# Analysis and simulation of relevant parameters for optimal wireless power transfer

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## Abstract

An important challenge in the wireless power transfer is the sizing of the coils for transmission and energy reception. The output power in a wireless power transfer system can be determined by analytical formulation; however, the effects of using some geometry or material for the transmitter and receiver coil assembly are not easily quantifiable by the analytical method. This work quantifies by numerical simulation the impact on output power changing the separation between the transmitter coil and receiver, materials, geometries and number of turns. The quantities obtained allowed to determine a model for coupling coefficient to compute optimal frequency for the power transfer. The analysis and evaluation of these parameters were developed through an electromagnetic simulator with finite element; the work considers planar circular and square coils. Experimental results were obtained in order to validate the proposed model to compute the wireless power transferred. The document contributes to identify the important parameters to be controlled or modified in the coils with the purpose to optimize the power transmission for a wireless system.

## Keywords

Coils Coupling factor Finite element method Magnetic energy Wireless power transfer## List of symbols

## Abbreviations

- AC
Alternating current

- AWG
American wire gauge

- FEM
Finite element method

- WPT
Wireless power transfer

## Symbols

*B*Magnetic field density (T)

- \(C_\mathrm{p}\), \(C_\mathrm{s}\)
Capacitor sides: primary and secondary

- \(D_\mathrm{e}\)
Outer diameter for circular coils or width of a square coil (mm)

*dx*Separation between coils (mm)

**H**Height

**F**Ferrite material

- \(I_\mathrm{p}\), \(I_\mathrm{s}\)
Current sides: primary and secondary (A)

*k*Coupling coefficient

- \(k_\mathrm{b}\)
Geometric factor

- \(k_\mathrm{o}\)
Optimal coupling coefficient

- \(L_\mathrm{p}\), \(L_\mathrm{s}\)
Inductance sides: primary and secondary (\(\upmu \hbox {H}\))

**M**Magnet

*M*Mutual inductance (\(\upmu \hbox {H}\))

**N**Original coils (circular coils)

**NS**Square coils

- \(P_\mathrm{f}\)
Power of the source (W)

- \(P_\mathrm{L}\)
Active power consumed by the load (W)

- \(R_\mathrm{p}\), \(R_\mathrm{s}\)
Resistance sides: primary and secondary (\(\Omega \))

*Rx*Receiver coil

*Tx*Transmitter coil

- \(V_\mathrm{f}\)
Voltage of power source

**W**Width

- \(w_\mathrm{o}\)
Optimal angular frequency (rad/s)

- \(w_\mathrm{p}\), \(w_\mathrm{s}\)
Resonant frequency sides: primary and secondary (MHz)

- \(X_\mathrm{M}\)
Magnetizing reactance (\(\Omega \))

- \(Z_\mathrm{p}\), \(Z_\mathrm{s}\)
Impedance sides: primary and secondary (\(\Omega \))

## Greek symbols

- \(\eta \)
Efficiency of the WPT

- \(\phi _{ij}\)
Magnetic flux lines produced by

*i*linking*j*coil

## Subscripts

*i*Transmitter coil

*j*Receiver coil

- p
Primary coil

- s
Secondary coil

## Notes

## References

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