Home / Examples / Electromagnetic Analysis [Hertz] / Example 13: Corrugated Waveguide

Example 13: Corrugated Waveguide

General

The dispersion curve of a corrugated waveguide are solved. The model has uniform structure in the depth direction.
The periodic boundary condition is applied in the 3D resonant analysis.
Unless specified in the list below, the default conditions will be applied.

Results will vary depending on Femtet version and the PC environment.

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

Analysis Conditions

Item	Settings
Solver	Electromagnetic Analysis [Hertz]
Analysis Type	Resonant Analysis

Mesh tab, Harmonic analysis tab and Open boundary tab are set as follows.

Tab	Setting Item	Settings
Mesh Tab	Element Type	2nd-order Element
Resonant Analysis	Number of Modes	5
	Approximated Frequency	0 [Hz]
	Input Power	1.0 [W]

Model

The ambient air is defined with a solid body. No boundary condition is set on the faces normal to Z axis.

The waveguide has a periodic structure. Cut out one unit to set the periodic boundary condition [PERIOD1] and [PERIOD2] to its cross sections.

The other faces are set with Electric wall PEC.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
4/Solid	AIR	000_Air(*)

* Available from the material DB

Boundary Conditions

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
MW/Face	Electric	Magnetic Wall	N/A
PERIOD1/Face	Symmetry/Continuity	Periodic	N/A
PERIOD2/Face	Symmetry/Continuity	Periodic	N/A
Outer Boundary Condition	Electric	Electric Wall	N/A

Boundary Pair

Boundary Condition Name/Topology	Boundary Condition Name/Topology	Boundary Condition Type	Settings
PERIOD1/Face	PERIOD2/Face	Translational	1 ≤ θ ≤ 359

Results

The phase difference of periodic boundary is varied in the range of 1 ≤ θ ≤ 359. The resonant frequencies are plotted for each angle.

The electric field at θ＝180.

This is the lowest - frequency resonant mode.

[Reference]

[1] Yu Zbu and Andreas Cangellaris, "Multigrid Finite Element Methods for Electromagnetic Field Modeling", The IEEE Press Series on Electromagnetic Wave Theory, pp. 396-397.