Mother Nature's reflection coefficient...
 

I believe that "Mother Nature's" voltage reflection coefficient is the well
known classical one, i.e.

rho = (Z - Zo)/(Z + Zo) is "Mother Nature's" reflection coefficient.

I believe this simply because it corresponds to the "image match"!

i.e. rho will be null when Z = Zo [NOT conj(Zo)], and is the condition for
there to be no reflected voltage wave.

Note: this is *NOT* the condition for a "conjugate match" i.e. maximum
power transfer does not result in a null voltage refelection coefficient in
the case of a general complex surge impedance Zo.

As a "thought experiment" to support my contention that

rho = (Z - Zo)/(Z + Zo)

Is "natural", consider the case of an infinitely long transmission line of
surge
impedance [characteristic impedance] Zo, where in general Zo may be complex
and not necessarily a real constant e.g. [Zo is not 50 Ohms resistive or
some other
such simple case.] i.e.

Zo = Zo(p) = sqrt((R + pL)/(G + pC))

Where, R, L, G and C are the primary parameters of the line and p is the
complex
frequency p = s + jw and the value of Zo is complex in general and may vary
with frequency p.

In this thought experiment consider that you are standing in the "center" of
this
infinitely long line of surge impedance Zo and that you cut said line with a
pair of
pliers.

Looking in one direction down the semi-infinite line you see a
driving point impedance equal to the surge impedance Zo of that
semi-infinite
line. Looking in the other direction you will also see a driving point
impedance equal to the surge impedance Zo of a semi-infinite line.

And so...

at the cut you have made, there is an "image match". i.e. at the
cut two equal driving point impedances Zo are facing each
other.

This is a Zo match, or "image match", it is not a conjugate match! In
a conjugate match Zo would be facing conj(Zo).

Now solder the cut back together and then consider a "wave" launched from
one end of this infinite line in one direction. If you have trouble
picturing this
situation just imagine it is Douglas Adams sitting on the patio of the
Restaurant
at the End of the Universe with his handy wave generator who launches the
wave!

Such a wave will move in one direction only on down that Zo line forever and
will never be reflected because there are no discontinuities over that
infinite
distance.

Now as the wave is passing the "cut" that you made in the center of that
infinite
line, quickly insert a reflectometer with internal reference impedance R =
Zo,
the characteristic surge impedance of the line.

This reflectometer will read a rho of:

rho = (Z - Zo)/(Z + Zo)

Where, since one sees Zo in both directions at the cut and so Z = Zo and
rho = 0, as it should of course indicate zero reflected voltage since there
are no
"reflections" on this infinite line with a wave travelling in only one
direction.

This is a very natural situation...

And so I maintain that "Mother Nature" favors the *definition*

rho = (Z - Zo)/(Z + Zo)

or as I like to write it rho = (Z - R)/(Z + R) since I like to use R
representing the
[R]eference impedance i.e. R = Zo because R is the [R]eference impedance
used
inside the reflectometer and whichmay or may not be equal to Zo as
appropriate for the
intended use.

I have no problem whatsoever with this definition of rho not being null
when there is a conjugate match.

In the general case for "Mother Nature's" reflection coefficient rho will
not be
zero when there is maximum power transfer.

In fact there may well be considerable reflected VAR's in that case...
VAR's being Volt Amperes Reactive, i.e. reactive power reflected at the
conjugate match point.

On the other hand, I have no argument with those who choose to define rho
as:

rho = (Z - conj(Zo))/(Z + conj(Zo))

just as long as they are consistent in it's use and the conclusions they
draw from
it. Here they will get a null rho for a conjugate match, and they will not
get a null
rho for an image match.

I can see situations in which such a defintion of rho using conj(Zo) might
be useful,
not necessary mind you, but perhaps more convenient for solving some
problems.

But I still maintain that defining rho in terms of the conjugate of Zo is
"unatural" and
that "Mother Nature" naturally likes the classical...

rho = (Z - Zo)/(Z + Zo)

because that is what she uses herself when she supports the natural
propagation of waves
on transmission lines.

Thoughts, comments?

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

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

But I still maintain that defining rho in terms of the conjugate of Zo is
"unatural" and
that "Mother Nature" naturally likes the classical...

rho = (Z - Zo)/(Z + Zo)

because that is what she uses herself when she supports the natural
propagation of waves
on transmission lines.

Thoughts, comments?

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

Do you ever notice the fleeting look of fear on the faces of
people as they suddenly recognize you as you walk down the street, Peter?
73,
Tom Donaly, KA6RUH

Tom:

[snip]
Do you ever notice the fleeting look of fear on the faces of
people as they suddenly recognize you as you walk down the street, Peter?
73,
Tom Donaly, KA6RUH
[snip]

Yes!!! Finally I'm recognized for what I am...

The Darth Vader of USENET.

Thanks,

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

On Tue, 26 Aug 2003 06:24:17 GMT, "Peter O. Brackett"
wrote:

Yes!!! Finally I'm recognized for what I am...

The Darth Vader of USENET.

Hi Darth,

When you run across your son, please keep it a family secret.

73's
Richard Clark, KB7QHC

Richard:

[snip]
"Richard Clark" wrote in message
...
On Tue, 26 Aug 2003 06:24:17 GMT, "Peter O. Brackett"
wrote:

Yes!!! Finally I'm recognized for what I am...

The Darth Vader of USENET.

Hi Darth,

When you run across your son, please keep it a family secret.

73's
Richard Clark, KB7QHC
[snip]

Actually I have two sons [That I know of?] which one do you refer to, the
"good" one or the "evil" one?

One som lives in Seattle [Tim], the other in San Francisco [Steve]... both
are inactive hams, both think I'm far too old and... irrelevant anyway.
Sigh... My wife gives me no respect, my sons give me no respect, the only
respect I get is from the denziens of this Newsgroup, and even then it's
only when I attempt to "terrorize" the group with tidbits of algebra! :-)

What?

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

My wife gives me no respect, my sons give me no respect, the only
respect I get is from the denziens of this Newsgroup, and even then it's
only when I attempt to "terrorize" the group with tidbits of algebra! :-)

What?

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


Canucks in exile rspect you tremendously. You would get even more respect if
you can proclaim Indialantic new DXCC entity. Does it have to do anything with
Indians, Indiana Jones, in Diana, Atlantis, dial, In Dial Antic or what?

Yuri da BUm in BMV (Buick really) by the see (if he can make it)

On Wed, 27 Aug 2003 21:19:47 GMT, "Peter O. Brackett"
wrote:

Well Indialantic By-the-Sea is a small town [pop ~2500] on the barrier
island about
....

Hi Peter,

And I thought it was there because it wasn't Indipacific or Indigulf.

73's
Richard Clark, KB7QHC

And I thought it was there because it wasn't Indipacific or Indigulf.

73's
Richard Clark, KB7QHC




Must be bacause of them reflected waves? Maybe bunch of dummies on the beach
would calm things down, like 1:1 :-)

Sounds like radio paradise Peter. We almost bought island in Maine, only to
find that there was erosion going on and environazis were oposed to any shoring
up of private property. It was like a dream, at the end of peninsula, separated
by abt 200 ft channel which would emerge at low tide and allow Jeep to get
through. Power and telephone feeding two cottages (low and high band), oh well!
Found another place at Cape Breton, I hope to fire up from there in some
contests, it is a park I believe.

73 Yuri

Yuri:

[snip]
Sounds like radio paradise Peter. We almost bought island in Maine, only
to
find that there was erosion going on and environazis were oposed to any
shoring
up of private property. It was like a dream, at the end of peninsula,
separated
by abt 200 ft channel which would emerge at low tide and allow Jeep to get
through. Power and telephone feeding two cottages (low and high band), oh
well!
Found another place at Cape Breton, I hope to fire up from there in some
contests, it is a park I believe.

73 Yuri
[snip]

We too have a Nova Scotia place [a condo] on the Halifax waterfront but I
don't have
any antennas up there yet either. I hope to have antennas up in both
places, i.e. Indialantic
and Halifax probably later in the New Year.

My current radio hobby project, fitting it in between consulting jobs. I'm
supposed to be fully
retired but find that I am only semi-retired :-). is to outfit my Expedition
with an IC-706 and a
Tarheels screwdriver both of which I bought just after Dayton. But I
haven't even drilled holes
in the Expedition yet.

Procrastination is ruining my hobby!

I've never been HF mobile, wanted to try that.

I was thinking I might like to try some DXpeditioning now that I am supposed
to have the time.

Sigh.

--
Peter K1PO [ex VE1AEX, VE3DZK, VE2POB]
Indialantic By-the-Sea, FL.