Re: NEC-LIST: Mutual Coupling Impedance from S parameters

At 04:59 PM 8/18/2004 -0500, Mohammad Amin wrote:
>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

Found my copy of AN95-1 ... The last page gives:
Z11 = ((1+s11)(1-s22)+s12s21)/((1-s11)(1-s22)- s12s21)
Z12 = 2S12 / ((1-s11)(1-s22)-s12s21)

the latter resembles your equation, if s12=s21

Note that these conversions are normalized to Z0! if you're doing your
calculations with a 50 ohm impedance, then you need to scale appropriately
(z12 actual = z12 * Z0).

James Lux, P.E.
Spacecraft Telecommunications Section
Jet Propulsion Laboratory, Mail Stop 161-213
4800 Oak Grove Drive
Pasadena CA 91109
tel: (818)354-2075
fax: (818)393-6875

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