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Sphere Resonator

Eigenmode Analysis Examples

Hexahedral mesh:

Tetrahedral mesh:

$image\Sphere_Resonator.gif$

General Description

This example demonstrates a simple eigenmode calculation. The structure is a vacuum sphere surrounded by perfectly conducting material. Q-factors are calculated in the postprocessing step.

Structure Generation

The background material is defined as perfectly conducting material, the units are changed to centimeters, gigahertz and nanoseconds, and the boundary conditions are set to "electric".

The cylindrical resonator is created by adding a solid sphere to the vacuum layer. Its dimensions are defined by a single parameter (radius "r"), so that its geometry can be changed easily.

Mesh Setting

Both the number of lines per wavelength and the lower mesh limit are increased to 20 for the hexahedral mesh. Curved element order property for the tetrahedral mesh is set to 2.

Solver Setup

The number of modes is changed in order to consider only three eigenmodes. When the eigenmode solver is started, the three lowest resonance frequencies of the structure are calculated. Please note that the first three modes are identical except for polarization.

Post Processing

The resulting mode information is listed in the navigation tree in the folder 2D/3D Results, subfolder Modes. Here the mode patterns as well as the corresponding eigenfrequencies can be found. The resonance frequencies are also stored in the logfile of the eigenmode solver. Depending on the radius "r" of the sphere the analytical solution of the first three eigenfrequencies can be written as

f_res = 0.4367 * c / r

(c = speed of light in the observed medium)

The default parameter settings (r = 10 cm) yields the following first resonance frequency: 1.3092 GHz

The quality factor is calculated using Post Processing: 2D/3D Field Post Processing Loss and Q . For a conductivity of 5.8*10^7 S/m, the analytical value for mode one is given by Q = 36850.

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