Gamma. Before somebody tells me.
 

Before somebody tells me there's something wrong with programs
LINE_ZIN and INPUT_Z I'd better put in a few words of explanation.

First of all there's nothing wrong with the programs. Both are
correct.

They both calculate the reflection coefficient Gamma for a given line
and given load impedance at a given frequency. One does it for coaxial
lines and the other for balanced-twin and open-wire lines.

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

With program LINE_ZIN enter the following -

Freq = 0.2 MHz
Conductor diameter = 0.2 mm
Conductor spacing = 10 mm
Line length = 119.25 metres
Velocity factor = 1.00
Load resistance = 0.00 ohms
Load reactance = + 552.6 ohms

From which we get -

Zo = 552.6 ohms
Gamma = 1.084
Angle of Gamma = -90.0 degrees
SWR at load end = 24.8
SWR at input end = Infinity

With program INPUT_Z enter the following -

Frequ = 0.2 MHz
Zo = 50 ohms
Line length = 100 metres
Inner conductor diameter = 0.73 mm (RG-58)
Velocity factor = 0.66
Load resistance = 0.00 ohms
Load reactance = +50.00 ohms

From which we get -

Gamma = 1.109
Angle of Gamma = -90.0 degrees
SWR at load end = 19.3

The reason for the abnormally high values of Gamma, and the SWR at the
input end being higher than the SWR at the load end, is that the line
impedance Zo is not purely resistive. It has a negative angle. Zo =
Ro - jXo.

There is a resonance between -jXo and + jXload which causes the
reflected wave to be greater than the incident wave. Hence Gamma
exceeds unity. The effect is not present when jXload is negative.

Gamma has a maximum value when +Xload = Zo as can be found by varying
Xload on either side of Zo.

At some distance back from the load the extraordinary high value of
SWR occurs (as demonstrated with program LINE_ZIN) due to that point
taking the place of the end of the line when Zo is purely resistive.

The true value of Zo = Ro+jXo can be found by making the line long
enough such that attenuation exceeds about 35 or 40 dB. Line input
impedance is then becomes equal to Zo.

It is the fact that Zo is never purely resistive which causes errors
when using the Smith Chart. Errors which the user can be entirely
unaware of. Coax lines are more prone to error than higher impedance
balanced-twin lines.

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

Gamma. Before somebody tells me.
 

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

Gamma. Before somebody tells me.
 

"Cecil Moore" wrote
That agrees with Chipman who says it only occurs in lossy lines.
============================================
Didn't you know ALL real lines are lossy?

Still, I'm pleased to hear Chipman agrees with me.
----
Reg.

Gamma. Before somebody tells me.
 

On Sat, 08 Apr 2006 01:34:33 GMT, Cecil Moore
wrote:

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.

But in theory, the line can have loss and this does not occur :-)

Gamma. Before somebody tells me.
 

"Cecil Moore" wrote
That agrees with Chipman who says it only occurs in lossy lines.
============================================
Didn't you know ALL real lines are lossy?

Still, I'm pleased to hear Chipman agrees with me.
----
Reg.

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

- - - - and perhaps I should add that I was well aquainted with the
behaviour of transmission lines well before Chipman wrote his book.
----
Reg.

Gamma. Before somebody tells me.
 

On Sat, 8 Apr 2006 18:05:39 +0100, "Reg Edwards"
wrote:

- - - - and perhaps I should add that I was well aquainted with the
behaviour of transmission lines well before Chipman wrote his book.

Did you scribble it on the last page of Noah's log?

Gamma. Before somebody tells me.
 

Reg Edwards wrote:
- - - - and perhaps I should add that I was well aquainted with the
behaviour of transmission lines well before Chipman wrote his book.

He wrote his book almost 40 years ago, Reg. Do you know
how old that makes you?
--
73, Cecil http://www.qsl.net/w5dxp

Gamma. Before somebody tells me.
 

"Cecil Moore" wrote
Reg Edwards wrote:
- - - - and perhaps I should add that I was well aquainted with
the
behaviour of transmission lines well before Chipman wrote his
book.

He wrote his book almost 40 years ago, Reg. Do you know
how old that makes you?

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

I may be in my 81st year but I DO know how old I am.

If Chipman wrote his book about 40 years ago then I was 40 years old
at the time. I have never written any books myself. I have never
attached sufficient importance to the subject matter. I educated
myself to enable me to do a job which was more interesting than merely
writing so-called bibles for a living.
----
Reg

Gamma. Before somebody tells me.
 

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.

The Zo of twisted pair ranges rom very nearly purely capacitive impedance of
several thousand kOhms at low frequencies to purely resistive near 100 Ohms
at the higher ends.

Analysis and design of systems that operate over this 5-6 decade range of
frequencies must perforce use complex Zo!

Smith's venerable chart is completely useless. Smith's Chart is only for
"amateurs" who use transmission lines in very limited ways.

The complex reflection coeficient in all of its' glory reigns supreme for
those practical and realistic design and application scenarios.

Thoughts, comments?

--
Pete k1po
Indialantic, FL.


"Wes Stewart" wrote in message
...
On Sat, 08 Apr 2006 01:34:33 GMT, Cecil Moore
wrote:

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.

But in theory, the line can have loss and this does not occur :-)

Gamma. Before somebody tells me.
 

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.

The Zo of twisted pair ranges rom very nearly purely capacitive impedance of
several thousand kOhms at low frequencies to purely resistive near 100 Ohms
at the higher ends.

Analysis and design of systems that operate over this 5-6 decade range of
frequencies must perforce use complex Zo!

Smith's venerable chart is completely useless. Smith's Chart is only for
"amateurs" who use transmission lines in very limited ways.

The complex reflection coeficient in all of its' glory reigns supreme for
those practical and realistic design and application scenarios.

Thoughts, comments?

--
Pete k1po
Indialantic, FL.


"Wes Stewart" wrote in message
...

On Sat, 08 Apr 2006 01:34:33 GMT, Cecil Moore
wrote:


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.

But in theory, the line can have loss and this does not occur :-)





How are you, Peter? Is this some kind of religious controversy? I can't
imagine hams having any use for twisted pair transmission lines, but
maybe you can give your lines some fractal qualities, or show how
current can flow four directions at the same time in the same place in
them or the voltage at any given point on one of them must have 25
possible values simultaneously, or that the impedance on a typical line
is proportional to the square root of Cecil's forearm. In fact, giving
them any qualities that are impossible will endear them to
the great post hog on this newsgroup and start a never ending thread.
73,
Tom Donaly, KA6RUH

Gamma. Before somebody tells me.
 

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.

Gamma. Before somebody tells me.
 

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
--

Gamma. Before somebody tells me.
 

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]

Gamma. Before somebody tells me.
 

"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

Gamma. Before somebody tells me.
 

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."

Gamma. Before somebody tells me.
 

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

Gamma. Before somebody tells me.
 

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
--

Gamma. Before somebody tells me.
 

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

Gamma. Before somebody tells me.
 

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

Gamma. Before somebody tells me.
 

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

Gamma. Before somebody tells me.
 

Peter, I am very familiar with what happens below 200 Khz.

Most of my transmission line progs cover from power freqs up to UHF.
And they only stop there because of problems with finding room on the
screen for numerical overflow and the programming trouble with
shifting decimal points around.

Very shortly I shall have a program about "Behaviour of Coaxial
Transmission Lines at Low Frequencies. It accepts frequencies in the
range 20 Hz to 5 MHz. Input data is kilo-Hertz in the range 0.02 to
5000. Originally I stopped at 500 KHz.

There's no point in extending frequency range up to 10 GHz because
there is no interest in the subject matter. Although the maths is
already built in. There's just not enough space on the screen.
Programs should be easy to use.

As a program writer yourself you should be familiar with all this.
----
Reg.
======================================

"Peter O. Brackett" wrote in message
nk.net...
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