# Near-field comparison: Voltage source vs Spherical Modes Source

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Dear Moderator,

Consider a half-wavelength strip dipole placed in the origin and oriented along the z-axis with the width along the y-axis.

Case 1: Dipole is excited at the (edge-)port with 2V. SWE coefficients up to order n = 10 are requested and exported in an .sph file.

Case 2: The structure is removed and the .sph file from case 1 is used as a source and placed in the origin. The equivalent 'virtual' dipole source has the same orientation as the meshed dipole with a voltage source from case 1.

Therefore, two problems are equivalent.

For a half-wave dipole, FF boundary is set at 2D^2/lambda = 0.5*lambda.

Consider the field request in a single point with different radii: (r, theta, phi) = (r, 90, 90)

Note that I am always requesting the Near Fields (for radii in both the near-field and the far-field).

For FF radii down to approximately 0.7*lambda, both ways yield the same results. For radii between 0.5*lambda and 0.7*lambda, fields obtained in these two ways start to diverge.

A numerical example:

- > Voltage source: E (0.5*lambda, 90, 90) = - 87.6389 - 86.2589 j.

- > SWE source: E (0.5*lambda, 90, 90) = - 87.2327 - 90.8919 j.

The difference is large, around 3 in magnitude and 2 degrees in phase.

To obtain this value from a set of SWE coefficients, one needs to either expand the field at a particular spherical coordinate using spherical harmonics and Hankel functions, or calculate the far-field first and use the spherical propagation factor exp(-jkr)/r for back-propagation. The former is more accurate for smaller radii. However, even if FEKO used the latter, radii between 0.5*lambda to 0.7*lambda are still in the antenna far-field. Therefore, the calculated fields should be more correct compared to the full-wave voltage source radiated pattern, which I hope we can take as a reference.

Furthermore, I compared the results to my own SWE code:

- > SWE2:  E (0.5*lambda, 90, 90) = - 87.6630 - 86.3141 j, which is much closer to the full-wave result.

So my questions are:

1) Why do the results using voltage source and equivalent spherical modes source differ in the 'closer' far-field region?

2) How does FEKO calculate the back-propagation from the SWE source? If the answer is using the  exp(-jkr)/r term, would it not be more natural to expand the fields using spherical harmonics and Hankel functions (since you already have the coefficients)? If FEKO does use the harmonic expansion, why does it give the incorrect value for the radii at the FF boundary.

The question is important for my research problem so I hope you will be able to answer.

Best regards,

Tomislav Marinovic (KU Leuven, Belgium)

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Dear tmarinovic

From the fact that you are referring to a complex quantity for the near field, I assume you are comparing only a single component. Could you please confirm which component this is (E_r, E_theta or E_phi)? Also, could you confirm the unit of the values you have mentioned? Are these in V/m?

In general, sampling near field calculations too close to a spherical mode source is not recommended.

Kind regards,

Johan H

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Dear Johan,

Thank you for a quick reply!

It is theta-component. Units are V/m since I am using Near Field request in FEKO.

I hope you can now answer to my questions.

BR,

Tomislav

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Dear tmarinovic

With your example I believe you are triggering:

WARNING 40147: Near fields for spherical modes are computed in the cut-off region beta*R < N, reduce spherical wave order N or increase distance R

Note that your OUT file should include details on the value for R for your specific example.

In Feko the spherical mode source is intended as an option to represent an antenna installed on a large platform for efficient simulations of the installed performance of such an antenna. Here the focus is specifically on efficient far field calculations and not on near field sampling relatively close to the antenna.

Details on Feko's implementation for spherical mode sources can be found under the "AS card" section starting on p986 of the Altair Feko User Manual. (UserManual.pdf located in the ..\help\feko\pdf folder of your Altair installation.) Unfortunately we are not able to go into more details regarding Feko's implementation - other than sharing this (publicly available) information.

Kind regards,

Johan H

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