EZ WAY 2 CONVERT S-PARAMETERS TO SERIES EQUIVALENT????
 

Hi,

I'm quite comfortable impedance matching to
large signal series equivalent impedances, when i
get them in data sheets. No problem, even when i
have to extrapolate a bit.

However, sometimes you only get scattering
parameters. So we could use this formula:

Z11=((1+s11)*(1-s22)+s12*s21)/((1-s11)
*(1-s22)-s12*s21)

Etcetera. But i don't wanna do vector
math all the time. And i also don't wanna
graph this gamma on the Smith chart by hand.

So i was wondering if there was a program
out there, that will do this calculation
for you?

Thanks in advance!


Dr. Slick

wrote in message
oups.com...
Etcetera. But i don't wanna do vector
math all the time. And i also don't wanna
graph this gamma on the Smith chart by hand.

So i was wondering if there was a program
out there, that will do this calculation
for you?

Not that I'm aware of, but it'd be trivial to code up in MatLab, MathCAD, or
even Excel if you wanted to...

Heck, even 'Windows Scripting,' which is really Visual BASIC, would work.
In the *NIX word, there's PERL, Rexx, etc...

Hi,

Agilent's (HP) AppCAD may be what you are looking for. The
current version is 3.02, I believe, and it is free.


Cheers - Joe

Joel Kolstad wrote:
wrote in message
oups.com...
Etcetera. But i don't wanna do vector
math all the time. And i also don't wanna
graph this gamma on the Smith chart by hand.

So i was wondering if there was a program
out there, that will do this calculation
for you?

Not that I'm aware of, but it'd be trivial to code up in MatLab,
MathCAD, or
even Excel if you wanted to...

Heck, even 'Windows Scripting,' which is really Visual BASIC, would
work.
In the *NIX word, there's PERL, Rexx, etc...


Well, i've never used Excel for vector algebra.

Could you throw something together on Excel, and send
me the file, so i know what you mean? If you could,
include the bi-linear transformation:

As i understand the Z11 formula
i stated, you will still get a vector
solution, so in essence the Z11 will
be a gamma reflection coefficient, or magnitude
(from 0 to 1) with an angle. So on top of that, you
will need to convert this gamma to
the complex series equivalent impedance,
which you can do graphically on the Smith, or
by using:

Gamma(Z11) = (ZL-Zo) / (ZL+Zo)

And letting Zo=characteristic impedance (assume
real! Usually 50 ohms), and then solving for ZL.


Slick

Z11 is the complex input impedance of a two-port network that has an
open-circuit at the output port. That is, the output current is zero.

v1=Z11* i1 + Z12 * i2
v2=Z21* i1 + Z22 * i2

Z11= v1 / i1 when i2=0
Z22= v2 / i2 when i1=0
Z12= v1 / i2 when i1=0
Z21= v2 / i1 when i2=0

Z11 should be confused with S11, which is the reflection coefficient at the
input port.

S11=[(Z11-1)(Z22+1)-Z12*Z21]
/ [(Z11+1)(Z22+1)-Z12*Z21]

Bill W0IYH

wrote in message
ups.com...

Joel Kolstad wrote:
wrote in message
oups.com...
Etcetera. But i don't wanna do vector
math all the time. And i also don't wanna
graph this gamma on the Smith chart by hand.

So i was wondering if there was a program
out there, that will do this calculation
for you?

Not that I'm aware of, but it'd be trivial to code up in MatLab,
MathCAD, or
even Excel if you wanted to...

Heck, even 'Windows Scripting,' which is really Visual BASIC, would
work.
In the *NIX word, there's PERL, Rexx, etc...


Well, i've never used Excel for vector algebra.

Could you throw something together on Excel, and send
me the file, so i know what you mean? If you could,
include the bi-linear transformation:

As i understand the Z11 formula
i stated, you will still get a vector
solution, so in essence the Z11 will
be a gamma reflection coefficient, or magnitude
(from 0 to 1) with an angle. So on top of that, you
will need to convert this gamma to
the complex series equivalent impedance,
which you can do graphically on the Smith, or
by using:

Gamma(Z11) = (ZL-Zo) / (ZL+Zo)

And letting Zo=characteristic impedance (assume
real! Usually 50 ohms), and then solving for ZL.


Slick

Joe McElvenney wrote:
Hi,

Agilent's (HP) AppCAD may be what you are looking for. The
current version is 3.02, I believe, and it is free.


Cheers - Joe


That's a good program, and there is tons of
stuff there.

But i'm not certain I can get large
signal impedances out of it. I mean,
when they give large signal impedances on
a data sheet, it's usually done by matching
the input and output on the bench, with
cut-and-try techniques, and then removing
the DUT, and using a VNA to measure the
what the transistor "sees" on both sides,
and then taking the conjugate of this, and
calling this the large signal impedance.
Matching to these usually gives you
good results.

How close Z11=((1+s11)*(1-s22)+s12*s21)/((1-s11)
*(1-s22)-s12*s21) will be to the stated large signal
impedances after you convert
it to a series equivalent impedance on the Smith
chart, I don't really know. It won't surpise me
if it doesn't come too close, as the s-parameters
are small signal.



Slick

wrote in message
oups.com...

How close Z11=((1+s11)*(1-s22)+s12*s21)/((1-s11)
*(1-s22)-s12*s21) will be to the stated large signal
impedances after you convert
it to a series equivalent impedance on the Smith
chart, I don't really know.

Note:

In the above formula Z11 should be replaced by
Z11 / Z0. In other words Z11 is "normalized" with respect to Z0 in this
formula. See the Gonzalez reference.

In a "normalized" Smith chart Z0=1.0.

Bill W0IYH

Well, i've never used Excel for vector algebra.

It's certainly nowhere near as clean as, e.g., Matlab or MathCAD, but it can
certainly do it. Look up the 'COMPLEX' function; it'll tell you you need to
install the 'Analysis ToolPak add-in' and under 'see also' point you to the
functions you'll need (e.g., IMSUM for complex arithmetic, etc.)

As i understand the Z11 formula
i stated, you will still get a vector
solution, so in essence the Z11 will
be a gamma reflection coefficient, or magnitude
(from 0 to 1) with an angle.

Right, or... just a regular old complex number. You can use IMABS and
IMARGUMENT to obtain the maginutde and angle of your complex number.

---Joel

William E. Sabin wrote:
wrote in message
oups.com...

How close Z11=((1+s11)*(1-s22)+s12*s21)/((1-s11)
*(1-s22)-s12*s21) will be to the stated large signal
impedances after you convert
it to a series equivalent impedance on the Smith
chart, I don't really know.

Note:

In the above formula Z11 should be replaced by
Z11 / Z0. In other words Z11 is "normalized" with respect to Z0 in
this
formula. See the Gonzalez reference.

In a "normalized" Smith chart Z0=1.0.

Bill W0IYH


You're correct according to Pozar.

I'm gonna assume that this was just a
typo on Gottlieb's part (pg.131, Practical
RF power Design Tech.), and what he really
meant to type was lowercase "z11", to show
it was normalized. (I have a feeling Gottlieb
just copied this out of another book, just like
i copied it from him! heheh...)

But you bring up a good point:
I might be barking up the wrong tree here if
Z11 or z11 is defined as the input impedance
when port 2 is open circuited.
This shouldn't be the same as the large
signal input impedance, when the output is
approximately conjugately matched.



Slick

Note:

In the above formula Z11 should be replaced by
Z11 / Z0. In other words Z11 is "normalized" with respect to Z0 in
this
formula. See the Gonzalez reference.

In a "normalized" Smith chart Z0=1.0.

Bill W0IYH

If the output is terminated with a 50 ohm pure resistance load then S11 is
the complex input reflection coefficient, 0 to 1.0. In an active circuit
(amplifier or oscillator) S11 can be outside these limits due to positive
internal DUT feedback.

Bill W0IYH