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# Example42Wireless 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.

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