near field to far field transformation (FDTD)

hi.
I have a basic question in FDTD.I know formula and concepts of Huygens surface and I know formulas of near field to far field transformation (NFTFF) and also I can write matlab codes for this purpose.but I have a simple question.
for NFTFF calculations,where I should place Huygens surface?before PML or in edge of PML?because as distance from antenna is increased,field amplitudes and then surface currents is decreased.therefore in antenna pattern calculation,amplitude of pattern is decreased.for example I should to have a far-field pattern in order of (0-10)dB,But I have -150 dB!.how solve this problem?do I should normalize fields on the Huygens surface to excitation source?
thanks...

In theory, any virtual box that enclosing your scattering object (or radiator) will generate the correct far field if you do it correctly. However, in numerical simulations, especially FDTD, you need to have a sense of "numerical". The FDTD calculated field very close the the PEC surface of the object has the worst accuracy due to the grid and central approximation. Thus putting the virtual box too close to the PEC object will decrease your far field accuracy as well. If put virtual box right on the PML it might give you some reflection error, unless your PML works really well. So it is a balance issue of where to choose your virtual box. Different software has different choices. You can research about this and give a good paper.

hi roderwh.how are you?
thanks for your reply in my topic of "near field to far field transformation (FDTD)"
I have another question.
in calculation of frequency domain equivalent surface currents for calculation of N_theta and L_phi at E_theta,do I must devide them to frequency domain excitation source amplitude?becuase in calculation of antenna pattern magnitude,I obtained -150 dB!my source amplitude is 1 VOLT and is a modulated gaussian pulse.but I obtained N_theta in order of 1e-8!
how solve this problem?
I wrote a 3D-FDTD code in matlab.
I calculate J and M currents in Huygens surface as following (for example):
"tmyxp is Mx current in xp plane in time domain" and "tjxzp is Jx current in zp plane in time domain".I calculeted them from E and H fields on the Huygens surface.
tmyxp(1,1,:, = 0.5*(Ez(ui,lj:uj-1,lk:uk-1)+Ez(ui,lj+1:uj,lk:uk-1));
tjxzp(1,:,:,1) = -0.25*(Hy(li:ui-1,lj:uj-1,uk)+Hy(li:ui-1,lj+1:uj,uk) ...
+ Hy (li:ui-1,lj:uj-1,uk-1) + Hy (li:ui-1,lj+1:uj,uk-1));
then I convert above parameters to frequency domain with fourier transform,but my answer is very small in magnitude.
do I must divide them frequency domain parameters to amplitude of frequency domain excitation source?

This is a typical normalization problem, yes you need to divide your far field value at that frequency by your excitation component at that frequency. For example, you have a gaussian pulse, when you FFT it, its spectrum is not even at all frequencies. So in order to be fair, we are always interested to see the pattern when the input is 1 at all frequencies. This is why you need the normalization by divide your frequency domain results with the FFT of your source signal. Hope this is clear.

thanks really.I will do according to your explanation.but there is an ambiguity.
what do you mean from far field data?E_theta and E_phi component or in calculation of fourier transform of equivalent surface currents on Huygens surface (i,e J and M currents)?

Ok, your J & M are transient data, and the far field (E_phi, E_theta) are also transient right? The calculation of E_phi E_theta is a convolution form, which requires all histories of J & M (See Allen's book). So your direct calculation of the far field is a transient solution. You need to FFT it in order to obtain a far field pattern at a particular frequency right?

yes,that is right.I have to FFT at a particular frequency.I found the solution.I get FFT of J and M currents on the Huygens surface and then obtained N_theta and L_phi at frequency domain.next,wrote E_theta relation and divide it to frequency domain excitation source at particular frequency.finally plot my antenna pattern.answer is true now.
thanks rodgerwxh!