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RCS of a sphere as function of frequency

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Introduction
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 :
σ= πr^2
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