Scattering matrix of lossy line

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
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Oliver Friedrich
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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

John Wood (Code 5550) e-mail: snipped-for-privacy@itd.nrl.navy.mil Naval Research Laboratory

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J. B. Wood

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