On Sun, 09 Apr 2006 21:09:07 GMT, "Tom Donaly"
wrote:

Peter O. Brackett wrote:

Gamma Fans:

One area of practical interest for which Zo is not "real" occurs over
[broad] ranges is in the area of application of the so-called "last mile"
[for you Newbies that might be "first mile" (grin)] of POTS (Plain Old
Telephone Service) twisted pair transmission lines to a variety of
communications "last mile" communications systems.

Over the frequency ranges of interest for telephone cable applications i.e.
from below 25Hz or so for some signalling and on up to several hundred kHz
or even a few MHz for xDSL applications such as ISDN BA and HDSL, T1,
etc..., the telephone twisted pair exhibits a Zo that varies all over the
map!

In this arena, complex Zo and highly variable Gamma is the norm, in this
twisted pair media and for those kinds of applications, unfortunately for
Mr. Smith Zo is NOT purely resistive.

Aren't you supposed to normalize the chart to Zo? Nothing Mr. Smith
said required Zo to be resistive.

On Sun, 09 Apr 2006 16:35:30 -0700, Wes Stewart
wrote:

On Sun, 09 Apr 2006 21:09:07 GMT, "Tom Donaly"
wrote:

Peter O. Brackett wrote:

Gamma Fans:

One area of practical interest for which Zo is not "real" occurs over
[broad] ranges is in the area of application of the so-called "last mile"
[for you Newbies that might be "first mile" (grin)] of POTS (Plain Old
Telephone Service) twisted pair transmission lines to a variety of
communications "last mile" communications systems.

Over the frequency ranges of interest for telephone cable applications i.e.
from below 25Hz or so for some signalling and on up to several hundred kHz
or even a few MHz for xDSL applications such as ISDN BA and HDSL, T1,
etc..., the telephone twisted pair exhibits a Zo that varies all over the
map!

In this arena, complex Zo and highly variable Gamma is the norm, in this
twisted pair media and for those kinds of applications, unfortunately for
Mr. Smith Zo is NOT purely resistive.

Aren't you supposed to normalize the chart to Zo? Nothing Mr. Smith
said required Zo to be resistive.


But most of the charts don't scale the area where the magnitude of the
reflection coefficient is greater than 1.

Owen
--

On Sun, 09 Apr 2006 23:42:56 GMT, Owen Duffy wrote:

On Sun, 09 Apr 2006 16:35:30 -0700, Wes Stewart
wrote:

On Sun, 09 Apr 2006 21:09:07 GMT, "Tom Donaly"
wrote:

Peter O. Brackett wrote:

Gamma Fans:

One area of practical interest for which Zo is not "real" occurs over
[broad] ranges is in the area of application of the so-called "last mile"
[for you Newbies that might be "first mile" (grin)] of POTS (Plain Old
Telephone Service) twisted pair transmission lines to a variety of
communications "last mile" communications systems.

Over the frequency ranges of interest for telephone cable applications i.e.
from below 25Hz or so for some signalling and on up to several hundred kHz
or even a few MHz for xDSL applications such as ISDN BA and HDSL, T1,
etc..., the telephone twisted pair exhibits a Zo that varies all over the
map!

In this arena, complex Zo and highly variable Gamma is the norm, in this
twisted pair media and for those kinds of applications, unfortunately for
Mr. Smith Zo is NOT purely resistive.

Aren't you supposed to normalize the chart to Zo? Nothing Mr. Smith
said required Zo to be resistive.


But most of the charts don't scale the area where the magnitude of the
reflection coefficient is greater than 1.

Most don't, but some do. [g]

"Cecil Moore" wrote in message
m...
Reg Edwards wrote:
But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.
--
73, Cecil http://www.qsl.net/w5dxp

Yes. A lossy line nas a non purely real (some X) Zo. Long distance power
grid lines are such.
73, Steve, K9DCI

On Mon, 10 Apr 2006 10:43:18 -0500, "Steve Nosko"
wrote:


"Cecil Moore" wrote in message
om...
Reg Edwards wrote:
But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.
--
73, Cecil http://www.qsl.net/w5dxp

Yes. A lossy line nas a non purely real (some X) Zo.

Or it doesn't.

Chipman also says, "It has already been noted that if the losses are
due equally to R and G, Zo is real, no matter how high the losses
are."

Wes Stewart wrote:
On Mon, 10 Apr 2006 10:43:18 -0500, "Steve Nosko"
wrote:


"Cecil Moore" wrote in message
. com...

Reg Edwards wrote:

But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.
--
73, Cecil http://www.qsl.net/w5dxp

Yes. A lossy line nas a non purely real (some X) Zo.


Or it doesn't.

Chipman also says, "It has already been noted that if the losses are
due equally to R and G, Zo is real, no matter how high the losses
are."



All you need is a line where R/L=G/C. This is the famous distortionless
line. It was probably invented long before Chipman. I don't know what
an amateur would want one for.
73,
Tom Donaly, KA6RUH

On Mon, 10 Apr 2006 10:25:07 -0700, Wes Stewart
wrote:

On Mon, 10 Apr 2006 10:43:18 -0500, "Steve Nosko"
wrote:


"Cecil Moore" wrote in message
. com...
Reg Edwards wrote:
But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.
--
73, Cecil http://www.qsl.net/w5dxp

Yes. A lossy line nas a non purely real (some X) Zo.

Or it doesn't.

Chipman also says, "It has already been noted that if the losses are
due equally to R and G, Zo is real, no matter how high the losses
are."


"Distortionless lines" are lines with purely resistive Zo, and they
include lossless lines and that class of lossy line.

Owen
--

Owen Duffy wrote:
"Distortionless lines" are lines with purely resistive Zo, and they
include lossless lines and that class of lossy line.

Re rho 1, Chipman is not talking about "distortionless
lines". He specifically states that it occurs when the reactive
portion of Z0 is of opposite sign to the load reactance.
--
73, Cecil http://www.qsl.net/w5dxp

Reg et al:

[snip]
The reason why both programs stop at 200 KHz has nothing to do with
the foregoing. It is due to skin effect not being fully operative at
lower frequencies which complicates calculations.
There are other programs which go down to audio and power frequencies.
----
Reg, G4FGQ
[snip]

It's a pity that your programs don't work all the way down to DC.

Maxwell's celebrated [I really should say Heaviside's] equations do!

Aside: It is Heaviside's vector formulation of Maxwell's complicated
quaternic formulation with which most of we [modern] "electricians" are most
familiar.

In fact the common/conventional mathematical formulation of the reflection
coefficient rho and its' magnitude gamma as derived from the
Maxwell/Heaviside equations are indeed valid from "DC to daylight".

Notwithstanding the views of some, there are indeed "reflected waves" at DC
and even these "DC reflections" are correctly predicted by the widely
accepted and celebrated common/conventional mathematical models of
electro-magnetic phenomena, formulated by Maxwell and Heaviside.

Reg I assume the reason for your programs failure to give [correct] answers
below 200 kHz is because your "quick and dirty" programs do not utilize full
mathematical models for skin effect below 200 kHz. As you know, solving
Maxwell's equations for analytical solutions of practical problems is
fraught with great difficulties and so often numerical techniques [MoM, FEM,
etc...] or empirical parametric methods are used.

Most [non-parametric] analytic skin effect models derived from Maxwell and
Heaviside's equations [such as those in Ramo and Whinnery] involve the use
of "transcendental" functions that although presented in a compact notation,
even still do not succumb to "simple" evaluation.

Surely though skin effect is easier to model below 200 kHz where the effect
becomes vanishingly smaller? And so I don't understand why your programs
cannot provide skin effects below 200 kHz.

If you are interested I can point you to some [lumped model] skin effect
models for wires [based upon concentric ring/cylindrical models] that,
although parametric and empirical, are very "compact" and easly evalutate
and which closely model skin effect, and other secondary effects such as
"proximity crowding", up to prescribed frequency limits as set by the
"parameters".

These models simply make empirical parametric corrections to the basic
R-L-C-G primary parameters by adding a few correction terms.

Thoughts, comments?

--
Pete k1po
Indialantic By-the-Sea, FL

Peter O. Brackett wrote:
. . .
Most [non-parametric] analytic skin effect models derived from Maxwell and
Heaviside's equations [such as those in Ramo and Whinnery] involve the use
of "transcendental" functions that although presented in a compact notation,
even still do not succumb to "simple" evaluation.

Surely though skin effect is easier to model below 200 kHz where the effect
becomes vanishingly smaller? And so I don't understand why your programs
cannot provide skin effects below 200 kHz.

If you are interested I can point you to some [lumped model] skin effect
models for wires [based upon concentric ring/cylindrical models] that,
although parametric and empirical, are very "compact" and easly evalutate
and which closely model skin effect, and other secondary effects such as
"proximity crowding", up to prescribed frequency limits as set by the
"parameters".

These models simply make empirical parametric corrections to the basic
R-L-C-G primary parameters by adding a few correction terms.

Thoughts, comments?

Calculation of skin effect in a round wire is simple, provided that you
have the ability to calculate various Bessel functions. Libraries in
Fortran are widely available, and probably in other languages also.
NEC-2 (and therefore EZNEC) does such a full calculation for evaluation
of wire loss. A side benefit of doing this is that you also get an
accurate evaluation of the internal inductance. However, in practical
terms, you can do quite well with the common skin depth approximation
based on the assumption that the wire diameter is at least several skin
depths, and an interpolation from there to the DC case.

Coaxial cable is more problematic than twinlead. Most analyses assume
that the resistance of the shield is negligible. But for an accurate
evaluation, you need to include it. At high frequencies it's simple, but
it's much more difficult at low frequencies than for a round wire, since
most equations you'll find require subtracting huge numbers from each
other, exceeding the capability of even double precision on modern PCs.
It's possible but requires some mathematical manipulation and trickery.

With coax at low frequencies, the fields from the two conductor currents
reach the outside of the cable. While they should still cancel, this
might cause some problems with the assumptions we normally make in the
analysis of coaxial transmission lines.

You're not likely to be able to do a very good job of predicting real
life transmission line behavior in any case, though, unless you account
for such real factors as the roughness of stranded conductors, braided
coax shield, and plated conductors. I'd also expect twinlead with solid
or punched polyethylene insulation between conductors to be somewhat
dispersive (that is, having a velocity factor which changes with
frequency), but I've never tried to measure it. Reg has said he's
measured many pieces of real cable and found its loss to agree with his
earlier coax program, but won't tell us where he buys it. Everything
I've ever been able to buy is considerably lossier.

Roy Lewallen, W7EL