Example42 Wireless Power Transfer Using Electromagnetic Resonance

General

The wireless power transfer using electromagnetic resonance with the open-end coils is analyzed.
The open boundary for low frequency analysis is used to improve the accuracy.
Unless specified in the list below, the default conditions will be applied.

Analysis Space

Item	Setting
Analysis Space	3D
Model Unit	m

Analysis Condition

Since the wavelength of the analysis frequency (25m) is much larger than the size of self-resonant coil (50 square cm), the absorbing boundary used for low frequency analysis is applied as an open boundary type.

Item	Setting
Solver	Electromagnetic analysis [Hertz]
Analysis Type	Harmonic analysis

Tab	Setting Item	Setting
Open Boundary	Type	Absorbing boundary (low frequencies)
Mesh	Frequency-Dependent Meshing	Reference frequency: 12[GHz] Select The conductor bodies thicker than the skin depth constitute the boundary condition
Harmonic Analysis	Sweep Type	Select “Linear step by division number”
	Sweep Setting	Minimum frequency: 11[MHz] Maximum frequency: 13[MHz] Division number: 200
	Frequency Sweep	Select Fast sweep S-parameter tolerance: 1×10-3

Model

The model consists of two open-end coils (Coil1 and Coil 2) and spherical air (Air).

The coils self resonate at around 12MHz. The size of the air domain is 2m in diameter that is much smaller than the wavelength at the self resonant frequency (25m).

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
1, 2/Solid	Coil1	008_Cu (*)
3/Solid	Air	000_Air *
4, 5/Solid	Coil2	008_Cu (*)

* Available from the material DB

Boundary Condition

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Setting
Port1/Face	Electric	Port	Reference impedance: 50Ω Integral path Set Path1
Port2/Face	Electric	Port	Reference impedance: 50Ω Integral path Set Path1
Outer Boundary Condition	Electric	Open boundary

Set up Mesher/Solver

Setting Item

Setting

Frequency-Dependent Meshing

Reference frequency: 12[GHz]

Select The conductor bodies thicker than the skin depth constitute the boundary condition

Results

The open-end coils (Coil1 and Coil2) are designed to self resonate at around 12MHz. From the S-parameters in the diagram below, it can be confirmed that they resonate at around 12MHz.

At around 12MHz, S21 is larger than S11, indicating that the power from Port1 is mostly transferred to Port2.

The efficiency is plotted (orange color) in the graph below with the following equation.

Efficiency = |S21| 2/ (1 – |S11|2)

In the graph, the result (blue color) of the conventional absorbing boundary is compared with the result (black color) of the absorbing boundary set at a sufficient distance of 10m from the wave source.

The wavelength of the analysis frequency is about 25m. The open boundary is located near the port, which is a wave source, at a distance of about 1m.

With the conventional absorbing boundary, the accuracy of the open boundary that is too close to the wave source is low. Consequently, the conventional absorbing boundary (blue) and the open boundary for low frequencies (orange)

show the difference in results.

By comparing with the result (black) where the absorbing boundary is set at a sufficient distance from the wave source, it is clear that the open boundary for low frequencies analysis achieves

highly accurate open boundary even though it is close to the wave source.

See other Electromagnetic Analysis examples.