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Cylinder Resonator

Eigenmode Analysis Examples

Hexahedral mesh:

Tetrahedral mesh:

$image\Cylinder_Resonator.gif$

General Description

This example demonstrates a simple eigenmode calculation. The structure is a cylinder with perfectly conducting walls and vacuum inside. 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 and megahertz, and the boundary conditions are set to "electric" in order to model perfectly conducting walls.

The cylindrical resonator is created by adding a solid cylinder to the vacuum layer. Its dimensions are defined by two parameters (length "l", and radius "r"), so that its geometry can be changed easily.

Mesh settings

Both the number of lines per wavelength and the lower mesh limit are increased to 15 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 mode 1 and mode 2 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 dimensions of the cylinder the analytical solution of the first two eigenfrequencies can be written as

f_res(TE_111) = 0.5 * c * sqrt((1/L)^2 + 0.344 * (1/r)^2)

f_res(TM_010) = 0.3828 * c / r

(c = speed of light in the observed medium)

The default parameter settings (l = 40 cm and r = 15 cm) yield the following first three resonance frequencies:

1.	695.686 MHz
2.	695.686 MHz
3.	765.090 MHz

The quality factors are calculated using 'Results/Loss and Q calculation'. For a conductivity of 5.8*10^7 S/m, the analytical values for mode one to three are given by

1.	Q = 40579
2.	Q = 40579
3.	Q = 42390

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