Hello,

No one has really derived the Reflection Coefficient,
either the "normal" or "conjugate" equation. This would
be key to our understanding of when you can use which equation.


What is not understood is how A/C/F got from:

Voltage R. C.= (Vr/Vi)e**(2*y*z)

where y=sqrt((R+j*omega*L)(G+j*omega*C))
and z= distance from load

To:

Voltage RC=(Z1-Z0)/(Z1+Z0) for purely real Zo
or Voltage RC=(Z1-Z0*)/(Z1+Z0)



Even Kurokawa doesn't show us how he gets the conjugate
equation. Email me to get the paper, his notation is confusing.


I have NO problems with the normalized formula,
AS LONG AS Zo IS PURELY REAL.


Nevertheless, even if you do believe the "normal"
equation is correct even with complex Zo, i'd still like
to see your derivation.

And please give us a derivation with VARIABLES ONLY.
The strong temptation to use specific numbers will only
lead us to incorrect conclusions like:

A**B=A+B, because it's true when A and B are equal to 2.



Slick

I looked back in one of the earlier chapters, where they originally do
reflection, and
using e**(+/-jyz)= cosyz +/- jsinyz they get

V(z)=(V+ + V-)cosyz -j(V+ - V-)sinyz
and
I(z)=Yo{(V+ - V-)cosyz -j(V+ + V-)sinyz}

a V(z)=V1cosyz + V2sinyz
}
}
b I(z)=-jY0V1sinyz + jY0V2cosyz

It says the equation is divided into two independent solutions for voltage
and current. I do not understand it. The brackets encompass both a and b.

Tam/WB2TT




"Dr. Slick" wrote in message
om...
Hello,

No one has really derived the Reflection Coefficient,
either the "normal" or "conjugate" equation. This would
be key to our understanding of when you can use which equation.


What is not understood is how A/C/F got from:

Voltage R. C.= (Vr/Vi)e**(2*y*z)

where y=sqrt((R+j*omega*L)(G+j*omega*C))
and z= distance from load

To:

Voltage RC=(Z1-Z0)/(Z1+Z0) for purely real Zo
or Voltage RC=(Z1-Z0*)/(Z1+Z0)



Even Kurokawa doesn't show us how he gets the conjugate
equation. Email me to get the paper, his notation is confusing.


I have NO problems with the normalized formula,
AS LONG AS Zo IS PURELY REAL.


Nevertheless, even if you do believe the "normal"
equation is correct even with complex Zo, i'd still like
to see your derivation.

And please give us a derivation with VARIABLES ONLY.
The strong temptation to use specific numbers will only
lead us to incorrect conclusions like:

A**B=A+B, because it's true when A and B are equal to 2.



Slick

From 'Fields and Waves in Communications Electronics' by Ramo Whinnery and
Van Duzer. section 1.16 and 1.23

start with positive moving wave plus negative moving wave = total to load
for both voltage and current, simple kirchoff's law summations at the
junction of the coax and load.
Vp+Vn=Vload (1)
Ip-In=Iload (2)
note that their convention is that current moving to the 'right' is positive
so the reflected 'negative' current wave is moving left which gives the
negative sign on the second term.

now use ohm's law to rewrite (2)

Vp/Zo - Vn/Zo = Vload/Zload (3)

then solving from (1) and (3) to get Vn/Vp

multiple (3) by Zload on both sides
Vp*Zload/Zo - Vn*Zload/Zo = Vload
substitute this for Vload in (1) to get:
Vp+Vn = Vp*Zload/Zo - Vn*Zload/Zo
group terms:
Vp-Vp*Zload/Zo = -Vn-Vn*Zload/Zo
factor:
Vp(1-Zload/Zo) = Vn(-1-Zload/Zo)
divide out terms
(1-Zload/Zo)/(-1-Zload/Zo) = Vn/Vp
multiply by Zo/Zo
(Zo-Zload)/(-Zo-Zload) = Vn/Vp
mulitply by -1/-1
(Zload-Zo)/(Zload+Zo) = Vn/Vp

therefo
rho = Vn/Vp = Zload-Zo/Zload+Zo

what could be simpler... apply kirchoff's and ohm's laws and a bit of
algebra.

Anyone interested in seeing the same derivation in perhaps slightly
different order can review my posting of 8-23 in the thread " A
subtle detail of reflection coefficient. . .". It includes a numerical
comparison of results using the derived formula with results using a
couple of alternative formulas. Of course, you can find a similar
derivation in nearly any electromagnetics or transmission line text. If
you do look it up, please note that I made an error (later corrected) in
stating that conjugately matching the line results in maximum power
transfer to the load. The condition for maximum power transfer for a
given source impedance is of course that the load impedance be the
complex conjugate of the impedance seen looking from the load back
toward the source.

Roy Lewallen, W7EL


David Robbins wrote:
From 'Fields and Waves in Communications Electronics' by Ramo Whinnery and
Van Duzer. section 1.16 and 1.23

start with positive moving wave plus negative moving wave = total to load
for both voltage and current, simple kirchoff's law summations at the
junction of the coax and load.
Vp+Vn=Vload (1)
Ip-In=Iload (2)
note that their convention is that current moving to the 'right' is positive
so the reflected 'negative' current wave is moving left which gives the
negative sign on the second term.

now use ohm's law to rewrite (2)

Vp/Zo - Vn/Zo = Vload/Zload (3)

then solving from (1) and (3) to get Vn/Vp

multiple (3) by Zload on both sides
Vp*Zload/Zo - Vn*Zload/Zo = Vload
substitute this for Vload in (1) to get:
Vp+Vn = Vp*Zload/Zo - Vn*Zload/Zo
group terms:
Vp-Vp*Zload/Zo = -Vn-Vn*Zload/Zo
factor:
Vp(1-Zload/Zo) = Vn(-1-Zload/Zo)
divide out terms
(1-Zload/Zo)/(-1-Zload/Zo) = Vn/Vp
multiply by Zo/Zo
(Zo-Zload)/(-Zo-Zload) = Vn/Vp
mulitply by -1/-1
(Zload-Zo)/(Zload+Zo) = Vn/Vp

therefo
rho = Vn/Vp = Zload-Zo/Zload+Zo

what could be simpler... apply kirchoff's and ohm's laws and a bit of
algebra.

"David Robbins" wrote in message ...
From 'Fields and Waves in Communications Electronics' by Ramo Whinnery and
Van Duzer. section 1.16 and 1.23

start with positive moving wave plus negative moving wave = total to load
for both voltage and current, simple kirchoff's law summations at the
junction of the coax and load.
Vp+Vn=Vload (1)
Ip-In=Iload (2)
note that their convention is that current moving to the 'right' is positive
so the reflected 'negative' current wave is moving left which gives the
negative sign on the second term.

now use ohm's law to rewrite (2)

Vp/Zo - Vn/Zo = Vload/Zload (3)



I believe this line (3) is only true if Zo is purely real.

If Zo is complex, i don't think you can apply
this.



then solving from (1) and (3) to get Vn/Vp

multiple (3) by Zload on both sides
Vp*Zload/Zo - Vn*Zload/Zo = Vload
substitute this for Vload in (1) to get:
Vp+Vn = Vp*Zload/Zo - Vn*Zload/Zo
group terms:
Vp-Vp*Zload/Zo = -Vn-Vn*Zload/Zo
factor:
Vp(1-Zload/Zo) = Vn(-1-Zload/Zo)
divide out terms
(1-Zload/Zo)/(-1-Zload/Zo) = Vn/Vp
multiply by Zo/Zo
(Zo-Zload)/(-Zo-Zload) = Vn/Vp
mulitply by -1/-1
(Zload-Zo)/(Zload+Zo) = Vn/Vp

therefo
rho = Vn/Vp = Zload-Zo/Zload+Zo

what could be simpler... apply kirchoff's and ohm's laws and a bit of
algebra.


Nice job David, nobody has done this yet. And done with variables,
as it needs to be done, and not with specific numbers.

I think this is correct for Zo is purely real.

I'd like to see the derivation for the conjugate equation,
which i have seen in Kurokawa, Besser, and the ARRL, among
other sources.


Slick

"Dr. Slick" wrote in message
om...
"David Robbins" wrote in message
...
From 'Fields and Waves in Communications Electronics' by Ramo Whinnery
and
Van Duzer. section 1.16 and 1.23

start with positive moving wave plus negative moving wave = total to
load
for both voltage and current, simple kirchoff's law summations at the
junction of the coax and load.
Vp+Vn=Vload (1)
Ip-In=Iload (2)
note that their convention is that current moving to the 'right' is
positive
so the reflected 'negative' current wave is moving left which gives the
negative sign on the second term.

now use ohm's law to rewrite (2)

Vp/Zo - Vn/Zo = Vload/Zload (3)



I believe this line (3) is only true if Zo is purely real.

If Zo is complex, i don't think you can apply
this.


yes you can. in sinusoidal steady state analysis as discussed in 'Basic
Circuit Theory' by Desoer and Kuh. in chapter 7 and specifically section 5
of that chapter they show the kirchoff current and voltage laws and ohms law
generalized for phasor representations of voltage and current and complex
impedances and admittances. those representations are perfectly valid in
that type of analysis.

In article ,
(Dr. Slick) wrote:

"David Robbins" wrote in message
...
From 'Fields and Waves in Communications Electronics' by Ramo Whinnery and
Van Duzer. section 1.16 and 1.23

start with positive moving wave plus negative moving wave = total to load
for both voltage and current, simple kirchoff's law summations at the
junction of the coax and load.
Vp+Vn=Vload (1)
Ip-In=Iload (2)
note that their convention is that current moving to the 'right' is positive
so the reflected 'negative' current wave is moving left which gives the
negative sign on the second term.

now use ohm's law to rewrite (2)

Vp/Zo - Vn/Zo = Vload/Zload (3)



I believe this line (3) is only true if Zo is purely real.

If Zo is complex, i don't think you can apply
this.

I swore that I wouldn't get into this one, but enough's enough.

Equation (1) is an application of Kirchoff's voltage law.
Equation (2) is an application of Kirchoff's current law.
Equation (3) results from (2) if you apply Ohm's law three times, to the
three terms in Equation (2).

Which of these three principles (Kirchoff's voltage law, Kirchoff's
current law, or Ohm's law) is the one you don't believe? Or do you
disbelieve more than one of the three?

David, ex-W8EZE

--
David or Jo Anne Ryeburn

To send e-mail, remove the letter "z" from this address.

"David or Jo Anne Ryeburn" wrote in message
...
In article ,
(Dr. Slick) wrote:

"David Robbins" wrote in message
...
From 'Fields and Waves in Communications Electronics' by Ramo Whinnery
and
Van Duzer. section 1.16 and 1.23

start with positive moving wave plus negative moving wave = total to
load
for both voltage and current, simple kirchoff's law summations at the
junction of the coax and load.
Vp+Vn=Vload (1)
Ip-In=Iload (2)
note that their convention is that current moving to the 'right' is
positive
so the reflected 'negative' current wave is moving left which gives
the
negative sign on the second term.

now use ohm's law to rewrite (2)

Vp/Zo - Vn/Zo = Vload/Zload (3)



I believe this line (3) is only true if Zo is purely real.

If Zo is complex, i don't think you can apply
this.

I swore that I wouldn't get into this one, but enough's enough.

Equation (1) is an application of Kirchoff's voltage law.
Equation (2) is an application of Kirchoff's current law.
Equation (3) results from (2) if you apply Ohm's law three times, to the
three terms in Equation (2).

Which of these three principles (Kirchoff's voltage law, Kirchoff's
current law, or Ohm's law) is the one you don't believe? Or do you
disbelieve more than one of the three?

now, now, take it easy on him... he didn't say he didn't believe kcl or kvl
or ohm's law... he just doesn't understand that they still do apply to
phasor notation used in sinusoidal steady state analysis. an easy
misunderstanding.

"David Robbins" wrote in message ...


I believe this line (3) is only true if Zo is purely real.

If Zo is complex, i don't think you can apply
this.

I swore that I wouldn't get into this one, but enough's enough.

Equation (1) is an application of Kirchoff's voltage law.
Equation (2) is an application of Kirchoff's current law.
Equation (3) results from (2) if you apply Ohm's law three times, to the
three terms in Equation (2).

Which of these three principles (Kirchoff's voltage law, Kirchoff's
current law, or Ohm's law) is the one you don't believe? Or do you
disbelieve more than one of the three?

now, now, take it easy on him... he didn't say he didn't believe kcl or kvl
or ohm's law... he just doesn't understand that they still do apply to
phasor notation used in sinusoidal steady state analysis. an easy
misunderstanding.


Gee, thanks David. I was wrong! This was a little review for me!
Hehe... owww..

But it still doesn't answer my question.

I don't think Kurokawa and Besser and the ARRL just pulled it
out of thin air.

And how do you explain the rho 1 for a passive network?
Shouldn't be possible. And neither should a negative SWR.

I'm not sure what is wrong with your derivation, but there
must be something that they are missing to not have the conjugate
in the numerator. Or there is a particular step that you cannot do
with complex impedances.

Again, the normal equation is only for purely real Zo, or
when Zo*=Zo. If Zo is complex, you have to use the conjugate
equation.

Could you email a scan of some of the pages? Not that it
would absolutely help me too much, but perhaps you are missing
something.


Slick

William E. Sabin wrote:
4) The determination that rho magnitude in a transmission line can be
greater than 1.0 is correct. In a passively loaded line fed by an
oscillator, where there is no positive feedback from load to oscillator,
there is no problem about a rho magnitude greater than 1.0.

But can |rho|=Sqrt(Pref/Pfwd) ever be greater than 1.0 for a
passive load?
--
73, Cecil http://www.qsl.net/w5dxp



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