Multilayer Substrate model - accuracy in lower frequencies

Georgios Kyriakou

Dear FEKO team,

I would like to ask a question regarding the simulation of an antenna structure in low frequencies. I am simulating a crossed dipole antenna in the frequency range 20MHz - 100MHz, which is purposed for radioastronomy applications. The antenna has a finite ground plane which I simulate as a rectangular surface, and an infinite lower half space of soil. Due to the required accuracy of the application, the soil which is underneath the antenna and which has been measured to have different complex permittivity at different depths, has to be modelled in multiple layers, so I used the option "Infinite multilayer substrate". The problem is that, as I have realized by using one layer and the options "Reflection Coefficient Approximation" and "Exact Sommerfeld Integrals", the latter one is the only accurate method for lower frequencies. When I switched to multilayer substrate and run the model, the solution for zenith Gain was closer to the results of the "Reflection coefficient approximation" for one layer, so I assume that this approach is also used for the multilayer substrate. 

My question is, is there any other way I can achieve the same accuracy as that of the "Exact Sommerfeld Integrals" in the low frequencies, when using a multilayer substrate? I even tried to model the first layers as finite cuboids of dielectric medium solved with FEM (hence a hybrid approach with MoM) but I get an error from the iterative solver BiCGSTAB:

"Maximum number of iterations reached without convergence" with a norm error of the order of O(0.1), whereas the criterion for convergence is O(10^-5)

I would appreciate any advice. Attached is an image of the comparison between "Reflection coefficient approximation" and "Exact Sommerfeld Integrals" where the discrepancy is visible, and an image of the multilayer substrate model which produces similar results as the "Reflection coefficient approximation".

Thanks in advance,

George

 

GGAMPALA

Hi Georgios, the planar multilayer substrate is not the same as reflection coefficient but similar to the homogeneous half space (Sommerfeld Integrals). Both these are using the planar Green's functions.

I don't think you are doing an apples-to-apples comparison with a half-space using reflection coefficient approximaiton and 3 dielectric layers with planar Green's functions. Here you have two additional thin layers on top of an infinitely think bottom layer whereas it's just a uniform half space with reflection coefficient approximaiton. If you remove the two thin layers from the planar multilayer substrate, the results will be similar to the homogeneous half space (Sommerfeld Integrals).

 

Georgios Kyriakou

Gopinath Gampala_21873 said:

Hi Georgios, the planar multilayer substrate is not the same as reflection coefficient but similar to the homogeneous half space (Sommerfeld Integrals). Both these are using the planar Green's functions.

I don't think you are doing an apples-to-apples comparison with a half-space using reflection coefficient approximaiton and 3 dielectric layers with planar Green's functions. Here you have two additional thin layers on top of an infinitely think bottom layer whereas it's just a uniform half space with reflection coefficient approximaiton. If you remove the two thin layers from the planar multilayer substrate, the results will be similar to the homogeneous half space (Sommerfeld Integrals).

 

Hi Gopinath, and thanks for your response.

There is no curve of the multilayer substrate in the attached diagram, I included it in a new one. As far as the comparison is concerned, I would expect that the 2 extra layers do not alter the result significantly since Dielectrics 1&2 do not have values extremely different from the infinite layer of Dielectric 3.

In fact as you can see in the new diagram the reflection coefficient approximation (of 1 layer) has ~1dB offset from the 2 other solutions, but what prompted me to ask is that "multilayer" and "reflection coefficient" have similar slope up to 60MHz. But since the method is the same for multilayer and Sommerfeld Integral, I must conclude that the slope is real and not an inaccuracy of the method of multilayer substrate.