1. Wireless Power 1
Wireless Power (March 2010)
Jenna Rock and Loren Schwappach
highly directional antennas have achieved efficiencies greater
Abstract: The idea of using strongly coupled magnetic than 95 percent. However, practical problems with this
resonances to wirelessly transfer power over large distances will approach include the large antenna sizes required and the
be introduced. This new idea was discovered by a group of MIT losses due to atmospheric absorption and free space.
professors and has far reaching implications on how power will
Another approach to providing wireless power which has
be transferred in future years. Along with presenting this idea, a
top level understanding of how this method of wireless power become quite popular this century is the use of inductive
transfer is provided. charging to transfer energy between two systems. Because
there must be a short gap between the two inducting coils, this
is considered a type of short distance wireless energy transfer
I. INTRODUCTION and impractical for separation of more than a few inches.
I MAGINE a future in which wireless power transfer
redefined the way people live and work. Imagine a world
where cell phones, household robots, music and multimedia III. RECENT DEVELOPMENTS
players, computers, automobiles, medical devices, and other In 2006 a bright group of Massachusetts Institute of
fixed and portable electronics were powered without ever Technology (MIT) theoretical physics professors led by Marin
being plugged into the wired power grid. This imagined world Soljačić developed a possible solution, using wireless power
is much closer to reality than one might think. A “tutorial” of transfer via strongly coupled magnetic resonances. Their
a method for providing wireless power via strongly coupled approach overcomes several major drawbacks that previously
magnetic resonances will be presented along with a discussion plagued the transmission of power wirelessly. These
of the implications. drawbacks can be summarized as: large energy wasted into
free space when using an omni-directional transmitter;
unobstructed line-of-sight required by lasers and highly
II. HISTORICAL INFORMATION directional antennas; and very close-range or very low-power
The concept of transferring power to the world wirelessly energy transfer as limited by magnetic induction. Their
was first experimented with by Nikola Tesla who lived from concept, which they refer to as “WiTricity” (as in Wireless
10 July 1856 – 7 January 1943. His experiments were with Electricity), uses strongly coupled magnetic resonances and
high power electromagnetic waves and he even managed to has been shown to improve the distance of magnetic induction
demonstrate lighting a bulb using wireless power at The power transfer by a factor of 106. In other words, non-
Chicago World’s Fair in 1893. Unfortunately, Tesla’s system resonant magnetic induction is almost a million times less
for providing wireless power required a clear line-of-site efficient than WiTricity. The significantly improved efficiency
between the transmitter and the receiver. Tesla even proposed of this approach greatly expands the potential applications
a system of using the earth’s ionosphere to store and which can harness this form of wireless energy. In order to
propagates wireless energy via electrical conduction, understand how wireless power transfer via strongly coupled
effectively lightning bolts. However, a means of controlling magnetic resonances works, an understanding of magnetic
and profiting from Tesla’s unconventional ideas could not be induction, inductive coupling, resonance, and resonant
envisioned in his time and thus were thought impractical and magnetic coupling is first needed.
financially irresponsible by his investors. Eventually Tesla’s
world changing ideas were abandoned and Tesla was labeled
as a mad scientist, bankrupted by his investors, and driven IV. TECHNICAL DETAILS
slowly into poverty and depression. A. Magnetic Induction
After Tesla’s death the driving force behind wireless Magnetic Induction is a fundamental idea used throughout
power transmission was the idea of using radio and microwave electronics. It is the process of developing a voltage across a
power transmission systems. NASA JPL Goldstone conductor (like copper) positioned in a shifting magnetic field
demonstrated long distance wireless power transmission by (the field moves around a fixed conductor), or conversely, a
successfully transmitting 34kw of electrical power at a conductor moving through a stationary magnetic field. It uses
distance of 1.5km with an efficiency of 82 percent on June 5, a loop or coil of conductive material like silver, gold or copper
1975. Since the demonstration, individual experiments using to carry an AC current and generate an oscillating
(corresponding to the alternating current) magnetic field as
shown in Figure 1. As electric current, I, flows though the

2. Wireless Power 2
wire, it produces to a changing magnetic field, B, which wraps induction (toothbrushes, etc.), yet the applications are limited
around the wire. As the current reverses in direction, the to a very small range. Michael Faraday, who is credited with
magnetic field also reverses its direction, thus achieving the the discovery of magnetic induction, stated that the
changing field required. electromotive force (EMF) produced around a closed loop is
directly related to the changing amount of the magnetic flux
through any surface bounded by its path. Faraday's Law of
electromagnetic induction is: E= -dφB/dt, where E is known in
physics as the electromotive force and φB is the magnetic
flux. Lenz's Law also states that: “the current in the loop is
always in such a direction as to oppose the change of magnetic
Figure 1: Magnetic field created on a single AC flux Ф(t) that produced it” [7]. The change in direction derived
conducting wire. [6] by Lenz's Law can be thought of as the result of the minus
sign in Faraday’s Law.
If a conductive loop (the transmitter) is driven by an AC
power source, it will quickly generate an oscillating magnetic
B. Coupling
field around the vicinity of the loop as shown by Figure 2. The
blue lines in the illustration represent the magnetic field that is The phenomenon of coupling is observed when energy is
being created when current flows through the loop. When the dynamically exchanged between two objects, whether
current reverses in direction, the magnetic field will also mechanical, thermal, electrical, or otherwise. Generically,
reverse in direction, thus providing an alternating field. coupling is the connection between a source of energy and a
consumer of energy – a mechanical example of coupling is a
car pulling a trailer via a ball coupling. Magnetic coupling (or
inductive coupling) is the use of magnetism to accomplish this
transfer of power. When a changing current flow in one
conductor induces a voltage across a second conductor,
coupling has been observed. Mutual inductance is a measure
Figure 2: Magnetic field on a coil. [6] of the amount of coupling that has occurred between two such
conductors. Wireless electricity, WiTricity, relies on magnetic
When a second conductive loop (the receiver) is brought coupling to eliminate all physical connections linking the
within close enough proximity to the first, it will quickly begin source and receiver and thus allows a wireless power
to capture a portion of the original loop’s oscillating magnetic connection between the two devices.
field. Thus the original (transmitting) loop will then induce or
generate an electrical current (flow of electrical energy) in the C. Resonance
second (receiving) coil as shown in Figure 3. The second
Resonance is the inclination of an object or system to
coil’s generated current may then be used to power connected
oscillate (vibrate) at larger amplitudes at some frequencies
devices. An electrical transformer (a device made of two coils
rather than at other frequencies. The natural frequencies are
in close proximity) is a device that uses this idea of magnetic
called the object or system’s resonant frequencies and can be
induction to transfer energy from a primary coil to its
used to accomplish amazing things. At resonant frequencies,
secondary coil without the coils being electrically wired
even microscopic, periodic, forces can eventually produce
together. It is used to “transform” the AC at one voltage to AC
large amplitude oscillations in like-resonant receiving devices.
at a different voltage, in other words it is used to step a voltage
The property of resonance exists in numerous different
up or down.
physical systems. Nikola Tesla described resonance as the
frequency at which energy can be most effectively added to an
oscillating system (like the earth’s Ionosphere). A child’s
playground swing is an outstanding example of an oscillating
system involving both potential and kinetic energy. This is
when a child swings back and forth at a constant rate
determined by the length of the swing. The child can increase
the energy in the swing system and thus make the swing go
higher by aligning his/her body with the movement of the
swing. In this example, the swing is moving at its mechanical
Figure 3: Basic Transformer. [6]
resonant frequency and the child’s synchronized movements
are effectively transferring energy into the swing system.
This type of electrical power transfer from one loop to the
Another popular example of resonance is an opera singer in an
other is known as magnetic induction and is the basis for
opera house shattering several wine glasses as she produces a
electrical transformers and electric generators. Many of
magnificent single note (frequency) for a sufficiently long
today’s electronic devices already use the concept of magnetic

3. Wireless Power 3
duration. All objects have natural resonant frequencies and in and the receiving coil was wired to a resistive load of a 60W
the opera singer example the wine glasses are acting as natural bulb. They used two single copper loops each with a
resonate receivers. The sound waves produced by the opera matching radius of 25 cm. The transmitting wire coil output a
singer are captured by the wine glasses and as the wine glasses 9.9MHz resonating magnetic field. The coils were separated
absorb the energy from the singer’s notes, they begin vibrating by a distance of 2 meters. Since the coils were resonant, the
and eventually shatter in an amazing display. current and charge density profiles were 90 degrees out of
phase from each other. Using electromagnetic theory, the
MIT group defined an effective inductance and effective
D. Resonant Magnetic Coupling
capacitance as follows:
Resonant magnetic coupling uses the efficient energy
µ0 drdr ' ( J (r ) J (r ' ))
transfer property of resonance in conjunction with oscillating
magnetic fields. Resonance requires the transmitter and
L=
4π I 0
2 ∫∫ r − r'
,
receiver to have the same natural frequency. Coupling
1 1 drdr ' ( ρ ( r ) ρ ( r ' ))
describes the transfer of energy. And magnetic waves enable
this coupling to be done wirelessly. The ability to wirelessly
=
C 4πε 0 q 0 2 ∫∫ r − r'
.
transmit power using this effect is the focus of the research
and demonstration by the MIT team in 2006.
Furthermore, this coupling can occur even around and Where J(r) is the spatial current and ρ(r) is the charge
through objects as illustrated in Figure 4. Non-conductive density. The group stated that the energy contained in the coil
materials simply do not affect the magnet waves. And is thus expressed as:
magnetic waves wrap around conductive materials but do not 1 2 1 2
U= L I0 = q0 .
impact them as the natural frequencies are not similar. 2 2C
The resulting resonant frequency is then defined as:
1
f0 = .
2π LC
Using their design constraints the MIT group was able to
build a demonstration, shown in Figure 5, and light up the
receiving 60W light bulb, effectively demonstrating wireless
power with approximately 50% efficiency. This 50%
efficiency is already several thousand times more efficient
than today’s batteries.
Figure 4: Wireless power transfer around an object. [6]
E. WiTricity
WiTricity, as discovered by a group of MIT professors lead
by Professor Marin Soljačić, uses a scheme where non-
radiating magnetic coupling is implemented using the non-
lossy stationary near-field (the region within a radius r << λ,
where λ = wavelength). WiTricity transmitters and receivers
use specially designed magnetic resonators as shown in Figure
5 that efficiently transfer power over relatively large distances
via the magnetic near-field. The MIT group revealed that
when the permittivity ε is large and field variations are slow,
the material absorption is related to the material loss tangent,
which allows the resonating field to couple at incredible
efficiencies. Figure 5: Professor Soljacic and the WiTricity team.
[1]
F. The MIT Experiment
The original MIT experiment validating the concept of G. Efficiency
WiTricity was demonstrated in 2006 and used two self- One of the most spectacular aspects of this system of
resonant coils. A self-resonating coil has its own natural transferring power wirelessly is that it is relatively highly
resonant frequencies. The transmitting coil was wired to an efficient. The MIT team used and confirmed the equation:
oscillating circuit; the two coils were coupled magnetically;

4. Wireless Power 4
PW devices that can be utilized in and out of the vicinity of a
η= , WiTricity power source. These two definitions can be applied
PS + PD + PW to the different products that use this power.
to calculate the efficiency of the system. The graph in Figure The possible applications of WiTricity in automatically
6 shows the theoretical and experimental efficiencies the MIT powering and charging today’s electronics are astonishing.
team found in their system. Applications for consumer electronics include automatic
charging and recharging of portable electronics (I-pods, cell
phones, controllers, laptops, etc.) in automobiles, homes,
offices, and WiTricity-enabled hot spots. Other consumer
applications include direct powering of immobile devices such
as digital pictures, home theater systems, flat screen
televisions, speakers, and desktop PC’s and peripherals.
Industrial applications include direct wireless power
interconnections across rotating and moving “joints” (e.g.,
robotics, packing equipment, assembly machine lines, and
tools) thus, doing away with costly and problematic wiring.
Other industrial applications include providing power
interconnections in harsh environments (mining, underwater,
etc.), and a wireless source for moving robotics and automatic
guided vehicles eliminating the need for expensive power
Figure 6: Theoretical and Experimental System wiring, complex mechanisms, and labor intensive charging.
Efficiency. [5] Applications in transportation include automatic wireless
powering for personal and commercial hybrid and future all-
The graph in Figure 6 compares three different things electric vehicles and eliminating the need for costly harnesses
related to the efficiency of the system. The teal shaded area and slip rings. There are also unconventional applications like
shows the theoretical prediction of maximum efficiency. The the powering of implantable medical devices and high tech
black squares show the calculated maximum. And the red military systems (e.g., military robotics, aircrafts, etc).
bars show the actual experimental values. WiTricity Corporation is hoping to bring such WiTricity
If the distance between the source and the receiving coil is transmitters and receivers to the consumer market as early as
“d”, then about 95% of the power can be transferred (with 2011.
appropriate coils and frequencies). However, if there is a
longer distance say “5d” only about 10% of the power can be
transferred. However, these are still impressive results, V. ADVANTAGES AND DISADVANTAGES
everything considered. As one of the MIT professors One of the things that will probably be on the tip of most
explained, “If I'm replacing an alkaline battery, if it's only 1% people’s tongue when they hear about this new way of
efficient it will still beat the pants off of a battery because transferring power is caution on the potential negative impacts
disposable battery power costs 350x grid power.” [2]. This this new method may have on the environment, especially
incredible amount of efficiency for transferring energy humans. The answer to this obvious question is another great
wirelessly has exciting implications. selling point for the technology. The WiTricity method of
providing wireless power transfer has insignificant effects on
H. WiTricity Products and Applications the environment and has almost no effect on humans since
they look like air to the resonating magnetic field. Figure 5
After the impressive research results were recorded by the
shows the MIT group standing between their huge inductive
WiTricity research team, a corporation was founded in 2007 to
coils, clearly not being affected in any way by the magnetic
develop ways for commercializing this new technology. The
field.
WiTricity Corporation has two different definitions in how
For the environmental side of things, the way these coils
their wireless project can be used. Their first definition is for
work in transferring energy the electricity stays on the sending
Direct Wireless Power. Direct Wireless Power is when all of
or receiving coils instead of radiating harmfully into the
the power that a system or device requires is provided without
environment, like many of today’s devices (take cell phones
wires, and without a chemical energy source such as batteries.
for example). Also, since the power is transferred by the
Direct Wireless Power is used when a device is always within
magnetic field there are no physical electrons being
the range of a WiTricity power source. The next definition is
transmitted into the air. The only thing that is escaping into
that of Automatic Wireless Charging. Automatic Wireless
the environment is the heat caused by the small resistance of
Charging is used when a system/device with a rechargeable
the wire as the current flows through the coils. Therefore, all
battery is able to charge itself, either while powered up or not,
of the power built on the coils that has not been absorbed by
without the need for a physical cord or battery change.
the receiving coils, is slowly dissipated as heat loss. In
Automatic Wireless Charging is for mobile systems and
addition, as WiTricity does not use radio waves, it does not

5. Wireless Power 5
interfere with Wi-Fi, cell phones, or other methods of [2] J. Dix. (2010). “Wireless power” Retrieved March 17,
communication. The reason why transferring power 2010, from
wirelessly like this does not hurt humans is again because no http://www.networkworld.com/news/2010/011210-
electrons are being radiated into the air. Since the power is witricity.html?page=1
being transferred by a magnetic field much smaller than the [3] A. Kurs., A. Karalis., R. Moffatt., P. Fisher., & M.
earth’s magnetic field it is perfectly safe for all earthly life, Soljacic. (2007). Wireless power transfer via strongly
including human life. Furthermore, since it is extremely coupled magnetic resonances”. Science Express. (n.d.).
difficult to get two unlike objects to perfectly resonate [4] A. Kurs. (2007). Wireless power transfer via strongly
magnetically with each other it is extremely unlikely for coupled magnetic resonances. Science. 317(7), 83,
[5] A. Karalis., J. Joannopoulos., & Marin Soljacic. (2007).
unwanted objects to interfere with the WiTricity method of
Efficient wireless non-radiative mid-range energy
wireless power transfer, making WiTricity safe for pace
transfer. Annals of Physics. 323(2008), 34-48.
makers and other small medical devices. This protection is
[6] WiTricity Corporation. (2010). WiTricity technology: the
also ensured because WiTricity Corporation technology uses basics. Retrieved March 20, 2010, from,
frequencies that are untouched by most of today’s devices. http://www.witricity.com/pages/technology.html
[7] Ulaby, F. Fundamentals of applied electromagnetics.
Upper Saddle River, NJ; Pearson Education Inc., 2007,
VI. VARIANTS AND EVOLUTION OF THE TECHNOLOGY pp. 528
While the development of “WiTricity” applications already
seems limitless, the concept is still in its birthing stage and
there are sure to be many improvements developed in the
technology in the coming years. During the development of
this report, the authors could already envision potential
additional applications/extensions. For example, an automatic
wireless charging device could transmit an “I need power”
signal periodically and a WiTricity transmission system could
listen for those requests and provide power as needed. This
could eliminate the need to have the WiTricity transmitter
continuously powered on. Another area that didn’t appear to
be explored is relay stations. The idea is to have
receive/transmit stations to extend the range of power without
additional wires – could such an idea replace wires between
power poles? What about power provided to a vehicle while it
was moving? Just as WiMax first was only a fixed wireless
technology before being enhanced to support mobile
applicaions, WiTricity might be enhanced to provide power to
vehicles while being driven. These are just a few rough ideas;
the WiTricity concept is bound to have numerous
improvements in the years ahead.
VII. CONCLUSION
WiTricity uses non-radiative magnetic resonant coupling to
achieve wireless power transfer over a million times more
efficient than inductive coupling. The idea of using
components’ natural resonant frequencies to couple induction
fields ensures efficient energy transfer and has global
applications. The MIT group that researched and
experimentally validated this concept in 2006 has already
begun developing applications for this technology. The
WiTricity Corporation hopes to bring this technology to the
consumer by 2011.
REFERENCES
[1] F. Hadley,. (2007). Goodbye wires. (PDF)
“MIT_WiTricity_Press_Release.pdf”