Peter O. Brackett wrote:
In summary, I believe that we agree completely, and that we were typing
at "cross purposes".


If this newsgroup had its own logo, it would surely be two crossed
porpoises.


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

It's often noted in texts that SWR is really a meaningless measure when
applied to lossy lines. So I wouldn't unduly worry about strange SWR
numbers for very lossy lines. Take a look at the analysis I just posted
on another thread, which gives voltages, currents, impedances, and
powers for an example case, and see if you can find anything wrong with
it. The calculation used for reflection coefficient is based on its
definition, namely reflected voltage divided by forward voltage. That
agrees with all the transmission line and electromagnetics texts I have,
which is getting to be quite a number now.

Roy Lewallen, W7EL

William E. Sabin wrote:

In simulation programs, transmission lines are solved for their two-port
parameters, and are then treated as lumped circuits in the actual
simulation, just like any lumped-element circuit. Which is a good way
to do it.

I notice that in the ARRL Antenna Book, 19th edition , on page 24-7, it
is stated with definite finality that the reflection coefficient formula
uses the complex conjugate of Zo in the numerator.
I also understand that this has been established by a "well-trusted
authority".

I have used Mathcad to calculate rho and VSWR for Reg's example, for
many values of X0 (imaginary part of Z0) from -0 to -250 ohms.

The data follows:

Note: |rho1*| is conjugated rho1, SWR1 is for |rho1*|, |rho2| is not
conjugated and SWR2 applies to |rho2|

X0.......|rho1*|..SWR1.....|rho2|..SWR2
-250..... 0.935...30.0.....1.865...-3.30
-200..... 0.937...30.8.....1.705...-3.80
-150..... 0.942...33.3.....1.517...-4.87
-100..... 0.948...37.5.....1.320...-7.25
-050..... 0.955...43.3.....1.131...-16.3
-020..... 0.959...47.6.....1.030...-76.5
-015..... 0.960...48.4.....1.010...-204
-012..... 0.960...48.9.....0.997....+/- infinity
-010..... 0.960...49.2.....0.990....+305
-004..... 0.961...76.3.....0.974....+76.3
0000..... 0.961...50.9.....0.961....+50.9

The numbers for not-conjugate rho are all over the place and lead to
ridiculous numbers for SWR. It is also obvious that for a low-loss line
it doesn't matter much. But values of rho greater than 1.0, on a Smith
chart correspond to negative values of resistance (see the data).

Something is wrong here that we are overlooking.

The use of conjugate rho is so much better behaved that I have some real
doubts about some of our conclusions on this matter.

What about it folks? How can we get to the bottom of this?

Bill W0IYH

"Roy Lewallen" wrote

It's often noted in texts that SWR is really a
meaningless measure when
applied to lossy lines.
=============================

In amateur SWR meter applications even the line is just
a figment of the imagination.

But that problem is easily solved - change the name
of the meter!
----
Reg

The equation in the ARRL Antenna Book is identical
to the equation for rho that is in the Power Wave
literature (see Gonzalez and also see Kurokawa).
Also, numerous literature sources describe how an
open-circuit generator with internal impedance Z0,
connected directly to load ZL, is actually a power
wave setup that leads to a rho formula that is
identical to the formula in the ARRL Antenna Book.
When calculating rho, it is not necessary to fool
around with the wave equations, because frequency
is constant and everything is steady-state.

Bill W0IYH



Also the same conjugate formula in Les Besser's
RF Fundamentals I, and Kurokawa, and the 1992 ARRL
general Handbook, which has NO term for Zo reactance, so
it assumes a purely real Zo.

This page also has the correct general formula:

http://www.zzmatch.com/lcn.html


Slick

A few days ago I posted a derviation of the (non-conjugate) formula for
voltage reflection coefficient on a transmission line. It required only
a few assumptions:

1. That the voltage reflection coefficient is the ratio of reverse to
forward voltage.
2. That the voltage at any point along the line, including the ends, is
the sum of the forward and reverse voltages, and that the current is the
sum of forward and reverse currents.
3. That the ratio of forward voltage to forward current, and the ratio
of reverse voltage to reverse current, equal the characteristic
impedance of the transmission line.

Given these assumptions, the derivation is a matter of straightforward
algebra.

For those promoting some other formula for voltage reflection
coefficient: Which of the above assumptions is false? What substitute
assumption is true? And what's *your* dervivation? Remember, we're
talking about transmission lines here, not a one- or two-port analysis
with a "reference impedance" instead of a transmission line, and where
there's no restriction that the total voltage and current are simply the
sum of the forward and reverse components.

Roy Lewallen, W7EL

Roy Lewallen wrote:
1. That the voltage reflection coefficient is the ratio of reverse to
forward voltage.
For those promoting some other formula for voltage reflection
coefficient: Which of the above assumptions is false?

Number 1 is not always true for s11, the s-parameter reflection
coefficient.

What substitute assumption is true?

For an s-parameter analysis, it's that s11 = b1/a1 when a2=0
Your definition above says that rho = b1/a1 no matter what
the value of a2. Some configurations have rho = s11 and some
don't.

There are differences between your transmission line analysis,
an s-parameter analysis, an h-parameter analysis, a y-parameter
analysis, or a z-parameter analysis. If they were all alike,
there would be no need for their separate existences. FYI:

s11=[(h11-1)(h22+1)-h12*h21]/[(h11+1)(h22+1)-h12*h21]

s11=[(1-y11)(1+y22)+y12*y21]/[(1+y11)(1+y22)-y12*y21]

s11=[(z11-1)(z22+1)-z12*z21]/[(z11+1)(z22+1)-z12*z21]

s11=Vref1/Vfwd1 when Vref2=0, i.e. Pref2=0
--
73, Cecil http://www.qsl.net/w5dxp



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Roy Lewallen wrote:
I tried really hard to say clearly that I'm speaking of transmission
lines and not one- or two-port analysis. How could I have phrased that
in a way it would be understood?

You can speak of anything you want. But a transmission line analysis
including a tuner and reflected waves *IS* a two-port analysis at the
tuner. It *IS* a one-port analysis at the load. There's just no getting
around it. Your transmission line analysis resembles a Z-parameter
analysis of one-port and two-port systems.
--
73, Cecil http://www.qsl.net/w5dxp



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"Roy Lewallen" wrote
I tried really hard to say clearly that I'm speaking
of transmission
lines and not one- or two-port analysis.

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

There's no difference between the two. If you produce
the symetrical S-matrix for a length of transmission
line, its 4 parameters contain complex hyperbolic
functions like (Ro+jXo)*Cosh(A+jB) . . . . . where A
is nepers and B is radians.

Whichever way you go, matrix-algebra or Heaviside, you
perform exactly the same set of calculations and, not
surpisingly, you end up with the same answers -
provided Zo in one place only is not followed with an
askerisk just to obtain another answer which is thought
to be more preferable.
---
Reg, G4FGQ

Roy:

[snip]
"Roy Lewallen" wrote in message
...
I tried really hard to say clearly that I'm speaking of transmission
lines and not one- or two-port analysis. How could I have phrased that
in a way it would be understood?
[snip]

!!!

Your phrasing is clear, but it is you that does not understand.

Since when has a transmission line NOT been a two port network?

A transmission line has two ports, period, end of story!

Why are you being so picayune about this issue? Something else must be
bothering
you here... I just can't figure out where you are coming from.

What is your purpose in differentiating between networks and transmission
lines?

As far as I understand an electrical network may consist of nothing more
than a simple transmission line, if so, what's your point?

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

Roy Lewallen wrote:
Someone, I don't even recall who now, noticed that the formula used for
calculating transmission line reflection coefficient allows a magnitude
greater than one when Z0 is complex. From there, the claim was made that
a reflection coefficient greater than one is impossible for a passive
network, since (they said) it implies the creation of energy.

I suspect the problem probably has something to do with squaring
the absolute magnitude of a complex voltage reflection coefficient.
Maybe only the real part should be squared to obtain the power
reflection coefficient?
--
73, Cecil http://www.qsl.net/w5dxp



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