camelot wrote:
Hello,
I'm have "little" doubt about s-parameter simulations. My
question is very simple but I do not know if the answer is the same.
The Thevenin theorem can be applied to a s-parameter simulation?
That is, if I do a simulation using a port P1 of 50 ohm where at valley
of the generator I've connected 2 impedences, one in parallel Z1 and
one in series Z2. Supposing I obtained S11 at frequency f1. Then I
incorporate the impedence Z2 (at frequency f1) in the port 1 impedence
(using Thevenin), can I obtain the same S11 parameters for f1 fequency?

From: "Fields and Waves ...", by Ramo and Whinnery:
"It must be emphasized, as in any Thevenin equivalent
circuit, that the equivalent circuit was derived to
to tell what happens in the *load* under different
*load* conditions, and significance cannot be automatically
attached to a calculation of power loss in the internal
impedance of the equivalent circuit."

Power loss in the internal impedance of the Thevenin
equivalent circuit is related to the s-parameters.
|s11|^2 is power reflected from the network input
divided by the power incident on the network input.
--
73, Cecil http://www.w5dxp.com

Thank you for your comments,
I'm doing some calculations and simulations in order to verify if I
can bypass representation problem of s-parameters in other ways rather
than the Thevenin one.
There is one thing I'd like to submit to your attention, the known
formula
S11=(Zin-Z0)/(Zin+Z0),
where Z0 is the port impedance and Zin the load, does not works if you
consider Z0 not pure real (usually 50 ohm) but composed by a real and
an imaginary part i.e. Z0 = a+jb.
Are there other known formulas for S11 for Z0 real+imaginary?

Camelot

"camelot" wrote in message
ups.com...
Thank you for your comments,
I'm doing some calculations and simulations in order to verify if I
can bypass representation problem of s-parameters in other ways rather
than the Thevenin one.
There is one thing I'd like to submit to your attention, the known
formula
S11=(Zin-Z0)/(Zin+Z0),
where Z0 is the port impedance and Zin the load, does not works if you
consider Z0 not pure real (usually 50 ohm) but composed by a real and
an imaginary part i.e. Z0 = a+jb.
Are there other known formulas for S11 for Z0 real+imaginary?

Camelot

http://www.rfcafe.com/references/electrical/s-h-y-z.htm

Also:

http://www.daycounter.com/Calculator...lculator.phtml

Regards,

Frank (VE6CB)

On Jan 29, 2:12 am, "camelot" wrote:
Thank you for your comments,
I'm doing some calculations and simulations in order to verify if I
can bypass representation problem of s-parameters in other ways rather
than the Thevenin one.
There is one thing I'd like to submit to your attention, the known
formula
S11=(Zin-Z0)/(Zin+Z0),
where Z0 is the port impedance and Zin the load, does not works if you
consider Z0 not pure real (usually 50 ohm) but composed by a real and
an imaginary part i.e. Z0 = a+jb.
Are there other known formulas for S11 for Z0 real+imaginary?

Camelot

Frank has already provided you with links to (I presume)
transformations to other linear two-port representations.

But I'm curious. Why do you think that the formula you wrote above
doesn't work when Z0 is complex? In what way do you think it does not
work?

I'm also curious why you would pick a complex reference impedance for
S-parameter work, but that's really a different issue.

Cheers,
Tom

Hi Tom,
well, after few researches on several books, I found that the formula
I provided by me works only for real Z0. The general formula valid in
case Z0 is complex is the follow:

S11=(Zin-Z0*)/(Zin+Z0)

Where Z0* is the conjugate of Z0. Obviously, if Z0 is real, the
conjugate coincide with the real one.
However, thank you for your interest ;-)

Camelot


But I'm curious. Why do you think that the formula you wrote above
doesn't work when Z0 is complex? In what way do you think it does not
work?

I'm also curious why you would pick a complex reference impedance for
S-parameter work, but that's really a different issue.

Cheers,
Tom

On Jan 30, 11:13 pm, "camelot" wrote:
Hi Tom,
well, after few researches on several books, I found that the formula
I provided by me works only for real Z0. The general formula valid in
case Z0 is complex is the follow:

S11=(Zin-Z0*)/(Zin+Z0)

Where Z0* is the conjugate of Z0. Obviously, if Z0 is real, the
conjugate coincide with the real one.
However, thank you for your interest ;-)

Camelot

But I'm curious. Why do you think that the formula you wrote above
doesn't work when Z0 is complex? In what way do you think it does not
work?

I'm also curious why you would pick a complex reference impedance for
S-parameter work, but that's really a different issue.

Cheers,
Tom


I'm not sure where you got it, but the formula with the complex
conjugate is NOT correct! The formula without complex conjugate is
correct, for complex Z and Z0, both.

That the formula using the complex conjugate is incorrect is trivial
to see: consider that a line terminated in a load equal to the line's
characteristic impedance (be it purely resistive, or complex) has no
reflection. That is, if load Z = Z0, there is no reflection. Then if
Z0 is complex and has a non-zero reactive component, your formula
yields S11 which is not zero, for a line which is terminated to have
no reflection. As far as I am concerned, that would be incorrect.
The original formula, without complex conjugate, yields the correct
answer for this case. Can you come up with a case where it is
incorrect?

Cheers,
Tom

Hi Tom,
as far as I am concerned, your observations are rights only if we are
talking about real quantities. If you have a load that is complex then
you obtain perfect matching (there is no reflection) only if Z0 is not
equal to Zin but it is the conjugate of Zin. If you remember, this is
the same condition valid for the maximum power transferring when the
load in complex. Do you agree with these considerations?

Regards,

Camelot



I'm not sure where you got it, but the formula with the complex
conjugate is NOT correct! The formula without complex conjugate is
correct, for complex Z and Z0, both.

That the formula using the complex conjugate is incorrect is trivial
to see: consider that a line terminated in a load equal to the line's
characteristic impedance (be it purely resistive, or complex) has no
reflection. That is, if load Z = Z0, there is no reflection. Then if
Z0 is complex and has a non-zero reactive component, your formula
yields S11 which is not zero, for a line which is terminated to have
no reflection. As far as I am concerned, that would be incorrect.
The original formula, without complex conjugate, yields the correct
answer for this case. Can you come up with a case where it is
incorrect?

Cheers,
Tom- Hide quoted text -

- Show quoted text -

camelot wrote:
If you have a load that is complex then
you obtain perfect matching (there is no reflection) only if Z0 is not
equal to Zin but it is the conjugate of Zin. If you remember, this is
the same condition valid for the maximum power transferring when the
load in complex. Do you agree with these considerations?

Are you saying that an SWR of 1:1 always accompanies
maximum power transfer?
--
73, Cecil http://www.w5dxp.com

On Jan 31, 11:52 pm, "camelot" wrote:
Hi Tom,
as far as I am concerned, your observations are rights only if we are
talking about real quantities. If you have a load that is complex then
you obtain perfect matching (there is no reflection) only if Z0 is not
equal to Zin but it is the conjugate of Zin. If you remember, this is
the same condition valid for the maximum power transferring when the
load in complex. Do you agree with these considerations?

Regards,

Camelot

OK, it is easy to see that a perfect match is NOT the conjugate, but
an impedance equal to the line's Z0. Consider an "infinitely long"
line. You know that the input impedance equals Z0 for all time, and
there can be no reflection. Whatever you send out just keeps going.

Now think about that line as two pieces, connected together. The
first piece is, say, 100 meters long, connected on one end to the
signal generator, and on the other end to the remaining piece of line,
still infinitely long. Now you have connected a load of Z0 (the
infinitely long piece) to a 100 meter section of line with
characteristic impedance Z0, and clearly there are no reflections
where the lines are connected together.

It should be clear that you can just as well replace the infinite
section of line with a load equal to Z0 (NOT equal to the conjugate of
Z0, if Z0 has a reactive part), and there will be no change in the
conditions in the 100 meter section between the Z0 load and the signal
generator.

You can arrive at EXACTLY the same conclusion if you consider the
current and voltage in a "forward" wave (including their phase
relationship) and the current and voltage in a load equal to Z0, and
the current and voltage in a load equal to the complex conjugate of
Z0. You will see that for a line of impedance Z0, only a load equal
to Z0 will have the correct voltage and current at its terminals to
match only a forward wave on the line, and thus allow for zero
reflected wave.

It is a separate, but related, issue to discuss exactly what the
matching should be to get the most power from a generator to a load
through a section of such line. But it should be clear that to have
zero reflection, zero S11, the load must equal Z0 and in general not
Z0* (though of course Z0=Z0* if Z0 is purely resistive).

Cheers,
Tom

In article .com,
"K7ITM" wrote:

On Jan 30, 11:13 pm, "camelot" wrote:
Hi Tom,
well, after few researches on several books, I found that the formula
I provided by me works only for real Z0. The general formula valid in
case Z0 is complex is the follow:

S11=(Zin-Z0*)/(Zin+Z0)


Hello, and I don't know where you obtained that formula but it's
incorrect. S11 in terms of a reflection coefficient is given by your
formula above but without the complex conjugate of Z0. I have seen
reflection coefficients in technical journals defined with a complex
conjugate Z0 as you have shown but that's not consistent with scattering
or transmission line theory (unless Z0 is real). I know it seems
counterintuitve but a source of complex Z0 would be matched (no
voltage/current reflections) to a transmission line having the same
characteristic impedance. This condition does not in general correspond
to the condition of maximum power transfer from source to line.
Conversely a line of complex Z0 impedance connected to a source of complex
Z0* impedance represents maximum power transfer from source to line but we
still have voltage and current "reflections" RELATIVE to Z0. What you
have to keep in mind is that incident (forward) and reflected
voltages/currents only have meaning when they are referenced to an
impedance, say Z0. And to monitor steady-state incident and reflected
waves you need to separate the steady-state voltage (or current) into
these components using a bridge or directional coupler (sampling devices
that are also designed to use Z0 (e.g. 50 + j0 ohms) as a reference).

In most applications what I've said is moot since line impedance is
usually real or very close to real and we are dealing with sources having
real or very close to real impedances. Under these conditions the matched
condition coincides with maximum power transfer.

If you want an in-depth treatment of what I've attempted to summarize I
recommend the chapter on circuit analysis in the "Electronic Designers'
Handbook", ed. E.J. Giacoletto, published by McGraw-Hill. Sincerely,

John Wood (Code 5550) e-mail:
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337