US 20100225175 A1 Abstract Described herein are embodiments of forming a wireless power transfer system which include locating a source high-Q resonator on one side of a solid object, where the solid object may be an object from the group consisting of a solid non-conducting wall, or a solid non-conducting window, locating a receiving high-Q resonator on the other side of the solid object, aligning a first position of the source resonator with a second position of the receiving resonator, and using the source resonator to create a magnetic field, and using the receiving resonator to receive the magnetic field, and to produce an output that includes power based on said receiving the magnetic field.
Claims(50) 1. A method, comprising
locating a source high-Q resonator on one side of a solid object, where the solid object is an object from the group consisting of a solid non-conducting wall, or a solid non-conducting window; locating a receiving high-Q resonator on the other side of the solid object; aligning a first position of the source resonator with a second position of the receiving resonator; and using the source resonator to create a magnetic field, and using the receiving resonator to receive the magnetic field, and to produce an output that includes power based on said receiving the magnetic field. 2. A method as in 3. A method as in 4. A method as in 5. A method as in 6. A method as in 7. A method as in 8. A method as in 9. A method as in 10. A method as in 11. A method as in 12. A system, comprising:
a source high-Q resonator, optimized for generating an AC magnetic field which stores energy in its near field; a transmitting circuit, coupled to said source resonator, and operative to receive power from an AC connection, and produces an output power which is coupled to said source resonator and drives said source resonator in a substantially resonant state; a receiving high-Q resonator optimized for receiving power from said AC magnetic field generated by said source resonator across a substantially solid object which is one of a solid non-conducting wall or non-conducting window; and a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output power based on said receiving by said receiving resonator. 13. A system as in 14. A system as in 15. A system as in 16. A system as in 17. A method as in 18. A wireless power bridge, comprising:
a transmitting unit receiving an AC power, and carrying out an AC to AC power conversion, and including an inductive loop, and; a resonant source high-Q resonator unit, separate from the transmitting unit and coupled to the transmitting unit, said source resonator unit composed of at least one wire loop and a principle capacitor as needed to achieve substantial resonance; said transmitting unit including a resonator tuning circuit to tune to a resonance frequency of the source resonator; a resonant receiving high-Q resonator unit, composed of at least one wire loop and another principle capacitor to achieve substantial resonance; a receiving unit, separate from said receiving resonator unit, and accommodating a power conversion and, having a resonator tuning and matching circuit to tune a resonance frequency of the receiving resonator and to match said receive power conversion to a source impedance of said receiving resonator. 19. A wireless power bridge as in 20. A wireless power bridge as in 21. A wireless power bridge as in 22. A wireless power bridge as in 23. A wireless power bridge as in 24. A method, comprising:
applying power from an AC outlet to a first high-Q resonator on a first side of a solid object, where the solid object is an object from the group consisting of a non-conducting solid wall, or a non-conducting solid window; generating a magnetic signal at said first resonator; receiving said magnetic signal on the second side of the solid object; and creating a power output on the second side of the solid object, in a second high-Q resonator, based on the generated magnetic signal. 25. A method, as in 26. A method, as in 27. A method, comprising:
locating a source high-Q resonator on one side of a solid object; locating a receiving high-Q resonator on the other side of the solid object; aligning a first position of the source resonator with a second position of the receiving resonator; and using the source resonator to create a magnetic field, and using the receiving resonator to receive the magnetic field, and to produce an output that includes power based on said receiving the magnetic field. 28. A method as in 29. A method as in 30. A method as in 31. A method as in 32. A method as in 33. A method as in 34. A method as in 35. A method as in 36. A method as in 37. A method as in 38. A method, comprising:
applying power from an AC outlet to a first high-Q resonator on a first side of a solid object, where the solid object is an object from the group consisting of a non-conducting solid wall, or a non-conducting solid window; generating a magnetic signal at said first resonator; receiving said magnetic signal on the second side of the solid object; and creating a power output on the second side of the solid object, in a second high-Q resonator, based on the generated magnetic signal. 39. A method as in 40. A method as in 41. A system, comprising;
a source high-Q resonator, optimized for generating an AC magnetic field which stores energy in its near field; a transmitting circuit, coupled to said source resonator, and operative to receive power from an AC connection, and produces an output power which is coupled to said source resonator and drives said source resonator in a substantially resonant state to create AC power wirelessly in a receiving high-Q resonator optimized for receiving power from said AC magnetic field that has a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output AC power based on said receiving by said receiving resonator. 42. A system, comprising:
a source high-Q resonator, optimized for generating an AC magnetic field which stores energy in its near field; a transmitting circuit, coupled to said source resonator, and operative to receive power from an AC connection, and produces an output power which is coupled to said source resonator and drives said source resonator in a substantially resonant state to create DC power wirelessly in a receiving high-Q resonator optimized for receiving power from said AC magnetic field that has a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output DC power based on said receiving by said receiving resonator. 43. A system, comprising:
a transmitting circuit, coupled to said source resonator, and operative to receive power from a DC connection, and produces an output power which is coupled to said source resonator and drives said source resonator in a substantially resonant state to create AC power wirelessly in a receiving high-Q resonator optimized for receiving power from said AC magnetic field that has a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output AC power based on said receiving by said receiving resonator. 44. A system, comprising:
a transmitting circuit, coupled to said source resonator, and operative to receive power from a DC connection, and produces an output power which is coupled to said source resonator and drives said source resonator in a substantially resonant state to create DC power wirelessly in a receiving high-Q resonator optimized for receiving power from said AC magnetic field that has a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output DC power based on said receiving by said receiving resonator. 45. A system as in 46. A system, comprising:
a receiving high-Q resonator optimized for receiving power from an AC magnetic field generated by a remote source high-Q resonator that has been created from an AC connection, said receiving resonator adapted for mounting adjacent a solid object, with said solid object between said receiving resonator and said source resonator; and a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output AC power based on said receiving by said receiving resonator. 47. A system, comprising:
a receiving high-Q resonator optimized for receiving power from an AC magnetic field generated by a remote source high-Q resonator that has been created from an DC connection, said receiving resonator adapted for mounting adjacent a solid object, with said solid object between said receiving resonator and said source resonator; and a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output AC power based on said receiving by said receiving resonator. 48. A system, comprising:
a receiving high-Q resonator optimized for receiving power from an AC magnetic field generated by a remote source high-Q resonator that has been created from an AC connection, said receiving resonator adapted for mounting adjacent a solid object, with said solid object between said receiving resonator and said source resonator; and a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output DC power based on said receiving by said receiving resonator. 49. A system, comprising:
a receiving high-Q resonator optimized for receiving power from an AC magnetic field generated by a remote source high-Q resonator that has been created from a DC connection, said receiving resonator adapted for mounting adjacent a solid object, with said solid object between said receiving resonator and said source resonator; and a receiving circuit, coupled to receive power that has been received by said receiving resonator, and to produce an output DC power based on said receiving by said receiving resonator. 50. A system as in Description This application is a continuation of U.S. patent application Ser. No. 12/688,339 ('339 application) filed Jan. 15, 2010, the entirety of which is incorporated herein by reference. The '339 application is a continuation of U.S. patent application Ser. No. 12/055,963 ('963 application), filed Mar. 26, 2008 the entirety of which is incorporated herein by reference. The '963 application claims the benefit of the following provisional applications, each of which is incorporated herein by reference in its entirety: U.S. Provisional Patent Application 60/908,383 filed Mar. 27, 2007; and U.S. Provisional Patent Application 60/908,666, filed Mar. 28, 2007. The '963 application is a continuation-in-part of co-pending United States patent application entitled WIRELESS NON-RADIATIVE ENERGY TRANSFER filed on Jul. 5, 2006 and having Ser. No. 11/481,077 ('077 application), the entirety of which is incorporated herein by reference. The '077 application claims the benefit of provisional application Ser. No. 60/698,442 filed Jul. 12, 2005 ('442 application), the entirety of which is incorporated herein by reference. The '963 application, pursuant to U.S.C. §120 and U.S.C. §363, is a continuation-in-part of International Application No. PCT/US2007/070892, filed Jun. 11, 2007, which is incorporated herein by reference in its entirety, and which claims priority to the following provisional applications, each of which is incorporated herein by reference in its entirety: U.S. Provisional Patent Application 60/908,383 filed Mar. 27, 2007; and U.S. Provisional Patent Application 60/908,666, filed Mar. 28, 2007. This invention was made with government support awarded by the National Science Foundation under Grant No. DMR 02-13282. The government has certain rights in this invention. The disclosure relates to wireless energy transfer. Wireless energy transfer may for example, be useful in such applications as providing power to autonomous electrical or electronic devices. Radiative modes of omni-directional antennas (which work very well for information transfer) are not suitable for such energy transfer, because a vast majority of energy is wasted into free space. Directed radiation modes, using lasers or highly-directional antennas, can be efficiently used for energy transfer, even for long distances (transfer distance L The rapid development of autonomous electronics of recent years (e.g. laptops, cell-phones, house-hold robots, that all typically rely on chemical energy storage) has led to an increased need for wireless energy transfer. The inventors have realized that resonant objects with coupled resonant modes having localized evanescent field patterns may be used for non-radiative wireless energy transfer. Resonant objects tend to couple, while interacting weakly with other off-resonant environmental objects. Typically, using the techniques described below, as the coupling increases, so does the transfer efficiency. In some embodiments, using the below techniques, the energy-transfer rate can be larger than the energy-loss rate. Accordingly, efficient wireless energy-exchange can be achieved between the resonant objects, while suffering only modest transfer and dissipation of energy into other off-resonant objects. The nearly-omnidirectional but stationary (non-lossy) nature of the near field makes this mechanism suitable for mobile wireless receivers. Various embodiments therefore have a variety of possible applications including for example, placing a source (e.g. one connected to the wired electricity network) on the ceiling of a factory room, while devices (robots, vehicles, computers, or similar) are roaming freely within the room. Other applications include power supplies for electric-engine buses and/or hybrid cars and medical implantable devices. In some embodiments, resonant modes are so-called magnetic resonances, for which most of the energy surrounding the resonant objects is stored in the magnetic field; i.e. there is very little electric field outside of the resonant objects. Since most everyday materials (including animals, plants and humans) are non-magnetic, their interaction with magnetic fields is minimal. This is important both for safety and also to reduce interaction with the extraneous environmental objects. In one aspect, an apparatus is disclosed for use in wireless energy transfer, which includes a first resonator structure configured to transfer energy with a second resonator structure over a distance D greater than a characteristic size L In some embodiments, the first resonator structure is configured to transfer energy to the second resonator structure. In some embodiments, the first resonator structure is configured to receive energy from the second resonator structure. In some embodiments, the apparatus includes the second resonator structure. In some embodiments, the first resonator structure has a resonant angular frequency ω In some embodiments Q
In some embodiments, the coupling to loss ratio In some such embodiments, D/L In some embodiments, Q
In some such embodiments, D/L In some embodiments, Q In some embodiments, the quantity κ/√{square root over (Γ In some embodiments, the energy transfer operates with an efficiency η In some embodiments, the energy transfer operates with a radiation loss η
In some embodiments, the energy transfer operates with a radiation loss η
In some embodiments, in the presence of a human at distance of more than 3 cm from the surface of either resonant object, the energy transfer operates with a loss to the human η
In some embodiments, in the presence of a human at distance of more than 10 cm from the surface of either resonant object, the energy transfer operates with a loss to the human η
In some embodiments, during operation, a device coupled to the first or second resonator structure with a coupling rate Γ In some embodiments, P In some embodiments, if the device is coupled to the first resonator, then ½≦[(Γ In some embodiments, the device includes an electrical or electronic device. In some embodiments, the device includes a robot (e.g. a conventional robot or a nano-robot). In some embodiments, the device includes a mobile electronic device (e.g. a telephone, or a cell-phone, or a computer, or a laptop computer, or a personal digital assistant (PDA)). In some embodiments, the device includes an electronic device that receives information wirelessly (e.g. a wireless keyboard, or a wireless mouse, or a wireless computer screen, or a wireless television screen). In some embodiments, the device includes a medical device configured to be implanted in a patient (e.g. an artificial organ, or implant configured to deliver medicine). In some embodiments, the device includes a sensor. In some embodiments, the device includes a vehicle (e.g. a transportation vehicle, or an autonomous vehicle). In some embodiments, the apparatus further includes the device. In some embodiments, during operation, a power supply coupled to the first or second resonator structure with a coupling rate Γ In some embodiments, if the power supply is coupled to the first resonator, then ½≦[(Γ In some embodiments, the apparatus further includes the power source. In some embodiments, the resonant fields are electromagnetic. In some embodiments, f is about 50 GHz or less, about 1 GHz or less, about 100 MHz or less, about 10 MHz or less, about 1 MHz or less, about 100 KHz or less, or about 10 kHz or less. In some embodiments, f is about 50 GHz or greater, about 1 GHz or greater, about 100 MHz or greater, about 10 MHz or greater, about 1 MHz or greater, about 100 kHz or greater, or about 10 kHz or greater. In some embodiments, f is within one of the frequency bands specially assigned for industrial, scientific and medical (ISM) equipment. In some embodiments, the resonant fields are primarily magnetic in the area outside of the resonant objects. In some such embodiments, the ratio of the average electric field energy to average magnetic filed energy at a distance D In some embodiments, the resonant fields are acoustic. In some embodiments, one or more of the resonant fields include a whispering gallery mode of one of the resonant structures. In some embodiments, one of the first and second resonator structures includes a self resonant coil of conducting wire, conducting Litz wire, or conducting ribbon. In some embodiments, both of the first and second resonator structures include self resonant coils of conducting wire, conducting Litz wire, or conducting ribbon. In some embodiments, both of the first and second resonator structures include self resonant coils of conducting wire or conducting Litz wire or conducting ribbon, and Q In some embodiments, one or more of the self resonant conductive wire coils include a wire of length l and cross section radius a wound into a helical coil of radius r, height h and number of turns N. In some embodiments, N=√{square root over (l In some embodiments, for each resonant structure r is about 30 cm, h is about 20 cm, a is about 3 mm and N is about 5.25, and, during operation, a power source coupled to the first or second resonator structure drives the resonator structure at a frequency f. In some embodiments, f is about 10.6 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments D/L In some embodiments, for each resonant structure r is about 30 cm, h is about 20 cm, a is about 1 cm and N is about 4, and, during operation, a power source coupled to the first or second resonator structure drives the resonator structure at a frequency f. In some embodiments, f is about 13.4 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments D/L In some embodiments, for each resonant structure r is about 10 cm, h is about 3 cm, a is about 2 mm and N is about 6, and, during operation, a power source coupled to the first or second resonator structure drives the resonator structure at a frequency f. In some embodiments, f is about 21.4 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments D/L In some embodiments, one of the first and second resonator structures includes a capacitively loaded loop or coil of conducting wire, conducting Litz wire, or conducting ribbon. In some embodiments, both of the first and second resonator structures include capacitively loaded loops or coils of conducting wire, conducting Litz wire, or conducting ribbon. In some embodiments, both of the first and second resonator structures include capacitively loaded loops or coils of conducting wire or conducting Litz wire or conducting ribbon, and Q In some embodiments, the characteristic size L
In some such embodiments, D/L In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure L
In some such embodiments, D/L In some embodiments, the characteristic size L
In some such embodiments, D/L In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure L
In some such embodiments, D/L In some embodiments, the characteristic size L
In some such embodiments, D/L In some embodiments, during operation, one of the resonator structures receives a usable power P
is less than about 5 Amps/√{square root over (Watts)} or less than about 2 Amps/√{square root over (Watts)}. In some embodiments, during operation, one of the resonator structures receives a usable power P
is less than about 2000 Volts/√{square root over (Watts)} or less than about 4000 Volts/√{square root over (Watts)}. In some embodiments, one of the first and second resonator structures includes a inductively loaded rod of conducting wire or conducting Litz wire or conducting ribbon. In some embodiments, both of the first and second resonator structures include inductively loaded rods of conducting wire or conducting Litz wire or conducting ribbon. In some embodiments, both of the first and second resonator structures include inductively loaded rods of conducting wire or conducting Litz wire or conducting ribbon, and Q In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure L
In some such embodiments, D/L In some embodiments, the characteristic size L
In some such embodiments, D/L In some embodiments, one of the first and second resonator structures includes a dielectric disk. In some embodiments, both of the first and second resonator structures include dielectric disks. In some embodiments, both of the first and second resonator structures include dielectric disks, and Q In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure is L
In some such embodiments, D/L In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure is L
In some such embodiments, D/L In some embodiments, at least one of the first and second resonator structures includes one of: a dielectric material, a metallic material, a metallodielectric object, a plasmonic material, a plasmonodielectric object, a superconducting material. In some embodiments, at least one of the resonators has a quality factor greater than about 5000, or greater than about 10000. In some embodiments, the apparatus also includes a third resonator structure configured to transfer energy with one or more of the first and second resonator structures, where the energy transfer between the third resonator structure and the one or more of the first and second resonator structures is mediated by evanescent-tail coupling of the resonant field of the one or more of the first and second resonator structures and a resonant field of the third resonator structure. In some embodiments, the third resonator structure is configured to transfer energy to one or more of the first and second resonator structures. In some embodiments, the first resonator structure is configured to receive energy from one or more of the first and second resonator structures. In some embodiments, the first resonator structure is configured to receive energy from one of the first and second resonator structures and transfer energy to the other one of the first and second resonator structures. Some embodiments include a mechanism for, during operation, maintaining the resonant frequency of one or more of the resonant objects. In some embodiments, the feedback mechanism comprises an oscillator with a fixed frequency and is configured to adjust the resonant frequency of the one or more resonant objects to be about equal to the fixed frequency. In some embodiments, the feedback mechanism is configured to monitor an efficiency of the energy transfer, and adjust the resonant frequency of the one or more resonant objects to maximize the efficiency. In another aspect, a method of wireless energy transfer is disclosed, which method includes providing a first resonator structure and transferring energy with a second resonator structure over a distance D greater than a characteristic size L In some embodiments, the first resonator structure is configured to transfer energy to the second resonator structure. In some embodiments, the first resonator structure is configured to receive energy from the second resonator structure. In some embodiments, the first resonator structure has a resonant angular frequency ω In some embodiments, the coupling to loss ratio
In some such embodiments, D/L In another aspect, an apparatus is disclosed for use in wireless information transfer which includes a first resonator structure configured to transfer information by transferring energy with a second resonator structure over a distance D greater than a characteristic size L In some embodiments, the first resonator structure is configured to transfer energy to the second resonator structure. In some embodiments, the first resonator structure is configured to receive energy from the second resonator structure. In some embodiments the apparatus includes, the second resonator structure. In some embodiments, the first resonator structure has a resonant angular frequency ω In some embodiments, the coupling to loss ratio
In some such embodiments, D/L In another aspect, a method of wireless information transfer is disclosed, which method includes providing a first resonator structure and transferring information by transferring energy with a second resonator structure over a distance D greater than a characteristic size L In some embodiments, the first resonator structure is configured to transfer energy to the second resonator structure. In some embodiments, the first resonator structure is configured to receive energy from the second resonator structure. In some embodiments, the first resonator structure has a resonant angular frequency ω In some embodiments, the coupling to loss ratio
It is to be understood that the characteristic size of an object is equal to the radius of the smallest sphere which can fit around the entire object. The characteristic thickness of an object is, when placed on a flat surface in any arbitrary configuration, the smallest possible height of the highest point of the object above a flat surface. The characteristic width of an object is the radius of the smallest possible circle that the object can pass through while traveling in a straight line. For example, the characteristic width of a cylindrical object is the radius of the cylinder. The distance D over which the energy transfer between two resonant objects occurs is the distance between the respective centers of the smallest spheres which can fit around the entirety of each object. However, when considering the distance between a human and a resonant object, the distance is to be measured from the outer surface of the human to the outer surface of the sphere. As described in detail below, non-radiative energy transfer refers to energy transfer effected primarily through the localized near field, and, at most, secondarily through the radiative portion of the field. It is to be understood that an evanescent tail of a resonant object is the decaying non-radiative portion of a resonant field localized at the object. The decay may take any functional form including, for example, an exponential decay or power law decay. The optimum efficiency frequency of a wireless energy transfer system is the frequency at which the figure of merit
is maximized, all other factors held constant. The resonant width (Γ) refers to the width of an object's resonance due to object's intrinsic losses (e.g. loss to absorption, radiation, etc.). It is to be understood that a Q-factor (Q) is a factor that compares the time constant for decay of an oscillating system's amplitude to its oscillation period. For a given resonator mode with angular frequency ω and resonant width Γ, the Q-factor Q=ω/2Γ. The energy transfer rate (κ) refers to the rate of energy transfer from one resonator to another. In the coupled mode description described below it is the coupling constant between the resonators. It is to be understood that Q Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. In case of conflict with publications, patent applications, patents, and other references mentioned incorporated herein by reference, the present specification, including definitions, will control. Various embodiments may include any of the above features, alone or in combination. Other features, objects, and advantages of the disclosure will be apparent from the following detailed description. Other features, objects, and advantages of the disclosure will be apparent from the following detailed description. Referring to It is to be understood that while two resonant objects are shown in the embodiment of Initially, we present a theoretical framework for understanding non-radiative wireless energy transfer. Note however that it is to be understood that the scope of the invention is not bound by theory. Coupled Mode Theory An appropriate analytical framework for modeling the resonant energy-exchange between two resonant objects 1 and 2 is that of “coupled-mode theory” (CMT). The field of the system of two resonant objects 1 and 2 is approximated by F(r,t)≈a
where ω _{1,2}). The coupling to loss ratio κ/√{square root over (Γ_{1}Γ_{2})} serves as a figure-of-merit in evaluating a system used for wireless energy-transfer, along with the distance over which this ratio can be achieved. The regime κ/√{square root over (Γ_{1}Γ_{1})}1 is called “strong-coupling” regime.
In some embodiments, the energy-transfer application preferably uses resonant modes of high Q=ω/2Γ, corresponding to low (i.e. slow) intrinsic-loss rates Γ. This condition may be satisfied where the coupling is implemented using, not the lossy radiative far-field, but the evanescent (non-lossy) stationary near-field. To implement an energy-transfer scheme, usually finite objects, namely ones that are topologically surrounded everywhere by air, are more appropriate. Unfortunately, objects of finite extent cannot support electromagnetic states that are exponentially decaying in all directions in air, since, from Maxwell's Equations in free space: {right arrow over (k)} Furthermore, in some embodiments, small Q In the following, we describe several examples of systems suitable for energy transfer of the type described above. We will demonstrate how to compute the CMT parameters ω In addition, as described below, Q Self-Resonant Conducting Coils In some embodiments, one or more of the resonant objects are self-resonant conducting coils. Referring to
is the maximum amount of positive charge accumulated in one side of the coil (where an equal amount of negative charge always also accumulates in the other side to make the system neutral) and I
where μ Losses in this resonant system consist of ohmic (material absorption) loss inside the wire and radiative loss into free space. One can again define a total absorption resistance R
where c=1/√{square root over (μ
is the electric-dipole moment of the coil and
is the magnetic-dipole moment of the coil. For the radiation resistance formula Eq. (5), the assumption of operation in the quasi-static regime (h,r λ=2πc/ω) has been used, which is the desired regime of a subwavelength resonance. With these definitions, the absorption and radiation quality factors of the resonance are given by Q^{abs}=Z/R_{abs }and Q^{rad}=Z/R_{rad }respectively.
From Eq. (2)-(5) it follows that to determine the resonance parameters one simply needs to know the current distribution j in the resonant coil. Solving Maxwell's equations to rigorously find the current distribution of the resonant electromagnetic eigenmode of a conducting-wire coil is more involved than, for example, of a standard LC circuit, and we can find no exact solutions in the literature for coils of finite length, making an exact solution difficult. One could in principle write down an elaborate transmission-line-like model, and solve it by brute force. We instead present a model that is (as described below) in good agreement (˜5%) with experiment. Observing that the finite extent of the conductor forming each coil imposes the boundary condition that the current has to be zero at the ends of the coil, since no current can leave the wire, we assume that the resonant mode of each coil is well approximated by a sinusoidal current profile along the length of the conducting wire. We shall be interested in the lowest mode, so if we denote by x the coordinate along the conductor, such that it runs from −l/2 to +l/2, then the current amplitude profile would have the form I(x)=I _{l}(x)=ρ_{o }sin(πx/l), and thus q_{o}=∫_{0} ^{l/2}dxρ_{o}|sin(πx/l)|=ρ_{o}l/π. Using these sinusoidal profiles we find the so-called “self-inductance” L_{s }and “self-capacitance” C_{s}, of the coil by computing numerically the integrals Eq. (2) and (3); the associated frequency and effective impedance are ω_{s }and Z_{s }respectively. The “self-resistances” R_{s}, are given analytically by Eq. (4) and (5) using
and therefore the associated Q The results for two particular embodiments of resonant coils with subwavelength modes of λ
Referring to _{1,2 }(x) and j_{1,2 }(x), total charges and peak currents respectively as q_{1,2 }and I_{1,2}, and capacitances and inductances respectively as C_{1,2 }and L_{1,2}, which are the analogs of ρ(x), j(x), q_{o}, I_{o}, C and L for the single-coil case and are therefore well defined, we can define their mutual capacitance and inductance through the total energy:
and the retardation factor of u=exp(iω|x−x′|/c) inside the integral can been ignored in the quasi-static regime D<<λ of interest, where each coil is within the near field of the other. With this definition, the coupling coefficient is given by κ=ω√{square root over (C _{κ} ^{−1}=(M_{C}/√{square root over (C_{1}C_{2})})^{−1}+(√{square root over (L_{1}L_{2})}/M_{L})^{−1}.
Therefore, to calculate the coupling rate between two self-resonant coils, again the current profiles are needed and, by using again the assumed sinusoidal current profiles, we compute numerically from Eq. (6) the mutual capacitance M
Referring to Table 2, relevant parameters are shown for exemplary embodiments featuring pairs or identical self resonant coils. Numerical results are presented for the average wavelength and loss rates of the two normal modes (individual values not shown), and also the coupling rate and figure-of-merit as a function of the coupling distance D, for the two cases of modes presented in Table 1. It can be seen that for medium distances D/r=10−3 the expected coupling-to-loss ratios are in the range κ/Γ˜2−70. Capacitively-Loaded Conducting Loops or Coils In some embodiments, one or more of the resonant objects are capacitively-loaded conducting loops or coils. Referring to _{s} ω→ω_{s}, as C_{p}→0.
In general, the desired CMT parameters can be found for this system, but again a very complicated solution of Maxwell's Equations is required. Instead, we will analyze only a special case, where a reasonable guess for the current distribution can be made. When C _{s}>C, then ω≈1/√{square root over (LC_{p})}ω_{s }and Z√√{square root over (L/C_{p})}Z_{s}, while all the charge is on the plates of the loading capacitor and thus the current distribution is constant along the wire. This allows us now to compute numerically L from Eq. (2). In the case h=0 and N integer, the integral in Eq. (2) can actually be computed analytically, giving the formula L=μ_{o}r[ ln(8 r/a)−2]N^{2}. Explicit analytical formulas are again available for R from Eq. (4) and (5), since I_{rms}=I_{o}, |p|≈0 and |m|=I_{o}Nπr^{2 }(namely only the magnetic-dipole term is contributing to radiation), so we can determine also Q^{abs}ωL/R_{abs }and Q^{rad}=ωL/R^{rad}. At the end of the calculations, the validity of the assumption of constant current profile is confirmed by checking that indeed the condition C_{p} C_{s} ωω_{s }is satisfied. To satisfy this condition, one could use a large external capacitance, however, this would usually shift the operational frequency lower than the optimal frequency, which we will determine shortly; instead, in typical embodiments, one often prefers coils with very small self-capacitance C_{s }to begin with, which usually holds, for the types of coils under consideration, when N=1, so that the self-capacitance comes from the charge distribution across the single turn, which is almost always very small, or when N>1 and h2 Na, so that the dominant self-capacitance comes from the charge distribution across adjacent turns, which is small if the separation between adjacent turns is large.
The external loading capacitance C
At lower frequencies it is dominated by ohmic loss and at higher frequencies by radiation. Note, however, that the formulas above are accurate as long as {tilde over (ω)} ω_{s }and, as explained above, this holds almost always when N=1, and is usually less accurate when N>1, since h=0 usually implies a large self-capacitance. A coil with large h can be used, if the self-capacitance needs to be reduced compared to the external capacitance, but then the formulas for L and {tilde over (ω)}, {tilde over (Q)} are again less accurate. Similar qualitative behavior is expected, but a more complicated theoretical model is needed for making quantitative predictions in that case.
The results of the above analysis for two embodiments of subwavelength modes of λ/r≧70 (namely highly suitable for near-field coupling and well within the quasi-static limit) of coils with N=1 and h=0 at the optimal frequency Eq. (7) are presented in Table 3. To confirm the validity of constant-current assumption and the resulting analytical formulas, mode-solving calculations were also performed using another completely independent method: computational 3D finite-element frequency-domain (FEFD) simulations (which solve Maxwell's Equations in frequency domain exactly apart for spatial discretization) were conducted, in which the boundaries of the conductor were modeled using a complex impedance ζ ^{−5 }for copper in the microwave). Table 3 shows Numerical FEFD (and in parentheses analytical) results for the wavelength and absorption, radiation and total loss rates, for two different cases of subwavelength-loop resonant modes. Note that for conducting material copper (σ=5.998·10^{7}S/m) was used. (The specific parameters of the plot in _{abs}≧1000 and Q^{rad}≧10000.
Referring to _{s}. In the case h=0, the coupling is only magnetic and again we have an analytical formula, which, in the quasi-static limit rDλ and for the relative orientation shown in _{L}√πμ_{o}/2·(r_{1}r_{2})^{2}N_{1}N_{2}/D^{3}, which means that Q_{κ}∝(D/√{square root over (r_{1}r_{2})})^{3 }is independent of the frequency ω and the number of turns N_{1}, N_{2}. Consequently, the resultant coupling figure-of-merit of interest is
which again is more accurate for N From Eq. (9) it can be seen that the optimal frequency {tilde over (ω)}, where the figure-of-merit is maximized to the value {tilde over (()}{tilde over (√)}{tilde over ((√{square root over (Q _{1 }and Q_{2 }peak. For same coils, it is given by Eq. (7) and then the figure-of-merit Eq. (9) becomes
Typically, one should tune the capacitively-loaded conducting loops or coils, so that their angular eigenfrequencies are close to {tilde over (ω)} within {tilde over (Γ)}, which is half the angular frequency width for which √{square root over (Q Referring to Table 4, numerical FEFD and, in parentheses, analytical results based on the above are shown for two systems each composed of a matched pair of the loaded coils described in Table 3. The average wavelength and loss rates are shown along with the coupling rate and coupling to loss ratio figure-of-merit κ/Γ as a function of the coupling distance D, for the two cases. Note that the average numerical Γ
Optimization of √{square root over (Q In some embodiments, the results above can be used to increase or optimize the performance of a wireless energy transfer system which employs capacitively-added coils. For example, the scaling of Eq. (10) with the different system parameters one sees that to maximize the system figure-of-merit κ/Γ one can, for example: -
- Decrease the resistivity of the conducting material. This can be achieved, for example, by using good conductors (such as copper or silver) and/or lowering the temperature. At very low temperatures one could use also superconducting materials to achieve extremely good performance.
- Increase the wire radius a. In typical embodiments, this action is limited by physical size considerations. The purpose of this action is mainly to reduce the resistive losses in the wire by increasing the cross-sectional area through which the electric current is flowing, so one could alternatively use also a Litz wire or a ribbon instead of a circular wire.
- For fixed desired distance D of energy transfer, increase the radius of the loop r. In typical embodiments, this action is limited by physical size considerations.
- For fixed desired distance vs. loop-size ratio D/r, decrease the radius of the loop r. In typical embodiments, this action is limited by physical size considerations.
- Increase the number of turns N. (Even though Eq. (10) is expected to be less accurate for N>1, qualitatively it still provides a good indication that we expect an improvement in the coupling-to-loss ratio with increased N.) In typical embodiments, this action is limited by physical size and possible voltage considerations, as will be discussed in following sections.
- Adjust the alignment and orientation between the two coils. The figure-of-merit is optimized when both cylindrical coils have exactly the same axis of cylindrical symmetry (namely they are “facing” each other). In some embodiments, particular mutual coil angles and orientations that lead to zero mutual inductance (such as the orientation where the axes of the two coils are perpendicular) should be avoided.
- Finally, note that the height of the coil h is another available design parameter, which has an impact to the performance similar to that of its radius r, and thus the design rules are similar.
The above analysis technique can be used to design systems with desired parameters. For example, as listed below, the above described techniques can be used to determine the cross sectional radius a of the wire which one should use when designing as system two same single-turn loops with a given radius in order to achieve a specific performance in terms of κ/Γ at a given D/r between them, when the material is copper (σ= Similar analysis can be done for the case of two dissimilar loops. For example, in some embodiments, the device under consideration is very specific (e.g. a laptop or a cell phone), so the dimensions of the device object (r _{s}=1.158 m, a_{s}≧5 mm _{s}=1.15 m, a_{s}≧33 mm _{s}=1.119 m, a_{s}≧7 mm _{s}=1.119 m, a_{s}≧52 mm _{s}=1.518 m, a_{s}≧7 mm _{s}=1.514 m, a_{s}≧50 mm _{s}=1.491 m, a_{s}≧5 mm _{s}=1.491 m, a_{s}≧36 mmOptimization of Q As will be described below, in some embodiments the quality factor Q of the resonant objects is limited from external perturbations and thus varying the coil parameters cannot lead to improvement in Q. In such cases, one may opt to increase the coupling to loss ratio figure-of-merit by decreasing Q -
- Increase the wire radii a
_{1 }and a_{2}. In typical embodiments, this action is limited by physical size considerations. - For fixed desired distance D of energy transfer, increase the radii of the coils r
_{1 }and r_{2}. In typical embodiments, this action is limited by physical size considerations. - For fixed desired distance vs. coil-sizes ratio D/√{square root over (r
_{1}r_{2})}, only the weak (logarithmic) dependence of the inductance remains, which suggests that one should decrease the radii of the coils r_{1 }and r_{2}. In typical embodiments, this action is limited by physical size considerations. - Adjust the alignment and orientation between the two coils. In typical embodiments, the coupling is optimized when both cylindrical coils have exactly the same axis of cylindrical symmetry (namely they are “facing” each other). Particular mutual coil angles and orientations that lead to zero mutual inductance (such as the orientation where the axes of the two coils are perpendicular) should obviously be avoided.
- Finally, note that the heights of the coils h
_{1 }and h_{2 }are other available design parameters, which have an impact to the coupling similar to that of their radii r_{1 }and r_{2}, and thus the design rules are similar.
- Increase the wire radii a
Further practical considerations apart from efficiency, e.g. physical size limitations, will be discussed in detail below. It is also important to appreciate the difference between the above described resonant-coupling inductive scheme and the well-known non-resonant inductive scheme for energy transfer. Using CMT it is easy to show that, keeping the geometry and the energy stored at the source fixed, the resonant inductive mechanism allows for ˜Q Inductively-Loaded Conducting Rods A straight conducting rod of length 2 h and cross-sectional radius a has distributed capacitance and distributed inductance, and therefore it supports a resonant mode of angular frequency ω. Using the same procedure as in the case of self-resonant coils, one can define an effective total inductance L and an effective total capacitance C of the rod through formulas (2) and (3). With these definitions, the resonant angular frequency and the effective impedance are given again by the common formulas ω=1/√{square root over (LC)} and Z=√{square root over (L/C)} respectively. To calculate the total inductance and capacitance, one can assume again a sinusoidal current profile along the length of the conducting wire. When interested in the lowest mode, if we denote by x the coordinate along the conductor, such that it runs from −h to +h, then the current amplitude profile would have the form I(x)=I In some embodiments, one or more of the resonant objects are inductively-loaded conducting rods. A straight conducting rod of length 2 h and cross-sectional radius a, as in the previous paragraph, is cut into two equal pieces of length h, which are connected via a coil wrapped around a magnetic material of relative permeability μ, and everything is surrounded by air. The coil has an inductance L _{s} ω→ω_{s}, as L_{c}→0.
In general, the desired CMT parameters can be found for this system, but again a very complicated solution of Maxwell's Equations is required. Instead, we will analyze only a special case, where a reasonable guess for the current distribution can be made. When L _{s}>L, then ω≈1/√{square root over (L_{c}C)}ω_{s }and Z≈√{square root over (L_{c}/C)}Z_{s}, while the current distribution is triangular along the rod (with maximum at the center-loading inductor and zero at the ends) and thus the charge distribution is positive constant on one half of the rod and equally negative constant on the other side of the rod. This allows us now to compute numerically C from Eq. (3). In this case, the integral in Eq. (3) can actually be computed analytically, giving the formula 1/C=1/(π∈_{o}h)[ln(h/a)−1]. Explicit analytical formulas are again available for R from Eq. (4) and (5), since I_{rms}=I_{o}, |p|=q_{o}h and |m|=0 (namely only the electric-dipole term is contributing to radiation), so we can determine also Q^{abs}=1/ωCR_{abs }and Q^{rad}=1/ωCR_{rad}. At the end of the calculations, the validity of the assumption of triangular current profile is confirmed by checking that indeed the condition L_{c} L_{s} ωω_{s }is satisfied. This condition is relatively easily satisfied, since typically a conducting rod has very small self-inductance L_{s }to begin with.
Another important loss factor in this case is the resistive loss inside the coil of the external loading inductor L
where the total wire length is l The external loading inductance L
Then, for the particular simple case L _{s}, for which we have analytical formulas, the total Q=1/ωC(R_{c}+R_{abs}+R_{rad}) becomes highest at some optimal frequency _{c}≈0.8 (μ_{o}σ^{2}r_{Bc} ^{3}/C)^{1/4}) At lower frequencies it is dominated by ohmic loss inside the inductor coil and at higher frequencies by radiation. Note, again, that the above formulas are accurate as long as {tilde over (ω)}ω_{s }and, as explained above, this is easy to design for by using a large inductance.
The results of the above analysis for two embodiments, using Brooks coils, of subwavelength modes of λ/h≧200 (namely highly suitable for near-field coupling and well within the quasi-static limit) at the optimal frequency {tilde over (ω)} are presented in Table 5. Table 5 shows in parentheses (for similarity to previous tables) analytical results for the wavelength and absorption, radiation and total loss rates, for two different cases of subwavelength-loop resonant modes. Note that for conducting material copper (σ=5.998·10
In some embodiments, energy is transferred between two inductively-loaded rods. For the rate of energy transfer between two inductively-loaded rods 1 and 2 at distance D between their centers, the mutual capacitance M _{s}. In this case, the coupling is only electric and again we have an analytical formula, which, in the quasi-static limit hDλ and for the relative orientation such that the two rods are aligned on the same axis, is 1/M_{C}≈½π∈_{o}·(h_{1}h_{2})^{2}/D^{3}, which means that Q_{κ}∝(D/P√{square root over (h_{1}h_{2})})^{3 }is independent of the frequency ω. Consequently, one can get the resultant coupling figure-of-merit of interest
It can be seen that the optimal frequency {tilde over (ω)}, where the figure-of-merit is maximized to the value {tilde over (()}{tilde over (√)}{tilde over ((√{square root over (Q _{1 }and Q_{2 }peak. Typically, one should tune the inductively-loaded conducting rods, so that their angular eigenfrequencies are close to {tilde over (ω)} within {tilde over (Γ)}, which is half the angular frequency width for which √{square root over (Q_{1}Q_{2})}/Q_{κ}>{tilde over (()}{tilde over (√)}{tilde over ((√{square root over (Q_{1}Q_{2})}/Q_{κ}))}/2.
Referring to Table 6, in parentheses (for similarity to previous tables) analytical results based on the above are shown for two systems each composed of a matched pair of the loaded rods described in Table 5. The average wavelength and loss rates are shown along with the coupling rate and coupling to loss ratio figure-of-merit κ/Γ as a function of the coupling distance D, for the two cases. Note that for Γ _{s }to make the triangular-current assumption a good one and computed M_{C }numerically from Eq. (6). The results show that for medium distances D/h=10−3 the expected coupling-to-loss ratios are in the range κ/Γ˜0.5−100.
Dielectric Disks In some embodiments, one or more of the resonant objects are dielectric objects, such as disks. Consider a two dimensional dielectric disk object, as shown in
The results for two TE-polarized dielectric-disk subwavelength modes of λ/r≧10 are presented in Table 7. Table 7 shows numerical FDFD (and in parentheses analytical SV) results for the wavelength and absorption, radiation and total loss rates, for two different cases of subwavelength-disk resonant modes. Note that disk-material loss-tangent Im{e}/Re{∈}= The required values of c, shown in Table 7, might at first seem unrealistically large. However, not only are there in the microwave regime (appropriate for approximately meter-range coupling applications) many materials that have both reasonably high enough dielectric constants and low losses (e.g. Titania, Barium tetratitanate, Lithium tantalite etc.), but also c could signify instead the effective index of other known subwavelength surface-wave systems, such as surface modes on surfaces of metallic materials or plasmonic (metal-like, negative-∈) materials or metallo-dielectric photonic crystals or plasmono-dielectric photonic crystals. To calculate now the achievable rate of energy transfer between two disks
Note that even though particular embodiments are presented and analyzed above as examples of systems that use resonant electromagnetic coupling for wireless energy transfer, those of self-resonant conducting coils, capacitively-loaded resonant conducting coils and resonant dielectric disks, any system that supports an electromagnetic mode with its electromagnetic energy extending much further than its size can be used for transferring energy. For example, there can be many abstract geometries with distributed capacitances and inductances that support the desired kind of resonances. In any one of these geometries, one can choose certain parameters to increase and/or optimize √{square root over (Q System Sensitivity to Extraneous Objects In general, the overall performance of particular embodiment of the resonance-based wireless energy-transfer scheme depends strongly on the robustness of the resonant objects' resonances. Therefore, it is desirable to analyze the resonant objects' sensitivity to the near presence of random non-resonant extraneous objects. One appropriate analytical model is that of “perturbation theory” (PT), which suggests that in the presence of an extraneous object e the field amplitude a
where again ω The frequency shift is a problem that can be “fixed” by applying to one or more resonant objects a feedback mechanism that corrects its frequency. For example, referring to As another example, referring to In various embodiments, other frequency adjusting schemes may be used which rely on information exchange between the resonant objects. For example, the frequency of a source object can be monitored and transmitted to a device object, which is in turn synched to this frequency using frequency adjusters as described above. In other embodiments the frequency of a single clock may be transmitted to multiple devices, and each device then synched to that frequency. Unlike the frequency shift, the extrinsic loss can be detrimental to the functionality of the energy-transfer scheme, because it is difficult to remedy, so the total loss rate Γ Capacitively-Loaded Conducting Loops or Coils In embodiments using primarily magnetic resonances, the influence of extraneous objects on the resonances is nearly absent. The reason is that, in the quasi-static regime of operation (r λ) that we are considering, the near field in the air region surrounding the resonator is predominantly magnetic (e.g. for coils with h2 r most of the electric field is localized within the self-capacitance of the coil or the externally loading capacitor), therefore extraneous non-conducting objects e that could interact with this field and act as a perturbation to the resonance are those having significant magnetic properties (magnetic permeability Re{μ}>1 or magnetic loss Im{μ}>0). Since almost all every-day non-conducting materials are non-magnetic but just dielectric, they respond to magnetic fields in the same way as free space, and thus will not disturb the resonance of the resonator. Extraneous conducting materials can however lead to some extrinsic losses due to the eddy currents induced on their surface.As noted above, an extremely important implication of this fact relates to safety considerations for human beings. Humans are also non-magnetic and can sustain strong magnetic fields without undergoing any risk. A typical example, where magnetic fields B˜1 T are safely used on humans, is the Magnetic Resonance Imaging (MRI) technique for medical testing. In contrast, the magnetic near-field required in typical embodiments in order to provide a few Watts of power to devices is only B˜10 One can, for example, estimate the degree to which the resonant system of a capacitively-loaded conducting-wire coil has mostly magnetic energy stored in the space surrounding it. If one ignores the fringing electric field from the capacitor, the electric and magnetic energy densities in the space surrounding the coil come just from the electric and magnetic field produced by the current in the wire; note that in the far field, these two energy densities must be equal, as is always the case for radiative fields. By using the results for the fields produced by a subwavelength (r λ) current loop (magnetic dipole) with h=0, we can calculate the ratio of electric to magnetic energy densities, as a function of distance D_{P }from the center of the loop (in the limit rD_{P}) and the angle θ with respect to the loop axis:
where the second line is the ratio of averages over all angles by integrating the electric and magnetic energy densities over the surface of a sphere of radius D _{p}=10 r=3 m the ratio of average electric to average magnetic energy density would be ˜12% and at D_{p}=3 r=90 cm it would be ˜1%, and for the loop of r=10 cm at a distance D_{p}=10 r=1 m the ratio would be ˜33% and at D_{p}=3 r=30 cm it would be ˜2.5%. At closer distances this ratio is even smaller and thus the energy is predominantly magnetic in the near field, while in the radiative far field, where they are necessarily of the same order (ratio→>1), both are very small, because the fields have significantly decayed, as capacitively-loaded coil systems are designed to radiate very little. Therefore, this is the criterion that qualifies this class of resonant system as a magnetic resonant system.
To provide an estimate of the effect of extraneous objects on the resonance of a capacitively-loaded loop including the capacitor fringing electric field, we use the perturbation theory formula, stated earlier, Γ Self-resonant coils are more sensitive than capacitively-loaded coils, since for the former the electric field extends over a much larger region in space (the entire coil) rather than for the latter (just inside the capacitor). On the other hand, self-resonant coils are simple to make and can withstand much larger voltages than most lumped capacitors. In general, different embodiments of resonant systems have different degree of sensitivity to external perturbations, and the resonant system of choice depends on the particular application at hand, and how important matters of sensitivity or safety are for that application. For example, for a medical implantable device (such as a wirelessly powered artificial heart) the electric field extent must be minimized to the highest degree possible to protect the tissue surrounding the device. In such cases where sensitivity to external objects or safety is important, one should design the resonant systems so that the ratio of electric to magnetic energy density u Dielectric Disks In embodiments using resonances that are not primarily magnetic, the influence of extraneous objects may be of concern. For example, for dielectric disks, small, low-index, low-material-loss or far-away stray objects will induce small scattering and absorption. In such cases of small perturbations these extrinsic loss mechanisms can be quantified using respectively the analytical first-order perturbation theory formulas All perturbations Γ where U=½∫d and depends linearly on the field tails E _{1-e}), at least for small perturbations, and thus the energy-transfer scheme is expected to be sturdy for this class of resonant dielectric disks. However, we also want to examine certain possible situations where extraneous objects cause perturbations too strong to analyze using the above first-order perturbation theory approach. For example, we place a dielectric disk c close to another off-resonance object of large Re{∈}, Im{∈} and of same size but different shape (such as a human being h), as shown in a, and a roughened surface of large extent but of small Re{∈}, Im{∈} (such as a wall w), as shown in b. For distances D_{h/w}/r=10^{−3 }between the disk-center and the “human”-center or “wall”, the numerical FDFD simulation results presented in a and 9 b suggest that, the disk resonance seems to be fairly robust, since it is not detrimentally disturbed by the presence of extraneous objects, with the exception of the very close proximity of high-loss objects. To examine the influence of large perturbations on an entire energy-transfer system we consider two resonant disks in the close presence of both a “human” and a “wall”. Comparing c, the numerical FDFD simulations show that the system performance deteriorates from κ/┌_{c}˜1−50 to κ[hw]/┌_{c[hw]}˜0.5−10 i.e. only by acceptably small amounts.
Inductively-loaded conducting rods may also be more sensitive than capacitively-loaded coils, since they rely on the electric field to achieve the coupling. System Efficiency In general, another important factor for any energy transfer scheme is the transfer efficiency. Consider again the combined system of a resonant source s and device d in the presence of a set of extraneous objects e. The efficiency of this resonance-based energy-transfer scheme may be determined, when energy is being drained from the device at rate Γ
where Γ
where fom Referring to Then from the source circuit at resonance (ω
and from the device circuit at resonance (ωL jωMI _{s} =I _{d}(R _{d}+R_{w})So by substituting the second to the first:
Now we take the real part (time-averaged powers) to find the efficiency:
which with Γ From Eq. (14) one can find that the efficiency is optimized in terms of the chosen work-drainage rate, when this is chosen to be Γ For example, consider the capacitively-loaded coil embodiments described in Table 4, with coupling distance D/r=7, a “human” extraneous object at distance D Overall System Performance In many cases, the dimensions of the resonant objects will be set by the particular application at hand. For example, when this application is powering a laptop or a cell-phone, the device resonant object cannot have dimensions larger that those of the laptop or cell-phone respectively. In particular, for a system of two loops of specified dimensions, in terms of loop radii r In general, in various embodiments, the primary dependent variable that one wants to increase or optimize is the overall efficiency η. However, other important variables need to be taken into consideration upon system design. For example, in embodiments featuring capacitively-loaded coils, the design may be constrained by, for example, the currents flowing inside the wires I In the following, we examine then the effects of each one of the independent variables on the dependent ones. We define a new variable wp to express the work-drainage rate for some particular value of fom _{s }and V_{s}), Γ_{work}/Γ_{d[e]}=√{square root over (1+fom_{[e]} ^{2})}>1wp=1 to increase the efficiency, as seen earlier, or Γ_{work}/Γ_{d[e]} 1wp>>1 to decrease the required energy stored in the device (and therefore I_{d }and V_{d}) and to decrease or minimize Q_{tot}=ψL_{d}/(R_{d}+R_{w})=ω/[2(Γ_{d}+Γ_{work})]. Similar is the impact of the choice of the power supply feeding rate Γ_{supply}, with the roles of the source and the device reversed.
Increasing N
required for given output power P With respect to frequency, again, there is an optimal one for efficiency, and Q One way to decide on an operating regime for the system is based on a graphical method. In Finally, one could additionally optimize for the source dimensions, since usually only the device dimensions are limited, as discussed earlier. Namely, one can add r Experimental Results An experimental realization of an embodiment of the above described scheme for wireless energy transfer consists of two self-resonant coils of the type described above, one of which (the source coil) is coupled inductively to an oscillating circuit, and the second (the device coil) is coupled inductively to a resistive load, as shown schematically in The parameters for the two identical helical coils built for the experimental validation of the power transfer scheme were h=20 cm, a=3 mm, r=30 cm, N=5.25. Both coils are made of copper. Due to imperfections in the construction, the spacing between loops of the helix is not uniform, and we have encapsulated the uncertainty about their uniformity by attributing a 10% (2 cm) uncertainty to h. The expected resonant frequency given these dimensions is f The theoretical Q for the loops is estimated to be ˜2500 (assuming perfect copper of resistivity ρ= The coupling coefficient κ can be found experimentally by placing the two self-resonant coils (fine-tuned, by slightly adjusting h, to the same resonant frequency when isolated) a distance D apart and measuring the splitting in the frequencies of the two resonant modes in the transmission spectrum. According to coupled-mode theory, the splitting in the transmission spectrum should be Δω=2√{square root over (κ As noted above, the maximum theoretical efficiency depends only on the parameter κ/√{square root over (Γ The power supply circuit was a standard Colpitts oscillator coupled inductively to the source coil by means of a single loop of copper wire 25 cm in radius (see In order to isolate the efficiency of the transfer taking place specifically between the source coil and the load, we measured the current at the mid-point of each of the self-resonant coils with a current-probe (which was not found to lower the Q of the coils noticeably.) This gave a measurement of the current parameters I Using this embodiment, we were able to transfer significant amounts of power using this setup, fully lighting up a 60 W light-bulb from distances more than 2 m away, for example. As an additional test, we also measured the total power going into the driving circuit. The efficiency of the wireless transfer itself was hard to estimate in this way, however, as the efficiency of the Colpitts oscillator itself is not precisely known, although it is expected to be far from 100%. Nevertheless, this gave an overly conservative lower bound on the efficiency. When transferring 60 W to the load over a distance of 2 m, for example, the power flowing into the driving circuit was 400 W. This yields an overall wall-to-load efficiency of ˜15%, which is reasonable given the expected ˜40% efficiency for the wireless power transfer at that distance and the low efficiency of the driving circuit. From the theoretical treatment above, we see that in typical embodiments it is important that the coils be on resonance for the power transfer to be practical. We found experimentally that the power transmitted to the load dropped sharply as one of the coils was detuned from resonance. For a fractional detuning Δf/f The power transfer was not found to be visibly affected as humans and various everyday objects, such as metallic and wooden furniture, as well as electronic devices large and small, were placed between the two coils, even when they drastically obstructed the line of sight between source and device. External objects were found to have an effect only when they were closer than 10 cm from either one of the coils. While some materials (such as aluminum foil, styrofoam and humans) mostly just shifted the resonant frequency, which could in principle be easily corrected with a feedback circuit of the type described earlier, others (cardboard, wood, and PVC) lowered Q when placed closer than a few centimeters from the coil, thereby lowering the efficiency of the transfer. We believe that this method of power transfer should be safe for humans. When transferring 60 W (more than enough to power a laptop computer) across 2 m, we estimated that the magnitude of the magnetic field generated is much weaker than the Earth's magnetic field for all distances except for less than about 1 cm away from the wires in the coil, an indication of the safety of the scheme even after long-term use. The power radiated for these parameters was ˜5 W, which is roughly an order of magnitude higher than cell phones but could be drastically reduced, as discussed below. Although the two coils are currently of identical dimensions, it is possible to make the device coil small enough to fit into portable devices without decreasing the efficiency. One could, for instance, maintain the product of the characteristic sizes of the source and device coils constant. These experiments demonstrated experimentally a system for power transfer over medium range distances, and found that the experimental results match theory well in multiple independent and mutually consistent tests. We believe that the efficiency of the scheme and the distances covered could be appreciably improved by silver-plating the coils, which should increase their Q, or by working with more elaborate geometries for the resonant objects. Nevertheless, the performance characteristics of the system presented here are already at levels where they could be useful in practical applications. Applications In conclusion, we have described several embodiments of a resonance-based scheme for wireless non-radiative energy transfer. Although our consideration has been for a static geometry (namely κ and Γ For example, in the macroscopic world, this scheme could potentially be used to deliver power to for example, robots and/or computers in a factory room, or electric buses on a highway. In some embodiments source-object could be an elongated “pipe” running above the highway, or along the ceiling. Some embodiments of the wireless transfer scheme can provide energy to power or charge devices that are difficult or impossible to reach using wires or other techniques. For example some embodiments may provide power to implanted medical devices (e.g. artificial hearts, pacemakers, medicine delivery pumps, etc.) or buried underground sensors. In the microscopic world, where much smaller wavelengths would be used and smaller powers are needed, one could use it to implement optical inter-connects for CMOS electronics, or to transfer energy to autonomous nano-objects (e.g. MEMS or nano-robots) without worrying much about the relative alignment between the sources and the devices. Furthermore, the range of applicability could be extended to acoustic systems, where the source and device are connected via a common condensed-matter object. In some embodiments, the techniques described above can provide non-radiative wireless transfer of information using the localized near fields of resonant object. Such schemes provide increased security because no information is radiated into the far-field, and are well suited for mid-range communication of highly sensitive information. A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Referenced by
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