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Brick Resonator

Eigenmode Analysis Examples

 

Hexahedral mesh:

 

Non-Optimized:

Optimized:

Tetrahedral mesh:

 

Non-Optimized:

Optimized:

 

 image\Brick_Resonator.gif

General Description

 

This example demonstrates a simple eigenmode calculation.  The structure is a rectangular box with perfectly conducting walls and vacuum inside. Q-factors are calculated in the postprocessing step.

The structure is used in four examples. Two of them use hexahedral mesh and the other two use tetrahedral mesh. The first and third example demonstrates the use of the optimizer together with the eigenmode solver.

 

Structure Generation

 

The background material is defined as perfectly conducting material, the units are changed to  millimeters, gigahertz and nanoseconds, and the boundary conditions are set to "electric" in order to model perfectly conducting walls. The box resonator is created as a brick shape. Its dimensions are  defined by three parameters (a, b and c), so that its geometry can be changed easily.

 

Solver Setup

 

When the eigenmode solver is started, a specific number of the lowest  resonance frequencies of the structure is calculated.  The relevant settings are defined using the default values, so that ten eigenmodes are considered.

 

Optimizer Setup (only for optimized brick)

 

The parameters considered for the optimization are listed here with its initial, minimum and maximum  values:

 

Parameter Name

Initial Value

Minimum Value

Maximum Value

Description

a

13

11

14

First brick edge

b

17

12

22

Second brick edge

c

20

12

22

Third brick edge

 

Six samples are chosen, since the ranges of the values a, b, and c are rather wide. As optimizer type the Quasi-Newton optimizer with support of interpolation of primary data is chosen.

The fundamental mode's frequency, which is supposed to be 10 GHz, is chosen as the first goal of the optimization. In order to increase the separation between the fundamental mode and the second mode, another optimizer goal is added: The frequency of mode 2 should exceed 14 GHz.

 

Post Processing

 

Non-optimized brick:

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 box (a*b*c) the analytical solution of the problem can be written as

 f_res(m,n,o) = 0.5 * c * sqrt( (m/a)^2 + (n/b)^2 + (o/c)^2 ) (c = speed of light in the observed medium).

 

The default parameter settings (a = 13 mm, b = 17 mm and c = 20 mm) yield the following first three resonance frequencies:

 

1.

11.5724 GHz

2.

13.7522 GHz

3.

14.5155 GHz

 

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 = 8075

2.

Q = 8377

3.

Q = 8886

 

Optimized brick:

After the optimization process has finished, a new set of parameters is available. From the results in the folders 2D/3D Results Mode 1 and 2D/3D Results Mode 2 it can be concluded that the optimization goals have been reached.

 



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