RCS of a sphere as function of frequency
This document presents a RCS simulation of a sphere with CAPITOLE-RCS. The model used is a simple sphere with a radius of 0.2 m. The Monostatic RCS calculation will be computed in one direction and for a frequency sweep from 10 MHz to 8 GHz.
Figure 1 – Sphere mesh model
1 – Geometry model
Use the sphere model described in « Getting Started with CAPITOLE-RCS » example.
The file is sphere200mm.step
2 – Simulation strategy
In this case, the frequency range is very large, from 10 MHz to 8 GHz.
Because CAPITOLE-RCS is based on a frequency domain method, it is not advised to use a single mesh for the whole frequency sweep. Instead, you should create several CAPITOLE-RCS projects for a sub-band of frequency range and using a mesh model suitable for this frequency range. Keep in mind that the mesh size should always λ/10 or less at the higher frequency.
|File name||Frequency Range||# of triangles||Mesh size||Solver||Calculation Time|
|sphere100.h5||10-100 MHz||1380||λ/1026 – λ/102||Full||3s|
|sphere1000.h5||100-1000 MHz||1380||λ/102 – λ/10||Full||29s|
|Sphere2000.h5||1000-2000 MHz||5426||λ/20 – λ/10||MLACA||1min42s|
|Sphere3000.h5||2000-3000 MHz||12194||λ/15 – λ/10||MLACA||4min22s|
|Sphere4000.h5||3000-4000 MHz||21664||λ/13 – λ/10||MLACA||7min6s|
|Sphere5000.h5||4000-5000 MHz||33858||λ/13 – λ/10||MLACA||11Min26s|
|Sphere8000.h5||5000-8000 MHz||136 264||λ/16 – λ/10||MLACA||1h15min18s|
The MLACA solver is the most efficient, because it uses a compression of impedance matrix. But at low frequency, the electric mesh size become smaller and it is impossible to use MLACA solver when mesh size is under λ/100, instead it is possible to use the Full solver.
All simulations were executed on a DELL server PowerEdge R920 with 4 CPUs Intel Xeon E7-8857 v2 3.0 GHz 12 cores, 512Go of memory
All projects file can be opened with POSTPRO3D at the same time. And a single graph can display all results.
Figure 2 – Sphere RCS as function of frequency
There are 3 regions of the RCS of a sphere. It can be observed on this graph.
The Rayleigh region, when λ>10 r
For a 0.2m sphere, it is until 150 MHz
The creeping wave effect occurs when λ=2πr
It corresponds to a frequency of 239 MHz where there is a maximum RCS.
The optical region starts when 2πr/λ>10
For a 0.2m sphere it corresponds to 2.39 GHz
Above this frequency, the RCS of the sphere is independant to the frequency and equal to :
For a 0.2m sphere, σ = -9 dBm²
And between, Rayleigh region and optical region, this is the Mie region.
Figure 3 – Rayleigh, Mie and Optical Region