NEC-LIST: Mutual Coupling Impedance from S parameters

Hi All,
 
The mutual coupling impedance between two antennas can be calculated by
representing these with an equivalent two port network. With active
impedance of antenna #1(Z1), while terminating antenna #2 with a passive
impedance ( Zp, say 0 or 50 ohms), the mutual coupling impedance can be
found using the formula Z1 = Z11-(Z12)^2/ (Z22+Zp). Here Z11 and
Z22 are self impedance ( For identical antennas, Z11 = Z22).
With two port network analyzer measurements, Z1 can be calculated from
S11, Zp is 50. If Z11, Z22 are known, Z12 can be calculated. (Likewise
admittances can be used)
 
However there is another formula for Z12 which uses directly S
parameters, that is:- Z12 = 2S12/{(1-S11)(1-S22)-(S12)^2}. I,m not
getting the same results from this formula as from the formula given
above.
 
(1) CAN SOMEONE POINT OUT THE DIFFERENCE BETWEEN THE TWO?
(2) GIVE REFERENCE WHERE ONE FORMULA IS DERIVED FROM ANOTHER?
(3) HAS SOMEONE USED SECOND FORMULA FOR MUTUAL IMPEDANCE CALCULATION?
 
Regards
MAM

                
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