsGroup
participants who seem to concentrate only upon short lossless,
distortionless
50 Ohm lines.

Being an RF guy, mostly, I am interested in
complex Z0 values of low loss lines, where
Imag(Z0) is no more than a few percent of
Real(Z0). I use exact equations in a Mathcad
program to get detailed answers. I find this
interesting and useful. The "classical" formula
for rho is quite satisfactory, for me.

Bill W0IYH

Peter O. Brackett wrote:

I would be willing to write such an article for QEX, however... not
without an invitation to do so. An unsolicted contribution would be a
lot of work on the part of anyone who undertook such a project and it
might all be for naught.

Personally I wouldn't do so without a clear indication from the editor
that such an article could be published. This is simply because time
is valuable and the fear that an unsolicited manuscript might be be
rejected simply because, although interesting, it would be of little
interest to the amateur radio community.

Looking at this from a writer and an editor's point of view (though
obviously not speaking for the editor of QEX)...

First of all, QEX is not an academic journal but a technical magazine.
The difference is that an academic journal has a guaranteed income from
college libraries, and thus can publish material that is stunningly
boring, provided only that it's original and of high academic merit.

QEX on the other hand has to earn its living by publishing articles that
are *interesting* and *useful* to subscribers. Every single issue will
determine whether a substantial fraction of subscribers decide to renew,
or not. This cold commercial fact tends to concentrate the editor's mind
- and it also improves the quality of articles that he or she chooses to
publish.

Editors don't like giving open-ended invitations to writers whose work
they don't already know. On the other hand, they love receiving e-mails
asking if they'd consider an article on a certain subject. The more
professional you are about this, by justifying why that article would be
interesting, outlining the topics you'd like to cover, showing that you
understand the needs of the magazine, and estimating an overall length
that's appropriate to both the topic and the magazine... why, the more
they'll like you.

Oh, by the way, that e-mail will also be read as a sample of your
writing style...

But even then, no editor will say "Go ahead - you write it, we'll
publish it." No self-respecting editor ever *should* say that! The best
any author can legitimately expect is an enthusiastic promise to
"consider it". It's then up to you to write an article that the editor
cannot refuse.

I can however provide professional technical references to anyone who
might have a sincere interest in learning about such things.

Very few people - even in this learned newsgroup - would be interested
in learning about the subject for its own academic sake. But enough
people have become intrigued by the topic of complex Zo to feel the
foundations of our understanding(?) of transmission lines shifting
underneath us. We now need to know which of the formulae and
relationships that we've been using are universally correct, and which
of them are actually only approximations. An article with that focus
really *would* be interesting!

An article really is needed now. Sorry, Walt, we can't go back to sleep
- the genie is out of the bottle, and only more understanding (not less)
will put it back. Reg's program is not the solution either. I'd trust
that particular program all the way, but I also want to understand
*why*, and using a program won't show me that.

What's needed here is more like an academic review article. Such
articles don't normally contain new, original results. The originality
of a good review consists in pulling together existing results from a
whole field of study and *explaining* what they mean.

Reviews generally shouldn't go into the same heavy detail as the
original references. For this particular topic, the mathematical level
of a magazine article would be a make-or-break issue... and another very
good reason why editors always say "Show me first." Academic papers tend
to deal in high-level general concepts that are already familiar to
academic readers, but that is not appropriate for an amateur readership.
To emphasize the difference, it's not that amateur readers are stupid
(far from it!) but that very few of us have covered this particular
academic territory. As an author, don't take us into there unless
there's absolutely no other way. If the same results can be obtained
using lower-level concepts such as Ohm's and Kirchhoff's laws, then -
for this readership - that's how it should be done.

The existence of academic papers would allow you to skip over some of
the heavy math, and keep your article interesting and moving forward.
For example, it's legitimate in an article of this kind to work with a
simplified example of a complex-Zo problem, derive a useful result, and
quote a reference that proves (at the expense of much heavier math) that
that result is actually a general one. A review-type article is one of
the few cases where the notorious "it can be shown that" is actually a
legitimate and useful tool to keep your story moving.



--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek

Bill:

[snip]
Being an RF guy, mostly, I am interested in
complex Z0 values of low loss lines, where
Imag(Z0) is no more than a few percent of
Real(Z0). I use exact equations in a Mathcad
program to get detailed answers. I find this
interesting and useful. The "classical" formula
for rho is quite satisfactory, for me.

Bill W0IYH
[snip]

That's the same approach most xDSL experts take
to complex Zo lines. Mathematical simulations
using say MatLab and such are used for designs.

The telephone twisted pair plant certainly has a
very complex Zo although it has extremely
high loss compared to most RF applications which
I know of.

Typically most lines world wide start out with
an approximate 1500 Ohm design basis. That
is the DC resistance of the lines are aimed at
no more than a DC resistance of 1500 Ohms
end to end. The R, L, C, and G primary parameters
of the line vary quite widely. Especially when
one considers there may be one or more
un removeable bridged taps [transmission line stubs]
floating across the line at unknown locations having
resonances directly in band!

A typical xDSL transceiver has a terminating
resistance of 100 Ohms... thus the transmitters
are attempting to transmit energy into a 100 Ohm
load at the end of 1500 Ohms of DC and even
higher at higher frequencies of loss!

Should the transmitter really be adjusted for
maximum power transfer, i.e. a conjugate
match into the local driving point impedance,
when most of the transmit power will be lost
heating up the line and never reach the load?

How will the poor suffering receiver be able to
copy weak signals from the far end of such
a line in the presence of the enormous QRM
from it's own transmitter blasting away on
the same pair it is listening on?

What kinds of line equalizers [tuners?] are used?
What kinds of echo cancellers are used?
What kinds of modulation are used?
What kinds of coding are used?
What is the bandwidth [bps/Hz] efficiency obtained?

Is any of this advanced technology
applicable to amateur radio of the future?

Is anyone interested?

What?

--
Peter K1PO
Indialantic By-the-Sea, FL.

Peter O. Brackett wrote:

Modern technology such as xDSL is in wide use on literally millions of
lines with extremely complex Zo world wide and has been made available
for very feasible prices! This is not academe! Such devices are very
practical, not academic, and have been developed within the industrial
community by thousands of practicising Engineers not academicians. A
lot of this very advanced work has been "exposed" in the Standards
Committee arenas of ETSI, ITU and ANSI. And so I consider this wide
exploitation of extremely complex Zo lines to be practical Engineering
and technology and not academic.

Fair point, Peter. Although the theory behind xDSL is still the province
of academic journals, this is a good example of theory into practice.

Even if we don't ever use the information within amateur radio purposes,
we may well have to deal with problems when it hasn't been implemented
correctly; so yes, we do need to know something about it.

The theory of transmission lines with complex Zo is where the two areas,
xDSL and amateur radio, touch and maybe overlap just a little. All the
more reason for writing an article!


--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek

| "Ian White, G3SEK" wrote:
|
| ...
| The difference is that an academic journal
| ...
| can publish material
| ...
| provided only that
| it's original and of high academic merit.
| ...
|

Dear Mr. Ian White,

This is an interesting point of view indeed,
which the last days
returns from time to time in my mind
so that I decided finally to ask you,
about it:

Is it a formal professional opinion,
or a deeper amateur hope of you?

Sincerely,

pez
SV7BAX

"Ian White, G3SEK" wrote in message ...
| Peter O. Brackett wrote:
|
| I would be willing to write such an article for QEX, however... not
| without an invitation to do so. An unsolicted contribution would be a
| lot of work on the part of anyone who undertook such a project and it
| might all be for naught.
|
| Personally I wouldn't do so without a clear indication from the editor
| that such an article could be published. This is simply because time
| is valuable and the fear that an unsolicited manuscript might be be
| rejected simply because, although interesting, it would be of little
| interest to the amateur radio community.
|
| Looking at this from a writer and an editor's point of view (though
| obviously not speaking for the editor of QEX)...
|
| First of all, QEX is not an academic journal but a technical magazine.
| The difference is that an academic journal has a guaranteed income from
| college libraries, and thus can publish material that is stunningly
| boring, provided only that it's original and of high academic merit.
|
| QEX on the other hand has to earn its living by publishing articles that
| are *interesting* and *useful* to subscribers. Every single issue will
| determine whether a substantial fraction of subscribers decide to renew,
| or not. This cold commercial fact tends to concentrate the editor's mind
| - and it also improves the quality of articles that he or she chooses to
| publish.
|
| Editors don't like giving open-ended invitations to writers whose work
| they don't already know. On the other hand, they love receiving e-mails
| asking if they'd consider an article on a certain subject. The more
| professional you are about this, by justifying why that article would be
| interesting, outlining the topics you'd like to cover, showing that you
| understand the needs of the magazine, and estimating an overall length
| that's appropriate to both the topic and the magazine... why, the more
| they'll like you.
|
| Oh, by the way, that e-mail will also be read as a sample of your
| writing style...
|
| But even then, no editor will say "Go ahead - you write it, we'll
| publish it." No self-respecting editor ever *should* say that! The best
| any author can legitimately expect is an enthusiastic promise to
| "consider it". It's then up to you to write an article that the editor
| cannot refuse.
|
| I can however provide professional technical references to anyone who
| might have a sincere interest in learning about such things.
|
| Very few people - even in this learned newsgroup - would be interested
| in learning about the subject for its own academic sake. But enough
| people have become intrigued by the topic of complex Zo to feel the
| foundations of our understanding(?) of transmission lines shifting
| underneath us. We now need to know which of the formulae and
| relationships that we've been using are universally correct, and which
| of them are actually only approximations. An article with that focus
| really *would* be interesting!
|
| An article really is needed now. Sorry, Walt, we can't go back to sleep
| - the genie is out of the bottle, and only more understanding (not less)
| will put it back. Reg's program is not the solution either. I'd trust
| that particular program all the way, but I also want to understand
| *why*, and using a program won't show me that.
|
| What's needed here is more like an academic review article. Such
| articles don't normally contain new, original results. The originality
| of a good review consists in pulling together existing results from a
| whole field of study and *explaining* what they mean.
|
| Reviews generally shouldn't go into the same heavy detail as the
| original references. For this particular topic, the mathematical level
| of a magazine article would be a make-or-break issue... and another very
| good reason why editors always say "Show me first." Academic papers tend
| to deal in high-level general concepts that are already familiar to
| academic readers, but that is not appropriate for an amateur readership.
| To emphasize the difference, it's not that amateur readers are stupid
| (far from it!) but that very few of us have covered this particular
| academic territory. As an author, don't take us into there unless
| there's absolutely no other way. If the same results can be obtained
| using lower-level concepts such as Ohm's and Kirchhoff's laws, then -
| for this readership - that's how it should be done.
|
| The existence of academic papers would allow you to skip over some of
| the heavy math, and keep your article interesting and moving forward.
| For example, it's legitimate in an article of this kind to work with a
| simplified example of a complex-Zo problem, derive a useful result, and
| quote a reference that proves (at the expense of much heavier math) that
| that result is actually a general one. A review-type article is one of
| the few cases where the notorious "it can be shown that" is actually a
| legitimate and useful tool to keep your story moving.
|
|
|
| --
| 73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
| Editor, 'The VHF/UHF DX Book'
| http://www.ifwtech.co.uk/g3sek