Home / Examples / Electromagnetic Analysis [Hertz] / Example 46: Skin Depth

Example 46: Skin Depth

General

It is confirmed that the skin depth calculated by Femtet matches the theoretical values.
Unless specified in the lists below, the default conditions will be applied.
Obtain this session's project file. (Right-click and choose 'Save link as')
Theoretically, skin depth is given by the following equation. The conditions of the example will yield a skin depth of 2 um using the theoretical equation.
(Conditions: frequency = 1 GHz; conductivity = 6.289e7 S/m; relative permeability = 1)
(1)

Analysis Condition

Item	Settings
Solver	Electromagnetic Analysis [Hertz]
Analysis Space	3D
Analysis Type	Harmonic Analysis
Unit	mm

Set the harmonic analysis and mesh tabs as follows.

Tab	Setting Item	Settings
Harmonic Analysis	Frequency	1×109 [Hz]
	Sweep Type	Single Frequency
	Frequency Sweep	Discrete Sweep
	Input	1.0 [W]
Mesh	General Mesh Size	1.0
	Adaptive Mesh	Deselect [Apply adaptive meshing].
	Frequency-Dependent Meshing	Deselect [The conductor bodies thicker than the skin depth constitute the boundary condition].

To accurately calculate the attenuation of electromagnetic waves in a conductor, set the mesh size to half the skin depth.
Deselect [Apply adapting meshing] since the electromagnetic field distribution is known in advance.
Deselect [The conductor bodies thicker than the skin depth constitute the boundary condition], since with this option selected, you will not be able to observe electromagnetic fields entering the conductor.

Model

The waveguide of parallel plates is modeled to propagate plane waves. When a plane wave is incident on a conductor, most of the wave is reflected from the conductor, but a small amount is incident.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	air	000_Air *
1/Sheet	conductor	003_Ag *

* Available from the material DB

Boundary Conditions

Boundary Condition Name/Topology

Tab

Boundary Condition Type

Settings

PORT/Face

Electric

Port

Reference Impedance: Select
[Use the characteristic impedance calculated from the port structure]

Number of Modes:

Number of Precalculated Modes: 5

Number of Modes Used in the Actual 3D Analysis: 1

Select Modes: None

Outer Boundary Condition

Electric

Magnetic Wall

Results

How to check skin depth is shown below.

Fig. 1 illustrates the electric field vectors of the result fields, indicating a slight penetration of electric fields into the conductor.

Fig. 1 Electric Field Vectors (Phase 0)

The contour of the absolute Z-component of an electric field is shown and its graph is illustrated below (Fig. 2).

The left figure of Fig. 2 shows the setting for the graph. The starting and ending points of the graph are positioned at the positions on the right figure of Fig. 2.

The starting and ending points are positioned at the surface of the conductor and away from the surface, respectively. The graph, therefore, indicates the variation in the strength of the electric field inside the conductor.

The number of divisions is set to 1000. As skin depth is determined from the graph, the precision of the obtained skin depth depends on the number of divisions of the graph.

Fig2. Graph Setting

Fig. 3 indicates the graph depicted with the setting of Fig. 2, with markers added. Place a marker on the surface of the conductor and read the value.

The value of 163.296 V/m is given. The skin depth is the depth at which the magnitude of electric fields reduces to 1/e times. The position where the magnitude of electric fields is 60.0073 (=163.296/e) indicates the point at the skin depth.

The graph indicates the position is 2 um from the surface.

The calculation result matches the theoretical value.

Fig.3 Calculation Result with Markers

Notes for Analysis

Determining a mesh size is important. In this example, where the skin depth is known, the mesh size can be set to half of the skin depth. If not, an optimal mesh size must be found.
Determining the analysis model size is also important. As explained above, the mesh size is determined based on the skin depth. If the model size is much larger than the skin depth, the calculation will require much more time for analysis.
In this example, cubic shapes of air and conductors are used for the models. However, an elongated model in the direction of electromagnetic wave propagation also allows for sufficient evaluation of the skin depth, resulting in a lower calculation load.
By setting Magnetic Wall to the exterior boundary condition, a plane wave can be excited.