(Tom Bruhns) wrote in message om...
So, when are you going to start using your own head and not depending
on others? When will you go through the simple set of equations to
find that Vr/Vf = (Zload-Zo)/(Zload+Zo), and there IS NO conjugate on
the Zo in the numerator? I went through all that long ago (several
years) when someone questioned it, and I trust my calcs. It happens
that they agree with those of many, many others.


Who agrees with you? Les Besser is an established authority, as is
the ARRL, and Pozar... i use their examples because I am not yet an
authority myself. Please do some more research before you type.
Hey, we are all standing on the shoulders of giants!

I certainly wouldn't want to stand on YOUR shoulders, though...



Which of the following do you not believe? Because if you believe it
all, then it's a couple VERY SIMPLE algebraic steps to get to the
equation for Vr/Vf.
1. On a TEM line, Vf/If = -Vr/Ir = Zo, which may be reactive.
2. On a TEM line, V=Vf+Vr and I=If+Ir.
3. Where a TEM line connects to a load, the equations in (1) and (2)
hold, and V=Zload*I -- because the net line voltage is the same as the
voltage across the load, and the net line current is the same as the
load current.

Please do us a favor and go do the algebra, and if you get what Besser
teaches, show us the steps, and we'll resolve the difference from what
we get. If you get what we get, then go take it up with Besser.

Cheers,
Tom


I've checked my results with MIMP, and the reflection coefficients
matched the equation:

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

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

Where * indicates conjugate."


A bit angry aren't we? Typical of one who has absolutely lost an
argument...

When you can show us your free energy device, we would love to see
it!


Slick


"Your Rage Has Imbalanced You!" - Lancelot

(Dr. Slick) wrote in message . com...
....
A bit angry aren't we? Typical of one who has absolutely lost an
argument...

Angry? Perhaps you are (the other part of the "we"), but I'm not.
Disappointed in you that you are unwilling to think for yourself and
go through the simple calculations. Understand what Ian wrote: there
IS no argument!

Cheers,
Tom

A big deal is being made of the general assumption that Z0 is real.

As anyone who has studied transmission lines in any depth knows, Z0 is,
in general, complex. It's given simply as

Z0 = Sqrt((R + jwL)/(G + jwC))

where R, L, G, and C are series resistance, inductance, shunt
conductance, and capacitance per unit length respectively, and w is the
radian frequency, omega = 2*pi*f. This formula can be found in virtually
any text on transmission lines, and a glance at the formula shows that
Z0 is, in general, complex.

It turns out that R is a function of frequency because of changing skin
depth, but it increases only as the square root of frequency. jwL, the
inductive reactance per unit length, however, increases in direct
proportion to frequency. So as frequency gets higher, jwL gets larger
more rapidly. For typical transmission lines at HF and above, jwL R,
so R + jwL ~ jwL. G represents the loss in the dielectric, and again for
typical cables, it's a negligibly small amount up to at least the upper
UHF range. Furthermore, G, initially very small, tends to increase in
direct proportion to frequency for good dielectrics like the ones used
for transmission line insulation. So the ratio of jwC to G stays fairly
constant, is remains very large, at just about all frequencies. The
approximation that jwC G is therefore valid, so G + jwC ~ jwC.

Putting the simplified approximations into the complete formula, we get

Z0 ~ Sqrt(jwL/jwC) = Sqrt(L/C)

This is a familiar formula for transmission line characteristic
impedance, and results in a purely real Z0. But it's very important to
realize and not forget that it's an approximation. For ordinary
applications at HF and above, it's adequately accurate.

Having a purely real Z0 simplifies a lot of the math involving
transmission lines. To give just a couple of examples, you'll find that
the net power flowing in a transmission line is equal to the "forward
power" minus the "reverse power" only if you assume a real Z0.
Otherwise, there are Vf*Ir and Vr*If terms that have to be included in
the equation. Another is that the same load that gives mininum
reflection also absorbs the most power; this is true only if Z0 is
assumed purely real. So it's common for authors to derive this
approximation early in the book or transmission line section of the
book, then use it for further calculations. Many, of course, do not, so
in those texts you can find the full consequences of the complex nature
of Z0. One very ready reference that gives full equations is _Reference
Data for Radio Engineers_, but many good texts do a full analysis.

Quite a number of the things we "know" about transmission lines are
actually true only if the assumption is made that Z0 is purely real;
that is, they're only approximately true, and only at HF and above with
decent cable. Among them are the three I've already mentioned, the
simplified formula for Z0, the relationship between power components,
and the optimum load impedance. Yet another is that the magnitude of the
reflection coefficient is always = 1. As people mainly concerned with
RF issues, we have the luxury of being able to use the simplifying
approximation without usually introducing significant errors. But
whenever we deal with formulas or situations that have to apply outside
this range, we have to remember that it's just an approximation and
apply the full analysis instead.

Tom, Ian, Bill, and most of the others posting on this thread of course
know all this very well. We have to know it in order to do our jobs
effectively, and all of us have studied and understood the derivation
and basis for Z0 calculation. But I hope it'll be of value to some of
the readers who might be misled by statements that "authorities" claim
that Z0 is purely real.

Roy Lewallen, W7EL

One more thing. I've never seen that conjugate formula for voltage
reflection coefficient and can't imagine how it might have been derived.
I've got a pretty good collection of texts, and none of them show such a
thing. If anyone has a reference that shows that formula and its
derivation from fundamental principles, I'd love to see it, and discover
how the author managed to get from the same fundamental principles as
everyone else but ended up with a different formula.

Roy Lewallen, W7EL

Roy:

[snip]
"Roy Lewallen" wrote in message
...
One more thing. I've never seen that conjugate formula for voltage
reflection coefficient and can't imagine how it might have been derived.
I've got a pretty good collection of texts, and none of them show such a
thing.
[snip]

You are absolutely correct Roy, that formula given by "Slick" is just plain
WRONG!

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

Always has been, always will be.

Where does that "Slick" guy get his information? And where does "Slick" get
off with all of his "potifications"??? I dunno... *He* thinks "Besser",
"Pozar" and
ARRL are authoritative sources for transmission line technology!!!

Me?

I have made a living as a professional Engineer designing transmission
equipment over
the past four decades, currently more than $4BB gross shipped to world wide
markets,
where the Zo I used is neither real, nor a constant!

And what is more... I have never consulted any of those three authorities
referenced by
"Slick". I certainly don't think of them as being authoritative, "cream
skimmers"
perhaps, but not certainly not authoritative.

I believe that "Slick" has gotta stop "pontificating" and start reading in
better circles...
much better!

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

"Peter O. Brackett" wrote in message nk.net...
Roy:

[snip]
"Roy Lewallen" wrote in message
...
One more thing. I've never seen that conjugate formula for voltage
reflection coefficient and can't imagine how it might have been derived.
I've got a pretty good collection of texts, and none of them show such a
thing.
[snip]

You are absolutely correct Roy, that formula given by "Slick" is just plain
WRONG!

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

Always has been, always will be.



As long as they are all purely real. Roy disagrees even when he
is wrong, because too many people read this NG, and it might make him
look bad (i.e., Not the All-Knowing Guru he pretends to be).




Where does that "Slick" guy get his information? And where does "Slick" get
off with all of his "potifications"??? I dunno... *He* thinks "Besser",
"Pozar" and
ARRL are authoritative sources for transmission line technology!!!



Bwa! HAah! Much, much, MUCH more than you will ever be!


Me?

I have made a living as a professional Engineer designing transmission
equipment over
the past four decades, currently more than $4BB gross shipped to world wide
markets,
where the Zo I used is neither real, nor a constant!


I feel sorry for your customers...



And what is more... I have never consulted any of those three authorities
referenced by
"Slick". I certainly don't think of them as being authoritative, "cream
skimmers"
perhaps, but not certainly not authoritative.


Dr. Besser kicks your ass backwards when it comes to RF knowledge.

And the ARRL is extremely well known. Pozar not so much, but the
guy is out there on the PhD level. I don't give a Sh** who you think
is an authority.

Look them up, they have way more credentials than either you or I.


I believe that "Slick" has gotta stop "pontificating" and start reading in
better circles...
much better!


Much better than the likes of you, then yes, you would certainly
be correct!

The conjugate formula is correct. If you believe in cancellation
of reactance. Why else would the magnitude rho (numerator of
Reflection Coefficient) be zero when Zload=Zo*???


Slick

Slick:

[snip]
[snip]

You are absolutely correct Roy, that formula given by "Slick" is just
plain
WRONG!

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

Always has been, always will be.
[snip]

After consideration, I must agree with Slick.

Slick is RIGHT and I was WRONG!

Slick please accept my apologies!!! I was wrong, and I admit it!

Indeed, the correct formula for the voltage reflection coefficient "rho"
when computed using a "reference impedance" R, which is say the, perhaps
complex, internal impedance R = r + jx of a generator/source which is loaded
by a perhaps complex load impedance Z = ro + j xo must indeed be:

rho = (Z - conj(R))/(Z + conj(R)) = (Z - r + jx)/(Z + r - jx)

For indeed as Slick pointed out elsewhere in this thread, how else will the
reflected voltage equal zero when the load is a conjugate match to the
generator.

Slick thanks for directing the attention of this "subtlety" to the
newsgroup, and again...

Slick, please accept my apologies, I was too quick to criticize!

Good work, and lots of patience... :-)

Regards,

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

Roy Lewallen wrote:
A big deal is being made of the general assumption that Z0 is real.

As anyone who has studied transmission lines in any depth knows, Z0 is,
in general, complex. It's given simply as

Z0 = Sqrt((R + jwL)/(G + jwC))

where R, L, G, and C are series resistance, inductance, shunt
conductance, and capacitance per unit length respectively, and w is the
radian frequency, omega = 2*pi*f. This formula can be found in virtually
any text on transmission lines, and a glance at the formula shows that
Z0 is, in general, complex.

A good approximation to Z0 is:

Z0 = R0 sqrt(1-ja/b)

where Ro = sqrt(L/C)
a is matched loss in nepers per meter.
b is propagation constant in radians per meter.

The complex value of Z0 gives improved accuracy in
calculations of input impedance and losses of
coax lines. With Mathcad the complex value is
easily calculated and applied to the various
complex hyperbolic formulas.

Reference: QEX, August 1996

Bill W0IYH

William E. Sabin wrote:

Roy Lewallen wrote:

A big deal is being made of the general assumption that Z0 is real.

As anyone who has studied transmission lines in any depth knows, Z0
is, in general, complex. It's given simply as

Z0 = Sqrt((R + jwL)/(G + jwC))

where R, L, G, and C are series resistance, inductance, shunt
conductance, and capacitance per unit length respectively, and w is
the radian frequency, omega = 2*pi*f. This formula can be found in
virtually any text on transmission lines, and a glance at the formula
shows that Z0 is, in general, complex.


A good approximation to Z0 is:

Z0 = R0 sqrt(1-ja/b)

where Ro = sqrt(L/C)
a is matched loss in nepers per meter.
b is propagation constant in radians per meter.

The complex value of Z0 gives improved accuracy in calculations of
input impedance and losses of coax lines. With Mathcad the complex value
is easily calculated and applied to the various complex hyperbolic
formulas.

Reference: QEX, August 1996

Bill W0IYH


The usage of complex conjugate Z0* becomes
significant when calculating very large values of
VSWR, according to some authors. But for these
very large values of standing waves, the concept
of VSWR is a useless numbers game anyway. For
values of VSWR less that 10:1 the complex Z0 is
plenty good enough for good quality coax.

W.C. Johnson points out on page 150 that the concept:

Pload = Pforward - Preflected

is strictly correct only when Z0 is pure
resistance. But the calculations of real power
into the coax and real power into the load are
valid and the difference between the two is the
real power loss in the coax. For these
calculations the complex value Z0 for moderately
lossy coax is useful and adequate.

The preoccupation with VSWR values is unfortunate
and excruciatingly exact answers involve more
nitpicking than is sensible.

Bill W0IYH

"William E. Sabin" sabinw@mwci-news wrote in message ...
....

The usage of complex conjugate Z0* becomes
significant when calculating very large values of
VSWR, according to some authors. But for these
very large values of standing waves, the concept
of VSWR is a useless numbers game anyway. For
values of VSWR less that 10:1 the complex Z0 is
plenty good enough for good quality coax.

My working definition for SWR is (1+|rho|)/|(1-|rho|)|. (Note the
overall absolute value in the denominator, so it never goes negative.)
Rho, of course, is Vr/Vf = (Zload-Zo)/(Zload+Zo), no conjugates. In
that way, when |rho|=1, that is, when |Vr|=|Vf|, SWR becomes infinite.
When |rho|1, SWR comes back down, and corresponds _exactly_ to the
Vmax/Vmin you would observe _IF_ you could propagate that Vr and Vf
without loss to actually establish standing waves you could measure.
I agree with Bill that all this is academic, but my working definition
seems to me to be consistent with the _concept_ of SWR, and does not
require me to be changing horses in mid-stream and remembering when to
use a conjugate and when not to. I _NEVER_ use Zo* in finding rho.
To me it's not so much a matter of nitpicking an area of no real
practical importance as coming up with a firm definition I don't have
to second-guess. Except on r.r.a.a., I don't seem to ever get into
discussions about such things, but my definitions are easy to state up
front so anyone I'm talking with can understand where I'm coming from
on them.


W.C. Johnson points out on page 150 that the concept:

Pload = Pforward - Preflected

is strictly correct only when Z0 is pure
resistance. But the calculations of real power
into the coax and real power into the load are
valid and the difference between the two is the
real power loss in the coax. For these
calculations the complex value Z0 for moderately
lossy coax is useful and adequate.

The preoccupation with VSWR values is unfortunate
and excruciatingly exact answers involve more
nitpicking than is sensible.

Agreed! And thanks for the reference re powers.

Cheers,
Tom