NEC-LIST: Complex Value of Coupling? Help Needed.

Dear All,

I am analyzing the performance of a 5 x 5 rectangular array using NEC2.
The method used is same as usual - Without any loading on any element,
sequentially excite each element, while reading the feed segment currents
of the other passive elements - to obtain the appropriate admittance
parameters.

The NEC file is:

CM THIS IS COMMENT CARD.
CE
GW 1 9 -0.205480 -1.414480 0.256850 -0.205480 -0.930880 0.256850 0.000100
GW 2 9 -0.102740 -1.414480 0.256850 -0.102740 -0.930880 0.256850 0.000100
GW 3 9 0.000000 -1.414480 0.256850 0.000000 -0.930880 0.256850 0.000100
GW 4 9 0.102740 -1.414480 0.256850 0.102740 -0.930880 0.256850 0.000100
GW 5 9 0.205480 -1.414480 0.256850 0.205480 -0.930880 0.256850 0.000100
GW 6 9 -0.205480 -0.828140 0.256850 -0.205480 -0.344540 0.256850 0.000100
GW 7 9 -0.102740 -0.828140 0.256850 -0.102740 -0.344540 0.256850 0.000100
GW 8 9 0.000000 -0.828140 0.256850 0.000000 -0.344540 0.256850 0.000100
GW 9 9 0.102740 -0.828140 0.256850 0.102740 -0.344540 0.256850 0.000100
GW 10 9 0.205480 -0.828140 0.256850 0.205480 -0.344540 0.256850 0.000100
GW 11 9 -0.205480 -0.241800 0.256850 -0.205480 0.241800 0.256850 0.000100
GW 12 9 -0.102740 -0.241800 0.256850 -0.102740 0.241800 0.256850 0.000100
GW 13 9 0.000000 -0.241800 0.256850 0.000000 0.241800 0.256850 0.000100
GW 14 9 0.102740 -0.241800 0.256850 0.102740 0.241800 0.256850 0.000100
GW 15 9 0.205480 -0.241800 0.256850 0.205480 0.241800 0.256850 0.000100
GW 16 9 -0.205480 0.344540 0.256850 -0.205480 0.828140 0.256850 0.000100
GW 17 9 -0.102740 0.344540 0.256850 -0.102740 0.828140 0.256850 0.000100
GW 18 9 0.000000 0.344540 0.256850 0.000000 0.828140 0.256850 0.000100
GW 19 9 0.102740 0.344540 0.256850 0.102740 0.828140 0.256850 0.000100
GW 20 9 0.205480 0.344540 0.256850 0.205480 0.828140 0.256850 0.000100
GW 21 9 -0.205480 0.930880 0.256850 -0.205480 1.414480 0.256850 0.000100
GW 22 9 -0.102740 0.930880 0.256850 -0.102740 1.414480 0.256850 0.000100
GW 23 9 0.000000 0.930880 0.256850 0.000000 1.414480 0.256850 0.000100
GW 24 9 0.102740 0.930880 0.256850 0.102740 1.414480 0.256850 0.000100
GW 25 9 0.205480 0.930880 0.256850 0.205480 1.414480 0.256850 0.000100
GS 0 0 1
GE 1
GN 0 0 0 0 10 0.005000
FR 0 1 0 0 292 1
EX 0 1 5 00 1.000000 -0.000000
XQ
EX 0 2 5 00 0.886385 -0.462950
XQ
EX 0 3 5 00 0.571355 -0.820703
XQ
EX 0 4 5 00 0.126496 -0.991967
XQ
EX 0 5 5 00 -0.347106 -0.937826
XQ
EX 0 6 5 00 1.000000 -0.000000
XQ
EX 0 7 5 00 0.886385 -0.462950
XQ
EX 0 8 5 00 0.571355 -0.820703
XQ
EX 0 9 5 00 0.126496 -0.991967
XQ
EX 0 10 5 00 -0.347106 -0.937826
XQ
EX 0 11 5 00 1.000000 -0.000000
XQ
EX 0 12 5 00 0.886385 -0.462950
XQ
EX 0 13 5 00 0.571355 -0.820703
XQ
EX 0 14 5 00 0.126496 -0.991967
XQ
EX 0 15 5 00 -0.347106 -0.937826
XQ
EX 0 16 5 00 1.000000 -0.000000
XQ
EX 0 17 5 00 0.886385 -0.462950
XQ
EX 0 18 5 00 0.571355 -0.820703
XQ
EX 0 19 5 00 0.126496 -0.991967
XQ
EX 0 20 5 00 -0.347106 -0.937826
XQ
EX 0 21 5 00 1.000000 -0.000000
XQ
EX 0 22 5 00 0.886385 -0.462950
XQ
EX 0 23 5 00 0.571355 -0.820703
XQ
EX 0 24 5 00 0.126496 -0.991967
XQ
EX 0 25 5 00 -0.347106 -0.937826
XQ
EN

Then I am plugging these Y parameters in the Cmax formula given in NEC
documentation i.e.

Cmax = [1 - sqrt(1-L^2)]/L,

to get maximum coupling between any 2 elements for such a rectangular array.

Now, I am also parametrically varying the separation between adjacent
elements from 0.1*lamda to 1.0*lamda, as also, for a given separation, I
am phasing the array beam from zenith to horizon (0 to 90 degrees) in
steps of 5 degrees. For each of these I have to generate a NEC file.

The above NEC file is when separation between adjacent elements is
0.1*lambda, and the excitations are such that the array, when
simultaneously excited with above mentioned excitations, will look at ~ 50
degrees from zenith. If you run this file, and calculate Cmax, you will
get some values of L > 1. Now, since

Cmax = [1 - sqrt(1-L^2)]/L,

where L = ( |Y12*Y21| ) / ( 2*Re(Y11)*Re(Y22) - Re(Y12*Y21) )

this gives me a complex value for Cmax. Basically, Cmax is a power
transfer ratio between the excited and passive antenna, and as such cannot
be complex.

The question is this:

For some NEC files, the Y parameters that NEC
provides me with, yields a value of "L" which is more than
"1". Is it at all possible for "L" to be greater than "1"? If no, what
does it indicate, I mean, what, if any, is the PHYSICAL SIGNIFICANCE of
"L"?

Kindly share your information about the above.

Thank you in advance.

Nikhil Mehta
Raman Research Institute
Sadashivnagar Bangalore 560 080

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