MAXIMIZING POWER YIELD FROM WIRELESS POWER MAGNETIC RESONATORS
Described herein are embodiments of a wireless power transmitter device for transmitting power to at least one highQ resonator that includes a first portion, formed of a highQ magnetic resonator, and a high frequency generation system, having a number of components, wherein at least one of said components is formed using a process which creates nanoscale features.
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 to 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 continuationinpart of copending U.S. patent application entitled WIRELESS NONRADIATIVE 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.
STATEMENT REGARDING GOVERNMENT FUNDINGThis invention was made with government support awarded by the National Science Foundation under Grant No. DMR 0213282. The government has certain rights in this invention.
BACKGROUNDThe 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 omnidirectional 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 highlydirectional antennas, can be efficiently used for energy transfer, even for long distances (transfer distance L_{TRANS}>>L_{DEV}, where L_{DEV }is the characteristic size of the device and/or the source), but require existence of an uninterruptible lineofsight and a complicated tracking system in the case of mobile objects. Some transfer schemes rely on induction, but are typically restricted to very closerange (L_{TRANS}<<L_{DEV}) or low power (˜mW) energy transfers.
The rapid development of autonomous electronics of recent years (e.g. laptops, cellphones, household robots, that all typically rely on chemical energy storage) has led to an increased need for wireless energy transfer.
SUMMARYThe inventors have realized that resonant objects with coupled resonant modes having localized evanescent field patterns may be used for nonradiative wireless energy transfer. Resonant objects tend to couple, while interacting weakly with other offresonant 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 energytransfer rate can be larger than the energyloss rate. Accordingly, efficient wireless energyexchange can be achieved between the resonant objects, while suffering only modest transfer and dissipation of energy into other offresonant objects. The nearlyomnidirectional but stationary (nonlossy) 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 electricengine buses and/or hybrid cars and medical implantable devices.
In some embodiments, resonant modes are socalled 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 nonmagnetic, 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_{2 }of the second resonator structure. In some embodiments, D is also greater than one or more of: a characteristic size L_{1 }of the first resonator structure, a characteristic thickness T_{1 }of the first resonator structure, and a characteristic width W_{1 }of the first resonator structure. The energy transfer is mediated by evanescenttail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure. The apparatus may include any of the following features alone or in combination.
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_{1}, a Qfactor Q_{1}, and a resonance width Γ_{1}, the second resonator structure has a resonant angular frequency ω_{2}, a Qfactor Q_{2}, and a resonance width Γ_{2}, and the energy transfer has a rate κ. In some embodiments, the absolute value of the difference of the angular frequencies ω_{1 }and ω_{2 }is smaller than the broader of the resonant widths Γ_{1 }and Γ_{2}.
In some embodiments Q_{1}>100 and Q_{2}>100, Q_{1}>300 and Q_{2}>300 , Q_{1}>500 and Q_{2}>500, or Q_{1}>1000 and Q_{2}>1000. In some embodiments, Q_{1}>100 or Q_{2}>100 , Q_{1}>300 or Q_{2}>300 , Q_{1}>500 or Q_{2}>500 , or Q_{1}>1000 or Q_{2}>1000.
In some embodiments, the coupling to loss ratio
In some such embodiments, D/L_{2 }may be as large as 2, as large as 3, as large as 5, as large as 7, or as large as 10.
In some embodiments, Q_{1}>1000 and Q_{2}>1000, and the coupling to loss ratio
In some such embodiments, D/L_{2 }may be as large as 2, as large as 3, as large as 5, as large as 7, as large as 10.
In some embodiments, Q_{κ}=ω/2κ is less than about 50, less than about 200, less than about 500, or less than about 1000. In some such embodiments, D/L_{2 }is as large as 2, as large as 3, as large as 5, as large as 7, or as large as 10.
In some embodiments, the quantity κ/√{square root over (Γ_{1}Γ_{2})} is maximized at an angular frequency {tilde over (ω)} with a frequency width {tilde over (Γ)} around the maximum, and the absolute value of the difference of the angular frequencies ω_{1 }and {tilde over (ω)} is smaller than the width {tilde over (Γ)}, and the absolute value of the difference of the angular frequencies ω_{2 }and {tilde over (ω)} is smaller than the width {tilde over (Γ)}.
In some embodiments, the energy transfer operates with an efficiency η_{work }greater than about 1%, greater than about 10%, greater than about 30%, greater than about 50%, or greater than about 80%.
In some embodiments, the energy transfer operates with a radiation loss η_{rad }less that about 10%. In some such embodiments the coupling to loss ratio
In some embodiments, the energy transfer operates with a radiation loss η_{rad }less that about 1%. In some such embodiments, the coupling to loss ratio
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_{h }of less than about 1%. In some such embodiments the coupling to loss ratio
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_{h }of less than about 0.2%. In some such embodiments the coupling to loss ratio
In some embodiments, during operation, a device coupled to the first or second resonator structure with a coupling rate Γ_{work }receives a usable power P_{work }from the resonator structure.
In some embodiments, P_{work }is greater than about 0.01 Watt, greater than about 0.1 Watt, greater than about 1 Watt, or greater than about 10 Watt.
In some embodiments, if the device is coupled to the first resonator, then ½≦[(Γ_{work}/Γ_{1})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦2, or ¼≦[(Γ_{work}/Γ_{1})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦4, or ⅛≦[(Γ_{work}/Γ_{1})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦8, and, if the device is coupled to the second resonator, then ½≦[(Γ_{work}/Γ_{2})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}23 2, or ¼[(Γ_{work}Γ_{2})^{2}−1]/(78 /√{square root over (Γ_{1}Γ_{2})})^{2}≦4, or ⅛≦[(Γ_{work}/Γ_{2})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦8.
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 nanorobot). In some embodiments, the device includes a mobile electronic device (e.g. a telephone, or a cellphone, 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_{supply }drives the resonator structure at a frequency f and supplies power P_{total}. In some embodiments, the absolute value of the difference of the angular frequencies ω=2πf and ω_{1 }is smaller than the resonant width Γ_{1}, and the absolute value of the difference of the angular frequencies ω=2πf and ω_{2 }is smaller than the resonant width Γ_{2}. In some embodiments, f is about the optimum efficiency frequency.
In some embodiments, if the power supply is coupled to the first resonator, then ½≦[(Γ_{supply}/Γ_{1})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦2, or ¼≦[(Γ_{supply}/Γ_{1}))^{2}−1]/κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦4, or ⅛≦[(Γ_{supply}/Γ_{1})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦8, and, if the power supply is coupled to the second resonator, then ½≦[(Γ_{supply}/Γ_{2})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦2, or ¼≦[(Γ_{supply}/Γ_{2})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦4, or ⅛≦[(Γ_{supply}/Γ_{2})^{2}−1]/(κ/√{square root over (Γ_{1}Γ_{2})})^{2}≦8.
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_{p }from the closest resonant object is less than 0.01, or less than 0.1. In some embodiments, L_{R }is the characteristic size of the closest resonant object and D_{p}/L_{R }is less than 1.5, 3, 5, 7, or 10.
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_{1}>300 and Q_{2}>300.
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^{2}−h^{2})}/2πr.
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_{R }is as large as about 2, 3, 5, or 8.
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_{R }is as large as about 3, 5, 7, or 10.
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_{R }is as large as about 3, 5, 7, or 10.
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_{1}>300 and Q_{2}>300.
In some embodiments, the characteristic size L_{R }of the resonator structure receiving energy from the other resonator structure is less than about 1 cm and the width of the conducting wire or Litz wire or ribbon of said object is less than about 1 mm, 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 380 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments, _{D/L}_{R }is as large as about 3, about 5, about 7, or about 10.
In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure L_{R }is less than about 10 cm and the width of the conducting wire or Litz wire or ribbon of said object is less than about 1 cm, 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 43 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7, or about 10.
In some embodiments, the characteristic size L_{R }of the resonator structure receiving energy from the other resonator structure is less than about 30 cm and the width of the conducting wire or Litz wire or ribbon of said object is less than about 5 cm, and, during operation, a power source coupled to the first or second resonator structure drives the resonator structure at a frequency f. In some such embodiments, f is about 9 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7, or about 10.
In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure L_{R }is less than about 30 cm and the width of the conducting wire or Litz wire or ribbon of said object is less than about 5 mm, 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 17 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7, or about 10.
In some embodiments, the characteristic size L_{R }of the resonator structure receiving energy from the other resonator structure is less than about 1 m, and the width of the conducting wire or Litz wire or ribbon of said object is less than about 1 cm, 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 5 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7, or about 10.
In some embodiments, during operation, one of the resonator structures receives a usable power P_{w }from the other resonator structure, an electrical current I_{s }flows in the resonator structure which is transferring energy to the other resonant structure, and the ratio
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_{w }from the other resonator structure, a voltage difference V_{s }appears across the capacitive element of the first resonator structure, and the ratio
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_{1}>300 and Q_{2}>300.
In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure L_{R }is less than about 10 cm and the width of the conducting wire or Litz wire or ribbon of said object is less than about 1 cm, 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 14 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7, or about 10.
In some embodiments, the characteristic size L_{R }of the resonator structure receiving energy from the other resonator structure is less than about 30 cm and the width of the conducting wire or Litz wire or ribbon of said object is less than about 5 cm, and, during operation, a power source coupled to the first or second resonator structure drives the resonator structure at a frequency f. In some such embodiments, f is about 2.5 MHz. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7, or about 10.
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_{1}>300 and Q_{2}>300.
In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure is L_{R }and the real part of the permittivity of said resonator structure ε is less than about 150. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7, or about 10.
In some embodiments, the characteristic size of the resonator structure receiving energy from the other resonator structure is L_{R }and the real part of the permittivity of said resonator structure ε is less than about 65. In some such embodiments, the coupling to loss ratio
In some such embodiments, D/L_{R }is as large as about 3, about 5, about 7.
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 evanescenttail 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_{2 }of the second resonator structure. In some embodiments, D is also greater than one or more of: a characteristic size L_{1 }of the first resonator structure, a characteristic thickness T_{1 }of the first resonator structure, and a characteristic width W_{1 }of the first resonator structure. The energy transfer is mediated by evanescenttail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure.
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_{1}, a Qfactor Q_{1}, and a resonance width Γ_{1}, the second resonator structure has a resonant angular frequency ω_{2}, a Qfactor Q_{2}, and a resonance width Γ_{2}, and the energy transfer has a rate κ. In some embodiments, the absolute value of the difference of the angular frequencies ω_{1 }and ω_{2 }is smaller than the broader of the resonant widths Γ_{1 }and Γ_{2}.
In some embodiments, the coupling to loss ratio
In some such embodiments, D/L_{2 }may be as large as 2, as large as 3, as large as 5, as large as 7, or as large as 10.
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_{2 }of the second resonator structure. In some embodiments, D is also greater than one or more of: a characteristic size L_{1 }of the first resonator structure, a characteristic thickness T_{1 }of the first resonator structure, and a characteristic width W_{1 }of the first resonator structure. The energy transfer is mediated by evanescenttail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure.
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_{1}, a Qfactor Q_{1}, and a resonance width Γ_{1}, the second resonator structure has a resonant angular frequency ω_{2}, a Qfactor Q_{2}, and a resonance width Γ_{2}, and the energy transfer has a rate κ. In some embodiments, the absolute value of the difference of the angular frequencies ω_{1 }and ω_{2 }is smaller than the broader of the resonant widths Γ_{1 }and Γ_{2}.
In some embodiments, the coupling to loss ratio
In some such embodiments, D/L_{2 }may be as large as 2, as large as 3, as large as 5, as large as 7, or as large as 10.
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_{2 }of the second resonator structure. In some embodiments, D is also greater than one or more of: a characteristic size L_{1 }of the first resonator structure, a characteristic thickness T_{1 }of the first resonator structure, and a characteristic width W_{1 }of the first resonator structure. The energy transfer is mediated by evanescenttail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure.
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}^{1}, a Qfactor ^{Q}^{1}, and a resonance width ^{Γ}^{1}, the second resonator structure has a resonant angular frequency ^{107 }^{2}, a Qfactor ^{Q}^{2}, and a resonance width ^{Γ}^{2}, and the energy transfer has a rate ^{κ}. In some embodiments, the absolute value of the difference of the angular frequencies ^{107 }^{1 }and ^{107}^{2 }is smaller than the broader of the resonant widths ^{Γ}^{1 }and ^{Γ}^{2}.
In some embodiments, the coupling to loss ratio
In some such embodiments, D/L_{2 }may be as large as 2, as large as 3, as large as 5, as large as 7, or as large as 10.
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, nonradiative 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 nonradiative 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 Qfactor (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 ^{107 } and resonant width ^{Γ}, the Qfactor ^{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}^{κ}^{=ω/2κ}.
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 nonradiative wireless energy transfer. Note however that it is to be understood that the scope of the invention is not bound by theory.
Coupled Mode TheoryAn appropriate analytical framework for modeling the resonant energyexchange between two resonant objects 1 and 2 is that of “coupledmode theory” (CMT). The field of the system of two resonant objects 1 and 2 is approximated by F(r,t)≈a_{1}(t)F_{1}(r)+a_{2}(t)F_{2}(r), where F_{1,2}(r) are the eigenmodes of 1 and 2 alone, normalized to unity energy, and the field amplitudes a_{1,2}(t) are defined so that a_{1,2}(t)^{2 }is equal to the energy stored inside the objects 1 and 2 respectively. Then, the field amplitudes can be shown to satisfy, to lowest order:
where ω_{1,2 }are the individual angular eigenfrequencies of the eigenmodes, Γ_{1,2 }are the resonance widths due to the objects' intrinsic (absorption, radiation etc.) losses, and κ is the coupling coefficient. Eqs. (1) show that at exact resonance (ω_{1}=ω_{2 }and Γ_{1}=Γ_{2}), the eigenmodes of the combined system are split by 2κ; the energy exchange between the two objects takes place in time ˜π/2κ and is nearly perfect, apart for losses, which are minimal when the coupling rate is much faster than all loss rates (κ>>Γ_{1,2}). The coupling to loss ratio κ/√{square root over (Γ_{1}Γ_{2})} serves as a figureofmerit in evaluating a system used for wireless energytransfer, along with the distance over which this ratio can be achieved. The regime κ/√{square root over (Γ_{1}Γ_{2 })}>>1 is called “strongcoupling” regime.
In some embodiments, the energytransfer application preferably uses resonant modes of high Q=ω/2Γ, corresponding to low (i.e. slow) intrinsicloss rates Γ. This condition may be satisfied where the coupling is implemented using, not the lossy radiative farfield, but the evanescent (nonlossy) stationary nearfield.
To implement an energytransfer 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)}^{2}=ω^{2}/c^{2 }where {right arrow over (k)} is the wave vector, ω the angular frequency, and c the speed of light. Because of this, one can show that they cannot support states of infinite Q. However, very longlived (socalled “highQ”) states can be found, whose tails display the needed exponential or exponentiallike decay away from the resonant object over long enough distances before they turn oscillatory (radiative). The limiting surface, where this change in the field behavior happens, is called the “radiation caustic”, and, for the wireless energytransfer scheme to be based on the near field rather than the far/radiation field, the distance between the coupled objects must be such that one lies within the radiation caustic of the other.
Furthermore, in some embodiments, small Q_{κ}=ω/2κ corresponding to strong (i.e. fast) coupling rate κ is preferred over distances larger than the characteristic sizes of the objects. Therefore, since the extent of the nearfield into the area surrounding a finitesized resonant object is set typically by the wavelength, in some embodiments, this midrange nonradiative coupling can be achieved using resonant objects of subwavelength size, and thus significantly longer evanescent fieldtails. As will be seen in examples later on, such subwavelength resonances can often be accompanied with a high Q, so this will typically be the appropriate choice for the possiblymobile resonant deviceobject. Note, though, that in some embodiments, the resonant sourceobject will be immobile and thus less restricted in its allowed geometry and size, which can be therefore chosen large enough that the nearfield extent is not limited by the wavelength. Objects of nearly infinite extent, such as dielectric waveguides, can support guided modes whose evanescent tails are decaying exponentially in the direction away from the object, slowly if tuned close to cutoff, and can have nearly infinite 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_{1,2}, Q_{1,2 }and Q_{κ}described above and how to choose these parameters for particular embodiments in order to produce a desirable figureofmerit κ/√{square root over (Γ_{1}Γ_{2})}=√{square root over (Q_{1}Q_{2})}/Q_{κ}. In particular, this figure of merit is typically maximized when ω_{1,2 }are tuned to a particular angular frequency {tilde over (ω)}, thus, if {tilde over (Γ)} is half the angularfrequency width for which √{square root over (Q_{1}Q_{2})}/Q_{κ} is above half its maximum value at {tilde over (ω)}, the angular eigenfrequencies ω_{1,2 }should typically be tuned to be close to {tilde over (ω)} to within the width {tilde over (Γ)}.
In addition, as described below, Q_{1,2 }can sometimes be limited not from intrinsic loss mechanisms but from external perturbations. In those cases, producing a desirable figureofmerit translates to reducing Q_{κ} (i.e. increasing the coupling). Accordingly we will demonstrate how, for particular embodiments, to reduce Q_{κ}.
SelfResonant Conducting CoilsIn some embodiments, one or more of the resonant objects are selfresonant 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_{0}=max {I(x)} is the maximum positive value of the linear current distribution, then I_{0}=ωq_{0}. Then, one can define an effective total inductance L and an effective total capacitance C of the coil through the amount of energy U inside its resonant mode:
where μ_{0 }and ε_{0 }are the magnetic permeability and electric permittivity of free space. With these definitions, the resonant angular frequency and the effective impedance are given by the common formulas ω=1/√{square root over (LC)} and Z=√{square root over (L/C)} respectively.
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_{abs }from the amount of power absorbed inside the wire and a total radiation resistance R_{rad }from the amount of power radiated due to electric and magneticdipole radiation:
where c=1/√{square root over (μ_{0}ε_{0})} and ζ_{0}=√{square root over (μ_{0}/ε_{0})} are the light velocity and light impedance in free space, the impedance with ζ_{c }is ζ_{c}=1/σδ=√{square root over (μ_{0}ω/2σ)} with σ the conductivity of the conductor and δ the skin depth at the frequency
is the electricdipole moment of the coil and
is the magneticdipole moment of the coil. For the radiation resistance formula Eq. (5), the assumption of operation in the quasistatic 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 conductingwire 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 transmissionlinelike 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 χ 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_{0 }cos (πx/l) , where we have assumed that the current does not vary significantly along the wire circumference for a particular χ, a valid assumption provided a<<r. It immediately follows from the continuity equation for charge that the linear charge density profile should be of the form ρ_{l}(x)=ρ_{0 }sin (πx/l), and thus
Using these sinusoidal profiles we find the socalled “selfinductance” L_{s }and “selfcapacitance” 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 “selfresistances” R_{s }are given analytically by Eq. (4) and (5) using
and therefore the associated Q_{s }factors may be calculated.
The results for two particular embodiments of resonant coils with subwavelength modes of λ_{s}/r≧70 (i.e. those highly suitable for nearfield coupling and well within the quasistatic limit) are presented in Table 1. Numerical results are shown for the wavelength and absorption, radiation and total loss rates, for the two different cases of subwavelengthcoil resonant modes. Note that, for conducting material, copper (σ=5.998·10 ̂−7 S/m) was used. It can be seen that expected quality factors at microwave frequencies are Q_{s}^{abs}≧1000 and Q_{s}^{rad}≧5000.
Referring to
and the retardation factor of u=exp(iωx−x′/c) inside the integral can been ignored in the quasistatic 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_{1}C_{2})}/2M_{C}+ωM_{L}/2√{square root over (L_{1}L_{2})}Q_{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 selfresonant 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_{C,s }and inductance M_{L,s }between two selfresonant coils at a distance D between their centers, and thus Q_{κ,s }is also determined.
Table 2Referring 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 figureofmerit 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 couplingtoloss ratios are in the range κ/Γ˜2−70.
CapacitivelyLoaded Conducting Loops or CoilsIn some embodiments, one or more of the resonant objects are capacitivelyloaded conducting loops or coils. Referring to
loading capacitor, the charge distribution ρ inside the wire is reduced, so C<C_{s}, and thus, from the charge conservation equation, the current distribution j flattens out, so L>L_{s}. The resonant frequency for this system is ω=1/√{square root over (L(C+C_{p}))}<ω_{s}=1/√{square root over (L_{s}C_{s})}, and I(x)→I_{0 }cos (πx/l) C→C_{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_{p}>>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_{0}r[1n (8r/a)−2]N^{2}. Explicit analytical formulas are again available for R from Eq. (4) and (5), since I_{rms}=I_{0}, p≈0 and m=I_{0}Nπr^{2 }(namely only the magneticdipole 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}>>ω<<ω_{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 selfcapacitance C_{s }to begin with, which usually holds, for the types of coils under consideration, when N=1, so that the selfcapacitance comes from the charge distribution across the single turn, which is almost always very small, or when N>1 and h>>2Na , so that the dominant selfcapacitance comes from the charge distribution across adjacent turns, which is small if the separation between adjacent turns is large.
The external loading capacitance C_{p }provides the freedom to tune the resonant frequency (for example by tuning A or d). Then, for the particular simple case h=0 , for which we have analytical formulas, the total Q=ωL/(R_{abs}+R_{rad}) becomes highest at the optimal frequency
reaching the value
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 selfcapacitance. A coil with large h can be used, if the selfcapacitance 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 nearfield coupling and well within the quasistatic 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 constantcurrent assumption and the resulting analytical formulas, modesolving calculations were also performed using another completely independent method: computational 3D finiteelement frequencydomain (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_{C}=√{square root over (μ_{0}ω/2σ)} boundary condition, valid as long as ζ_{C}/ζ_{0}<<1(<10^{−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 subwavelengthloop resonant modes. Note that for conducting material copper (σ=5.998·10^{7}S/m) was used. (The specific parameters of the plot in
Referring to
which again is more accurate for N_{1}=N_{2}=1.
From Eq. (9) it can be seen that the optimal frequency {tilde over (ω)}, where the figureofmerit is maximized to the value , is that where √{square root over (Q_{1}Q_{2})} is maximized, since Q_{κ} does not depend on frequency (at least for the distances D<<λ of interest for which the quasistatic approximation is still valid). Therefore, the optimal frequency is independent of the distance D between the two coils and lies between the two frequencies where the singlecoil Q_{1 }and Q_{2 }peak. For same coils, it is given by Eq. (7) and then the figureofmerit Eq. (9) becomes
Typically, one should tune the capacitivelyloaded 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_{1}Q_{2})}/Q_{κ}>.
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 figureofmerit κ/Γ as a function of the coupling distance D, for the two cases. Note that the average numerical Γ^{rad }shown are again slightly different from the singleloop value of
Optimization of √{square root over (Q_{1}Q_{2})}/Q_{κ}
In some embodiments, the results above can be used to increase or optimize the performance of a wireless energy transfer system which employs capacitivelyloaded coils. For example, the scaling of Eq. (10) with the different system parameters one sees that to maximize the system figureofmerit 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 crosssectional 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. loopsize 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 couplingtoloss 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 figureofmerit 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 singleturn 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=5.998·10^{7}S/m):
D/r=5, κ/Γ≧10, r=30 cma≧9 mm
D/r=5, κ/Γ≧10, r=5 cma≧3.7 mm
D/r=5, κ/Γ≧20, r=30 cma≧20 mm
D/r=5, κ/Γ≧20, r=5 cma≧8.3 mm
D/r=10, κ/Γ≧1, r=30 cma≧7 mm
D/r=10, κ/Γ≧1, r=5 cma≧2.8 mm
D/r=10, κ/Γ≧3, r=30 cma≧25 mm
D/r=10, κ/Γ≧3, r=5 cma≧10 mm
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_{d},h(_{d},a_{d}, N_{d}) are very restricted. However, in some such embodiments, the restrictions on the source object (r_{s}, h_{s}, a_{s}, N_{s}) are much less, since the source can, for example, be placed under the floor or on the ceiling. In such cases, the desired distance is often well defined, based on the application (e.g. D˜1 m for charging a laptop on a table wirelessly from the floor). Listed below are examples (simplified to the case N_{s}=N_{d}=1 and h_{s}=h_{d}=0) of how one can vary the dimensions of the source object to achieve the desired system performance in terms of κ/√{square root over (Γ_{s}Γ_{d})}, when the material is again copper (σ=5.998·10^{7}S/m):
D=1.5 m, κ/√{square root over (Γ_{s}Γ_{d})}≧15, r_{d}=30 cm, a_{d}=6 mmr_{s}=1.158 m, a_{s}≧5 mm
D=1.5 m, κ/√{square root over (Γ_{s}Γ_{d})}≧30, r_{d}=30 cm, a_{d}=6 mmr_{s}=1.15 m, a_{s}≧33 mm
D=1.5 m, κ/√{square root over (Γ_{s}Γ_{d})}≧1, r_{d}=5 cm, a_{d}=4 mmr_{s}=1.119 m, a_{s}24 7 mm
D=1.5 m, κ/√{square root over (Γ_{s}Γ_{d})}≧2, r_{d}=5 cm, a_{d}=4 mmr_{s}=1.119 m, a_{s}≧52 mm
D=2 m, κ/√{square root over (Γ_{s}Γ_{d})}≧10, r_{d}=30 cm, a_{d}=6 mmr_{s}=1.518 m, a_{s}≧7 mm
D=2 m, κ/√{square root over (Γ_{s}Γ_{d})}≧20, r_{d}=30 cm, a_{d}=6 mmr_{s}=1.514 m, a_{s}≧50 mm
D=2 m, κ/√{square root over (Γ_{s}Γ_{d})}≧0.5, r_{d}=5 cm, a_{d}=4 mmr_{s}=1.491 m, a_{s}≧5 mm
D=2 m, κ√{square root over (Γ_{s}Γ_{d})}≧1, r_{d}=5 cm, a_{d}=4 mmr_{s}=1.491 m, a_{s}≧36 mm
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 figureofmerit by decreasing Q_{κ} (i.e. increasing the coupling). The coupling does not depend on the frequency and the number of turns. Therefore, the remaining degrees of freedom are:

 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. coilsizes 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.
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 resonantcoupling inductive scheme and the wellknown nonresonant 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^{2 }(˜10^{6}) times more power delivered for work at the device than the traditional nonresonant mechanism. This is why only closerange contactless mediumpower (˜W) transfer is possible with the latter, while with resonance either closerange but largepower (˜kW) transfer is allowed or, as currently proposed, if one also ensures operation in the stronglycoupled regime, mediumrange and mediumpower transfer is possible. Capacitivelyloaded conducting loops are currently used as resonant antennas (for example in cell phones), but those operate in the farfield regime with D/r>>1, r/λ˜1, and the radiation Q's are intentionally designed to be small to make the antenna efficient, so they are not appropriate for energy transfer.
InductivelyLoaded Conducting RodsA straight conducting rod of length 2h and crosssectional 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 selfresonant 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_{0}cos(πx/2h), since it has to be zero at the open ends of the rod. This is the wellknown halfwavelength electric dipole resonant mode.
In some embodiments, one or more of the resonant objects are inductivelyloaded conducting rods. A straight conducting rod of length 2h and crosssectional 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_{c}, which is added to the distributed inductance of the rod and thus modifies its resonance. Note however, that the presence of the centerloading inductor modifies significantly the current distribution inside the wire and therefore the total effective inductance L and total effective capacitance C of the rod are different respectively from L_{s }and C_{s}, which are calculated for a selfresonant rod of the same total length using a sinusoidal current profile, as in the previous paragraph. Since some current is running inside the coil of the external loading inductor, the current distribution j inside the rod is reduced, so L<L_{s}, and thus, from the charge conservation equation, the linear charge distribution ρ_{l }flattens out towards the center (being positive in one side of the rod and negative in the other side of the rod, changing abruptly through the inductor), so C>C_{s}. The resonant frequency for this system is ω=1/√{square root over ((L+L_{c})C)}<ω_{s}=1/√{square root over (L_{s}C_{s})}, and I(x)→I_{0 }cos(πx/2h)L→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_{c}>>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 centerloading 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/(πε_{0}h) [1n(h/a)−1] . Explicit analytical formulas are again available for R from Eq. (4) and (5), since I_{rms}=I_{0}, p=q_{0}h and m=0 (namely only the electricdipole 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}ω<<ω_{s }is satisfied. This condition is relatively easily satisfied, since typically a conducting rod has very small selfinductance 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_{c }and it depends on the particular design of the inductor. In some embodiments, the inductor is made of a Brooks coil, which is the coil geometry which, for fixed wire length, demonstrates the highest inductance and thus quality factor. The Brooks coil geometry has N_{Bc}, turns of conducting wire of crosssectional radius a_{Bc }wrapped around a cylindrically symmetric coil former, which forms a coil with a square crosssection of side r_{Bc }, where the inner side of the square is also at radius r_{Bc }(and thus the outer side of the square is at radius 2r_{Bc}), therefore N_{Bc}≈(r_{Bc}/2a_{Bc})^{2}. The inductance of the coil is then L_{c}=2.0285μ_{0}r_{Bc}N_{Bc}^{2}≈2.0285μ_{0}r_{Bc}^{5}/8a_{Bc}^{4 }and its resistance
where the total wire length is l_{Bc}≈2π(3r_{Bc}/2)N_{Bc}≈3πr_{Bc}^{3}/4a_{Bc}^{2 }and we have used an approximate squareroot law for the transition of the resistance from the dc to the ac limit as the skin depth varies with frequency.
The external loading inductance L_{c }provides the freedom to tune the resonant frequency. (For example, for a Brooks coil with a fixed size r_{Bc}, the resonant frequency can be reduced by increasing the number of turns N_{Bc }by decreasing the wire crosssectional radius a_{Bc}. Then the desired resonant angular frequency ω=1/√{square root over (L_{c}C )} is achieved for a_{Bc}≈(2.0285μ_{0}r_{Bc}^{5}ω^{2}C)^{1/4 }and the resulting coil quality factor is Q_{c}≈0.169μ_{0}σr_{Bc}^{2}ω/√{square root over (1+ω^{2}μ_{0}σ√{square root over (2.0285μ_{0}(r_{Bc}/4)^{5}C)})}).Then, for the particular simple case L_{c}>>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 {tilde over (w)}, reaching the value {tilde over (Q)}, both determined by the loadinginductor specific design. (For example, for the Brookscoil procedure described above, at the optimal frequency {tilde over (Q)}≈Q_{c}≈0.8(μ_{0}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 nearfield coupling and well within the quasistatic 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 subwavelengthloop resonant modes. Note that for conducting material copper (σ=5.998·10^{7}S/m) was used. The results show that, in some embodiments, the optimal frequency is in the lowMHz microwave range and the expected quality factors are Q^{abs}≧1000 and Q^{rad}≧100000.
In some embodiments, energy is transferred between two inductivelyloaded rods. For the rate of energy transfer between two inductivelyloaded rods 1 and 2 at distance D between their centers, the mutual capacitance M_{c }can be evaluated numerically from Eq. (6) by using triangular current distributions in the case ω<<ω_{s}. In this case, the coupling is only electric and again we have an analytical formula, which, in the quasistatic limit h<<D<<λ and for the relative orientation such that the two rods are aligned on the same axis, is 1/M_{c}≈½πε_{0}·(h_{1}h_{2})^{2}/D^{3}, which means that Q_{κ}∝(D/√{square root over (h_{1}h_{2})})^{3 }is independent of the frequency ω. Consequently, one can get the resultant coupling figureofmerit of interest
It can be seen that the optimal frequency {tilde over (ω)}, where the figureofmerit is maximized to the value is that where √{square root over (Q_{1}Q_{2})} is maximized, since Q_{κ} does not depend on frequency (at least for the distances D<<λ of interest for which the quasistatic approximation is still valid). Therefore, the optimal frequency is independent of the distance D between the two rods and lies between the two frequencies where the singlerod Q_{1 }and Q2 peak.
Typically, one should tune the inductivelyloaded 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}>/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 figureofmerit κ/Γ as a function of the coupling distance D, for the two cases. Note that for Γ^{rad }the singlerod value is used. Again we chose L_{c}>>L_{s }to make the triangularcurrent 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 couplingtoloss ratios are in the range κ/Γ˜0.5−100.
Table 6 Dielectric DisksIn 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 TEpolarized dielectricdisk 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 subwavelengthdisk resonant modes. Note that diskmaterial losstangent Im{ε}/Re{ε}=10^{−4 }was used. (The specific parameters corresponding to the plot in
The required values of ε, shown in Table 7, might at first seem unrealistically large. However, not only are there in the microwave regime (appropriate for approximately meterrange 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 ε could signify instead the effective index of other known subwavelength surfacewave systems, such as surface modes on surfaces of metallic materials or plasmonic (metallike, negativeε) materials or metallodielectric photonic crystals or plasmonodielectric photonic crystals.
To calculate now the achievable rate of energy transfer between two disks 1 and 2, as shown in
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 selfresonant conducting coils, capacitivelyloaded 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_{1}Q_{2})}/Q_{κ} or, if the Q's are limited by external factors, to increase and/or optimize for Q_{κ}.
System Sensitivity to Extraneous ObjectsIn general, the overall performance of particular embodiment of the resonancebased wireless energytransfer 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 nonresonant 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_{1}(t) inside the resonant object 1 satisfies, to first order:
where again ω_{1 }is the frequency and Γ_{l }the intrinsic (absorption, radiation etc.) loss rate, while κ_{11−e }is the frequency shift induced onto 1 due to the presence of e and Γ_{1−e }is the extrinsic due to e (absorption inside e, scattering from e etc.) loss rate. The firstorder PT model is valid only for small perturbations. Nevertheless, the parameters κ_{11−e}, Γ_{1−e }are well defined, even outside that regime, if a_{1 }is taken to be the amplitude of the exact perturbed mode. Note also that interference effects between the radiation field of the initial resonantobject mode and the field scattered off the extraneous object can for strong scattering (e.g. off metallic objects) result in total radiation—Γ_{1−e}'s that are smaller than the initial radiation—Γ_{1 }(namely Γ_{1−e }is negative).
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 energytransfer scheme, because it is difficult to remedy, so the total loss rate Γ_{1[e]}=Γ_{1}+Γ_{1−e }(and the corresponding figureofmerit κ_{[e]}/√{square root over (Γ_{1[e]}Γ_{2[e]})}, where κ_{e} the perturbed coupling rate) should be quantified.
CapacitivelyLoaded Conducting Loops or CoilsIn embodiments using primarily magnetic resonances, the influence of extraneous objects on the resonances is nearly absent. The reason is that, in the quasistatic 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 h<<2r most of the electric field is localized within the selfcapacitance of the coil or the externally loading capacitor), therefore extraneous nonconducting 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 I/m{μ}>0). Since almost all everyday nonconducting materials are nonmagnetic 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 nonmagnetic and can sustain strong magnetic fields without undergoing any risk. A typical example, where magnetic fields B˜1T are safely used on humans, is the Magnetic Resonance Imaging (MRI) technique for medical testing. In contrast, the magnetic nearfield required in typical embodiments in order to provide a few Watts of power to devices is only B˜10^{−4}T, which is actually comparable to the magnitude of the Earth's magnetic field. Since, as explained above, a strong electric nearfield is also not present and the radiation produced from this nonradiative scheme is minimal, it is reasonable to expect that our proposed energytransfer method should be safe for living organisms.
One can, for example, estimate the degree to which the resonant system of a capacitivelyloaded conductingwire 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 r<<D_{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}. From Eq. (12) it is obvious that indeed for all angles in the near field (x<<1) the magnetic energy density is dominant, while in the far field (x>>1) they are equal as they should be. Also, the preferred positioning of the loop is such that objects which may interfere with its resonance lie close to its axis (θ=0), where there is no electric field. For example, using the systems described in Table 4, we can estimate from Eq. (12) that for the loop of r=30 cm at a distance 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}=3r=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 capacitivelyloaded 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 capacitivelyloaded loop including the capacitor fringing electric field, we use the perturbation theory formula, stated earlier, Γ_{1−c}^{abs}=ω_{1}/4·∫d^{3}rIm{ε_{c}(r)}E_{1}(r)^{2}/U with the computational FEFD results for the field of an example like the one shown in the plot of
Selfresonant coils are more sensitive than capacitivelyloaded 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, selfresonant 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_{e}/u_{m }is reduced or minimized at most of the desired (according to the application) points in the surrounding space.
Dielectric DisksIn embodiments using resonances that are not primarily magnetic, the influence of extraneous objects may be of concern. For example, for dielectric disks, small, lowindex, lowmaterialloss or faraway 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 firstorder perturbation theory formulas All perturbations
Γ_{1−e}^{rad}=ω_{1}∫d^{3}rRe{ε_{e}(r)}E_{1}(r)^{2}/U
Γ_{1−c}^{abs}=ω_{1}/4·∫d^{3}rIm{ε_{c}(r)}E_{1}(r)^{2}/U
where U=½∫d^{3}rε(r)E_{1}(r)^{2 }is the total resonant electromagnetic energy of the unperturbed mode. As one can see, both of these losses depend on the square of the resonant electric field tails E_{1 }at the site of the extraneous object. In contrast, the coupling rate from object 1 to another resonant object 2 is, as stated earlier,
κ=ω_{1}/2·∫d^{3}rε_{2}(r)E_{2}*(r)E_{1}(r)/∫d^{3}rε(r)E_{1}(r)^{2 }
and depends linearly on the field tails E_{1 }of 1 inside 2. This difference in scaling gives us confidence that, for, for example, exponentially small field tails, coupling to other resonant objects should be much faster than all extrinsic loss rates (κ>>Γ_{1−e}), at least for small perturbations, and thus the energytransfer 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 firstorder perturbation theory approach. For example, we place a dielectric disk c close to another offresonance object of large Re{ε}, Im{ε} and of same size but different shape (such as a human being h), as shown in
Inductivelyloaded conducting rods may also be more sensitive than capacitivelyloaded 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 resonancebased energytransfer scheme may be determined, when energy is being drained from the device at rate Γ_{work }for use into operational work. The coupledmodetheory equation for the device fieldamplitude is
where Γ_{d[e]}=Γ_{d[e]}^{rad}+Γ_{d[e]}^{abs}=Γ_{d[e]}^{rad}+(Γ_{d}^{abs}+Γ_{d−e}^{abs}) is the net perturbeddevice loss rate, and similarly we define Γ_{s[e]} for the perturbedsource. Different temporal schemes can be used to extract power from the device (e.g. steadystate continuouswave drainage, instantaneous drainage at periodic times and so on) and their efficiencies exhibit different dependence on the combined system parameters. For simplicity, we assume steady state, such that the field amplitude inside the source is maintained constant, namely a_{s}(t)=A_{s}e^{−iωt}, so then the field amplitude inside the device is a_{d}(t)=A_{d}e^{−iωt }with A_{d}/A_{s}=iκ_{[e]}/.(Γ_{d[e]}+Γ_{work}). The various timeaveraged powers of interest are then: the useful extracted power is P_{work}=2Γ_{work}A_{d}^{2}, the radiated (including scattered) power is P_{rad}=2Γ_{s[e]}^{rad}A_{s}^{2}+2Γ_{d[e]}^{rad}A_{d}^{2}, the power absorbed at the source/device is P_{s/d}=2Γ_{s/d}^{abs}A_{s/d}^{2}, and at the extraneous objects P_{e}=2Γ_{se}^{abs}A_{s}^{2}+2Γ_{de}^{abs}A_{d}^{2}. From energy conservation, the total timeaveraged power entering the system is P_{total}=P_{work}+P_{rad}+P_{s}+P_{d}+P_{e}. Note that the reactive powers, which are usually present in a system and circulate stored energy around it, cancel at resonance (which can be proven for example in electromagnetism from Poynting's Theorem) and do not influence the powerbalance calculations. The working efficiency is then:
where fom_{[e]}=κ_{[e]}/√{square root over (Γ_{s[e]}Γ_{d[e]})} is the distancedependent figureofmerit of the perturbed resonant energyexchange system. To derive Eq. (14), we have assumed that the rate Γ_{supply}, at which the power supply is feeding energy to the resonant source, is Γ_{supply}=Γ_{s[e]}+κ^{2}/(Γ_{d[e]}+Γ_{work}) such that there are zero reflections of the fed power P_{total }back into the power supply.
Example Capacitivelyloaded Conducting LoopsReferring to
Then from the source circuit at resonance (ωL_{s}=1/ωC_{s}):
and from the device circuit at resonance (ωL_{d}=1/ωC_{d}):
0=I_{d}(R_{d}+R_{ω})−jωMI_{s}jωMI_{s}=I_{d}(R_{d}+R_{ω})
So by substituting the second to the first:
Now we take the real part (timeaveraged powers) to find the efficiency:
which with Γ_{work}=R_{ω}/2L_{d}, Γ_{d}=R_{d}/2L_{d}, Γ_{s}=R_{s}/2L_{s}, and κ=ωM/2√{square root over (L_{s}L_{d})}, becomes the general Eq. (14). [End of Example]
From Eq. (14) one can find that the efficiency is optimized in terms of the chosen workdrainage rate, when this is chosen to be Γ_{work}/Γ_{d[e]}=Γ_{supply}/Γ_{s[e]}=√{square root over (1+fom_{[e]}^{2})}>1. Then, η_{work }is a function of the fom_{[e]} parameter only as shown in
For example, consider the capacitivelyloaded coil embodiments described in Table 4, with coupling distance D/r=7, a “human” extraneous object at distance D_{h }from the source, and that P_{work}=10W must be delivered to the load. Then, we have (based on
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 cellphone, the device resonant object cannot have dimensions larger that those of the laptop or cellphone respectively. In particular, for a system of two loops of specified dimensions, in terms of loop radii r_{s,d }and wire radii a_{s,d }, the independent parameters left to adjust for the system optimization are: the number of turns N_{s,d}, the frequency f, the workextraction rate (load resistance) Γ_{work }and the powersupply feeding rate Γ_{supply}.
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 capacitivelyloaded coils, the design may be constrained by, for example, the currents flowing inside the wires I_{s,d }and the voltages across the capacitors V_{s,d}. These limitations can be important because for ˜Watt power applications the values for these parameters can be too large for the wires or the capacitors respectively to handle. Furthermore, the total loaded Q_{tot}=ωL_{d}/(R_{d}+R_{w}) of the device is a quantity that should be preferably small, because to match the source and device resonant frequencies to within their Q's, when those are very large, can be challenging experimentally and more sensitive to slight variations. Lastly, the radiated powers P_{rad,s,d }should be minimized for safety concerns, even though, in general, for a magnetic, nonradiative scheme they are already typically small.
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 workdrainage rate for some particular value of fom_{[e]}, through Γ_{work}/Γ_{d[e]}=√{square root over (1+wp·fom_{[e]}^{2})}. Then, in some embodiments, values which impact the choice of this rate are: Γ_{work}/Γ_{d[e]}=1wp=0 to minimize the required energy stored in the source (and therefore I_{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}=ωL_{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_{s }and N_{d }increases κ/√{square root over (Γ_{s}Γ_{d})} and thus efficiency significantly, as seen before, and also decreases the currents I_{s }and I_{d}, because the inductance of the loops increases, and thus the energy
required for given output power P_{work }can be achieved with smaller currents. However, increasing N_{d }increases Q_{tot}, P_{rad,d }and the voltage across the device capacitance V_{d}, which unfortunately ends up being, in typical embodiments one of the greatest limiting factors of the system. To explain this, note that it is the electric field that really induces breakdown of the capacitor material (e.g. 3 kV/mm for air) and not the voltage, and that for the desired (close to the optimal) operational frequency, the increased inductance L_{d }implies reduced required capacitance C_{d }, which could be achieved in principle, for a capacitivelyloaded device coil by increasing the spacing of the device capacitor plates d_{d }and for a selfresonant coil by increasing through h_{d }the spacing of adjacent turns, resulting in an electric field (≈V_{d}/d_{d }for the former case) that actually decreases with N_{d}; however, one cannot in reality increase d_{d }or h_{d }too much, because then the undesired capacitance fringing electric fields would become very large and/or the size of the coil might become too large; and, in any case, for certain applications extremely high voltages are not desired. A similar increasing behavior is observed for the source P_{rod,s }and V_{s }upon increasing N_{s}. As a conclusion, the number of turns N_{s }and N_{d }have to be chosen the largest possible (for efficiency) that allow for reasonable voltages, fringing electric fields and physical sizes.
With respect to frequency, again, there is an optimal one for efficiency, and Q_{tot }is approximately maximum, close to that optimal frequency. For lower frequencies the currents get worse (larger) but the voltages and radiated powers get better (smaller). Usually, one should pick either the optimal frequency or somewhat lower.
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_{s }and a_{s }in the set of independent variables and optimize with respect to these too for all the dependent variables of the problem (we saw how to do this only for efficiency earlier). Such an optimization would lead to improved results.
Experimental ResultsAn experimental realization of an embodiment of the above described scheme for wireless energy transfer consists of two selfresonant 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_{0}=10.56±0.3 MHz, which is about 5% off from the measured resonance at around 9.90 MHz.
The theoretical Q for the loops is estimated to be ˜2500 (assuming perfect copper of resistivity ρ=1/σ=1.7×10^{−8}Ωm) but the measured value is 950±50. We believe the discrepancy is mostly due to the effect of the layer of poorly conducting copper oxide on the surface of the copper wire, to which the current is confined by the short skin depth (˜20 μm) at this frequency. We have therefore used the experimentally observed Q (and Γ_{1}=Γ_{2}=Γ=ω/(2Q) derived from it) in all subsequent computations.
The coupling coefficient κ can be found experimentally by placing the two selfresonant coils (finetuned, 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 coupledmode theory, the splitting in the transmission spectrum should be Δω=2√{square root over (κ^{2}−Γ^{2})}. The comparison between experimental and theoretical results as a function of distance when the two the coils are aligned coaxially is shown in
As noted above, the maximum theoretical efficiency depends only on the parameter κ/√{square root over (Γ_{1}Γ_{2})}=κ/Γ, plotted as a function of distance in
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 midpoint of each of the selfresonant coils with a currentprobe (which was not found to lower the Q of the coils noticeably.) This gave a measurement of the current parameters I_{1 }and I_{2 }defined above. The power dissipated in each coil was then computed from P_{1,2}=ΓLI_{1,2}^{2}, and the efficiency was directly obtained from η=P_{work}/(P_{1}+P_{2}+P_{work}). To ensure that the experimental setup was well described by a twoobject coupledmode theory model, we positioned the device coil such that its direct coupling to the copper loop attached to the Colpitts oscillator was zero. The experimental results are shown in
Using this embodiment, we were able to transfer significant amounts of power using this setup, fully lighting up a 60 W lightbulb 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 walltoload 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_{0 }of a few times the inverse loaded Q, the induced current in the device coil was indistinguishable from noise.
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 longterm 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 silverplating 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.
ApplicationsIn conclusion, we have described several embodiments of a resonancebased scheme for wireless nonradiative energy transfer. Although our consideration has been for a static geometry (namely κ and Γ_{e }were independent of time), all the results can be applied directly for the dynamic geometries of mobile objects, since the energytransfer time κ^{−1 }(˜1 μs−1 ms for microwave applications) is much shorter than any timescale associated with motions of macroscopic objects. Analyses of very simple implementation geometries provide encouraging performance characteristics and further improvement is expected with serious design optimization. Thus the proposed mechanism is promising for many modem applications.
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 sourceobject 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 interconnects for CMOS electronics, or to transfer energy to autonomous nanoobjects (e.g. MEMS or nanorobots) 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 condensedmatter object.
In some embodiments, the techniques described above can provide nonradiative wireless transfer of information using the localized near fields of resonant object. Such schemes provide increased security because no information is radiated into the farfield, and are well suited for midrange 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.
Claims
1. A wireless power transmitter device for transmitting power to at least one highQ resonator, comprising:
 a first portion, formed of a highQ magnetic resonator, and a high frequency generation system, having a number of components, wherein at least one of said components is formed using a process which creates nanoscale features.
2. A device as in claim 1, wherein said features include an inductor.
3. A device as in claim 1, wherein said features include a capacitor.
4. A wireless power receiver device for receiving power from at least one highQ resonator, comprising:
 a receiver portion, formed of plural electrical components, a highQ magnetic receiving resonator, and a power output part,
 wherein at least one of said electrical components is formed using a process which creates mechanical nanoscale features forming said plural electrical components.
5. A receiver as in claim 4, wherein said feature includes an inductor.
6. A receiver as in claim 4, wherein said feature includes a capacitor.
7. A wireless power transmitting device for transmitting power to at least one highQ resonator, comprising:
 a first portion, formed of a highQ magnetic resonator, and a high frequency generation system, having a number of components, wherein at least one of said components is formed using a mechanical process.
8. A device as in claim 7, wherein said components include an inductor.
9. A device as in claim 7, wherein said components include a capacitor.
10. A wireless power receiving device for receiving power from at least one highQ resonator, comprising:
 a receiver portion, formed of plural electrical components, a highQ magnetic receiving resonator, and a power output,
 wherein at least one of said electrical components is formed using a mechanical process which creates mechanical features forming said plural electrical components.
11. A receiver as in claim 10, wherein said feature includes an inductor.
12. A receiver as in claim 10, wherein said feature includes a capacitor.
Type: Application
Filed: Mar 18, 2010
Publication Date: Jul 8, 2010
Inventors: Aristeidis Karalis (Boston, MA), Andre B. Kurs (Chestnut Hill, MA), Robert Moffatt (Reston, VA), John D. Joannopoulos (Belmont, MA), Peter H. Fisher (Cambridge, MA), Marin Soljacic (Belmont, MA)
Application Number: 12/726,742
International Classification: H01F 38/14 (20060101); H03H 7/01 (20060101);