NEC-LIST: antenna isolation and Maximum Coupling calculation

Dear all,

I have a question about the calculation of the isolation between two
antennas and the maximum coupling calculation in NEC2/NEC4.
Consider for example two bowtie antennas, 1.5 m length, positioned 30 m
apart ('side by side'). I want to calculate the isolation between these
two antennas. NEC2/NEC4 can do a maximum coupling calculation. In this
calculation, the antenna impedances are matched by NEC to obtain maximum
coupling. That is not what I want, I want to know the antenna isolation
with the antenna loads as they are, hence no matching. Therefore, I have
calculated the isolation, using the currents calculated by NEC, and as a
check, compared it to results from the Maximum Coupling calculation. I
had expected that the Maximum Coupling calculation would result in a
larger coupling, hence less isolation. To my surprise: the calculations
showed the opposite, the Maximum Coupling being about 5 to 10 dB lower
than the result from my own calculation.

This is how I did the calculation:
I give antenna 1 a 1.0 V voltage source and no load. Antenna 2 has a
load of 50 ohm (no voltage source). The current in the source segement
of antenna 1 gives me Y11, the current in antenna 2 Y21. Next I can do
the same calculation with 1.0 V on antenna 2 (and still the load of 50
ohm), and the voltage source of antenna 1 removed (really removed, not
V1 = 0 V, I know that then NEC does not short-circuit it). From this
calculation, the current in antenna 2 gives me Y22 and the current in
antenna 1 Y12. Now I have the Y matrix and by taking the inverse, the Z
matrix is obtained. The source and victim currents (respectively antenna
1 and antenna 2) are obtained from the first calculation with antenna 1
excited. The transmitted power form the source antenna (antenna 1) is:
Ptr = 1/2 |I1|^2 Re(Z1d)
with Z1d the driving point impedance of antenna 1: Z1d = Z11 - Z21^2/Z22
  (note that when the coupling is small: Z1d =~Z11)
The received power on the victim antenna (antenna 2) is:
Pre = 1/2 |I2|^2 Re(Z22)
And the coupling (or isolation) is: Pre/Ptr (and in dB by taking the
10*log10 of this).

For the maximum coupling calculation, both antennas were unloaded (since
the Maximum Coupling calculation is supposed to determine the
conjugately matched load for optimum coupling).
I did these calculations over a frequency range from 60 to 120 MHz (the
antenna is in resonance at ~100 MHz), segment length 0.3 m (1/10
wavelength at 100 MHz).
The Maximum Coupling was between -41 and -39 dB, the isolation from my
own calculation between -34.5 and -30.5 dB.
I did the same calculation for two 1.5m dipole antennas. For this
configuration, I see that above 80 MHz, my own calculation results in
more coupling than the Maximum Coupling Calculation. (For the range of
60 - 120 MHz, the Maximum Coupling is between -39 and -33.5 dB and the
isolation from my own calculation between -43.5 and -33 dB.)

Could anyone comment on this ?
Is there a mistake in my calculation ?
Is the Maximum Coupling Calculation in NEC correct ?
Or am I misinterpreting the Maximum Coupling calculation ?
I would appreciate your comments.

regards,

Rogier van Aken.

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