Wireless charging

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Wireless charging is currently becoming a hot topic for marketing, consequently, for a design as well. However, wireless energy transfer principle is not new and already well-known. Specifically, this principle is used in electromechanical apparatus such as transformers. The only difference is that in a transformer transferring and receiving coils are motionlessly mounted on a static part, magnetic yoke, which guides the magnetic field from one coil to another. Therefore, it is possible to say that the energy is transferred via the specific magnetic path. However, there is a special class of electromechanical devices that indeed implement wireless energy transfer – electrical machines. They transfer the energy from static to rotating part or vice versa through a real, physical air gap.
As so, we can conclude that wireless energy transfer systems have a solid background and can be investigated by a standard package of design tools. Wireless chargers, which are widely advertised today, are conventional air transformers that may (or may not) contain magnetic paths. Normally, the transmitting part (primary coil) is fixed while the receiving part (secondary coil) is located in a mobile device and can take different positions relative to a primary coil. The mutual location of coils is directly impacting the charging efficiency. Coils can be of a different shape, but most commonly they are either square or circular (as the one in the picture).

Axisymmetric wireless charger
Axisymmetric wireless charger

Coils of the charger are rarely located alone in the air as the stray magnetic field they emit is harmful for electronic devices. Several protective measures are available. One of them is to place a highly conductive thin plate at the back of a coil. Eddy currents induced in the back plate will counter-react the stray field behind the coil, thus, protecting electronics. Another option is to mount coils in magnetic yokes that will concentrate and guide the magnetic flux. If necessary, these measures can be combined.

We are going to summarize main milestones that a designer of a wireless charger shall reach. Although any of modeling packages can be used, we prefer QuickField software for the analysis due to its user-friendliness, speed and calculation power. We will analyze a transformer with concentric coils and magnetic yokes. Dimensions (in millimeters) and axisymmetric FEM model are shown in pictures below.

Dimensions of a model
Dimensions of a model

Axisymmetric FEM model with mesh
Axisymmetric FEM model with mesh

Wireless energy transfer system requires power electronics for its power supply. On a schematics of an equivalent circuit below there is a block of AC source at a primary side. It incorporates an alternating voltage source, rectifier and inverter that supplies an alternating voltage of desired frequency. Secondary side has a rectifier AC to DC that supplies a direct voltage to a battery and a load Rload (if it is powered on). Resistance R1 and inductance L1 represent the primary, transmitting coil of the charger. It is coupled with secondary, receiving coil designated as R2 and L2 via the mutual inductance M.

Equivalent circuit of a wireless charger
Equivalent circuit of a wireless charger

Wireless energy transfer system operates at high frequencies, in the range of kHz, which is limited by power electronics capabilities. The higher frequency provides a higher voltage, thus, more power on the secondary side. However, at such frequencies reactances of a circuit significantly increase limiting currents magnitude in primary and secondary circuits, so decreasing the transferring power. A common way to improve the behavior of the circuit is to add capacitances C1 and C2 to operate in resonance mode. Although this capacitances can be straightforwardly estimated from the equation ω0 = 1/√C1·L1  = 1/√C2·L2 , on practice it becomes quite tricky. Taking into account the fact of non-linear magnetic characteristic of iron and the eddy-current effects in conductors and back plates, a variation of inductance is observed. Thus, the designer needs to thoroughly analyze the circuit at the rated operation point to determine and fix the values of capacitors.

In our example of wireless charger we take several assumptions: the operation frequency f = 10 kHz does not cause noticeable eddy current effects in copper strands and iron yokes have a constant relative permeability μr = 1000. With these assumptions QuickField easily calculates the self- and mutual-inductances. In our case they are L1 = L2 = 22.65 μH and M = 20.80 μH. Based on obtained inductances the capacitances are C1 = C2 = 11.20 μF.

In order to decrease the calculation time the power electronics parts were neglected in the model. As so, a following external circuit was created in QuickField.

Equivalent circuit omitting power electronics
Equivalent circuit omitting power electronics

Power supply is provided by an alternating current source of magnitude Î1 = 4 A. Load is modeled by Rload = 1 Ω. Under this conditions with the presence of both capacitors maximum transferred power to the load is P2 = 12.69 W while the apparent power on the primary side S1 = 13.67 VA. Thus, the circuit efficiently transfers the energy through the air by magnetic field, as shown on animation.

Magnetic field between coils
QuickField simulation: Magnetic field between coils

In conclusion, wireless chargers, or wireless energy transfer systems in general, have a transformer theory in its core. Novel aspects come from a fact of air gap between coils and presence of power electronics at primary and secondary side. This brings new challenges in design, such as the effects of mutual positioning of coils and high frequency effects. A much deeper study is required to analyze how the mutual alignment, secondary coil orientation, supply frequency influences the charger. Depending on the application a designer will take a lot of engineering decisions. However, it is possible to make one step towards this process already now by downloading and investigating the model for this example here.

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