Rho = (Zload-Zo*)/(Zload+Zo), for complex Zo
 

Hello,

Consider a source impedance of Zo=50+j200 and Zl=0-j200.

Since these are both series equivalent impedances, Zo
is like a 50 ohm resistor with a series inductor, and Zl
is like a series capacitor.

At ONE test frequency, the inductive and capacitive
reactances will cancel out (series resonance). When this happens,
is will be equivalent to Zo=50 and Zl=0, which is a short.

If you incorrectly use the "normal" equation for rho (when
Zo is complex), you will get:

Rho = (Zload-Zo)/(Zload+Zo) = (-50-j400)/50
= 403.1 /_ -97 degrees

So some silly people on this NG think that a
short will reflect a voltage 403.1 times the incident voltage,
which is absolutely insane.


Now try the correct "conjugate" equation (for complex
Zo):

Rho = (Zload-Zo*)/(Zload+Zo) = -50/50= -1

Which is exactly what you should get for a short,
a full reflection with a phase shift of 180 degrees, but the ratio
can never be more than one for a passive network.




And consequently, the ratio of the reflected to incident
powers can also never be more than 1 for a passive network:

If you use ratios, it doesn't matter whether you use
peak or RMS voltages.

([Vpeak.incident/Vpeak.reflected])=
([Vrms.incident/Vrms.reflected])=sqrt(Pi/Pr)=[rho]

This is because the sqrt(2) is in the numerator and denominator.
And the 2 (after squaring) is also factored out in the Power RC!

And...the Zo is also factored out for Power RC!

The Zo is not needed for the Power RC, because the
impedance of the source is identical to the load for the
reflected power! Sure, you use the Zo in relation to Zl to
get rho, but once you get rho, you have the power RC.

Hah! the plot thickens a bit....


Slick

On 6 Sep 2003 04:37:43 -0700, (Dr. Slick) wrote:

Hello,

Consider a source impedance of Zo=50+j200 and Zl=0-j200.

Since these are both series equivalent impedances, Zo
is like a 50 ohm resistor with a series inductor, and Zl
is like a series capacitor.

At ONE test frequency, the inductive and capacitive
reactances will cancel out (series resonance). When this happens,
is will be equivalent to Zo=50 and Zl=0, which is a short.

If you incorrectly use the "normal" equation for rho (when
Zo is complex), you will get:

Rho = (Zload-Zo)/(Zload+Zo) = (-50-j400)/50
= 403.1 /_ -97 degrees

So some silly people on this NG think that a
short will reflect a voltage 403.1 times the incident voltage,
which is absolutely insane.


Now try the correct "conjugate" equation (for complex
Zo):

Rho = (Zload-Zo*)/(Zload+Zo) = -50/50= -1

Which is exactly what you should get for a short,
a full reflection with a phase shift of 180 degrees, but the ratio
can never be more than one for a passive network.




And consequently, the ratio of the reflected to incident
powers can also never be more than 1 for a passive network:

If you use ratios, it doesn't matter whether you use
peak or RMS voltages.

([Vpeak.incident/Vpeak.reflected])=
([Vrms.incident/Vrms.reflected])=sqrt(Pi/Pr)=[rho]

This is because the sqrt(2) is in the numerator and denominator.
And the 2 (after squaring) is also factored out in the Power RC!

And...the Zo is also factored out for Power RC!

The Zo is not needed for the Power RC, because the
impedance of the source is identical to the load for the
reflected power! Sure, you use the Zo in relation to Zl to
get rho, but once you get rho, you have the power RC.

Hah! the plot thickens a bit....


Hmm.... so you manually typed off page 13 of some
transmission line school book, so
what was the purpose of your exercise?
Typing skill increase?

Or did I miss something?

w.
--
On the Internet nobody knows that I am a dog.

In article ,
(Dr. Slick) wrote:

Hello,

Consider a source impedance of Zo=50+j200 and Zl=0-j200.
******

(1) A *source* impedance of Z_0 = 50 + 200j is easily arranged. A
*transmission line surge impedance* of Z_0 = 50 + 200j is impossible;
surge impedances of transmission lines must have angles between - Pi/4
radians and + Pi/4 radians.

Since these are both series equivalent impedances, Zo
is like a 50 ohm resistor with a series inductor, and Zl
is like a series capacitor.

At ONE test frequency, the inductive and capacitive
reactances will cancel out (series resonance). When this happens,
is will be equivalent to Zo=50 and Zl=0, which is a short.
**********

(2) Not equivalent in any reasonable sense. 50 and 50 + 200j aren't equal,
nor are - 200j and 0 equal.

If you incorrectly use the "normal" equation for rho (when
Zo is complex), you will get:

Rho = (Zload-Zo)/(Zload+Zo) = (-50-j400)/50
= 403.1 /_ -97 degrees

(3) You forgot the factor of 50 in the denominator. The quantity you are
calculating above is approximately a magnitude of 8.062257748 at an angle
of about - 97.12501636 degrees. Of course this is silly for a value of rho
(but not as silly as 403.1 at an angle of - 97 degrees). However see my
comment (1) above.

So some silly people on this NG think that a
short will reflect a voltage 403.1 times the incident voltage,
which is absolutely insane.

(4) I hope most readers believe the way to calculate rho when Z_L = 0 is
rho = (Z_L - Z_0)/(Z_L + Z_0) = (0 - Z_0)/(0 + Z_0) = - 1.

Hah! the plot thickens a bit....

Yes, it does.

David, ex-W8EZE

--
David or Jo Anne Ryeburn

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

"Dr. Slick" wrote:

Hello,

Consider a source impedance of Zo=50+j200 and Zl=0-j200.

An excellent example.

Since these are both series equivalent impedances, Zo
is like a 50 ohm resistor with a series inductor, and Zl
is like a series capacitor.

At ONE test frequency, the inductive and capacitive
reactances will cancel out (series resonance). When this happens,
is will be equivalent to Zo=50 and Zl=0, which is a short.

If you incorrectly use the "normal" equation for rho (when
Zo is complex), you will get:

Rho = (Zload-Zo)/(Zload+Zo) = (-50-j400)/50
= 403.1 /_ -97 degrees

Corrected arithmetic error - -1-j8 = 8.062/_ -97.125

So some silly people on this NG think that a
short will reflect a voltage 403.1 times the incident voltage,
which is absolutely insane.

Now try the correct "conjugate" equation (for complex
Zo):

Rho = (Zload-Zo*)/(Zload+Zo) = -50/50= -1

Which is exactly what you should get for a short,
a full reflection with a phase shift of 180 degrees, but the ratio
can never be more than one for a passive network.

So for this example using the 'revised' rho Vr = -Vi
so the voltage across the capacitor would be Vi + Vr = 0 .

Let us do some circuit analysis.

As you say above, the equivalent circuit is 3 elements in
series: a 50 ohm resister, a +j200 ohm inductor and -j200
ohm capacitor.

Let us apply 1 volt to this circuit...
Total impedance
50+j200+0-j200 = 50 ohms
Total current (volts/impedance)
1/50 = .02 A
Voltage across resistor
.02 * 50 = 1 V
Voltage across inductor
.02 * (0+j200) = 4/_ 90 Volts
Voltage across capacitor (the load)
.02 * (0-j200) = 4/_ -90

Now for the check...
Vi = 0.5 V
With classic rho
Vr = 0.5 * 8.062/_ -97.125 = 4.031/_ -97.125
Vload = Vi+Vr = 0.5 + 4.031/_ -97.125 = 4/_ -90
The same as computed using circuit theory.

With revised rho
Vr = -.5
Vload = 0.5 -0.5 = 0

Which is more useful?
classic rho which properly predicts the voltage across the load
or
revised rho which just provides some number

I know which one I'd pick.

The thing to remember is that in circuits with inductors it is
very easy to achieve voltages greater than any of the supplies.

....Keith

"Dr. Slick" wrote in message
om...
(Dr. Slick) wrote in message
. com...

Rho = (Zload-Zo)/(Zload+Zo) = (-50-j400)/50
= 403.1 /_ -97 degrees



Oops! that should be Rho = 8.06 /_ -97 degrees.

Forgot to divide by 50.

A multiple of 8 is still insane for a short.


Slick

you really don't understand resonances do you.

and you obviously haven't read and understood the paper that derived the
'power wave reflection coefficient' that you are misapplying to voltage and
current waves.

In article ,
(Dr. Slick) wrote:

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

Hello,

Consider a source impedance of Zo=50+j200 and Zl=0-j200.
******

(1) A *source* impedance of Z_0 = 50 + 200j is easily arranged. A
*transmission line surge impedance* of Z_0 = 50 + 200j is impossible;
surge impedances of transmission lines must have angles between - Pi/4
radians and + Pi/4 radians.


Ok, a source impedance then.

In that case you shouldn't be using a formula intended to apply to the
surge impedance of a transmission line.

I don't fully understand why your last statement needs to be so.

I assume that by "last statement" you mean

"A *transmission line surge impedance* of Z_0 = 50 + 200j is impossible;
surge impedances of transmission lines must have angles between - Pi/4
radians and + Pi/4 radians."

This follows immediately from the formula Z_0 = sqrt((R + jwL)/(G + jwC)),
the facts that none of w, R, L, G, or C are negative, the way angles work
when one divides complex numbers and takes square roots, and the fact that
the real part of Z_0 can't be negative (which decides which of the two
square roots should be used).

Where do you stand David?

I believe that algebra speaks for itself. I believe that whether a model
accurately depicts reality has to be tested by experiment. And I believe
that when many such experiments have been previously carried out, all
confirming the accuracy of the depiction, any claim that the model is
inaccurate and that another one is accurate has to be supported with
extraordinarily strong empirical evidence.

David, ex-W8EZE

--
David or Jo Anne Ryeburn

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

"David Robbins" wrote in message ...
"Dr. Slick" wrote in message
m...
(David or Jo Anne Ryeburn) wrote in message
.. .


ok, i quit... i have shown several times that the calculation of vswr from
rho only applies in ideal lines, you can not use it in lossy lines because
of the simplifications that went into deriving it. if you insist on harping
on this point how can you ever open your eyes to see the rest of the errors
in your calculations.



25' of RG-8 isn't THAT lossy.

Once again, where and when and how did you do a measurement? When
you get a rho greater than 1, the VSWR = (1 + |rho|)/(1 - |rho|) gives
ridiculous
NEGATIVE SWRs. And rho WILL give you the SWR, assuming your
tranmission
isn't extremely lossy. This is why people say that the SWR meter has
to
be at the antenna, instead of at the end of 100' of RG-58.

You are quitting because you can't really answer this question.


Slick

"David Robbins" wrote in message ...

I did read some of Kurokawas paper, and it IS a bit confusing.
Have you figured it out David?

Please tell us how the conjugate equation was derived.

Please explain where the fallacy of my logic lies for you.


Slick

it wasn't derived, it was defined. formula (1) defines the power waves.
formula (11) defines the 'power wave reflection coefficient' in terms of the
two waves in (1). it is then just algebra to rearrange the terms to get the
formula in (12).


Please show us if he correctly defines formula (1) and why. And i'd also
like to see if someone can derive these:

ai= (Vi+Zi*Ii)/(2*sqrt(Re(Zi))
bi= (Vi-conj(Zi)*Ii)/(2*sqrt(Re(Zi))

For what he calls the incident and reflected power waves.

And he does say that this is also the voltage RC when Zi is real and
positive.

And then he does square the MAGNITUDE of this, to get the Power RC.




i have given up on convincing any one on here that this equation can not be
applied to voltage and current waves on lossy lines. unfortunately it will
give the right answers but for the wrong reason on ideal lines. so go read
the paper, understand what he is doing, and realize that it is a different
domain than the 'classical' voltage and current waves that have been used
for many years and work just fine.


You are giving up because you don't understand the paper either.


Slick

"Dr. Slick" wrote in message
om...
"David Robbins" wrote in message
...
"Dr. Slick" wrote in message
m...
(David or Jo Anne Ryeburn) wrote in message
.. .


ok, i quit... i have shown several times that the calculation of vswr
from
rho only applies in ideal lines, you can not use it in lossy lines
because
of the simplifications that went into deriving it. if you insist on
harping
on this point how can you ever open your eyes to see the rest of the
errors
in your calculations.



25' of RG-8 isn't THAT lossy.

Once again, where and when and how did you do a measurement? When
you get a rho greater than 1, the VSWR = (1 + |rho|)/(1 - |rho|) gives
ridiculous
NEGATIVE SWRs. And rho WILL give you the SWR, assuming your
tranmission
isn't extremely lossy. This is why people say that the SWR meter has
to
be at the antenna, instead of at the end of 100' of RG-58.

You are quitting because you can't really answer this question.


Slick
you really are hopeless... that formula for VSWR is not valid when the line
has losses, and you can only get rho 1 when the line has losses.... see the
catch 22????

"David Robbins" wrote in message ...


Please show us if he correctly defines formula (1) and why. And i'd
also
like to see if someone can derive these:

ai= (Vi+Zi*Ii)/(2*sqrt(Re(Zi))
bi= (Vi-conj(Zi)*Ii)/(2*sqrt(Re(Zi))

For what he calls the incident and reflected power waves.

re-read my reply above until you understand it... (1) is GIVEN, it is the
starting point, he DEFINED ai and bi to be those values... the then goes on
for several paragraphs explaining why he thinks those are better waves than
other types of waves.


Well, I certainly didn't expect you to provide the derivation,
but maybe someone else can.

And there is the point that if Zi is real and positive, the
power wave is actually a voltage wave.


Slick

"Dr. Slick" wrote in message
om...
"David Robbins" wrote in message
...


Please show us if he correctly defines formula (1) and why. And
i'd
also
like to see if someone can derive these:

ai= (Vi+Zi*Ii)/(2*sqrt(Re(Zi))
bi= (Vi-conj(Zi)*Ii)/(2*sqrt(Re(Zi))

For what he calls the incident and reflected power waves.

re-read my reply above until you understand it... (1) is GIVEN, it is
the
starting point, he DEFINED ai and bi to be those values... the then goes
on
for several paragraphs explaining why he thinks those are better waves
than
other types of waves.


Well, I certainly didn't expect you to provide the derivation,
but maybe someone else can.

no, no one can derive something that is defined... it is a given. it is the
author's choice to define waves the way he wants, and then to define
whatever he wants to all his reflection coefficient from those waves. that
does not mean it can be generalized to other waves. the waves defined that
result in the normal reflection coefficient happen to be a simple solution
to a second order partial differential equation that results when you
analyze the voltage or current waves in a transmission line.... a different
type of wave, requiring a different reflection coefficient... and never the
twain shall meet!

"Dr. Slick" wrote:

wrote in message ...
The passive network you provided in your first post fulfills this
requirement if you define 'power RC' as |rho|^2.

I disagree that the voltage RC will be greater than 1.

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

It is not nearly that tricky. 'Revised' rho, as you state,
predicts 0 Volts across the capacitor. This will be easy to
measure with any AC voltmeter that can handle your test frequency.

I predict, using circuit theory, that if you excite the
test circuit with a 1 Volt sinusoid at a frequency that
makes the impedances j200 and -j200, that you will measure
4 Volts across the capacitor, not 0. This aligns with the
result expected from 'classic' rho.

....Keith

PS Please consider dispensing with the insults. They do not
further the discussion and are quite unbecoming.

Somebody said -

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

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

No problem !

The fixed standard arm of the rho bridge (instead of a 50-ohms resistor) can
be just a very long length of transmission line of input impedance Zo =
Ro+jXo which, of course, varies with frequency in exactly the required
manner.

Or, as I often did 50 years back, make an artificial lumped-LCR line
simulating network to any required degree of accuracy.
----
Reg

"Dr. Slick" wrote:

wrote in message ...

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

It is not nearly that tricky. 'Revised' rho, as you state,
predicts 0 Volts across the capacitor. This will be easy to
measure with any AC voltmeter that can handle your test frequency.

Perhaps, but i'm interested in the forward and reflected
waves, which you can only get with directional couplers on a line of
the same Z as the Zo, i suspect. So even if you get 0 volts, there
are still fwd and rev waves.

But what if you do not get zero volts. Sort of messes up the
'revised' rho theory a bit, does it not?

I predict, using circuit theory, that if you excite the
test circuit with a 1 Volt sinusoid at a frequency that
makes the impedances j200 and -j200, that you will measure
4 Volts across the capacitor, not 0. This aligns with the
result expected from 'classic' rho.

Go ahead and bench test it, and let us know what you find.

Rummage. Rummage. Rummage.
2.2 uH +/- 10%, 100 pf tolerance unknown, 33 ohms +/- 5%

R = 34 measured
L = 2.2 uH
C = 100 pF
But wait, there will be a scope probe across C, vendor says
15 pF nominal when compenstaed for a 15 pF scope input, but
the scope input is 20 pF. Oh well, use 15 pF anyway. So:
C = 115 pF

f = 10.006 MHz
Zres = 34 + j0
Zind = 0 + j138.3
Zcap = 0 - j138.3

But it is always wise to predict the outcome before the measurements...

So let's use a 1 Volt sinusoid at 10.006 MHz.

From circuit theory:
Ires = 0.02941 + j0 A
Vcap = 4.067 /_ -90 V

From 'classic' rho:
Vi = 0.5 V
rho = (Zl-Z0)/(Zl+Z0)
= ((0 -j138.3)-(34+j138.3))/((0 -j138.3)+(34+j138.3))
= 8.1965/_ -97.0
Vr = Vi * rho
= 0.5 * 8.1965/_ -97.0
= 4.09826/_ -97.0 V
Vcap = Vload = Vi + Vr
= 0.5 + 4.09826/_ -97.0
= 4.067/_ 90.0 V

So I expect the magnitude of the voltage to be 4.067 volts.

But wait, there are a whole bunch of tolerances so that is
unlikely to be the voltage, so what is the expected range?

We are not sure of the capacitor tolerance but it is unlikely
to be better than 10% and the scope probe is unknown, so let's
call it 10%.
The resistor was measured at 34 +/- 1 digit + meter error, so
5% is probably good.

So if the capacitor is 10% high and resistor is 5% low the
error would be 1.1/.95 = 1.16 or about 16%. So if the
result is within 16% of 4.067 it will be consistent with
expectations.

First adjust frequency for resonance
f = 10.14 MHz, tolerably close to the predicted 10.006 MHz.

And the measured voltage across the capacitor is...

Hold on, before revealing the answer....

In the interests of minimizing the wiggle room, perhaps you
would be so kind as to provide your prediction for the voltage
across the capacitor. Using 'revised' rho, in a previous post
I recall you predicted 0 volts. Is this still your expectation?

....Keith

David Robbins wrote:

wrote in message ...
"Dr. Slick" wrote:

wrote in message
...

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

It is not nearly that tricky. 'Revised' rho, as you state,
predicts 0 Volts across the capacitor. This will be easy to
measure with any AC voltmeter that can handle your test frequency.

Perhaps, but i'm interested in the forward and reflected
waves, which you can only get with directional couplers on a line of
the same Z as the Zo, i suspect. So even if you get 0 volts, there
are still fwd and rev waves.

But what if you do not get zero volts. Sort of messes up the
'revised' rho theory a bit, does it not?

the 'revised' rho predicts zero reflect 'power waves' as defined by
kurokawa... it says nothing about voltage or current waves.

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

This could work, I supposed, but this discussion started with an
assertion that 'classic' rho was WRONG because it resulted in
more reflected power than incident. My contention is that
'classic' rho is correct and yields the correct voltages regardless
of the results obtained when |rho|^2 is used to predict powers.

If kurokawa wishes to introduce a new rho to solve these problems
in a different manner, that is fine, but he would have reduced
confusion significantly if he had not called it rho.

....Keith

And that's the whole crux of the problem -- the mistaken assumption that
the "reflected power" can never exceed the "forward power". Once you
accept that erroneous idea as a fact, you're stuck with some very
problematic dilemmas that no amount of fancy pseudo-math and alternate
reflection coefficient equations can extract you from. A very simple
derivation, posted here and never rationally disputed, clearly shows
that the total average power consists of "forward power" (computed from
Vf and If), "reflected power" (computed from Vr and Ir), and another
average power term (from Vf * Ir and Vr * If) whenever Z0 is complex.
The only solid and inflexible rule is that these three always have to
add up to the total average power. Not that the "forward power" always
has to equal or exceed the "reflected power". It's in that false
assumption that the problem lies.

Roy Lewallen, W7EL

wrote:

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

This could work, I supposed, but this discussion started with an
assertion that 'classic' rho was WRONG because it resulted in
more reflected power than incident. My contention is that
'classic' rho is correct and yields the correct voltages regardless
of the results obtained when |rho|^2 is used to predict powers.

If kurokawa wishes to introduce a new rho to solve these problems
in a different manner, that is fine, but he would have reduced
confusion significantly if he had not called it rho.

...Keith

wrote in message ...
David Robbins wrote:

wrote in message
...
"Dr. Slick" wrote:

wrote in message
...

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

It is not nearly that tricky. 'Revised' rho, as you state,
predicts 0 Volts across the capacitor. This will be easy to
measure with any AC voltmeter that can handle your test frequency.

Perhaps, but i'm interested in the forward and reflected
waves, which you can only get with directional couplers on a line of
the same Z as the Zo, i suspect. So even if you get 0 volts, there
are still fwd and rev waves.

But what if you do not get zero volts. Sort of messes up the
'revised' rho theory a bit, does it not?

the 'revised' rho predicts zero reflect 'power waves' as defined by
kurokawa... it says nothing about voltage or current waves.

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

even worse... the 'new' one is based on kurokawa's specific definition of a
'power wave'. this 'power wave' is obviously defined to avoid some of the
discussion we have been having when talking about forward and reflected
powers, but it is not 'power' as discussed in most other places. it is
instead a contrived wave formula specifically chosen to make power
calculations easier as kurokawa states just before defining the forward and
reflected 'power waves' as:

a=(V+ZI)/2sqrt(|ReZ|) and
b=(V+Z*I)/2sqrt(|ReZ|)
(subscripts 'i' left off all terms for readability)

these definitions of course make it harder to calculate the underlying volta
ges and currents, but make it easy to calculate power and power reflections
from a multi port network as you simply define the 'power wave reflection
coeficient' as s=b/a and the 'power reflection coefficient' as |s|^2. note,
at no point does kurokawa use rho. In one point just after defining s (eqn
11) and expanding it by substitution to s=(Zl-Zo*)/(Zl+Zo) (eqn 12) and
further into R,X terms (eqn 13) it is compared to the significance of the
'conventional voltage reflection coefficient', there is no mention that this
should replace the 'conventional' rho, nor that it should give the same
results.

i think the more important thing now is to point out to the arrl the error
of using that form of the reflection coefficient in place of the
'conventional' one in the latest antenna book so it doesn't become gospel in
the future.

Reg:

[snip]
The fixed standard arm of the rho bridge (instead of a 50-ohms resistor)
can
be just a very long length of transmission line of input impedance Zo =
Ro+jXo which, of course, varies with frequency in exactly the required
manner.

Or, as I often did 50 years back, make an artificial lumped-LCR line
simulating network to any required degree of accuracy.
----
Reg
[snip]

Caution... take care, the "reflection police" may get ya!

Roy and Dave took me to task on another thread for even suggesting just such
an
approach. A semi-infinite line!!! Hmph... no way they were gonna let me
get away
with that. Roy wanted to know what "semi-infinite" was!!!

Dave even told me that my idea of having a lumped approximation to Zo was
impossible!
This was a completd surprise to me since over 300,000 units of an xDSL
transceiver I
recently designed for the commercial marketplace and which have all been
shipped
and installed by BellSouth, Verizon, SBC and other such unknowing folks
incorporates
just exactly that kind of circuitre!

Hmmmm... I guess I lucked out and none of those customers noticed I was
balancing \
a lumped approximation of Zo against a real distributed complex Zo!

:-)

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

Chipman, page 138, presents an equation for the power at any point 'z' on a
line that involves Zo and considers the case where Zo = Ro+jXo. He then
derives two equations: one for the real component of the power Pr measured
at any point 'z' on a line and another for the imaginary component of power
Pi at that point. Watts and VARs . . .

Each equation contains three terms. The second equation for Pi and the third
term in both equations vanish when the value of Xo is zero. The condition
that the real part never be negative is shown to be that Xo/R0 is equal to
or less than unity.

He first, however, derives the reflection coefficient for the point 'z'
which is stated as p(z) = (Z(z) - Zo)/(Z(z) + Zo) and Zo is defined to be a
complex number. Some authors have referred to this as "Classical Rho."

Chipman's interpretation of this equation for Pr of three terms is that the
first term represents the real power for the incident wave alone at a point
'z'; the second term relates to the real power in the reflected wave at that
same point; and the third term (which vanishes for real Zo) represents "an
interaction between the reflected and incident waves." This is in effect the
third term that Roy obtained using Vf * Ir and Vr * If.

Thus on a line with real Zo, the net average power in the load is always
given by Pf - Pr. However, with lossy lines having Xo not equal to zero, all
three terms of the equation must be taken into account in determining the
net power at any point along the line. And thus, Pr and Pf alone do not
describe the load power.

He further states that passive terminations exist which can result in
classical rho achieving a value of 2.41 "without there being any implication
that the power level of the reflected wave is greater than that of the
incident wave." The physical example is that of the resonance obtained by
conjugate matching of the Xo-component of the line with the load and the
attendant "resonant rise in voltage.".

The existence of this third term is, I believe, what much of the discussion
has talked around and attempted to avoid confronting by involving all manner
of arcane definitions and interpretations to "prove" that the net power
delivered to a load cannot be other than Pf-Pr and that Pf is always larger
than Pr.

Note that this work is not mine - I am merely reporting the gist of
Chipman's derivations and interpretations due to the scarcity of his book.

This plus Roy's presentation is enough for me . . .

--
73/72, George
Amateur Radio W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13QE
"Starting the 58th year and it just keeps getting better!"






"Roy Lewallen" wrote in message
...
And that's the whole crux of the problem -- the mistaken assumption that
the "reflected power" can never exceed the "forward power". Once you
accept that erroneous idea as a fact, you're stuck with some very
problematic dilemmas that no amount of fancy pseudo-math and alternate
reflection coefficient equations can extract you from. A very simple
derivation, posted here and never rationally disputed, clearly shows
that the total average power consists of "forward power" (computed from
Vf and If), "reflected power" (computed from Vr and Ir), and another
average power term (from Vf * Ir and Vr * If) whenever Z0 is complex.
The only solid and inflexible rule is that these three always have to
add up to the total average power. Not that the "forward power" always
has to equal or exceed the "reflected power". It's in that false
assumption that the problem lies.

Roy Lewallen, W7EL

wrote:

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

This could work, I supposed, but this discussion started with an
assertion that 'classic' rho was WRONG because it resulted in
more reflected power than incident. My contention is that
'classic' rho is correct and yields the correct voltages regardless
of the results obtained when |rho|^2 is used to predict powers.

If kurokawa wishes to introduce a new rho to solve these problems
in a different manner, that is fine, but he would have reduced
confusion significantly if he had not called it rho.

...Keith

| George, W5YR wrote:
| ...
| The condition
| that the real part never be negative
| is shown to be
| that Xo/R0 is equal to
| or less than unity.
| ...

Unfortunately,
I am afraid this is
_not_
the case at all.

Exactly, the related lines have as follows:

"The condition that Pr should never become negative is that
|p(z)|^2 + 2(Xo/Ro) Im p(z) = 1
Expanding p(z) from (7.33) with Zo = Ro + jXo and Z(z) = R(z) + jX(z),
it is easily found that this reduces to the condition |Xo/Ro| =1,
which has already been seen to be true."

Mrs. yin,SV7DMC, who has repeated, checked and solved
all of this book materials, except perhaps a few,
forewarns of that:
Every time Chipman says "easily", probably implies
"as I heard or read or something like that".
How else can someone explains,
why the proof of every such claim by him,
it happens to be a so cumbersome one?

This is true especially this time.

If someone follows the Chipman's hint,
the equivalent condition at which "easily" arrives
is only Z(z) = 0.
[e.g. in the thread
'Complex Z0 - Power : A Proof' - The Missing Step]


After that,
this last condition is unquestionably valid at the terminal load,
when we impose Z(l) = Zt = Rt +jXt, with Rt = 0.

At every other point it is still an unproven, open, problem,
at least to me.

But there is a chance to finish with this matter...

According to Mr. Tarmo Tammaru/WB2TT
in the thread 'Complex line Z0: A numerical example':

"I did a search, and came up with a Robert A Chipman, age 91, in Toledo OH.
From my recollection, the age is about right, and Toledo is where I saw him"


Therefore,
I think it is the most appropriate time,
someone curious enough of you,
who leaves somewhere near by him,
to go and ask him about it.

Is there any volunteer?

Sincerely,

pez
SV7BAX

"David Robbins" wrote in message
...

i think the more important thing now is to point out to the arrl the error
of using that form of the reflection coefficient in place of the
'conventional' one in the latest antenna book so it doesn't become gospel
in
the future.


I have contacted n6bv and he reports they have already changed the 20th
edition of the Antenna Book back to the 'conventional' rho and changed the
power analysis to use the full hyperbolic formlations for voltage or current
to calculate the line loss.

Reflection-cooefficient bridges have been around for the last ONE HUNDRED &
FIFTY YEARS.

They have always incorporated artificial lines, or line simulators, or real
lines in the standard or reference arm of the bridge.

The reflection-coefficient bridge was used to locate faults on the first
oceanic telegraph cables by comparing the faulty cable with an artificial
version maintained at the terminal station specially for the purpose. An
artificial fault was moved along the artificial cable until the bridge was
balanced. The wideband signal generator was a 100-volt wet battery and a
telegraph key. The bridge unbalance indicator was a mirror galvanometer
using a light beam 5 or 6 feet in length and a sensitivity measured in
nano-amps.

The equipment was mounted on a mahogany bench, housed in beautifully
polished mahogany cases. Electrical connections were made by copper bars
between brass screw terminals, all changes in direction of bars were at
90-degrees. All brass and copper surfaces not needed for electrical
connections were brightly polished and coated with a clear laquer. The
overall appearance of the test room was a work of art, produced by a master
of his electrical and mechanical skills, with a quiet pride in the knowledge
that no-one else could possibly better improve operating efficiency of the
station and the cables which radiated from it in various directions under
the
ever-restless waves.

The same arrangement was used to locate oceanic cable faults in the 1970's.
I designed a fault locating test equipment with 10:1 bridge ratio arms which
saved space in the artificial line rack. The artificial line matched the
real
line from 1/10th Hz to 50 Hz. Cables had amplifiers every 20 or 30 miles
which also had to be simulated in the articial line.

For a 100 years or more, new multipair phone and other cable types have been
acceptance tested with reflection-coefficient bridges. One pair in the cable
is exhaustively tested for everything the test engineer can think of to make
sure there's nothing wrong with it. The known good pair is then used as the
standard arm of the bridge and each of the other 1023 pairs in the cable is
compared with it in the other arm of the bridge. It is a very sensitive
method of detecting cable faults. Care must be taken to terminate each pair
with its Zo. If standing waves are present then a dry high-resistance
faulty soldered joint might not be detected if it is located at a current
minimum.

Pulse-echo cable-fault locating test sets use a network to simulate the very
wideband line input impedance Ro + jXo. It is essential to balance-out in a
bridge the high amplitude transmitted pulse which would otherwise paralyse
the echo receiver

And for many years amateurs have unknowingly used reflection-coefficient
bridges immediately at the output of their transmitters. They have been
incorrectly named by get-rich-quick salesmen as SWR, forward and reflected
power meters. These quantities exist only in the users' imaginations and the
meter doesn't actually measure any of them.

A more appropriate name for the instrument is a TLI. (Transmitter Loading
Indicator). A pair of red and green LEDs would suffice to answer the
question " Is the load on the transmitter near enough to 50 ohms resistive
or is it not near to 50 ohms resistive ? "
---
Reg, G4FGQ

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

"Peter O. Brackett" wrote
Reg:
[snip]
The fixed standard arm of the rho bridge (instead of a 50-ohms resistor)
can
be just a very long length of transmission line of input impedance Zo =
Ro+jXo which, of course, varies with frequency in exactly the required
manner.

Or, as I often did 50 years back, make an artificial lumped-LCR line
simulating network to any required degree of accuracy.
----
Reg
[snip]

Caution... take care, the "reflection police" may get ya!

Roy and Dave took me to task on another thread for even suggesting just
such
an
approach. A semi-infinite line!!! Hmph... no way they were gonna let me
get away
with that. Roy wanted to know what "semi-infinite" was!!!

Dave even told me that my idea of having a lumped approximation to Zo was
impossible!
This was a completd surprise to me since over 300,000 units of an xDSL
transceiver I
recently designed for the commercial marketplace and which have all been
shipped
and installed by BellSouth, Verizon, SBC and other such unknowing folks
incorporates
just exactly that kind of circuitre!

Hmmmm... I guess I lucked out and none of those customers noticed I was
balancing \
a lumped approximation of Zo against a real distributed complex Zo!

:-)

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

Reg wrote:
"For 100 years or more, new multipair phone and other cable types have
been acceptance tested with reflection coefficient bridges. One pair in
the cable is exhaustively tested for everything the test engineer can
think of to make sure there`s nothing wrong with it.."

Why bridge test a cable pair that has continuity and accessible
terminals?

I would rather measure the transmission characteristics that I might
use.

The impedance of a 2-wire circuit may be of interest for balancing a
term-set, but that is usually accomplished by adjusting the balance
network by trial and error for the best balance or for most transhybrid
loss. Another option is to accept a compromise fallback network which
gives whatever hybrid balance results, good or bad.

One can locate a line fault by using:
wavelength = V / f

Where multiple repeaters are in a chain, as in Reg`s undersea cables,
each repeater can generate its own unique pilot tone. One can check the
tones to determine where the chain is broken. I`ve done that with
terrestrial microwave systems and recorded the tone interruptions on a
multichannel event recorder with synchronized timing marks. Whenever an
outage occurs, time, location, and duration are charted.

For a rough check on local telephone loops in the swirtched telephone
system here, the phone company had a dial-up tone oscillator in its
central offices. More significantly, other subscribers can be dialed up
to determine the quality of the connections that can be made.

Data circuits often have a loop-back capability in data modems, used to
determine error rate. This is another way to evaluate circuits.

For broadcast program lines, and other leased circuits, the phone
company will treat the line to meet specifications. The customer then
tests his own circuits to make sure he is getting what he pays for.

There are "silent" test systems for multipair cables which test with
tones outside the audible range. These can evaluate attenuation and
cross-talk and these can be related to the similar values in the audible
range.

SWR is a function of reflection strength. I see no problem in labeling a
reflection strength as SWR, even though there may not be enough cable
for a standing wave pattern. I think TLI would be a fine meter name too.

Best regards, Richard Harrison, KB5WZI

I would rather measure the transmission characteristics that I might
use.

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

You've never acceptance tested a 20-mile long phone cable, 542-pairs,
88mH-loaded every 2000 yards.

There are so many things which can go wrong with it you can't believe it.

For example, it is a waste of time measuring line attenuation (loss) on all
542 pairs as a means of detecting a possible imperfection in any one pair.

Very serious defects, sufficient to disrupt normal service, can be entirely
overlooked if attenuation is measured just at one or two frequencies as a
check to see if loss is between specified performance limits. Loss is so
small on transmission lines it is very difficult to measure accurately. It
can get lost in temperature changes especially on overhead lines.

I know - I've done it !

It is obvious the most sensitive of ALL measuring instruments is a bridge
used to compare one value with another, good with bad. The bad sticks out
like a sore thumb even if it is only a teeny bit bad.
---
Reg.

Where multiple repeaters are in a chain, as in Reg`s undersea cables,
each repeater can generate its own unique pilot tone. One can check the
tones to determine where the chain is broken.

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

How does each repeater generate its unique pilot tone when a trawler or
earthquake breaks the inner conductor. Or do you have another way of
powering repeaters at the bottom of mid-atlantic?

Reg, G4FGQ

One can locate a line fault by using:
wavelength = V / f

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

How do you manage at the lower frequencies when velocity is a function of
frequency ?
---
Reg

On Tue, 16 Sep 2003 01:02:49 +0000 (UTC), "Reg Edwards"
wrote:

One can locate a line fault by using:
wavelength = V / f

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

How do you manage at the lower frequencies when velocity is a function of
frequency ?
---
Reg


Inventing new problems? Old wine in new bottles more like it ;-)

The velocity to the nearest geo-synchronous satellite is close enough
to constant that it doesn't matter. One repeating station and it is
quite obvious when it is dead (solves the parking problem for the next
one to replace it too).

GEOS too far away? Use LEOS instead and talk around the dead one
(it's going to fall into the sea/Australia/China/Canada anyway).

And for those still in love with wire are promises from nanotechnology
to tether satellites to earth in the future (power generation for
cheap - life expectancy for the guy that throws the switch is nil
however).

73's
Richard Clark, KB7QHC

On Mon, 15 Sep 2003 22:42:00 -0500, Cecil Moore
wrote:

Chipman never said the reflected power can be greater than the forward power
into a passive load.

Hi Cecil,

You are the only one to just have suggested he did. Others (in total
wide-eyed innocence) may have drawn that faulty conclusion by
inference, but they also have missed the boat on many other issues.

73's
Richard Clark, KB7QHC

I would like to emphasize that
the Uniform Transmission Line Theory valid relation

|Xo/Ro| = 1

is _not_ used
in any step in the proof of

R(l) = Rt = 0.

This is obvious
from the derivation
in the referenced thread.

Sincerely,

pez
SV7BAX

On Tue, 16 Sep 2003 10:06:52 -0500, Cecil Moore
wrote:

Richard Clark wrote:

wrote:
Chipman never said the reflected power can be greater than the forward power
into a passive load.

You are the only one to just have suggested he did.

Because of a death in the family, I entered the discussion late, but
I thought that was what Roy was asserting using his calculations,
that fP - rP was a negative value.

Hi Cecil,

Then you should respond to that posting. The reason for this
suggestion is that you now continue to make speculative assertions
pegged against two names in a discussion where you are admittedly in
the dark.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
Then you should respond to that posting. The reason for this
suggestion is that you now continue to make speculative assertions
pegged against two names in a discussion where you are admittedly in
the dark.

Richard, why are you trying to hold me to a higher standard than to
which you hold yourself?
--
73, Cecil http://www.qsl.net/w5dxp



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On Tue, 16 Sep 2003 12:36:56 -0500, Cecil Moore
wrote:

Richard Clark wrote:
Then you should respond to that posting. The reason for this
suggestion is that you now continue to make speculative assertions
pegged against two names in a discussion where you are admittedly in
the dark.

Richard, why are you trying to hold me to a higher standard than to
which you hold yourself?

Hi Cecil,

So, is your interest in pursuing unrelated matters here, or posting to
the original technical discussion you can only guess at?

When I offered discussion employing Chipman's comments, I posted them
to those who showed interest, to those who showed they were versed
with the author, to those who showed inquiry into his credentials,
to those who showed ignorance to his specific limitations of requiring
the source Z to match the line and a host of other specifics all
offered in direct response unlike you. I can tell you who has a copy
available, who has shown interest in obtaining a copy, who has a copy
in transit from an Australian vendor, and who has asked about the
author as being a former instructor of theirs. And none of these
individuals has yet to respond to simple but necessary observations by
Chipman of the requirement of the Source Z. Do you join that throng?

If these low standards have the bar set to high for you....

73's
Richard Clark, KB7QHC