received power in dipole antenna ?

i designed a wire dipole antenna in FEKO and simulated it . i found it directivity by using the equation
Directivity = 2/(cosθ1-cosθ2) . θ1,θ2 are the 3db points of elevation plane of the dipole antenna. i got θ1 as 51.6 degree and θ2 as 128.6 degree hence my directivity becomes 1.6129 dbi. i found the aperture of the dipole antenna from the equation Ae = D*λ²/4*pi i got Ae as 0.5134 (my frequency is 74.9481 Mhz ). i constructed two equal dipole antenna in FEKO . i placed two dipole antenna 2 Meter apart . the first dipole is feed by 1 V 50 Ohm voltage source so i calculated the transmitted power by the equation Ptx = V²/R i got it as 0.02 watt. i calculated the received power in the second antenna by the equation Pr =Pt*Gt*Ae/4pi*r² my i got Gt above (i took Gt and Directivity are same) calculation as 1.6129 dbi , r= 2 meter then i got Pr =0.000328 i converted in to db as 10*log(p2/p1) i got S12 as -17 db. but i got S12 in FEKO as -14.28 Db.
is my calculations wrong? if it wrong how can i calculate the received power in the second dipole antenna theoretically ?? why there is more than 2 db difference in calculations ??:shock:

The quoted equation is only valid in far field, 2 m is clearly near field. That's at least one possible explanation for deviation.

For a more exact caluculation of transmission in near field, refer to antenna theory text books, e.g. Balanis.

FvM said:

The quoted equation is only valid in far field, 2 m is clearly near field. That's at least one possible explanation for deviation.

For a more exact caluculation of transmission in near field, refer to antenna theory text books, e.g. Balanis.

Click to expand...

Thank you for your replay. if my distance R in far field then my equations are correct ?

i increased the distance between them by 10 meter. then i got s12 as -31.80 db and i got -26.78 db in feko
there is approximately 6 db difference. is my equations correct??? did i missed anything??