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#112
August 26th 03, 08:27 PM
 Jim Kelley Posts: n/a

W5DXP wrote:

Jim Kelley wrote:

W5DXP wrote:
I don't think there's anything to argue about. From _Optics_, by Hecht:
"We define the reflectance R to be the ratio of the reflected power to
the incident power."

He certainly wasn't including Max Born and Emil Wolf when he said "We".
They define reflectance in terms of indices of refraction i.e.
(n1-n2)/(n1+n2).

The Reflectance is equal to the square of the amplitude reflection
coefficient.
R = Ir/Ii = [(n1-n2)/(n1+n2)]^2

Again, Born and Wolf disagree with Hecht. They define Reflectivity as
being the square of the reflection coefficient.

Hecht says the definition "leads to" the last term above.

Certainly he didn't feel that some relative amounts of power are what
determine the indices of refraction of the system. That would be
ridiculous.

73, ac6xg
#113
August 26th 03, 11:35 PM
 David Robbins Posts: n/a

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

...

Incorrect. You need the conjugate in the numerator if the Zo is
complex. If it is purely real, WHICH MOST TEXTS ASSUME, then you can
use the normal equation.

sorry, the derivation for the table in the book i sent before is for the
general case of a complex Zo. they then go on to simplify for an ideal

line
and for a nearly ideal line... nowhere does a conjugate show up.

sorry, i don't have time for this. its really quite simple, just apply
kirchoff's and ohm's laws at the connection point and it falls right out.

When they say "ideal line" do they mean purely real?

yes, purely real with no loss terms.

and that reference you give is not for a load on a transmission line, it

is
different animal.

Not at all really. The impedance seen by the load can be from
either a source or a source hooked up with a transmission line. It
doesn't matter with this equation.

the reference you gave is looking at a generator connected to a load. true,
it doesn't matter if there is a transmission line in between the generator
and the 'load' but the impedance being used is the one transformed back to
the generator end of the line, not the one at the far end of the line... so
basically that equation is not a transmission line equation, it is a
generator to load reflection calculation done to maximize power not to
satisfy kirchoff.

#114
August 27th 03, 12:40 AM
 Richard Clark Posts: n/a

On Tue, 26 Aug 2003 22:35:29 -0000, "David Robbins"
wrote:
the reference you gave is looking at a generator connected to a load. true,
it doesn't matter if there is a transmission line in between the generator
and the 'load' but the impedance being used is the one transformed back to
the generator end of the line, not the one at the far end of the line... so
basically that equation is not a transmission line equation, it is a
generator to load reflection calculation done to maximize power not to
satisfy kirchoff.

Hi David,

If it is time invariant (linear), it doesn't matter.

73's
Richard Clark, KB7QHC
#115
August 27th 03, 12:51 AM
 Tom Bruhns Posts: n/a

Richard Clark wrote in message . ..

The scenario begins:

"A 50-Ohm line is terminated with a load of 200+j0 ohms.
The normal attenuation of the line is 2.00 decibels.
What is the loss of the line?"

Having stated no more, the implication is that the source is matched
to the line (source Z = 50+j0 Ohms). This is a half step towards the
full blown implementation such that those who are comfortable to this
point (and is in fact common experience) will observe their answer and

"A = 1.27 + 2.00 = 3.27dB"

Interesting. I'd first have asked if the line was really 50 ohms,
completely nonreactive. If so, L/C=R/G and I'd have said A=3.266dB.
If the line was just 50 ohms nominal, then I can think of at least one
scenario in which A=0.60dB. And I can think of another in which A=
5.2dB. The definition I have used for loss in those cases is
A=-10*log10(P1/P2), where P2 is the power delivered to the (line+load)
excitation. The answer, given that definition, never depends on
source impedance of the driving source. Of course it could with a
different definition, for example involving the maximum available
power from the source, but that just confuses the issue by lumping
"(source) mismatch loss" with acutal line loss, as has been pointed
out before.

Cheers,
Tom

#116
August 27th 03, 01:15 AM
 Peter O. Brackett Posts: n/a

Roy:

[snip]
"Roy Lewallen" wrote in message
...
In transmission line analysis, we're not free to rescale the forward and
reverse voltage waves, unless we also scale all the voltages, currents
and powers accordingly. The forward and reverse waves have to add to the
total voltage in the line and at its ends, and the ratio of each
component to the corresponding current component has to equal the Z0 of
the line.

[snip]

I agree, that's why I say the definition of rho with Zo and not the
conjugate is
actually Mother Natures definition. Simply because that's the way the
solution
to the wave equation [The Telegraphists Equation] turns out.

[snip]
It's quite apparent that in S parameter analysis you're quite
free to scale them as you wish, as you have. Vendelin et al didn't just
scale them, but chose a set of V+ and V- which aren't even related to a
and b by the same constant.

[snip]

Actually you are free!

Just define the waves a and b as any linear combination of i and v and as
long as the linear combination is non-singular you will be just fine! You
can Engineer systems to your hearts content and get all the right answers.
[It's sort of like the assumption of current flow in conductors from + to -,
even though we "know" electrons flow the other way, it always
gives us the correct Engineering answers, so who cares!]

[snip]
basic principles. And from it or other methods, we can conclude that
when a transmission line is terminated in its characteristic impedance,
there is no reflection of the voltage (or current) wave. When it's
terminated in the complex conjugate of its characteristic impedance, or
any other impedance except its characteristic impedance, there is a
reflection.

Roy Lewallen, W7EL

[snip]

Roy my friend we are in violent agreement!

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

#117
August 27th 03, 01:23 AM
 Peter O. Brackett Posts: n/a

Cecil:

[snip]
The scaling is defined by the s-parameter specification. Nobody is
free "to scale them as you wish". For instance, a1 is defined as:

(V1+I1*Z0)/2*Sqrt(Z0)
--
73, Cecil http://www.qsl.net/w5dxp

[snip]

I like that definition best of all in a theoretical setting... but be
prepared...
there are many others to be found in the literature.

Even though I like the definition you have shown above, I find the
definitions...

a = v + Zo*i and b = v - Zo*i

To be very convenient in practice since they correspond to a very easy to
understand, visualize and manipulate single Operational Amplifier
reflectometer
circuit.

As long as the relationship between v and i and a and b are simple linear
combinations
without singularities, i.e. the transformation matrix M which allows you to
transform between
the [a, b] vectors and the [i, v] vectors is non-singular then you are just
fine, as long as
you remain consistent with your initial definition. You can perform
reliable and accurate
Engineering with any definition of the "waves" [a, b] that are a suitable
linear combination of the
"electricals" [i, v].

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

#118
August 27th 03, 01:27 AM
 Peter O. Brackett Posts: n/a

Richard:

[snip]
I know you eschew academic references in favor of "first principles,"
but others may want more material than the simple puzzle aspect.
They can consult "Transmission Lines & Networks," Walter C. Johnson,
Chapter 13, "Insertion Loss and Reflection Factors." But lest those
who go there for the answer, I will state it is from another
reference, Johnson simply is offered as yet another reference to
balance the commonly unstated inference of SWR mechanics being
conducted with a Z matched source. "Transmission Lines," Robert
Chipman is another (and not the source of the puzzle either).

73's
Richard Clark, KB7QHC

[snip]

I hear you...

I don't eschew academic references, but when it comes to systems
Engineering, I do try to follow what our great President Regan once said,
"Trust, but Verify!"

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

#119
August 27th 03, 01:33 AM
 Peter O. Brackett Posts: n/a

Roy:

[snip]
You didn't show differently in your analysis, and no one has stepped
forward with a contrary proof, derivation from known principles, or
numerical example that shows otherwise.

Roy Lewallen, W7EL

[snip]

Yes I did. I guess that you missed that post.

I'll paste a little bit of that posting here below so that you can see it
again.

[begin paste]
We are discussing *very* fine points here, but...

[snip]
ratio of the reflected to incident voltage as rho = b/a would yeild the
usual formula:

rho = b/a = (Z - R)i/(Z + R)i = (Z - R)/(Z+ R).

In which no conjugates appear!

Now if we take the internal/reference impedance R to be complex as R = r +
jx then for a "conjugate match" the unknown Z would be the conjugate of the
internal/reference impedance and so that would be:

Z = r - jx

Thus the total driving point impedance faced by the incident voltage a would
be 2r:

R + Z = r + jx + r - jx = 2r

and the current i through Z would be i = a/2r with the voltage v across Z
being v = a/2.

Now the reflected voltage under this conjugate match would not be zero,
rather it would be:

b = (Z - R)i = ((r - jx) - (r + jx))i = (r - r -jx -jx)i = -2jxi = -2jxa/2r
= -jax/r

and the reflection coefficient value under this conjugate match would be
simply:

b/a = rho = - jx/r

Thus I conclude that, under the classical definitions, when one has a
"conjugate match" [i.e. maximum power transfer] the reflected voltage and
the reflection coefficient are not zero.
:
:
In summary:

Under the classical definition of rho = (Z - R)/(Z + R) rho will be not be
zero for a "conjugate match" and in fact there will be a "residual"
reflected voltage of -jx/r times the incident voltage at a conjugate match.
The only time the classical definition of rho and the reflected voltage is
null is for an "image match" when the load equals the reference impedance.
:
:
Unless one changes ones definition of the reflected voltage/reflection
coefficient to utilize the conjugate of the internal impedance as the
"reference" impedance then the reflected voltage is not zero at a conjugate
match. End of story.
[snip]

Regards,

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

#120
August 27th 03, 01:42 AM
 W5DXP Posts: n/a

Jim Kelley wrote:
Again, Born and Wolf disagree with Hecht. They define Reflectivity as
being the square of the reflection coefficient.

From the IEEE dictionary: "reflectivity - The reflectance of the surface
of a material so thick that the reflectance does not change with increasing
thickness" Looks like Born and Wolf are wrong.
--
73, Cecil http://www.qsl.net/w5dxp

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