Remember Me?

 Reg Edwards Posts: n/a Peter, what an excellent, straight-forward, plain
-English, explanation. And you didn't enlist the
aid of a single guru. Not even Terman or the
ARRL handbook. ;o)
-----
Reg

 Dr. Slick Posts: n/a "Peter O. Brackett" wrote in message link.net...
Slick:

[snip]
And not the complex conjugate of Z0.

:
:
This is ABSOLUTELY WRONG!

The reflection coefficient is zero only when the Zload
is the conjugate of the Zo.

Go look it up in any BASIC RF book!

Slick

[snip]

Easy now boy! You'r almost as bad as me!

ok...taking some deep breaths here... It is entirely possible, in fact I know this to be true, that there can be
more than one *definition* of "the reflection coefficient". And so... one
cannot say definitively that one particular defintion is WRONG.

But we need a definite definition, otherwise everyone has their
own standard, so when i say "reflection coefficient", you will will
know what i mean, not something else.

When i say "Elephant", hopefully the same animal pops into your

If the definition of the reflection coefficient is given as rho = (Z - R)/(Z
+ R) then that's what it is. This particular definition corresponds to the
situation which results in rho being null when the unknown Z is equal to the
reference impedance R, i.e. an "image match". If the definition is given as
rho = (Z - conj(R))/(Z + conj(R)) then rho will be null when the unknown Z
is equal to the conjugate of the reference impedance conj(R), i.e. a
"conjugate match".

Correction: rho = (Z - conj(R))/(Z + (R)), the conjugate being
only in the denominator.

Slick
 Dr. Slick Posts: n/a Roy Lewallen wrote in message ...
I'm eagerly awaiting your analysis showing how and why it's wrong. Or
simply which of the statements and equations I wrote are incorrect, and
what the correct statement or equation should be and why. Or even a
simple numerical example that illustrates the relationship between
reflection and power transfer.

I think Reg put it best:

"Dear Dr Slick, it's very easy.

Take a real, long telephone line with Zo = 300 - j250 ohms at 1000 Hz.

Load it with a real resistor of 10 ohms in series with a real
inductance of
40 millihenrys.

The inductance has a reactance of 250 ohms at 1000 Hz.

If you agree with the following formula,

Magnitude of Reflection Coefficient of the load, ZL, relative to line
impedance

= ( ZL - Zo ) / ( ZL + Zo ) = 1.865 which exceeds unity,

and has an angle of -59.9 degrees.

The resulting standing waves may also be calculated.

Are you happy now ?"
---
Reg, G4FGQ

If it were not for Reg pointing out this example, i wouldn't have
researched and corrected my original, "purely real" Zo post with the
more general conjugate Zo formula.

And i researched it because i knew that you cannot have a R.C.
greater than one for a passive network (you can only have a R.C.
greater than one for an active network, which would be a "return gain"
instead of a "return loss"), so i knew that when Zo is complex, my
original post must have been wrong.

Roy, you and i have been slinging mud at each other, but i do
respect the things you have taught me, and i do thank you for deriving
the uV/meter equation for dipoles.

But i want you to know that i'm not doing this for my ego. Didn't
i admit that calling antennas "transducers" was a better word than
"transformers", albiet 2 transducers make 1 transformer?

I have yet to see you admit that someone else has a point.

Intelligent people can be close-minded, that is for certainly, in
which case, their intelligence is blunted.

Slick
 Dr. Slick Posts: n/a "David Robbins" wrote in message ...
"Dr. Slick" wrote in message
...
Roy Lewallen wrote in message

...

A. The one just posted by Peter, (Zl - Z0conj) / (Zl + Z0conj)

B. Slick's, (Zl - Z0conj) / (Zl + Z0)

This is the correct formula.

it is??? -10 points and repeat last week's homework.

Who are you to correct my homework? Look it up yourself

It's absolutely the correct formula

For passive circuits, 0=[rho]=1,

And strictly speaking: Reflection Coefficient =
(Zl-Zo*)/(Zl+Zo)

Where * indicates conjugate.

C. The one in all my texts and used by practicing engineers, (Zl - Z0) /
(Zl + Z0)

This formula is correct too, but only because most texts assume a
purely real Zo.

F+, and take the whole class again.

Slick

 Tdonaly Posts: n/a I ain't like most engineers boy, and i'm certainly more edumacated than
you!

You don't know Sh**!

Slick

Hi, Garvin, you old gwee.
Does your family know you're monkeying around like this on
the net?
73,
Tom Donaly, KA6RUH
 W5DXP Posts: n/a Roy Lewallen wrote:
I've never seen the (voltage) reflection coefficient defined as anything
other than the ratio of reflected voltage to forward voltage. Do you
have any reputable source that defines it differently?

s11 is a reflection coefficient that has the special condition that
a2 must be equal zero. When a2 is not equal zero, the s11 reflection
coefficient and the apparent reflection coefficient are not the same.
--
73, Cecil http://www.qsl.net/w5dxp

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 Roy Lewallen Posts: n/a Thank you. That is, of course, for a two port network. Since we've been
talking strictly about a one-port case (I think, anyway), let me
rephrase the question. Do you have any reputable source that defines the
reflection coefficient for a one-port network as anything other than Vr/Vf.

Although it's not really relevant to the discussion at hand, I believe a
valid argument could be made that if a2 isn't equal to zero, then S11
isn't a reflection coefficient at all. It surely isn't the reflection
coefficient at port 1, anyway. But it's a point I'll happily concede in

Roy Lewallen, W7EL

W5DXP wrote:
Roy Lewallen wrote:

I've never seen the (voltage) reflection coefficient defined as
anything other than the ratio of reflected voltage to forward voltage.
Do you have any reputable source that defines it differently?

s11 is a reflection coefficient that has the special condition that
a2 must be equal zero. When a2 is not equal zero, the s11 reflection
coefficient and the apparent reflection coefficient are not the same.

 Dan Posts: n/a Now that the various typo mistakes have been corrected, and putting
aside for the moment the name calling and ad hominem arguments, could
it be that _both_ sides in this discussion are correct? Camp 'A' says
that the reflection coefficient is computed the classical way, without
using Zo conjugate, and offers various mathematical proofs and
discussions of infinitely long lines. Camp 'B' says the reflection
coefficient is computed with Zo* (Zo conjugate) in the numerator, and
offers explanations dealing with the conservation of energy and
maximum transfer of power.

Both sides may be correct since they are talking about _two different_
meanings for the term "reflection coefficient." One has to do with
voltage (or current) traveling waves and the other has to do with
power. Quoting two references:

###

From Chipman, "Theory and Problems of Transmission Lines," 1968:

Section 7.1, Reflection coefficient for voltage waves:
[Discussion and math, then] ...
rho = (ZL - Zo) / (ZL + Zo)

Section 7.6, Complex characteristic impedance
[Various mathematical manipulations, then] ... "the maximum possible
value for |rho| is found to be 1 + sqrt(2) or about 2.41. ... [T]he
principal of conservation of energy is not violated even when the
magnitude of the [voltage wave] reflection coefficient exceeds unity."

[then more math, then] ... "The conclusion is somewhat surprising,
though inescapable, that a transmission line can be terminated with a
[voltage wave] reflection coefficient whose magnitude is as great as
2.41 without there being any implication that the power level of the
reflected wave is greater than that of the incident wave."

[then a discussion of a source with internal impedance Zo connected to
a line with characteristic impedance also Zo that is terminated with a
load of impedance ZL, then] "... more power will be delivered to a
terminal load impedance Zo* [conjugate of Zo] that produces a
reflected [voltage] wave on the line than to a terminal load impedance
Zo that produces no reflected [voltage] wave."

So Chipman states quite clearly that zero reflected voltage wave
magnitude does _not_ mean maximum power transfer. On the contrary,
maximum power is transferred only when there is a non-zero voltage
wave reflection (assuming a complex Zo line). Counter arguments along
the lines of "Well that doesn't seem right to me so therefore Chipman
must be wrong" don't carry much weight given Chipman's credentials.

###

From Kurokawa, "Power Waves and the Scattering Matrix," IEEE
Transactions on Microwave Theory and Techniques, March 1965:

Section 2, explanation of and mathematical definition of the concept
of "power waves," explicitly noted by the author to be distinct from
the more commonly discussed voltage and current traveling waves.

Section 3, definition of the reflection coefficient [for power waves]:
s = (ZL - Zo*) / (ZL + Zo)
with a footnote "[Only w]hen Zo is real and positive this is the
voltage wave reflection coefficient." Kurokawa takes pains to make it
clear that his "s" power wave reflection coefficient is not the same
as the (usually rho or Gamma) voltage wave reflection coefficient.

Section 9, comparison with [voltage and current] traveling waves:
"... since the [voltage or current] traveling wave reflection
coefficient is given by (ZL - Zo) / (ZL + Zo) [note no conjugate] and
the maximum power transfer takes place when ZL=Zo*, ... it is only
when there is a certain reflection in terms of [voltage or current]
traveling waves that the maximum power is transferred from the line to

So Kurokawa agrees with Chipman concerning the condition for maximum
power transfer. Kurokawa also defines two different reflection
coefficients, both in the same paper.

[In some of the above quotes I have altered the subscript letter
assigned to Z, merely for consistency between the two references.]

###

So, it seems to me, everybody can agree as long as it is understood
that there are different meanings for the term "reflection
coefficient." One meaning, and its mathematical definition, applies
to voltage or current waves. The other, with a slightly different
mathematical definition, applies to the power transfer from a line to
a load. They are one and the same only when the reactive portion of
Zo (Xo) is ignored. It may or may not be acceptable to do so,
depending on the attenuation of the line and the frequency. Lossy
lines and lower frequencies yield more negative values for the Xo
component of Zo.

You can use Reg's COAXPAIR or my TLDetails program to do the math and
show concrete examples. Try something like 100 feet of RG-174 at 0.1
MHz, terminated with loads equivalent to Zo and then Zo conjugate, and
compare the rho (or SWR) figures versus the power delivered to the
load for each case. When the termination equals Zo conjugate, note
that the total dB loss is actually _less_ than the matched line loss.
As counter intuitive as this may sound, Chipman offers an explanation
on page 139. (And as others are sure to point out, this makes
absolutely no difference in practical applications and is of academic
interest only.)

Copy of the Kurokawa paper, in pdf format, available on request via
private email. I've obtained copies of Chipman, on two separate
occasions, from Powell's in Portland.

Dan, AC6LA
www.qsl.net/ac6la/
 David Robbins Posts: n/a "Dr. Slick" wrote in message
om...
"David Robbins" wrote in message

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

...

A. The one just posted by Peter, (Zl - Z0conj) / (Zl + Z0conj)

B. Slick's, (Zl - Z0conj) / (Zl + Z0)

This is the correct formula.

it is??? -10 points and repeat last week's homework.

Who are you to correct my homework? Look it up yourself

i did, and its wrong.... but you cut off my reference in your reply. there
is no conjugate term in the complete solution for a real line.

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