Styrke Gamer

Using self-resonant coils in a strongly coupled regime, we experimentally demonstrated efficient nonradiative power transfer over distances up to 8 times the radius of the coils. We were able to transfer 60 watts with ~40% efficiency over distances in excess of 2 meters. We present a quantitative model describing the power transfer, which matches the experimental results to within 5%. We discuss the practical applicability of this system and suggest directions for further study. I n the early 20th century, before the electrical-wire grid, Nikola Tesla (1) devoted much effort toward schemes to transport power wire-lessly. However, typical embodiments (e.g., Tesla coils) involved undesirably large electric fields. The past decade has witnessed a surge in the use of autonomous electronic devices (laptops, cell phones, robots, PDAs, etc.). As a consequence, interest in wireless power has reemerged (2-4). Radiative transfer (5), although perfectly suitable for transferring information, poses a number of difficulties for power transfer applications: The efficiency of power transfer is very low if the radiation is omnidirectional, and unidirectional radiation requires an uninterrupted line of sight and sophisticated tracking mechanisms. A recent theoretical paper (6) presented a detailed analysis of the feasibility of using resonant objects coupled through the tails of their nonradiative fields for midrange energy transfer (7). Intuitively, two resonant objects of the same resonant frequency tend to exchange energy efficiently, while dissipating relatively little energy in extraneous off-resonant objects. In systems of coupled resonances (e.g., acoustic, electromagnetic, magnetic, nuclear), there is often a general "strongly coupled" regime of operation (8). If one can operate in that regime in a given system, the energy transfer is expected to be very efficient. Midrange power transfer implemented in this way can be nearly omnidirectional and efficient, irrespective of the geometry of the surrounding space, with low interference and losses into environmental objects (6). The above considerations apply irrespective of the physical nature of the resonances. Here, we focus on one particular physical embodiment: magnetic resonances (9). Magnetic resonances are particularly suitable for everyday applications because most of the common materials do not interact with magnetic fields, so interactions with environmental objects are suppressed even further. We were able to identify the strongly coupled regime in the system of two coupled magnetic resonances by exploring nonradiative (near-field) magnetic resonant induction at megahertz frequencies. At first glance, such power transfer is reminiscent of the usual magnetic induction (10); however, note that the usual nonresonant induction is very inefficient for midrange applications. Overview of the formalism. Efficient mid-range power transfer occurs in particular regions of the parameter space describing resonant objects strongly coupled to one another. Using coupled-mode theory to describe this physical system (11), we obtain the following set of linear equations: a : m ðtÞ ¼ ðiw m − G m Þa m ðtÞ þ ∑ n≠m ik mn a n ðtÞ þ F m ðtÞ ð1Þ where the indices denote the different resonant objects. The variables a m (t) are defined so that the energy contained in object m is |a m (t)| 2 , w m is the resonant angular frequency of that isolated object, and G m is its intrinsic decay rate (e.g., due to absorption and radiated losses). In this framework, an uncoupled and undriven oscilla-tor with parameters w 0 and G 0 would evolve in time as exp(iw 0 t-G 0 t). The k mn = k nm are coupling coefficients between the resonant objects indicated by the subscripts, and F m (t) are driving terms. We limit the treatment to the case of two objects, denoted by source and device, such that the source (identified by the subscript S) is driven externally at a constant frequency, and the two objects have a coupling coefficient k. Work is extracted from the device (subscript D) by means of a load (subscript W) that acts as a circuit resistance connected to the device, and has the effect of contributing an additional term G W to the unloaded device object's decay rate G D. The overall decay rate at the device is therefore G′ D = G D + G W. The work extracted is determined by the power dissipated in the load, that is, 2G W |a D (t)| 2. Maximizing the efficiency h of the transfer with respect to the loading G W , given Eq. 1, is equivalent to solving an impedance-matching problem. One finds that the scheme works best when the source and the device are resonant, in which case the efficiency is h ¼