Wireless energy transfer across variable distances
Described herein are embodiments of transferring electromagnetic energy that includes a first electromagnetic resonator receiving energy from an external power supply, said first resonator having a resonant frequency ω 1 , an intrinsic loss rate Γ 1 , and a first Q-factor Q 1 =ω 1 L 1 /(R 1ohm +R 1rad ), generating an oscillating near field region, a second electromagnetic resonator being positioned at variable distances from said first resonator and not electrically wired to said first resonator, said second resonator having a resonant frequency ω 2 , an intrinsic loss rate Γ 2 , and a second Q-factor Q 2 =ω 2 L 2 /(R 2ohm +R 2rad ). Electromagnetic energy may be transferred from said first resonator to said second resonator over a variable distance D that may be within the near-field region of the first resonator structure, and wherein R 1ohm >R 1rad , and R 2ohm >R 2rad .
1. A method of transferring electromagnetic energy comprising:
providing a first electromagnetic resonator receiving energy from a power supply, said first electromagnetic resonator having a resonant frequency ω 1 , an intrinsic loss rate Γ 1 , an inductance L 1 , an ohmic component of resistance R 1ohm , a radiative component of resistance R 1rad , and a first Q-factor Q 1 =ω 1 L 1 /(R 1ohm +R 1rad ), and generating a near field region comprising a temporally oscillating magnetic field;
providing a second electromagnetic resonator being positioned at variable distances from said first electromagnetic resonator and not electrically wired to said first electromagnetic resonator, said second electromagnetic resonator having a resonant frequency ω 2 , an intrinsic loss rate Γ 2 , an inductance L 2 , an ohmic component of resistance R 2ohm , a radiative component of resistance R 2rad , and a second Q-factor Q 2 =ω 2 L 2 /(R 2ohm +R 2rad ); and
wirelessly transferring electromagnetic energy from said first electromagnetic resonator to said second electromagnetic resonator over a variable distance D as the second electromagnetic resonator moves freely within the near-field region, and wherein R 1ohm >R 1rad , and R 2ohm >R 2rad and at least one of Q 1 and Q 2 is greater than 100.
2. The method of claim 1 , wherein the distance between the resonators is greater than 5 cm.
3. The method of claim 1 , wherein the distance between the resonators is greater than 10 cm.
4. The method of claim 1 , wherein the distance between the resonators is larger than a characteristic size of the smaller of the first electromagnetic resonator and the second electromagnetic resonator.
5. The method of claim 1 , wherein each resonator comprises an electrical conductor shaped into one or more loops wound in substantially a single plane circumscribing a substantially planar area.
6. The method of claim 5 , wherein the loops of the electrical conductors of each of the first electromagnetic resonator and the second electromagnetic resonator are in substantially the same plane.
7. The method of claim 5 , wherein a line drawn from the center of the first electromagnetic resonator to the center of the second electromagnetic resonator is substantially normal to the circumscribed planar area of each resonator.
8. The method of claim 5 , wherein a line drawn from the center of the first electromagnetic resonator to the center of the second electromagnetic resonator is substantially parallel to the circumscribed planar area of each resonator.
9. The method of claim 5 , wherein a line drawn from the center of the first electromagnetic resonator to the center of the second electromagnetic resonator forms a different angle to the surface area circumscribed by the first electromagnetic resonator than to the circumscribed planar area of each resonator.
10. The method of claim 1 , wherein Q 1 and Q 2 are each greater than 100.
11. The method of claim 1 , wherein √{square root over (Q 1 Q 2 )}>100.
12. A system of transferring electromagnetic energy comprising:
a first electromagnetic resonator receiving energy from a power supply, said first electromagnetic resonator having a resonant frequency ω 1 , an intrinsic loss rate Γ 1 , an inductance L 1 , an ohmic component of resistance R 1ohm , a radiative component of resistance R 1rad , and a first Q-factor Q 1 =ω 1 L 1 /(R 1ohm +R 1rad ), and generating a near field region comprising a temporally oscillating magnetic field;
a second electromagnetic resonator being positioned at variable distances from said first electromagnetic resonator and not electrically wired to said first electromagnetic resonator, said second electromagnetic resonator having a resonant frequency ω 2 , an intrinsic loss rate Γ 2 , an inductance L 2 , an ohmic component of resistance R 2ohm , a radiative component of resistance R 2rad , and a second Q-factor Q 2 =ω 2 L 2 /(R 2ohm +R 2rad ),
wherein the first and second electromagnetic resonators are coupled to wirelessly transfer electromagnetic energy from said first electromagnetic resonator to said second electromagnetic resonator over a variable distance D as the second electromagnetic resonator moves freely within the near-field region, and wherein R 1ohm >R 1rad , and R 2ohm >R 2rad and at least one of Q 1 and Q 2 is greater than 100.
13. The system of claim 12 , wherein the distance between the resonators is greater than 5 cm.
14. The system of claim 12 , wherein the distance between the resonators is greater than 10 cm.
15. The system of claim 12 , wherein the distance between the resonators is larger than a characteristic size of the smaller of the first electromagnetic resonator and the second electromagnetic resonator.
16. The system of claim 12 , wherein each resonator comprises an electrical conductor shaped into one or more loops wound in substantially a single plane circumscribing a substantially planar area.
17. The system of claim 16 , wherein the loops of the electrical conductors of each of the first electromagnetic resonator and the second electromagnetic resonator are in substantially the same plane.
18. The system of claim 16 , wherein a line drawn from the center of the first electromagnetic resonator to the center of the second electromagnetic resonator is substantially normal to the circumscribed planar area of each resonator.
19. The system of claim 16 , wherein a line drawn from the center of the first electromagnetic resonator to the center of the second electromagnetic resonator is substantially parallel to the circumscribed planar area of each resonator.
20. The system of claim 16 , wherein a line drawn from the center of the first electromagnetic resonator to the center of the second electromagnetic resonator forms a different angle to the surface area circumscribed by the first electromagnetic resonator than to the circumscribed planar area of each resonator.
21. The system of claim 12 , wherein Q 1 and Q 2 are greater than 100.
22. The system of claim 12 , wherein √{square root over (Q 1 Q 2 )}>100.