 Electromagnetic Fields in Wireless Power Transmission Requires a Wolfram Notebook System

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Wireless power transmission makes use of a pair of magnetically coupled coils, each in series with a capacitor. The characteristic frequency is discussed in the companion Demonstration "Wireless Power Transmission." The present Demonstration is concerned with the electromagnetic fields associated with a wireless transmission system. The parameters are the following (as defined in the companion Demonstration):

[more] , , ,  , (corresponding to , , , )

Maximum power is transmitted at the resonance frequency .

The instantaneous input voltage and currents , can be defined from the corresponding phaser solution of the circuit equation. The field of the coaxial coil system can be readily analyzed using the vector potential , which is a linear function of and . Assuming a near field, the electric and magnetic fields can be obtained by and , respectively. The power flow through space is given by the Poynting vector .

The field in the - plane is shown for a selected frequency and phase (i.e., time). The electric field perpendicular to the - plane is not shown. The magnetic field and Poynting vectors are shown by blue and orange arrows, respectively. The color indicates the magnitude of the energy density . All of these are plotted on a logarithmic scale.

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Contributed by: Y. Shibuya (January 2015)
Open content licensed under CC BY-NC-SA

Snapshots   Details

In the case of resonance (Snapshots 1 or 2), substantial power emanates from the coils due to the enhanced currents. Notice that the power flows to coil 2 even at the instant (Snapshot 2). The energy and power level are constrained in the off-resonance condition, as seen in Snapshot 3.

References

 J. Garnica, R. A. Chinga, and J. Lin, "Wireless Power Transmission: From Far Field to Near Field," Proceedings of the IEEE, 101(6), 2013 pp. 1321–1331. doi:10.1109/JPROC.2013.2251411.

 J. D. Jackson, Classical Electrodynamics, 3rd ed., Hoboken, NJ: John Wiley, 1998.