Scattering matrix of lossy line

[Oliver Friedrich]

Hallo,

I need the S-parameter model of a lossy line of arbitrary characteristic
impedance ZL which differs from my system impedance Z0=50 described by
the typical line parameters ZL and gamma.

I have found several literature where this is done for the A-parameters
of a lossy line, but never with the S-parameters.

Also I'm wondering why there is lots of transformation tables between the
different kinds of twoport parameters (Z,Y,A,H,...) but the S-Parameters
are missing all the time. What could be the fundamental reason for this?

I have found one citation where there are formulas for transforming S->A.
I have solved this set for S with help of Mathematica, so there shouldn't
be any errors, input has been verified several times. But replacing the
A-parameters and Z0 with their physical units (a simple plausibility
check when doing such things) yields nonsense units for the S-Parameters
(s11=0,s12=0,s21=0.5,s22=0) But the same unit check holds for the
original S->A equations.

So I suspect my book to be wrong, maybe typing errors.

1) Can anyone provide me with a symbolic S-Parameter model of a lossy
line (with R, L, G, C)?

2) Can anyone provide me a verified transformation from A->S which sure
is correct?

Thank you for your help



--
Regards

Oliver Friedrich

My email has no x!

 

[J. B. Wood]

In article <Xns9813853443D89oliverfriedrichtzmde@129.143.4.4>, Oliver
Friedrich <xoliver.friedrich@tzm.dex> wrote:

Hallo,

I need the S-parameter model of a lossy line of arbitrary characteristic
impedance ZL which differs from my system impedance Z0=50 described by
the typical line parameters ZL and gamma.

I have found several literature where this is done for the A-parameters
of a lossy line, but never with the S-parameters.

Also I'm wondering why there is lots of transformation tables between the
different kinds of twoport parameters (Z,Y,A,H,...) but the S-Parameters
are missing all the time. What could be the fundamental reason for this?

Hello, and one reason is that s-parameters are port
termination-dependent. The lossy transmission line can be represented as
a two-port referenced to ZL for s-parameters purposes. Here are the 4
s-parameters from the z-parameters:

s11 = ((z11 - z01)*(z22 + z02) - z12*z21)/delta

s12 = 2*z01*z02/delta

s21 = 2*z02*z21/delta

s22 = ((z11 + z01)*(z22 - z02) - z12*z21)/delta

where, in the case of the transmission line,

delta = (z11 + z01)*(z22 + z02) - z12*z21
z01 = z02 = ZL <-- This is the termination dependence.
z12 = z21

The above formulas and many other parameter conversions are from the
"Electronics Designers' Handbook" by L.J. Giacoletto and published by
McGraw-Hill.

Once you understand s-parameters, the conversions are not that difficult
and can be accomplished via matrix math. Software like Mathcad handles
matrices with complex number coefficients quite readily but you can also
do it with an MS Excel Spreasheet. Hope this helps. Sincerely,

I have found one citation where there are formulas for transforming S->A.
I have solved this set for S with help of Mathematica, so there shouldn't
be any errors, input has been verified several times. But replacing the
A-parameters and Z0 with their physical units (a simple plausibility
check when doing such things) yields nonsense units for the S-Parameters
(s11=0,s12=0,s21=0.5,s22=0) But the same unit check holds for the
original S->A equations.

So I suspect my book to be wrong, maybe typing errors.

1) Can anyone provide me with a symbolic S-Parameter model of a lossy
line (with R, L, G, C)?

2) Can anyone provide me a verified transformation from A->S which sure
is correct?

Thank you for your help

John Wood (Code 5550) e-mail: wood@itd.nrl.navy.mil
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337