Re: NEC-LIST: antenna isolation and Maximum Coupling calculation

John B. Wood wrote:
> Hello, Rogier. You're not determining the y (admittance) parameters
> correctly. At a given frequency two closely-coupled antennas can be
> treated as a two-port passive network. The admittance (y) parameters
> are determined as follows:
>
> y11 = i1/v1 with v2 = 0 (antenna #2 feedpoint is short-circuited)
>
> y12 = i1/v2 with v1 = 0 (antenna #1 feedpoint is short-circuited)
>
> y21 = i2/v1 with v2 = 0
>
> y22 = i2/v2 with v1 = 0
>
> Note that for this network y12 = y21. At no time should you be
> terminating either antenna feedpoint with 50 ohms. Following a
> determination of the y parameters, the maximum coupling may be
> calculated as follows:
>
> Max Coupling = [1-Sqrt(1-L^2)]/L
>
> where L = MAG(y12*y21)/[2*Real(y11)*Real(y22) - Real(y21*y21)]
>
> Of course if you change frequency you will have to use NEC to obtain a
> new set of y parameters. Hope this helps. Sincerely,

Thank you for your constructive comments, they have helped me to solve
my problem.

For anyone interested, let me explain:
I have determined the admittance with the method outlined by John Wood.
Note that because of the symmetry in my examples: Y11 = Y22. When I
calculate the maximum coupling with the formula listed above, the result
is the same as the maximum coupling calculated by NEC. So these results
are consistent.

The next step is to determine the currents in both antennas when the
victim antenna (no. 2) is terminated with a load (50 ohm for example).
Then the voltage over the load is:
V2 = -I2*Rload (note the minus sign)
Rload is the load with which antenna 2 is terminated. The currents must
now satisfy:
I1 = Y11*V1 - Y12*Rload*I2
I2 = Y21*V1 - Y22*Rload*I2
(note: Y11, Y12 etc. are still the same as just determined from the
calculation without extra loads).
Solving these equations for I1 and I2 leads to:
I1 = Y11*V1 - (Y12^2*Rload*V1)/(1+Y22*Rload)
I2 = Y21*V1/(1+Y22*Rload)

The transmitted power is:
Ptr = |I1|*|V1|
and the received power is:
Pre = |I2|^2*Rload
The coupling is:
Pre/Ptr = |Y21^2/[(Y11+Y11*Y22*Rload-Y21^2*load)*(1+Y22*load)]|*Rload
(I have used Matlab for the last step in this derivation)

The results from these calculations (with Rload = 50 ohm) are now always
lower than the 'Maximum Coupling', as expected. (for the range 60 - 120
MHz, the difference ranges from 0 to 20 dB)

Best regards,
Rogier van Aken.

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