Wireless power

This self-oscillating design uses a Colpitts oscillator to generate an AC sine wave output from the rectified and stabilized DC input. On switch-on, the transistor Q1 is turned on by the bias resistors on its base connection and the capacitor C1 starts to charge up. The increasing voltage across C1 generates an increasing magnetic field in the inductor L. Once the capacitor C1 is fully charged, the voltage across the inductor L is constant and the magnetic field starts to collapse. This induces a voltage across it that is higher than the supply voltage, turning off Q1 via C2 and holding it off until the magnetic field in the inductor has dissipated. The cycle then begins again. The resulting waveform through the inductor is approximately a sine wave. The resonant frequency of a Colpitts oscillator is given by:



The matching receiver coil must be accurately positioned to intercept the resulting magnetic field generated by the transmitter coil. The induced AC voltage is rectified and used to trickle-charge the rechargeable batteries. As the battery voltage rises, the voltage drop across the resistor R_charge reduces and the charging LED extinguishes.
The maximum power transmission (minimum losses) can be calculated from:



Where Q is the system quality factor:



And k the coupling coefficient between the transmitting inductance L_T and the receiving inductance L_R, which is derived from:



Where n_T and n_R are the number of turns of each coil respectively and P_RT is the permeance between them (equivalent to the magnetic conductivity), which in turn is derived from:



Where μ₀ is the permeability of air, A is the cross-sectional area and l is the magnetic path length.
The oscillator frequency, ƒ, can be chosen to be high (100s of kHz) to keep Q high and therefore the efficiency high, but it should not be too high to avoid EMC issues, relaxation losses and other ohmic losses due to the skin effect.
It follows that if the two coils are placed in close proximity then the magnetic path length will be small and the permeance high, giving a higher mutual inductance and a higher coupling coefficient, k. In the case of the rechargeable toothbrush, the spigot design accurately positions the transmitting coil around the ferrite core of the receiving coil to maximise the power transmission, as can be seen from the original patent application drawing from 1964 below:



The electric toothbrush charger is a special case of near-field wireless power transfer system. The mechanical design means that coil alignment is not an issue, safety is not critical as the power transferred is very low and the simple oscillator circuit keeps the cost down, which is ssential for a mass-produced consumer product.

Inductive chargers for mobile phones or other rechargeable devices are much more complex. Some of the most commonly used wireless power transfer open standards are Qi (pronounced “chee”) and the Power Matters Alliance (PMA) standards for inductive charging or the Airfuel Alliance for magnetic resonance power transfer.

Resonant wireless power transfer

Resonant inductive coupling uses three or more often four coils. The intermediary coils are resonant tank circuits with a capacitor in series with the winding. The resonance windings act as “magnetic lenses”, boosting the magnetic field from the transmitting coil and concentrating the received field for the receiving coil. If even only a small part of the transmitted alternating magnetic field is intercepted by the receiver resonator, it will pick up some of the energy, so separation distance and alignment is not so critical. Resonant power transmission applications include battery-less smartcards, RFID tags and near-field communication systems. Data communication and adaptive feedback is typically via Bluetooth:



Inductive wireless power transfer



Inductive charging is more efficient than resonant charging but more sensitive to coil alignment, so the choice between them is mostly application specific. The transmission range is limited to around 50mm, reducing to 5-10mm if the transmitter or receiver coils are not perfectly aligned, although multiple coils and/or adaptive controllers can be used to make the alignment less critical.



The energy transfer follows a square law in the Z direction (coil separation), a roughly linear relationship for lateral misalignment (coils not perfectly overlapping) and a non-linear relation-ship for angular misalignment (receiver tilted with respect to the transmitter coil).

Unlike the simple electric toothbrush charger, inductive charging systems such as Qi use flat coils with no magnetic cores and runs at higher frequencies (typically between 0.1MHz and 1MHz). This allows higher power transfer rates from 3W up to 70W or more, but then creates the problem of unwanted or hazardous induced voltages in any conductive metallic objects placed into the magnetic field. This hazard is eliminated by bidirectional data communication between the transmitter and receiver so that the full output power is only activated after the receiver has been properly identified as a Qi-compatible device and that there are no metallic obstacles in the way.

Communication is achieved by the receiver generating coded load pulses which the transmitter can detect and decode (Fig. 6).



A further advantage of data communication is that the receiver can send a received signal strength value back to the transmitter to form a closed loop control system to handle load transients, misalignments and fault conditions. Other systems use a separate radio link to transmit data back to the transmitter.

Wireless charging is nowadays most commonly used to recharge mobile phones, but it also has a place in industry for IoT applications. For example, consider a remote sensor module that is hermetically sealed against liquids, contaminants and vapours with no external connectors. It could be placed next to a piece of heavy industrial equipment and transmit local environment sensor readings such as ambient temperature, magnetic field strength, acoustic noise levels or shock/vibration via a data link that uses an on-board chip antenna. The system could be powered from an internal supercapacitor or rechargeable battery whose voltage is monitored and transmitted along with the other data. Once the internal power source becomes drained, the whole sensor module is removed to a safe environment and placed on a recharging pad to recharge the internal energy store. Thus wireless charging is not just a “gimmick” for industrial applications; it could become an accepted element in many harsh environment applications.

PCB Inductive power transfer

A small amount of power (1-2W) can be transferred across the isolation barrier using a coreless transformer formed from adjacent PCB spiral tracks. The dielectric strength of FR4 PCB material is 800V-1500V/mil, so a standard 4 layer PCB with 40 mils between layer 2 and layer 3 will have an isolation voltage of at least 30kVDC (care must be taken with vias to maintain a minimum separation).



The inductance of two overlying PCB spirals was worked out by Wheeler in 1928:





Where μ₀ is the permeability of FR4 which is typically around 1, d is the inner diameter of the spiral, D is the outer diameter and n the number of turns.

The mutual inductance between the overlaid spirals is given by:



Where the coupling coefficient, K, is typically 0.5 to 0.6 for two layers separated by 40 mils of FR4.

The efficiency is not high (around 25%), but the advantage of fully automated production and high isolation makes PCB coreless transformers a useful technique.

Practical Tip: Inductive coupling for wireless data rather than power transfer can also be useful to replace the optocoupler in the feedback circuit in a conventional AC/DC converter or to communicate fault conditions from the secondary to the primary across the isolation barrier.

With the rise of digital power supplies, the output regulation as well as the synchronous rectification timing can be digitally controlled from the primary side microcontroller using such simple inductive coupling across the isolation barrier. As the system is symmetrical, bi-directional data can be sent by duplicating the transmitter and receiver circuitry on both sides.

The implementation is relatively straightforward using a four-layer PCB : two opposing loops are formed from the PCB tracks on the top and bottom layers to create the transmitting and receiving coils and the data is transmitted by modulating the high frequency drive signal.

The electrical insulation is guaranteed by the PCB material and as both loops is embedded and shielded with ground planes above and below, the transfer characteristic is largely independent of moisture, dirt, interference or other environmental conditions. Even so, some signal conditioning is usually required to ensure data integrity.



The PCB track connections are transmission lines that have to be impedance matched with the transmitter and receiver amplifiers to avoid unwanted reflections. The PCB material (FR4) acts as a dielectric between the trace carrying the RF signal and the ground plane with characteristic impedance (in ohms)





For a standard PCB, the dielectric constant, ℇ, is equal to 4, so if the 1 ounce copper track is 20 mil wide and the PCB thickness is 10 mil, the resulting impedance will be 50 Ohms. For a 75 Ohm impedance, reduce the track thickness to 8.3 mils.

The PCB transmission lines will also have a characteristic capacitance [pF/in] of:



And a propagation delay [in ps/in] of :



For multilayer PCBs where the tracks are embedded between two ground or power planes, the above relationships need to be modified slightly:



Multilayer PCB characteristic impedance [ohms]:



Multilayer PCB characteristic capacitance [pF/in]:



Multilayer PCB propagation delay [ps/in]:



NOTE: PCB dimensions are still commonly defined in imperial measurements (inch, mils), so these have been used here instead of the metric system.