As of the Feko 2023.1 release, the characteristic mode analysis (CMA) method is now able to support impedance boundary conditions and skin effect approximations. The skin effect approximation constitutes an efficient way to simulate thin material layers and shielding walls, while avoiding the full geometric modelling of each layer, provided that the thickness of the layer is sufficiently small. CMA is a computational tool used to uncover the inherent tendencies of a structure to radiate, store or dissipate energy by decomposing the system matrix into a set of eigenmodes also called characteristic modes. In other words, CMA offers a valuable physical insight over the EM phenomena of the device. It would be suitable to remind that the characteristic eigenvalue can be interpreted in terms of reactive-radiated and dissipated-radiated power ratios as:

For instance, it is common practice to use copper or other highly conducting materials to manufacture the metallic parts of an RF device or create imperfect conducting shields. The typical plating copper thickness is usually less than 0.01 mm and practically orders of magnitude lower than the effective wavelength. Thus, the full geometrical modelling of the copper layer using SEP would be highly inefficient and possibly inaccurate in an EM simulation. To this end, the impedance boundary conditions, or skin effects can save the day by avoiding the geometric modelling of such thin material layers, while maintaining a reasonable accuracy for a successful simulation.

To demonstrate the usefulness of the new feature, we load the “*A.4 Monopole Antenna on a Finite Ground Plane*” model from the example guide in CADFEKO and add a characteristic mode configuration requesting for 15 characteristic modes. We copy the current and far field requests from the standard configuration into the characteristic mode configuration. At first, we use the model with perfect electric conductors as it is by default. In this case there are no dissipation effects, and the imaginary parts of the eigenvalues are zero. Next, we replace the perfect electric conductor with copper from the Feko material library. In this case, it should be noted that the structure of the grounded monopole is now presenting some power dissipation, and the imaginary parts of the eigenvalues are now non-zero. We can observe that modes 6 and 11 showcase the highest magnitudes of modal weighting coefficients and these two modes are also able to approximately recreate the current and field distributions of the standard configuration as can be seen in the results below.

*click on the image to enlarge*

Lastly, we use a cylindrical dielectric resonator antenna (CDRA) as our next example. The metallic faces of the substrate (ground plane and feedline) are made of copper (metallic medium) which is imported from the Feko material library. The copper thickness is set to ts = 0.035 mm. The constitutive parameters of the substrate material are ϵr,s = 2.22, tan δs = 0.002. The substrate height is hs = 0.8 mm and the radius is rs = 10.5 mm. The constitutive parameters of the resonator material are ϵr = 42 and tan δ = 0.0015. The height of the resonator is h = 4.6 mm and its radius is α = 3.8 mm. The slot dimensions are ls = 5 mm and ws = 0.8 mm. This structure contains the lossy dielectric materials of the resonator and the substrate as well as the lossy conductor of the ground plane and feedline. Namely, there are multiple reasons for the existence of power dissipation effects. The CDRA is lit by an incident plane wave from the z-direction with a polarisation aligned with the feeding slot. In this example, we try to uncover the radiation characteristics of the HEM11δ hybrid mode that resonates at 5 GHz. The eigenvalue real and imaginary parts are shown in log scale. The modal weighting coefficient and the monostatic RCS are both spiking at 5 GHz, where HEM11δ resonates.

*click on the image to enlarge*

Moreover, we observe the weighted summation of the equivalent magnetic current densities of modes 2 and 6 at 5 GHz. The resulting equivalent magnetic current is approximating the induced equivalent magnetic current of the standard configuration. For clarity, the conducting faces of the structure are filtered out.

*click on the image to enlarge*

All the examples are attached in the "*CMA_article_for_2023.1_material.zip*" file.