Solving the scattered field from bodies of various shapes and material properties is a very common problem in electromagnetic theory. The radar cross section (RCS) of spheroids with various material properties and of different axial ratios are investigated in [1] and [2], respectively. Here perfectly electrical conducting (PEC) spheroids of different axial ratios are considered as well as spheres with different material properties.
Figure 1 shows two spheroid FEKO models. The oblate spheroid is formed by sweeping an ellipse around its short axis, and the prolate spheroid by sweeping an ellipse around its long axis. Using the definitions in Figure 1 of lengths a and c, the axial ratio is defined as c/a and oblate spheroids have an axial ratio smaller than 1 while prolate spheroids have an axial ratio larger than 1.
Figure 1: Spheroid FEKO models


(a) Oblate spheroid 
(b) Prolate spheroid 




When computing the bistatic RCS an incident plane wave approaches the object along the zaxis. For all axial ratios the length a is kept at a constant value such that k_{0}a = 3, where k_{0} is the wavenumber in free space. Figure 2 shows the RCS computed for PEC spheroids of different axial ratios.
Figure 2: RCS for PEC spheroids of different axial ratios


(a) Oblate spheroids 
(b) Prolate spheroids 




With the axial ratio held constant at 1.0 (i.e. perfect spheres) the material properties are varied and the RCS shown in Figure 3. Notice that the RCS for each material is normalized to the area πa^{2} for direct comparison as the RCS at different frequencies are also compared in the case of fiberglass. As before a is chosen such that k_{0}a = 3. The material properties used are shown in Table 1.
Figure 3: RCS for spheres with different material properties 


Table 1: Material properties of spheroids 

Material 
Relative permittivity 
Conductivity 

Aluminium 
1.0 
3.538e7 
Fiberglass (1MHz) 
5.3 
1.111e9 
Fiberglass (10MHz) 
5.0 
1.111e9 
References
[1] 
P.P. Lemos, A.N. magoulas, I.K. Hatzilau, "Electromagnetic Scattering
from Real Scatterers: Impact of Material Electrical Characteristics to
the Scattered Field", Hellenic Naval Academy, Greece. 
[2]

P.P. Lemos, A.N. magoulas, I.K. Hatzilau, "Shape Dependence of the
Scattered Electromagnetic Field of Spheroidal Real Scatterers",
Hellenic Naval Academy, Greece. 