General Applicability of the Technique

Source and surface discretization for the MoM.
Surface Equivalence Principle.
Volume Equivalence Principle.
Special Greens function for planar multilayered media.
Dielectrically coated wires.

The MoM is applicable to problems involving currents on metallic and dielectric structures and radiation in free space. The structures are electrically small and are typically made of metals, although special extensions allow the inclusion of dielectrics, either as layered dielectrics or as finite sized shapes.

Technical Foundation

The MoM is a full wave solution of Maxwell's integral equations in the frequency domain. An advantage of the MoM is that it is a "source method" meaning that only the structure in question is discretised, not free space as with "field methods". Boundary conditions do not have to be set and memory requirements scale proportional to the size of the geometry in question and the required solution frequency. The following special extensions have been included in FEKO's MoM formulation to enable the modelling of magnetic and dielectric media.

Surface Equivalence Principle (SEP)

The SEP introduces equivalent electric and magnetic currents on the surface of a closed dielectric body. The surface of such bodies can be arbitrarily shaped and is discretised using triangles.

Volume Equivalence Principle (VEP)

The VEP allows the creation of dielectric bodies from cuboids. More basis functions are typically required than for the SEP, but neighbouring cuboids may have differing electric and magnetic properties.

Planar Green's Functions for Multilayered Media

Multilayered dielectric media may be modelled with Green's functions, e.g. substrates for microstrip. The special Green's function formulation implements 2D infinite planes with finite thickness to handle each layer of the dielectric. Conducting surfaces and wires inside the dielectric layers have to be discretised, but not the dielectric planes themselves. Metallic surfaces and wires can be arbitrarily oriented in the media and are allowed to cross multiple layers. Calculations are sped up with interpolation tables.

Thin Dielectric Sheets

Multiple layers of thin dielectric and anisotropic sheets can be analysed as a single layer in FEKO. Typical applications are the analysis of radome covered antennas and windscreens of automobiles.

Dielectrically Coated Wires

FEKO implements two methods for the modelling of dielectric and magnetic coatings on wires:

• Popovic's formulation modifies the radius of the metallic wire core to change the capacitive loading on the wire, while simultaneously adding a corresponding inductive load. The method is restricted in that the loss factor of the layer has to be identical to the loss factor of the surrounding medium.
• Pure dielectric layers (i.e. relative permeability of the layer equals that of the surrounding medium) should be modelled with the equivalence theorem where the effect of the dielectric layering is accounted for by a volume polarisation current. The only restriction on the method is that the layering may not be magnetic.
  

Real Ground

Real ground can be modelled with the reflection coefficient approximation or the exact Sommerfeld formulation.

Periodic Boundary Condition (PBC)

Infinite periodic structures with periodicity in either one or two dimensions may be modelled with the PBC feature. The structures can consist of metallic surfaces and thin dielectric sheets. The PBC method is based upon the periodic version of the free space Green function and can thus be used together with an infinite perfect electric or magnetic conducting surface, but not together with dielectric layers. A typical application is the analysis of frequency selective surfaces.

Typical Application of the MoM

Typical applications of the MoM include wire antennas, antennas mounted on structures, etc.

Fields in a delta port driven waveguide magic-T