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.

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

Thank you for your help