## Wireless Power (Wiki)

Wireless power or wireless energy transmission is the transmission of electrical energy from a power source to an electrical load without man-made conductors. Wireless transmission is useful in cases where interconnecting wires are inconvenient, hazardous, or impossible. The problem of wireless power transmission differs from that of wireless telecommunications, such as radio. In the latter, the proportion of energy received becomes critical only if it is too low for the signal to be distinguished from the backgroundnoise.[1]  With wireless power, efficiency is the more significant parameter. A large part of the energy sent out by the generating plant must arrive at the receiver or receivers to make the system economical.

The most common form of wireless power transmission is carried out using direct induction followed by resonant magnetic induction. Other methods under consideration areelectromagnetic radiation in the form of microwaves or lasers[2] and electrical conduction through natural media.[3]

## Electric energy transfer

Main article: Coupling (electronics)

An electric current flowing through a conductor, such as a wire, carries electrical energy.  When an electric current passes through a circuit there is an electric field in the dielectricsurrounding the conductor; magnetic field lines around the conductor and lines of electric force radially about the conductor.[4]

In a direct current circuit, if the current is continuous, the fields are constant; there is a condition of stress in the space surrounding the conductor, which represents stored electric and magnetic energy, just as a compressed spring or a moving mass represents stored energy. In an alternating current circuit, the fields also alternate; that is, with every half wave of current and of voltage, the magnetic and the electric field start at the conductor and run outwards into space with the speed of light.[5] Where these alternating fields impinge on another conductor a voltage and a current are induced.[4]

Any change in the electrical conditions of the circuit, whether internal[6] or external[7] involves a readjustment of the stored magnetic and electric field energy of the circuit, that is, a so-called transient. A transient is of the general character of a condenser discharge through an inductive circuit. The phenomenon of the condenser discharge through an inductive circuit therefore is of the greatest importance to the engineer, as the foremost cause of high-voltage and high-frequency troubles in electric circuits.[8]

Electromagnetic induction is proportional to the intensity of the current and voltage in the conductor which produces the fields and to the frequency. The higher the frequency the more intense the induction effect. Energy is transferred from a conductor that produces the fields (the primary) to any conductor on which the fields impinge (the secondary). Part of the energy of the primary conductor passes inductively across space into secondary conductor and the energy decreases rapidly along the primary conductor. A high frequency current does not pass for long distances along a conductor but rapidly transfers its energy by induction to adjacent conductors. Higher induction resulting from the higher frequency is the explanation of the apparent difference in the propagation of high frequency disturbances from the propagation of the low frequency power of alternating current systems. The higher the frequency the more preponderant become the inductive effects that transfer energy from circuit to circuit across space. The more rapidly the energy decreases and the current dies out along the circuit, the more local is the phenomenon.[4]

The flow of electric energy thus comprises phenomena inside the conductor[9] and phenomena in the space outside the conductor—the electric field—which, in a continuous current circuit, is a condition of steady magnetic and dielectric stress, and in an alternating current circuit is alternating, that is, an electric wave launched by the conductor[4] to become far-field electromagnetic radiation traveling through space with the speed of light.

In electric power transmission and distribution, the phenomena inside the conductor are of main importance, and the electric field of the conductor is usually observed only incidentally.[10] Inversely, in the use of electric power for radio telecommunications it is only the electric and magnetic fields outside of the conductor, that is far-field electromagnetic radiation, which is of importance in transmitting the message. The phenomenon in the conductor, the current in the launching structure, is not used.[4]

The electric charge displacement in the conductor produces a magnetic field and resultant lines of electric force. The magnetic field is a maximum in the direction concentric, or approximately so, to the conductor. That is, a ferromagnetic body[11] tends to set itself in a direction at right angles to the conductor. The electric field has a maximum in a direction radial, or approximately so, to the conductor. The electric field component tends in a direction radial to the conductor and dielectric bodies may be attracted or repelled radially to the conductor.[12]

The electric field of a circuit over which energy flows has three main axes at right angles with each other:

1. The magnetic field, concentric with the conductor.
2. The lines of electric force, radial to the conductor.
3. The power gradient, parallel to the conductor.

Where the electric circuit consists of several conductors, the electric fields of the conductors superimpose upon each other, and the resultant magnetic field lines and lines of electric force are not concentric and radial respectively, except approximately in the immediate neighborhood of the conductor. Between parallel conductors they are conjugate of circles.  Neither the power consumption in the conductor, nor the magnetic field, nor the electric field, are proportional to the flow of energy through the circuit. However, the product of the intensity of the magnetic field and the intensity of the electric field is proportional to the flow of energy or the power, and the power is therefore resolved into a product of the two components i and e, which are chosen proportional respectively to the intensity of the magnetic field and of the electric field. The component called the current is defined as that factor of the electric power which is proportional to the magnetic field, and the other component, called the voltage, is defined as that factor of the electric power which is proportional to the electric field.[12]

In radio telecommunications the electric field of the transmit antenna propagates through space as a radio wave and impinges upon the receive antenna where it is observed by its magnetic and electric effect.[12] Radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X rays and gamma rays are shown to be the same electromagnetic radiation phenomenon, differing one from the other only in frequency of vibration.[4][13]

### Electromagnetic induction

Energy transfer by electromagnetic induction is typically magnetic but capacitive coupling can also be achieved.

#### Electrodynamic induction method

The electrodynamic induction wireless transmission technique is near field over distances up to about one-sixth of the wavelength used. Near field energy itself is non-radiative but some radiative losses do occur. In addition there are usually resistive losses. With electrodynamic induction, electric current flowing through a primary coil creates a magnetic fieldthat acts on a secondary coil producing a current within it. Coupling must be tight in order to achieve high efficiency. As the distance from the primary is increased, more and more of the magnetic field misses the secondary.  Even over a relatively short range the inductive coupling is grossly inefficient, wasting much of the transmitted energy.[14]

This action of an electrical transformer is the simplest form of wireless power transmission. The primary and secondary circuits of a transformer are not directly connected. Energy transfer takes place through a process known as mutual induction. Principal functions are stepping the primary voltage either up or down and electrical isolation. Mobile phone andelectric toothbrush battery chargers, and electrical power distribution transformers are examples of how this principle is used. Induction cookers use this method. The main drawback to this basic form of wireless transmission is short range. The receiver must be directly adjacent to the transmitter or induction unit in order to efficiently couple with it.

The application of resonance increases the transmission range somewhat. When resonant coupling is used, the transmitter and receiver inductors are tuned to the same natural frequency. Performance can be further improved by modifying the drive current from a sinusoidal to a nonsinusoidal transient waveform.[15] In this way significant power may be transmitted between two mutually-attuned LC circuits having a relatively low coefficient of coupling. Transmitting and receiving coils are usually single layer solenoids or flat spirals with series capacitors, which, in combination, allow the receiving element to be tuned to the transmitter frequency.

Common uses of resonance-enhanced electrodynamic induction are charging the batteries of portable devices such as laptop computers and cell phones, medical implants andelectric vehicles.[16][17][18] A localized charging technique[19] selects the appropriate transmitting coil in a multilayer winding array structure.[20] Resonance is used in both the wireless charging pad (the transmitter circuit) and the receiver module (embedded in the load) to maximize energy transfer efficiency. This approach is suitable for universal wireless charging pads for portable electronics such as mobile phones. It has been adopted as part of the Qi wireless charging standard.

It is also used for powering devices having no batteries, such as RFID patches and contactless smartcards, and to couple electrical energy from the primary inductor to the helical resonator of Tesla coil wireless power transmitters.

#### Electrostatic induction method

Main article: Capacitive coupling
 The illumination of two exhausted tubes by means of a powerful, rapidly alternating electrostatic field created between two vertical metal sheets suspended from the ceiling on insulating cords.  This involves the physics of electrostatic induction.[21][22][23]

Electrostatic induction or capacitive coupling is the passage of electrical energy through a dielectric. In practice it is an electric field gradient or differential capacitance between two or more insulated terminals, plates, electrodes, or nodes that are elevated over a conducting ground plane. The electric field is created by charging the plates with a high potential, high frequency alternating current power supply. The capacitance between two elevated terminals and a powered device form a voltage divider.

The electric energy transmitted by means of electrostatic induction can be utilized by a receiving device, such as a wireless lamp.[24][25][26] Nikola Tesla demonstrated the illumination of wireless lamps by energy that was coupled to them through an alternating electric field.[21][27][28]

"Instead of depending on electrodynamic induction at a distance to light the tube . . . [the] ideal way of lighting a hall or room would . . . be to produce such a condition in it that an illuminating device could be moved and put anywhere, and that it is lighted, no matter where it is put and without being electrically connected to anything. I have been able to produce such a condition by creating in the room a powerful, rapidly alternating electrostatic field. For this purpose I suspend a sheet of metal a distance from the ceiling on insulating cords and connect it to one terminal of the induction coil, the other terminal being preferably connected to the ground. Or else I suspend two sheets . . . each sheet being connected with one of the terminals of the coil, and their size being carefully determined. An exhausted tube may then be carried in the hand anywhere between the sheets or placed anywhere, even a certain distance beyond them; it remains always luminous."[29]

The principle of electrostatic induction is applicable to the electrical conduction wireless transmission method.

“In some cases when small amounts of energy are required the high elevation of the terminals, and more particularly of the receiving-terminal D', may not be necessary, since, especially when the frequency of the currents is very high, a sufficient amount of energy may be collected at that terminal by electrostatic induction from the upper air strata, which are rendered conducting by the active terminal of the transmitter or through which the currents from the same are conveyed."[30]

Far field methods achieve longer ranges, often multiple kilometer ranges, where the distance is much greater than the diameter of the device(s). The main reason for longer ranges with radio wave and optical devices is the fact that electromagnetic radiation in the far-field can be made to match the shape of the receiving area (using high directivity antennas or well-collimated laser beam) thereby delivering almost all emitted power at long ranges. The maximum directivity for antennas is physically limited by diffraction.

#### Beamed power, size, distance, and efficiency

The dimensions of the components may be dictated by the distance from transmitter to receiver, the wavelength and the Rayleigh criterion or diffraction limit, used in standardradio frequency antenna design, which also applies to lasers. In addition to the Rayleigh criterion Airy's diffraction limit is also frequently used to determine an approximate spot size at an arbitrary distance from the aperture.

The Rayleigh criterion dictates that any radio wave, microwave or laser beam will spread and become weaker and diffuse over distance; the larger the transmitter antenna or laser aperture compared to the wavelength of radiation, the tighter the beam and the less it will spread as a function of distance (and vice versa). Smaller antennae also suffer from excessive losses due to side lobes. However, the concept of laser aperture considerably differs from an antenna. Typically, a laser aperture much larger than the wavelength induces multi-moded radiation and mostly collimators are used before emitted radiation couples into a fiber or into space.

Ultimately, beamwidth is physically determined by diffraction due to the dish size in relation to the wavelength of the electromagnetic radiation used to make the beam. Microwave power beaming can be more efficient than lasers, and is less prone to atmospheric attenuation caused by dust or water vapor losing atmosphere to vaporize the water in contact.

Then the power levels are calculated by combining the above parameters together, and adding in the gains and losses due to the antenna characteristics and the transparency anddispersion[disambiguation needed] of the medium through which the radiation passes. That process is known as calculating a link budget.

#### Microwave method

 An artist's depiction of a solar satellite that could send electric energy by microwaves to a space vessel or planetary surface.

Power transmission via radio waves can be made more directional, allowing longer distance power beaming, with shorter wavelengths of electromagnetic radiation, typically in the microwave range. A rectenna may be used to convert the microwave energy back into electricity. Rectenna conversion efficiencies exceeding 95% have been realized. Power beaming using microwaves has been proposed for the transmission of energy from orbiting solar power satellites to Earth and the beaming of power to spacecraft leaving orbit has been considered.[2][31]

Power beaming by microwaves has the difficulty that for most space applications the required aperture sizes are very large due todiffraction limiting antenna directionality. For example, the 1978 NASA Study of solar power satellites required a 1-km diameter transmitting antenna, and a 10 km diameter receiving rectenna, for a microwave beam at 2.45 GHz.[32] These sizes can be somewhat decreased by using shorter wavelengths, although short wavelengths may have difficulties with atmospheric absorption and beam blockage by rain or water droplets. Because of the "thinned array curse," it is not possible to make a narrower beam by combining the beams of several smaller satellites.

For earthbound applications a large area 10 km diameter receiving array allows large total power levels to be used while operating at the low power density suggested for human electromagnetic exposure safety. A human safe power density of 1 mW/cm2 distributed across a 10 km diameter area corresponds to 750 megawatts total power level. This is the power level found in many modern electric power plants.

Following World War II, which saw the development of high-power microwave emitters known as cavity magnetrons, the idea of using microwaves to transmit power was researched. By 1964 a miniature helicopter propelled by microwave power had been demonstrated.[33]

Japanese researcher Hidetsugu Yagi also investigated wireless energy transmission using a directional array antenna that he designed. In February 1926, Yagi and Uda published their first paper on the tuned high-gain directional array now known as the Yagi antenna. While it did not prove to be particularly useful for power transmission, this beam antenna has been widely adopted throughout the broadcasting and wireless telecommunications industries due to its excellent performance characteristics.[34]

Wireless high power transmission using microwaves is well proven. Experiments in the tens of kilowatts have been performed at Goldstone in California in 1975[35][36][37] and more recently (1997) at Grand Bassin on Reunion Island.[38] These methods achieve distances on the order of a kilometer.

#### Laser method

 With a laser beam centered on its panel of photovoltaic cells, a lightweight model plane makes the first flight of an aircraft powered by a laser beam inside a building at NASA Marshall Space Flight Center.

In the case of electromagnetic radiation closer to visible region of spectrum (10s of microns (um) to 10s of nm), power can be transmitted by converting electricity into a laser beam that is then pointed at a solar cell receiver[39] This mechanism is generally known as "power beaming" because the power is beamed at a receiver that can convert it to usable electrical energy.

Advantages of laser based energy transfer compared with other wireless methods are:[40]

1. collimated monochromatic wavefront propagation allows narrow beam cross-section area for energy transmission over large ranges.
2. compact size of solid state lasers-photovoltaics semiconductor diodes fit into small products.
3. no radio-frequency interference to existing radio communication such as Wi-Fi and cell phones.
4. control of access; only receivers illuminated by the laser receive power.

Its drawbacks are:

1. Laser radiation is hazardous, even at low power levels it can blind people and animals, and at high power levels it can kill through localized spot heating
2. Conversion to light, such as with a laser, is inefficient
3. Conversion back into electricity is inefficient, with photovoltaic cells achieving 40%–50% efficiency.[41] (Note that conversion efficiency is rather higher with monochromatic light than with insolation of solar panels).
4. Atmospheric absorption, and absorption and scattering by clouds, fog, rain, etc., causes losses, which can be as high as 100% loss
5. As with microwave beaming, this method requires a direct line of sight with the target.

The laser "powerbeaming" technology has been mostly explored in military weapons[42][43][44] and aerospace[45][46] applications and is now being developed for commercial andconsumer electronics Low-Power applications. Wireless energy transfer system using laser for consumer space has to satisfy Laser safety requirements standardized under IEC 60825.

To develop an understanding of the trade-offs of Laser ("a special type of light wave"-based system):

1. Propagation of a laser beam[47][48][49] (on how Laser beam propagation is much less affected by diffraction limits)
2. Coherence and the range limitation problem (on how spatial and spectral coherence characteristics of Lasers allows better distance-to-power capabilities[50])
3. Airy disk (on how wavelength fundamentally dictates the size of a disk with distance)
4. Applications of laser diodes (on how the laser sources are utilized in various industries and their sizes are reducing for better integration)

Geoffrey Landis[51][52][53] is one of the pioneers of solar power satellite[54] and laser-based transfer of energy especially for space and lunar missions. The continuously increasing demand for safe and frequent space missions has resulted in serious thoughts on a futuristic space elevator[55][56] that would be powered by lasers. NASA's space elevator would need wireless power to be beamed to it for it to climb a tether.[57]

NASA's Dryden Flight Research Center has demonstrated flight of a lightweight unmanned model plane powered by a laser beam.[58] This proof-of-concept demonstrates the feasibility of periodic recharging using the laser beam system and the lack of need to return to ground.

### Electrical conduction

 The Tesla coil wireless transmitter U.S. Patent 1,119,732
 Means for long conductors of electricity forming part of an electric circuit and electrically connecting said ionized beam to an electric circuit. Hettinger 1917 -(U.S. Patent 1,309,031)
Main article: World Wireless System

#### Disturbed charge of ground and air method

The wireless transmission of alternating current electricity through the earth with an equivalent electrical displacement through the air above it achieves long ranges that are superior to the resonant electrical induction methods and favorably comparable to the electromagnetic radiation methods.[59]  Electrical energy can be transmitted through inhomogeneous Earth with low loss because the net resistance between earth antipodes is less than 1 ohm.[3]  The electrical displacement takes place predominantly by electrical conduction through the oceans, and metallic ore bodies and similar subsurface structures.  The electrical displacement is also by means of electrostatic induction through the more dielectric regions such as quartz deposits and other non-conducting minerals.[60][61]  Receivers are energized by currents through the earth while an equivalent electric displacement occurs in the atmosphere.[62]

This energy transfer technique is suitable for transmission of electrical power in industrial quantities and also for wireless broadband telecommunications.  The Wardenclyffe Tower project was an early commercial venture for trans-Atlantic wireless telephony and proof-of-concept demonstrations of global wireless power transmission using this method.[63] The facility was not completed due to insufficient funding.[64]

##### Terrestrial transmission line with atmospheric return

Single wire with Earth return electrical power transmission systems rely on current flowing through the earth plus a single wire insulated from the earth to complete the circuit. In emergencies high-voltage direct current power transmission systems can also operate in the 'single wire with earth return' mode. Elimination of the raised insulated wire, and transmission of high-potential alternating current through the earth with an atmospheric return circuit is the basis of this method of wireless electrical power transmission.

The atmospheric conduction method depends upon the passage of electrical current through the earth, and through the uppertroposphere and the stratosphere.[65]  Current flow is induced by electrostatic induction up to an elevation of approximately 3 miles (4.8 km) above Earth's surface.[66][67] Electrical conduction and the flow of current through the upper atmospheric strata starting at a barometric pressure of approximately 130 millimeters of mercury is made possible by the creation of capacitively coupled discharge plasma through the process of atmospheric ionization.[68][69][70] In this way electric lamps can be lit and electric motors turned at moderate distances. The transmitted energy can be detected at much greater distances.[71]

A global system for "the transmission of electrical energy without wires" called the World Wireless System, dependent upon the high electrical conductivity of plasma and the high electrical conductivity of the earth, was proposed as early as 1904.[72][73]

##### Terrestrial single-conductor surface wave transmission line

The basic transmitter used for the terrestrial single-conductor earth resonance method is identical to that used for the atmospheric conduction method.[74][75]

The fundamental earth resonance frequency is approximately 11.78 Hz.[76]  A higher harmonic of this fundamental frequency is used.[77]

"The frequency should be smaller then twenty thousand per second, though shorter waves might be practicable"[78][79][80][81]

Observations have been made that may be inconsistent with a basic tenet of physics related to the scalar derivatives of the electromagnetic potentials[82][83][84][85][86][87][88] that are presently considered to be nonphysical.[89]

## Timeline of wireless power

• 1961: William C. Brown publishes an article exploring possibilities of microwave power transmission.[108][109]
• 1968: Peter Glaser proposes wirelessly transmitting solar energy captured in space using "Powerbeaming" technology.[110][111] This is usually recognized as the first description of a solar power satellite.
• 1973: The world's first passive RFID system is demonstrated at Los-Alamos National Lab.[112]
• 1975: Goldstone Deep Space Communications Complex does experiments in the tens of kilowatts.[35][36][37]
• 1998: RFID tags are powered by electrodynamic induction over a few feet.[citation needed]
• 1999: Prof. Shu Yuen (Ron) Hui and Mr. S.C. Tang file a patent on "Coreless Printed-Circuit-Board (PCB) transformers and operating techniques", which form the basis for future planar charging surface with "vertical flux" leaving the planar surface. The circuit uses resonant circuits for wireless power transfer. EP(GB)0935263B
• 2000: Prof. Shu Yuen (Ron) Hui invent a planar wireless charging pad using the "vertical flux" approach and resonant power transfer for charging portable consumer electronic products. A patent is filed on "Apparatus and method of an inductive battery charger,” PCT Patent PCT/AU03/00 721, 2000.
• 2001 Prof. Shu Yuen (Ron) Hui and Dr. S.C. Tang file a patent on "Planar Printed-Circuit-Board Transformers with Effective Electromagnetic Interference (EMI) Shielding". The EM shield consists of a thin layer of ferrite and a thin layer of copper sheet. It enables the underneath of the future wireless charging pads to be shielded with a thin EM shield structure with thickness of typically 0.7mm or less. U.S. Patent 6,501,364.
• 2001: Prof. Ron Hui's team demonstrate that the coreless PCB transformer can transmit power close to 100W in ‘A low-profile low-power converter with coreless PCB isolation transformer, IEEE Transactions on Power Electronics, Volume: 16 Issue: 3 , May 2001. A team of Philips Research Center Aachen, led by Dr. Eberhard Waffenschmidt, use it to power an 100W lighting device in their paper "Size advantage of coreless transformers in the MHz range" in the European Power Electronics Conference in Graz.
• 2002: Prof. Shu Yuen (Ron) Hui extends the planar wireless charging pad concept using the vertical flux approach to incorporate free-positioning feature for multiple loads. This is achieved by using a multilayer planar winding array structure. Patent were granted as "Planar Inductive Battery Charger", GB2389720 and GB 2389767.[citation needed]
• 2005: Prof. Shu Yuen (Ron) Hui and Dr. W.C. Ho publish their work in the IEEE Transactions on a planar wireless charging platform with free-positioning feature. The planar wireless charging pad is able to charge several loads simultaneously on a flat surface.[citation needed]
• 2007: A localized charging technique is reported by Dr. Xun Liu and Prof. Ron Hui for the wireless charging pad with free-positioning feature. With the aid of the double-layer EM shields enclosing the transmitter and receiver coils, the localized charging selects the right transmitter coil so as to minimize flux leakage and human exposure to radiation.[citation needed]
• 2007: Using electrodynamic induction the WiTricity physics research group, led by Prof. Marin Soljacic at MIT, wirelessly power a 60W light bulb with 40% efficiency at a 2 metres (6.6 ft) distance with two 60 cm-diameter coils.[113]
• 2008: Bombardier offers a new wireless power transmission product PRIMOVE, a system for use on trams and light-rail vehicles.[114]
• 2008: Intel reproduces the original 1894 implementation of electrodynamic induction and Prof. John Boys group's 1988 follow-up experiments by wirelessly powering a nearby light bulb with 75% efficiency.[115]
• 2008: Greg Leyh and Mike Kennan of the Nevada Lightning Laboratory publish a paper on the disturbed charge of ground and air method of wireless power transmission with circuit simulations and test results showing an efficiency greater than can be obtained using the electrodynamic induction method.[59]
• 2009: Palm (now a division of HP) launches the Palm Pre smartphone with the Palm Touchstone wireless charger.
• 2009: A Consortium of interested companies called the Wireless Power Consortium announce they are nearing completion for a new industry standard for low-power (which is eventually published in August 2010) inductive charging.[116]
• 2009: An Ex approved Torch and Charger aimed at the offshore market is introduced.[117] This product is developed by Wireless Power & Communication, a Norway based company.
• 2009: A simple analytical electrical model of electrodynamic induction power transmission is proposed and applied to a wireless power transfer system for implantable devices.[118]
• 2009: Lasermotive uses diode laser to win \$900k NASA prize in power beaming, breaking several world records in power and distance, by transmitting over a kilowatt more than several hundred meters.[119]
• 2009: Sony shows a wireless electrodynamic-induction powered TV set, 60 W over 50 cm[120]
• 2010: Haier Group debuts “the world's first” completely wireless LCD television at CES 2010 based on Prof. Marin Soljacic's follow-up research on the 1894 electrodynamic induction wireless energy transmission method and the Wireless Home Digital Interface (WHDI).[121]
• 2010: System On Chip (SoC) group in University of British Columbia develops a highly efficient wireless power transmission systems using 4-coils. The design is optimized for implantable applications and power transfer efficiency of 82% is achieved.[122]
• 2012: "Bioelectromagnetics and Implantable Devices" group in University of Utah, USA develops an efficient wireless power and data transfer system for biomedical Implants. Presented design achieves more than twice the efficiency and frequency bandwidth compared to conventional inductive link approach. Design approach is extendable to other industrial "smart" wireless power transfer system.[123]
• 2012: Christopher Tucker, Kevin Warwick and William Holderbaum of the University of Reading, UK develop a highly-efficient, compact power transfer system safe for use in human proximity. The design is simple and uses only a few components to generate stable currents for biomedical implants. It resulted from research that directly attempted to extend Tesla’s 1897 wireless power work.[124]
• 2013: Multi-coil based wireless power transfer system is proposed to reduce the variation in power transfer efficiency and data bandwidth with coupling variation. Such systems can compensate the effect of coil misalignment on system performance.[125][126]
• 2013: The concept of a virtual waveguide controlled by ordered magnetic fields for wireless power transmission is proposed. [127]

Books
• Walker, J., Halliday, D., & Resnick, R. (2011). Fundamentals of physics. Hoboken, NJ: Wiley.
• Hu, A. P. (2009). Wireless/Contactless power supply: Inductively coupled resonant converter solutions. Saarbrücken, Germany: VDM Verlag Dr. Müller.
• Valone, T. (2002). Harnessing the wheelwork of nature: Tesla's science of energy. Kempton, Ill: Adventure Unlimited Press.
• General Electric Co. (1915). General Electric review, Volume 18. "Wireless Transmission of Energy" By Elihu Thomson. General Electric Company, Lynn. (ed. Lecture by Professor Thomson, National Electric Light Association, New York.)
• Steinmetz, C. P. (1914). Elementary lectures on electric discharges, waves and impulses, and other transients. New York: McGraw-Hill book co., inc.
• Louis Cohen (1913). Formulae and tables for the calculation of alternating current problems. McGraw-Hill.
• Kennelly, A. E. (1912). The application of hyperbolic functions to electrical engineering problems: Being the subject of a course of lectures delivered before the University of London in May and June 1911. London: University of London Press.
• Orlich, E. M. (1912). Die Theorie der Wechselströme.
• Fleming, J. A. (1916) The principles of electric wave telegraphy and telephony. London: Longmans, Green and Co.
• Fleming, J. A. (1911). Propagation of electric currents in telephone & telegraph conductors. New York: Van Nostrand.
• Franklin, W. S. (1909). Electric waves: An advanced treatise on alternating-current theory. New York: Macmillan Co.
Patents

## References

1. ^ A radio transmitter can produce waves having a power of several kilowatts or even megawatts but this energy scatters in all directions. Only a small fraction, less than a millionth part, of the transmitted energy is received. However, this is sufficient to yield the intelligence.
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It is intended to give practical demonstrations of these principles with the plant illustrated. . . . An inexpensive instrument, not bigger than a watch, will enable its bearer to hear anywhere, on sea or land, music or song, the speech of a political leader . . . delivered in some other place, however distant. . . . Millions of such instruments can be operated from but one plant of this kind. More important than all of this, however, will be the transmission of power, without wires, which will be shown on a scale large enough to carry conviction.
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I have to say here that when I filed the applications of September 2, 1897, for the transmission of energy in which this method was disclosed, it was already clear to me that I did not need to have terminals at such high elevation. . . .
At that time I was absolutely sure that I could put up a commercial plant, if I could do nothing else but what I had done in my laboratory on Houston Street; but I had already calculated and found that I did not need great heights to apply this method. My patent says that I break down the atmosphere "at or near" the terminal. If my conducting atmosphere is 2 or 3 miles above the plant, I consider this very near the terminal as compared to the distance of my receiving terminal, which may be across the Pacific. . . .
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"The earth is 4,000 miles radius. Around this conducting earth is an atmosphere. The earth is a conductor; the atmosphere above is a conductor, only there is a little stratum between the conducting atmosphere and the conducting earth which is insulating. . . . Now, you realize right away that if you set up differences of potential at one point, say, you will create in the media corresponding fluctuations of potential. But, since the distance from the earth's surface to the conducting atmosphere is minute, as compared with the distance of the receiver at 4,000 miles, say, you can readily see that the energy cannot travel along this curve and get there, but will be immediately transformed into conduction currents, and these currents will travel like currents over a wire with a return. The energy will be recovered in the circuit, not by a beam that passes along this curve and is reflected and absorbed, . . . but it will travel by conduction and will be recovered in this way
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78. ^ ART OF TRANSMITTING ELECTRICAL ENERGY THROUGH THE NATURAL MEDIUMS, April 17, 1906, Canadian Patent No. 142,352, August 13, 1912.
Three requirements seem to be essential to the establishment of the resonating condition.
First. The earth’s diameter passing through the pole should be an odd multiple of the quarter wave length – that is, of the ratio between the velocity of light – and four times the frequency of the currents.
Second. It is necessary to employ oscillations in which the rate of radiation of energy into space in the form of hertzian or electromagnetic waves is very small. To give an idea, I would say that the frequency should be smaller then twenty thousand per second, though shorter waves might be practicable. The lowest frequency would appear to be six per second, in which case there will be but one node, at or near the ground-plate, and, paradoxical as it may seem, the effect will increase with the distance and will be greatest in a region diametrically opposite the transmitter. With oscillations still slower the earth, strictly speaking, will not resonate, but simply act as a capacity, and the variation of potential will be more or less uniform over its entire surface.
Third. The most essential requirement is, however, that irrespective of frequency the wave or wave-train should continue for a certain interval of time, which I have estimated to be not less then one-twelfth or probably 0.08484 of a second and which is taken in passing to and returning from the region diametrically opposite the pole over the earth’s surface with a mean velocity of about four hundred and seventy-one thousand two hundred and forty kilometers per second [471,240 km/sec].
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These three requirements, as stated are in agreement with his numerous experimental observations. . . . we would point out that the specification does not deal with theories, but with facts which applicant has experimentally observed and demonstrated again and again, and in the commercial exploitation of which he is engaged.
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