Coplanar energy transfer

Abstract

An external transmitter inductive coil can be provided in, on, or with a belt designed to be placed externally around a part of a body of a patient. An implantable device (such as a VAD or other medical device) that is implanted within the patient's body has associated with a receiver inductive coil that gets implanted within that part of the patient's body along with the device. The externally-located transmitter inductive coil inductively transfers electromagnetic power into that part of the body and thus to the receiver inductive coil. The implanted receiver inductive coil thus wirelessly receives the inductively-transferred electromagnetic power, and operates the implant.

Claims

1. A system for wirelessly powering a ventricular assist device (VAD) implanted within a body of a patient, comprising: a receiver inductive coil associated with the VAD and configured to be disposed in the pleural cavity of the patient's body to wirelessly receive inductively-transferred electromagnetic power and provide that received power to the VAD; and a transmitter inductive coil comprising one or more turns of electrically-conductive material that are configured to surround the pleural cavity by being disposed externally and completely around a part of the patient's body within which the pleural cavity is located, the transmitter inductive coil configured to inductively transfer electromagnetic power to the receiver inductive coil.

2. The system of claim 1 wherein at least one capacitor is associated with the transmitter inductive coil to form a transceiver resonance structure.

3. The system of claim 1 wherein at least one capacitor is associated with the receiver inductive coil to form a receiver resonance structure.

4. The system of claim 1 wherein the transmitter inductive coil comprises a transceiver capable of both transmitting and receiving.

5. The system of claim 1 wherein the receiver inductive coil uses a coil of the VAD to adjust to an ideal working point of the receiver inductive coil.

6. The system of claim 1 further comprising a second receiver inductive coil and wherein the two receiver inductive coils are coupled in series and function together as a single receiver inductive coil.

7. The system of claim 1 further comprising a circuit associated with the receiver inductive coil and wherein the circuit detects the resonance frequency of the receiver inductive coil and locks the resonance frequency of the transmitter inductive coil to the resonance frequency of the receiver inductive coil.

8. The system of claim 1 further comprising a circuit associated with the transmitter inductive coil and wherein the circuit compensates and keeps the resonance frequency of the transmitter inductive coil locked to the resonance frequency of the receiver inductive coil when the shape and thus the impedance of the transmitter inductive coil changes.

9. The system of claim 1 wherein a DC-to-DC converter associated with the VAD automatically adjusts to provide a substantially constant and optimum load to the receiver inductive coils.

10. The system of claim 9 wherein the DC-to-DC converter is located between a motor of the VAD and the receiver inductive coil.

11. A system for wirelessly powering a ventricular assist device (VAD) implanted within a body of a patient, comprising: a receiver inductive coil associated with the VAD and configured to be disposed in a left pleural cavity of the patient's body to wirelessly receive inductively-transferred electromagnetic power and provide that received power to the VAD; a second receiver inductive coil associated with the VAD and configured to be disposed in a right pleural cavity of the patient's body to wirelessly receive the inductively-transferred electromagnetic power and provide that received power to the VAD; and a transmitter inductive coil comprising one or more turns of electrically-conductive material that are configured to surround the left and right pleural cavities by being disposed externally and completely around a part of the patient's body within which the left and right pleural cavities are located, the transmitter inductive coil configured to inductively transfer electromagnetic power to the receiver inductive coils.

12. The system of claim 11 wherein at least one capacitor is associated with the receiver inductive coils to form a receiver resonance structure.

13. The system of claim 12 wherein at least one capacitor is associated with each of the receiver inductive coils to form receiver resonance structures.

14. The system of claim 11 wherein the receiver inductive coils use a coil of the VAD to adjust to an ideal working point of the receiver inductive coils.

15. The system of claim 14 wherein each of the receiver inductive coils uses a coil of the VAD to adjust to an ideal working point of a respective receiver inductive coil.

16. The system of claim 11 further comprising a circuit associated with the receiver inductive coils and wherein the circuit detects the resonance frequency of the receiver inductive coils and locks the resonance frequency of the transmitter inductive coil to the resonance frequency of the receiver inductive coils.

17. The system of claim 11 wherein a DC-to-DC converter associated with the VAD automatically adjusts to provide a substantially constant and optimum load to the receiver inductive coils.

18. The system of claim 11 wherein at least one capacitor is associated with the transmitter inductive coil to form a transceiver resonance structure.

19. The system of claim 11 wherein the transmitter inductive coil comprises a transceiver capable of both transmitting and receiving.

20. The system of claim 11 further comprising a circuit associated with the transmitter inductive coil and wherein the circuit compensates and keeps the resonance frequency of the transmitter inductive coil locked to the resonance frequency of the receiver inductive coils when the shape and thus the impedance of the transmitter inductive coil changes.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the drawing(s), like reference characters generally refer to the same or similar parts throughout the different views. The drawings are intended to illustrate the details of one or more embodiments according to the invention and/or the principles of the invention.

(2) FIG. 1 depicts an external belt 102 surrounding an implantable receiver coil 101; the belt can be opened and closed using a buckle 103.

(3) FIG. 2 shows an implantable circuit with a DC-to-DC converter coupled to the implantable receiver resonance structure 202. The load R.sub.1 can be a VAD or any other power consuming implantable device.

(4) FIG. 3 is a graph showing a relationship between output power and load resistance.

(5) FIG. 4 shows an alternative circuit coupled to the implantable receiver coil. The circuit has the same resonance structure 202 but uses the inductiveness of the implant VAD 402 and controller 401 as a DC to DC.

(6) FIG. 5 is a circuit that can be used to lock the external transceiver resonance frequency to the implanted receiver resonance frequency.

(7) FIG. 6 is another circuit that can be used to lock the external transceiver resonance frequency to the implanted receiver resonance frequency.

(8) FIG. 7 shows ring coil 701 implanted in the bottom of the pericardium sack 702.

(9) FIG. 8 shows two ring coil 801 implanted in the bottom of the pulmonary cage.

(10) FIG. 9 shows stent base ring coil 901 located in the descending aorta 902.

(11) FIG. 10 shows a model circuit for calculating the efficiency of energy transmission.

(12) FIG. 11 shows a schematic of a series-loaded receiver circuit.

(13) FIG. 12 shows a schematic of a parallel-loaded receiver circuit.

(14) FIG. 13 shows a schematic whereby a simple single-phase rectifying circuit is added to a receiver.

(15) FIG. 14 is a flow chart of coarse and fine resonance frequency detection.

(16) FIG. 15 is a flow chart of coarse and fine frequency base power control.

(17) FIG. 16 shows a configurable capacitor for use with a circuit for locking the external transceiver resonance.

DESCRIPTION

(18) The invention relates to an external transmitter inductive coil that can be provided in, on, or with a belt designed to be placed externally around a part of a body of a patient. Referring to FIG. 1, a surrounding belt 102 is depicted with a medical stent 101 therewithin. The stent 101 has built into it or incorporated within it a receiver coil of one or more turns of electrically-conductive material such as copper wire, for example. The belt 102 has in or on it, around its entire length, one or more turns of a transmitter coil. Like the receiver coil, the transmitter coil can have one or more turns of electrically-conductive material such as copper wire, for example. Together, the external belt 102 with the transmitter coil and the implantable medical device (such as a stent) with the receiver coil, can be considered a wireless power transfer system. In use, the transmitter coil is located externally around the chest of a patient or around some other part of the patient's body such as an arm, a leg, a head, or another part of the patient's torso, and the receiver is implanted within that part of the patient's body, such that electromagnetic power inductively transmitted from the surrounding coil of the belt 102 reaches and is wirelessly received by the patient-implanted receiver coil from all angles and directions.

(19) This physical arrangement of the external surrounding transmitter coil and the internally implanted receiver coil (that is disposed at least partially within an imaginary plane cutting through the patient's body and that is formed or defined by the surrounding external transmitter coil) can be referred to as a coplanar arrangement. And the system of the external transmitter coil and the implanted receiver coil thus can be referred to as a coplanar energy transfer (CET) system.

(20) CET is different than a known and common technique referred to as transcutaneous energy transfer (TET). TET only transfers energy through an area of the skin of a patient to a shallowly-implanted receiver just under that area of the skin. CET, in sharp contrast, involves surrounding the implanted receiver coil by placing or wrapping a transmitter coil completely around the part of the patient's body within which the receiver coil is implanted. If the receiver coil is disposed within the brain of the patient, for example, then CET involves disposing the transmitter coil externally around the corresponding part of the head of the patient such that an imaginary plane defined by the surrounding transmitter coil extends through at least a portion of the brain-implanted receiver coil. If the receiver coil is instead implanted within the descending aorta of the patient's vasculature, CET involves disposing the transmitter coil externally around the corresponding part of the patient's chest such that the imaginary plane defined by the surrounding transmitter coil extends through at least a portion of the aorta-implanted receiver coil. These are just two examples of where the transmitter and receiver coils could be located, and other locations are possible such as the arm or the leg of a patient.

(21) The stent 101 of FIG. 1 has built into it or incorporated within it the receiver coil, as indicated previously, and in this regard it is noted that the receiver inductive coil can comprise one or more electrically conductive fibers or strands that are among the various fibers or strands that together constitute the stent 101. These fibers or strands that comprise the receiver inductive coil can be electrical wires and can be coated with an electrical insulator. The receiver inductive coil can be built into or incorporated within the stent 101 in a variety of other ways.

(22) In one embodiment, the receiver coil is not built into the device with which it is associated. In this embodiment, the implantable receiver coil is operatively connected (such as by an electrical wire connection) to the implantable device to be able to provide wirelessly-received power to the implanted device but otherwise could be physically separate from and not an integral part of the device itself.

(23) In another embodiment, the receiver coil is built into the device with which it is associated.

(24) In one embodiment, the receiver coil is a stent 101 as shown in FIG. 1 as the device with which the implantable receiver coil is associated,

(25) In addition to VADs, the receiver coil can be associated with a variety of other types of implantable devices, including, for example, a constant glucose meter (CGM), a blood-pressure sensing device, a pulse sensing device, a pacemaker, implantable cardioverter defibrillators (IDC), digital cameras, capsule endoscopies, implanted slow release drug delivery systems (such as implanted insulin pump) a nerve stimulator, or an implanted ultrasound device.

(26) In operation, the CET system generates lower radio-frequency (RF) energy densities than TET systems. Because CET uses a surrounding external belt-like transmitter coil, the RF energy that is inductively transmitted into the patient's body from the transmitter coil is spread out and not concentrated or focused into or onto a particular spot or area of the patient's body. Using CET, the transmitted energy is spread out over the external transmitter coil of the CET, resulting in transmitted field strength and power density levels that are lower than TET systems. Also using a surrounding external belt-like transmitter coil eliminate misalignment problem and reduce dramatically the misplacement problems.

(27) It is noted that a power source must be associated with the external transmitter coil to provide that coil with the power that it will then wirelessly transmit for receipt by the implanted receiver coil. A controller unit also typically will be provided to regulate the operation of the transmitter coil Like the transmitter coil, both the power source and the controller will be external to the patient. The external source can be an AC current source, and the transmitter coil can be electrically connected to the AC current source. It also is noted that the transmitter coil can be a transceiver—that is, capable of both transmitting and receiving.

(28) Providing an Optimal Load to the Receiver Resonance Structure:

(29) In one embodiment according to the invention, the device with which the implantable receiver coil is associated is a ventricular assist device (VAD). In this embodiment a DC-to-DC converter is employed to provide an optimal load to the receiver inductive coil. The DC-to-DC converter is designed to automatically adjust to provide a constant or substantially constant selected optimum load to the receiver inductive coil. Typically, the DC-to-DC converter is implanted within the patient's body along with the receiver inductive coil and the VAD.

(30) FIG. 2 shows a DC-to-DC converter disposed between the receiver inductive coil and the resonance structure 202 (on the left) and a load R.sub.L (on the right). Load 201 may be a VAD or a constant glucose meter, or another implantable device described herein. As shown in FIG. 2, the circuit can also include a half or full-wave rectification (i.e., using a diode or diode bridge). As shown in FIG. 2, resonance structure 202 is formed by the receiver inductive coil and a capacitor. However the external transmitter inductive coil may also be associated with a capacitor to form a transmitter or transceiver resonance structure.

(31) The optimum load can be determined with reference to FIG. 3 which shows a relationship between power harvesting (W) and an R.sub.load value for a particular circuit, where R.sub.load is the internal resistance of whatever load is associated with the receiver inductive coil. While merely exemplary, the graph of FIG. 3 shows that the best power harvesting for the circuit is 80 Ohms or about 80 Ohms. A load with a resistance lower than 80 Ohms will reduce the voltage on the load and thereby reduce the harvested power, and a load with a resistance higher than 80 Ohms will reduce the current and thereby reduce the harvested power. The shape of the curve in the graph of FIG. 3 is determined by the function (26), provided below. In the case of a VAD, the resistive load represented by the VAD's motor will change as the mechanical load on the motor changes, and the depicted circuit (in FIG. 2) with the DC-to-DC converter is what is used to automatically adjust and provide a substantially constant and optimum load to the receiver inductive coil.

(32) In case of medical implant with high inductive load, like a VAD or implanted slow release drug delivery system that uses a motor, an alternative to the circuit of FIG. 2 is the circuit shown in FIG. 4. The circuit of FIG. 4 can be employed to adjust to an ideal working point of the receiver inductive coil (or, more accurately, of the receiver resonance structure which, as described above, is the combination of the receiver coil and its associated capacitor) when the device with which the implantable receiver coil is associated is a VAD.

(33) An implant with a brushless DC motor, like a VAD, needs adjustable power control to receive exactly the needed mechanical power. As shown in FIG. 3 and by function (26) below and as described above, the best power harvesting is achieved with the optimum R.sub.load. In this situation, a high quality motor controller, such as MOTION EN Speed Controller Series SC 1801 F (Faulhaber GmbH & Co. KG, Schönaich, Germany), can be used as a DC-to-DC converter for adjusting the R.sub.load to the optimum value using PWM (pulse width modulation). As shown in FIG. 4, a voltage and motor PWM controller 401 gives full control over the working point without any additional measures.

(34) By controlling the voltage and the DC-to-DC rate, the optimum R.sub.load can be achieved. The brushless DC motor of the VAD can be simulated with an equivalent resistor and inductor circuit. The speed of the motor is controlled using PWM as the motor input voltage, and the duty cycle is adjusted according to the needed speed. The coils of the VAD's motor flat the current just as is done in DC-to-DC voltage conversion. In this way, the VAD's motor is used as a DC-to-DC converter, and the reflected motor load is dependent on the conversion rate.

(35) Adding a voltage sensor with voltage control adds the capability to select the voltage in the receiver circuit. This gives full control on the reflected load (using the PWM mechanism) and on the used power by controlling the voltage (using the voltage control). For example, a LPC1102 chip can be used for (NXP Semiconductors N.V., Eindhoven, Netherlands) voltage sensing while an internal PWM engine and can control the voltage by using a transistor like SI8409DB (NXP Semiconductors) for closing the inline from the resonance structure 202.

(36) The voltage control can be done in several ways. One example is harvesting control on/off measured, as shown in FIG. 4, in the implanted receiver electronics itself. Another example is transmitting power control in the external transmitter/transceiver primary electronics that closes the loop according to the V.sub.sense in the receiver.

(37) Locking the Receiver and the Transmitter:

(38) Once placed within the body of a patient, the receiver coil shape can be distorted or modified from its at-rest shape and also can move over time to some extent as the patient moves, all depending on the particular location internally within the patient's body where the receiver coil is placed. With changing of its shape, the resonance frequency of the receiver coil changes. It is important for the transceiver resonance structure to be able to automatically find the receiver's resonance and adjust the transceiver's resonance to that found for the receiver and lock to that found resonance. In other words, the transceiver must have the capability to detect the receiver's resonance frequency and then lock to that detected receiver's resonance frequency.

(39) As described in FIG. 14 and in FIG. 15 the transceiver can detect the receiver's resonance frequency in two phases. First, in a coarse phase, when no pre-detected frequency is available, the transceiver uses a fast frequency detection process to roughly detect the receiver resonance frequency or else just start at some predetermined frequency. Second, in a fine phase that occurs after the coarse phase, the transceiver uses an ongoing process of fine tuning to detect the receiver resonance frequency.

(40) The main difference between the two procedures is the simplicity of the solution. FIG. 15 describes a very simple system where the coarse phase detects roughly the resonance, which then becomes the minimum frequency limit. (The system of FIG. 15 doesn't use the resonance frequency exactly, it uses a frequency above (or below) the resonance and then controls the transfer power by tuning the frequency). This is a simple system and it can work in strong coupling environment like the CET system. In other instances, when the coupling is lower due to distance or receiver/transceiver size/quality it is necessary to use the exact resonance frequency to be able to transfer the needed power.

(41) FIG. 14 describes the fine process that occurs after the first coarse adjust approximately determines the transmitter resonance. In the coarse phase, a microcontroller (MCU) associated with the transceiver resonance structure can have preliminary information about the receiver resonance frequency. The MCU will change the transceiver's driver frequency one after the other and detect the root mean square (RMS) current in the one or more coils of the transceiver. At the end of this phase, the MCU has the result of the entire frequency spectrum, and it can automatically select (as a result of its software programming) the best first coarse frequency, F.sub.coarse.

(42) After the coarse phase, the fine phase begins, in which the MCU's software programming dictates the selected frequency from the coarse phase as the best known resonance, F.sub.best. Once in the fine phase, the MCU stores the RMS current, adds single F.sub.delta to the previous frequency and stores that RMS current. By comparing these two RMS currents, the transceiver's MCU determines whether to add F.sub.delta or to reduce F.sub.delta from the previous F.sub.best. The equation used is as follows: F.sub.best=F.sub.best+/−F.sub.delta. Then, the tranceiver's resonance frequency is locked to the receiver's resonance frequency until the next fine phase process occurs. The fine phase process can occur periodically every T.sub.fine.

(43) Locking the transceiver resonance to the detected receiver resonance involves the transceiver coil automatically adjusting its capacitors, which can be accomplished using either the circuit shown in FIG. 5, or the circuit shown in FIG. 6, each of which is a resonance LC (inductance and capacitance) structure.

(44) In the circuit of FIG. 5, the MCU forces a fix frequency by generating P.sub.out pulse in the requested frequency and push the driver circuit. In so doing, the MCU thereby calibrates the configurable capacitor to get resonance. The MCU receives the feedback phase, and adjusts it to the resonance. In resonance, the feedback phase P.sub.in should be exact as the generated one P.sub.out. The MCU then compares the output P.sub.out to the input P.sub.in to validate the resonance. The MCU should adjust the capacitors according to the phase until P.sub.in=P.sub.out

(45) In the circuit of FIG. 6, the circuit is a self-oscillating circuit, and thus is always in resonance, however the MCU can adjust the frequency by changing the capacitors. The MCU can add capacitors to the capacitors array or remove capacitors as described in FIG. 16.

(46) Although FIGS. 5 and 6 show two particular circuits that can be used, it is noted that a variety of variants of phase locked loop (PLL) algorithms and implementing circuits can be used to compensate for impedance changes of the coils by adjusting capacitor value.

(47) Placement in a Patient's Body of the Receiver Resonance Structure:

(48) The receiver inductive coil can be placed within the body of a patient at a variety of internal locations. FIGS. 7, 8, and 9 illustrate three particular examples of a placement location inside the body of a patient.

(49) As shown in FIG. 7, the receiver coil 701 may be placed in the base of the flat part of the pericardia 702, which surrounds the heart 704. The main added value in placing the receiver coil 701 in the pericardia 702 with a VAD is that the pericardia 702 is relatively flat and open in typical VAD surgery. The receiver coil 701 can be glued to the pericardia 702 boundaries, e.g., with surgical glue.

(50) In FIG. 8, it is shown that the receiver coil 801 of a VAD can be placed in the pulmonary cage. One advantage of placing the coil 801 in the pulmonary cage is that the VAD will not disturb the magnetic power harvesting, and that pulmonary cage is relatively easy to access during the VAD surgery.

(51) As shown in FIG. 9, the receiver coil 901 may also be placed in an artery 902. The Aorta or the Vena Cava are particularly well-suited for placement of the receiver coil 901 because each is oriented vertically with respect to a plane that cuts in a cross section through the torso of the patient. Placement of the receiver coil 901 in the Aorta or the Vena Cava also allows the receiver coil 901 to be associated with an implantable stent.

(52) Further Disclosure Related to Providing an Optimum Load to the Receiver Resonance Structure:

(53) Having presented various details of various embodiments according to the invention, some theory, equations, and calculations relevant to providing an optimum load to the receiver resonance structure will now be presented.

(54) The ratio between the distance D from the transmitting coil to receiving coil and the wavelength λ is as follows:

(55) $\begin{array}{cc}\frac{D}{\lambda }=\frac{\mathrm{Df}}{c},& \left(1\right)\end{array}$
where f is the transmitting frequency and c=3.Math.10.sup.8 m/s is the speed of light.

(56) Given that the maximum distance D.sub.max does not exceed 0.4 m and the working frequency is f=100 kHz, the ratio D.sub.max/λ=0.00013<<1. Thus, we can conclude that the receiving coil is in the quasi-static area, and we can neglect the effects of the phase difference due to the wave propagation.

(57) The amplitude of the voltage induced in the receiving coil according to the Faraday's law [1] is as follows:

(58) $\begin{array}{cc}{v}_r\left(t\right)=-\frac{d\Phi }{dt}=-\frac{d}{dt}\left(B.Math.a\right),& \left(2\right)\end{array}$
where Φ is the magnetic flux through the receiving coil, B is the magnetic flux density, and a is the effective area of the receiving coil.

(59) To estimate the maximum induced voltage (2), assume that the receiving coil is located coaxially with the transmitting coil at its center, where the magnetic flux density B can be calculated as follows [1]:

(60) $\begin{array}{cc}B=\frac{{\mu }_r{\mu }_0{I}_t{N}_t}{2R_t}\sin \left(2\pi ft\right),& \left(3\right)\end{array}$
where μ.sub.r is the relative permeability of media, μ.sub.0=4π10.sup.7 V.Math.s/(A.Math.m) is the permeability of vacuum, I.sub.t is the amplitude of the current in the transmitting coil, and R.sub.t and N.sub.t are the radius and number of turns of the transmitting coil correspondingly.

(61) The effective area of the receiving coil can be calculated as follows:
a=πR.sub.r.sup.2N.sub.r,  (4)
where R.sub.r and N.sub.r are the radius and the number of turns of the receiving coil correspondingly.

(62) Substituting (3) and (4) into (2) and differentiating with respect to the time, gives the following expression for the amplitude of the voltage induced in the receiving coil:

(63) $\begin{array}{cc}{V}_r=2\pi f\frac{{\mu }_r{\mu }_0{I}_t{N}_t}{2R_t}{\mathrm{\pi R}}_r^2{N}_r.& \left(5\right)\end{array}$

(64) The transmitting and the receiving coils can be seen as two coupled inductors, as follows:

(65) $\begin{array}{cc}\{\begin{array}{c}{v}_t=L_t\frac{d{i}_t}{dt}-M\frac{d{i}_r}{dt}\\ v_r=-M\frac{d{i}_t}{dt}+L_r\frac{d{i}_r}{dt}\end{array},& \left(6\right)\end{array}$
where v.sub.t and v.sub.r are the transmitter and receiver coils voltages, i.sub.t and i.sub.r their currents, and M is the mutual inductance.

(66) Assuming that the current in both coils is a sine-wave of frequency ω=2πf, (6) can be written as follows:

(67) $\begin{array}{cc}\{\begin{array}{c}{v}_t=j\omega L_t{i}_t-j\omega {\mathrm{Mi}}_r\\ v_r=-j\omega {\mathrm{Mi}}_t+j\omega L_r{i}_r\end{array}.& \left(7\right)\end{array}$

(68) The mutual inductance M can be found from the open circuit experiment, where i.sub.r=0:

(69) $\begin{array}{cc}\{\begin{array}{c}{v_t.Math.}_{i_r=0}=j\omega L_t{i}_t\\ {v_r.Math.}_{i_r=0}=-j\omega {\mathrm{Mi}}_t\end{array}.& \left(8\right)\end{array}$

(70) Rearranging the second equation of (8) with respect to M and substituting (2)-(5) gives us:

(71) $\begin{array}{cc}M{|}_{i_r=0}=-\frac{v_r}{j\omega i_t}=-\frac{-\frac{d}{dt}\left(B.Math.a\right)}{j\omega i_t}=\frac{{\mu }_r{\mu }_0{N}_t}{2R_t}\pi R_r^2{N}_r=3.9\mu H.& \left(9\right)\end{array}$

(72) The value of M obtained in (9) increases as a function of the relative permeability μ.sub.r of the receiver core.

(73) For the purpose of efficiency calculation, assume that the transmitter coil is loaded with a series resonant capacitor and the receiver coil is loaded to form a series resonant circuit as describe in FIG. 10.

(74) The transmitter current is calculated using the coupled-inductor model (7), as follows:

(75) $\begin{array}{cc}{i}_t=\frac{v_s}{R_t+\frac{{\left(\omega M\right)}^2}{R_r+R_L}},& \left(24\right)\end{array}$
where v.sub.s=2V.sub.DD/π is the effective voltage of the source V.sub.dr at the first harmonic of the excitation frequency, R.sub.t is the active resistance of the transmitter coil, R.sub.r the active resistance of the receiver coil, and R.sub.L is the load resistance.

(76) The amplitude of the load voltage is given by:

(77) 0$\begin{array}{cc}{V}_L=\frac{2\omega {\mathrm{MV}}_{\mathrm{DD}}\text{/}\pi }{R_t+\frac{{\left(\omega M\right)}^2}{R_r+R_L}}.Math.\frac{R_L}{R_r+R_L}=\frac{2\omega {\mathrm{MV}}_{\mathrm{DD}}\text{/}\pi }{R_t\left(R_r+R_L\right)+{\left(\omega M\right)}^2}.Math.R_L,& \left(25\right)\end{array}$
where V.sub.DD is the supply voltage of the half-bridge driver of the transmitter.

(78) From here, the load power is given by:

(79) $\begin{array}{cc}{P}_L=\frac{V_L^2}{2R_L}=\frac{2{\left(\omega {\mathrm{MV}}_{\mathrm{DD}}\text{/}\pi \right)}^2{R}_L}{{\left(R_t\left(R_r+R_L\right)+{\left(\omega M\right)}^2\right)}^2}.& \left(26\right)\end{array}$

(80) Differentiating (26) with respect to R.sub.L gives the load resistance that maximizes the load power, as follows:

(81) $\begin{array}{cc}{R}_{\mathrm{Lopt}}=R_r+\frac{{\left(\omega M\right)}^2}{R_t}.& \left(27\right)\end{array}$

(82) Substituting (27) into (26) yields:

(83) $\begin{array}{cc}{P}_{\mathrm{Lopt}}=0.5\frac{{\left(V_{\mathrm{DD}}\text{/}\pi \right)}^2{\left(\omega M\right)}^2/R_t}{R_t{R}_r+{\left(\omega M\right)}^2}.& \left(28\right)\end{array}$

(84) Rearranging (28) with respect to the driver voltage gives:

(85) $\begin{array}{cc}{V}_{\mathrm{DD}}=\frac{\pi }{\omega M}\sqrt{2P_{\mathrm{Lopt}}{R}_t\left(R_t{R}_r+{\left(\omega M\right)}^2\right)}.& \left(29\right)\end{array}$

(86) The input power is:

(87) $\begin{array}{cc}{P}_t=\frac{V_{\mathrm{DD}}}{2\pi }{\int }_0^{\pi \text{/}\omega }{i}_t\left(t\right)dt=2{\left(\frac{V_{\mathrm{DD}}}{\pi }\right)}^2\frac{R_r+R_L}{R_t\left(R_r+R_L\right)+{\left(\omega M\right)}^2},& \left(30\right)\end{array}$
while its optimal value considering (27) is:

(88) $\begin{array}{cc}{P}_{\mathrm{topt}}={\left(\frac{V_{\mathrm{DD}}}{\pi }\right)}^2\frac{2R_r+{\left(\omega M\right)}^2\text{/}{R}_t}{R_t{R}_r+{\left(\omega M\right)}^2}.& \left(31\right)\end{array}$

(89) Dividing (29) by (31) gives the efficiency of the wireless power transmission corresponding to the optimum load resistance:

(90) $\begin{array}{cc}{\eta }_{\mathrm{opt}}=\frac{P_{\mathrm{Lopt}}}{P_{\mathrm{topt}}}=0.5\frac{1}{1+\frac{2R_r{R}_t}{{\left(\omega M\right)}^2}}.& \left(32\right)\end{array}$

(91) The general expression for the efficiency is:

(92) $\begin{array}{cc}\eta =\frac{P_L}{P_t}=\frac{{\left(\omega M\right)}^2}{R_t\left(R_r+R_L\right)+{\left(\omega M\right)}^2}.Math.\frac{R_L}{R_r+R_L}.& \left(33\right)\end{array}$

(93) Differentiating (33) with respect to R.sub.L gives the load resistance that maximizes the efficiency:

(94) $\begin{array}{cc}{R}_{L\eta \max }=\sqrt{R_r^2+\frac{{\left(\omega M\right)}^2{R}_r}{R_t}}.& \left(34\right)\end{array}$

(95) The maximum efficiency can be calculated by substituting (34) into (33).

(96) 0$\begin{array}{cc}{\eta }_{\max }=0.5\frac{1}{1+\frac{2R_r{R}_t}{{\left(\omega M\right)}^2}}.& \left(32\right)\end{array}$

(97) The maximum efficiency and maximum load power for the parallel-loaded receiver is identical to that of the series one. The optimal load resistance and maximizing the efficiency for the parallel-loaded receiver differ from (27) and (34). However, the derivation is similar. The specific formulae for the load resistance is not developed here and instead we find the optimal resistance using computer simulations tool like PSPICE® (Cadence Design Systems, San Jose, Calif.), a full-featured, native analog and mixed-signal circuit simulation tool.

(98) The circuit shown in FIG. 11 is a series-loaded receiver. The source Vdr is built from two BUZ11 N-MOSFETs driven by the IR2111 gate driver. The 0.1 Ohm resistor is used for the transmitter current monitoring. Both the transmitter and receiver capacitors are chosen with low ESR. The load resistance is chosen as R.sub.L=0.5 Ohm, and the driver voltage V.sub.DD=12 V. Substituting these values and the other setup parameters (R.sub.t=1 Ohm, R.sub.r=0.65 Ohm, M=2.056 μH) into (26) gives for P.sub.L=3.16 W. The measured voltage amplitude on the load resistance is 1.75 V, which corresponds to P.sub.L=3.1 W. The input power drawn from the power supply is P.sub.in=V.sub.DD/π.Math.I=12/3.14.Math.2.8=10.7 W. The efficiency is η=P.sub.L/P.sub.in=28%. It is noted that the load resistance is not optimized for the maximum output power.

(99) The circuit shown in FIG. 12 is a parallel-loaded receiver. The source V2 is built from two BUZ11 N-MOSFETs driven by the IR2111 gate driver. The 0.1 Ohm resistor is used for the current monitoring. Both the transmitter and receiver capacitors are chosen with low ESR. Substituting the model parameters into (29) gives V.sub.DD=11.5 V for P.sub.L=5 W. Computer simulations have shown that the maximum load power of 4.85 W is obtained for R.sub.L=80 Ohm. This result closely correlates with laboratory measurements, where an output power of 4.5 W was measured for V.sub.DD=12 V. The input power drawn from the power supply is P.sub.in=V.sub.DD/π.Math.I=12/3.14.Math.4.2=16.05 W. The efficiency is η.sub.7=P.sub.L/P.sub.in=28%.

(100) Inserting a simple single-phase rectifying circuit before R4, as shown in the circuit in FIG. 13, takes about 0.2 W dissipated on the diode with 2 A peak diode current and 44 V peak diode reverse voltage. The peak voltage on the receiver capacitor is 25 V, and the peak voltage on the transmitter capacitor is 500 V.

(101) Various modifications may be made to the embodiments disclosed herein. The disclosed embodiments and details should not be construed as limiting but instead as illustrative of some embodiments and of the principles of the invention.

INCORPORATION BY REFERENCE

(102) References and citations to other documents, such as patents, patent applications, patent publications, journals, books, papers, web contents, have been made throughout this disclosure. All such documents are hereby incorporated herein by reference in their entirety for all purposes.

EQUIVALENTS

(103) The invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The foregoing embodiments are therefore to be considered in all respects illustrative rather than limiting on the invention described herein. Scope of the invention is thus indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.