Design of wireless power transfer system via magnetic resonant coupling at 13.56 m hz

Proceedings of IOE Graduate Conference, Vol. 1, Nov 2013 202
Design of Wireless Power Transfer System via
Magnetic Resonant Coupling at 13.56MHz
Ajay Kumar Sah
Department of Electronics and Computer Engineering, IOE, Central Campus, Pulchowk, Tribhuvan University, Nepal
ajayshah2005@yahoo.com
Abstract: Power is a must to modern systems. Power transmission through wires is common. But not in
every field can wires be used because of certain limitations. The implantable biomedical devices like
pacemakers, cardiac defibrillators, and artificial hearts require power supply for long term operation. The
required power is supplied by driveline cable or by battery. WPT greatly reduces the risk of infection by
eliminating the driveline cable which otherwise needs to puncture the skin to provide power and also saves
the valuable space inside a person’s body in case of battery powered. In such fields, what we need is wireless
transmission. Wireless transmission is useful in cases where instantaneous or continuous energy transfer is
needed, but interconnecting wires are inconvenient, hazardous, or impossible. In this paper, a simple design
method of a wireless power transfer system using 13.56 MHz ISM band is proposed. The proposed wireless
power transfer system consists of rectifier, oscillator, power amplifier, power coil, load coil and two
intermediate coils as transmitter antenna and receiver antenna inserted between power coil and load coil.
Keywords: Wireless Power Transfer, Resonant coupling, Oscillator, Intermediate coils, Power transfer
efficiency.
1. INTRODUCTION
Power is very important to modern systems. From the
smallest sensors, bionic implants, laptops, consumer
products to satellites and oil platforms, it is important to
be able to deliver power means other than classical wires
or transmission lines. Wireless transmission is useful in
cases where instantaneous or continuous energy transfer
is needed, but interconnecting wires are inconvenient,
hazardous, or impossible sometimes. In case of biological
implants, there must be a battery or an energy storage
element present that can receive and hold energy. This
element takes up valuable space inside a person’s body. In
case of satellites, UAVs and oil platforms, solar panels,
fuel cells or combustion engines are currently used to
supply power [1].
The history of wireless power transmission dates back to
the late 19th century with the prediction that power could
be transmitted from one point to another in free space by
Maxwell in his “Treatise on Electricity and Magnetism”.
Heinrich Rudolf Hertz performed experimental validation
of Maxwell’s equation which was a monumental step in
the direction. However, Nikola Tesla’s experiments are
often considered as being some of the most serious
demonstrations of the capability of transferring power
wirelessly even with his failed attempts to send power to
space [2].
There are three types of Wireless Power Transfer (WPT):
radiative transfer, inductive transfer, and resonant
coupling. Radiative transfer, although suitable for
exchanging information, can transfer only small power
(several millwatts), because a majority of energy is
wasted into free space. Directive radiative transfer using
highly directional antennas can be efficiently used for
power transfer, even for long distances, but requires
existence of an uninterruptible line-of-sight and has
harmful influences on human body. On the other hand,
inductive coupling can transfer power with very high
efficiency but in a very short range (just in several
centimetres) [2].
The last type of WPT, resonant coupling, can transfer
high power at the medium range (several meters).
Recently, MIT proposed a new scheme based on strongly
coupled magnetic resonances, thus presenting a potential
breakthrough for a midrange wireless energy transfer. The
fundamental principle is that resonant objects exchange
energy efficiently, while non-resonant objects do not. The
scheme is carried with a power transfer of 60 W and has
RF-to-RF coupling efficiency of 40% for a distance of 2
m, which is more than three times the coil’s diameter. We
expect that coupled magnetic resonances will make
possible the commercialization of a midrange wireless
power transfer [3]-[5].
2. RELATED THEORY
A. Resonant frequency
Resonance is a phenomenon that causes an object to
vibrate when energy of a certain frequency is applied. In
physics, resonance is the tendency of a system (usually a
linear system) to oscillate with larger amplitude at some
frequencies than at others. These are known as the
system’s resonant frequencies. In these particular
frequencies, small periodic driving forces can even
produce oscillations having large amplitude. The resonant
frequency is calculated from (1).

Figure 1: Resonant frequency
(1)
Where, L and C are respectively the inductance and
capacitance of the tuned circuit.
B. Quality Factor (Q)
In physics and engineering the Quality factor (Q-factor) is
a dimensionless parameter that describes the
characteristics of an oscillator or a resonator, or
equivalently, characterizes a resonator’s bandwidth
relative to its centre frequency [1]. Higher Q indicates the
stored energy of the oscillator is relative of a lower rate of
energy loss and the oscillations die out more slowly. So it
can be stated that, oscillators with high quality factors
have low damping so that a pendulum rings longer, in
case of a pendulum example.
Figure 2: Bandwidth versus frequency
The above graph is the representation of the bandwidth,
Δf, of a damped oscillator energy versus frequency. The
higher the Q, the narrower and ‘sharper’ the peak is foΔf.
Sinusoidal signal driven resonators having higher Q
factors resonate with greater amplitudes (at the resonant
frequency) but have a smaller range of frequencies around
that frequency for which they resonate; the range of
frequencies for which the oscillator resonates is called the
bandwidth. Thus, a high Q tuned circuit in a radio
receiver would be more difficult to tune, but would have
more selectivity.
In an ideal series RLC circuit and in a tuned
radio frequency receiver (TRF) the Q factor can be
written as shown in (2).
(2)
Where, R, L and C are respectively the resistance,
inductance and capacitance of the tuned circuit.
C. Necessity of Impedance Matching
The resonance frequency changes as the coupling factor
changes, and the maximum efficiency power transfer
occurs at the resonance frequency. However, when this
wireless power transfer system is applied in the MHz
range (which allows smaller antennas), the usable
frequency range is bounded by the Industrial-Scientific-
Medical(ISM) band as shown in Figure 3. According to
the ISM band, the usable frequency ranges are extremely
narrow. For example, at 13.56MHz, the usable frequency
range is 13.56MHz±7kHz [6].
Figure 3: ISM Band
As a result, to apply this technology in restricted
frequency ranges such as the MHz range, the frequency of
the power source must be fixed at a usable range, and the
system has to be tuned so that its resonance frequency
matches the frequency of the power source.
D. Basic Theory of Impedance Matching
Impedance Matching is a technique commonly used in
power transfer systems and communication systems to
improve the efficiency of the system. It usually involves
inserting a matching network (such as an LC circuit) to
minimize the power reflection ratio to the power source of
the system. In Figure 4, the power transferred to the load
is written as (3) when the impedance of the power source
is defined as Zsource and that of the load is defined as
Zload. The power transferred to the load reaches its
maximum when Zsource=Z*load, as in (4). Therefore, the
circuit is considered matched and the maximum
efficiency achieved when the impedance of the load from

the source's point of view matches Zsource, and vice
versa [1].
Figure 4: Theory of impedance matching
(3)
(4)
The Impedance matching circuit can be considered as a
two-port network that can be described with (5). The
matching conditions are satisfied when the parameters
satisfy (6) & (7).
(5)
(6)
(7)
E. Equivalent Circuit diagram of the WPT System
Figure 5: Equivalent circuit of WPT system
Figure 5 shows the circuit representation of the WPT
system as modelled above. The schematic is composed of
four resonant circuits corresponding to the four coils.
These coils are connected together via a magnetic field,
characterized by coupling coefficients k12, k23, and k34.
Because the strengths of cross couplings between the
power & Rx coils and the load & Tx coils are very weak,
they can be neglected in the following analysis.
Theoretically, the coupling coefficient (also called
coupling factor) has a range from 0 to 1. If all magnetic
flux generated from a transmitting coil is able to reach a
receiving coil, the coupling coefficient would be “1”. On
the contrary, the coefficient would be represented as “0”
when there is no interaction between them. Actually, there
are some factors identifying the coupling coefficient. It is
effectively determined by the distance between the coils
and their relative sizes. It is additionally determined by
shapes of the coils and orientation (angle) between them.
The coupling coefficient can be calculated by using a
given formula
(8)
Where M12 is mutual inductance between coil “1” and
coil “2” and note that 0 ≤ k12 ≤ 1. Referring to the circuit
schematic, an AC power source with output impedance of
Rs provides energy for the system via the power coil.
Normally, the AC power supply can be a power amplifier
which is useful to measure a transmission and reflection
ratio of the system. Hence, a typical value of Rs, known
as the output impedance of the power amplifier is 50 Ω.
The power coil can be modelled as an inductor L1 with a
parasitic resistor R1. A capacitor C1 is added to make the
power coil resonate at the desirable frequency. The Tx
coil is a helical coil with many turns represented as an
inductor L2 with parasitic resistance R2. Geometry of the
Tx coil determines its parasitic capacitance such as stray
capacitance, which is represented as C2. Since this kind
of capacitance is difficult to be accurately predicted, for
fixed size of the coil, a physical length, which impacts the
self inductance and the parasitic capacitance, has been
manually adjusted in order to fit the resonant frequency as
desired. In the receiver side, the Rx coil is modelled
respectively by L3, R3 and C3. The load coil and the
connected load are also performed by L4, R4 and RL. A
capacitor C4 also has the same role as C1, so that the
resonant frequency of the load coil is defined. When the
frequency of sinusoidal voltage source VS is equal to the
self-resonant frequency of the resonators, their
impedances are at least. In other words, currents of the
coils would be at their most and energy can be delivered
mostly to the receiving coil. Otherwise, energy of the
transmitting power source would be dissipated in the
power coil circuit itself, resulting in the very low
efficiency. In general, setting the frequency of AC supply
source same as the natural resonant frequency of the
transceiver coils is one of the key points to achieve a
higher performance of the system.
The circuit model offers a convenient way to
systematically analyze the characteristic of the system. By
applying circuit theory Kirchhoff‘s Voltage Law (KVL)
to this system, with the currents in each resonant circuit
chosen as illustrated in Figure 5, a relationship between
currents through each coil and the voltage applied to the
power coil can be captured.
The system model can be considered as a two-port
network. To analyze this kind of system, S – parameter is
a suitable candidate. Actually, S21 is a vector referring to
a ratio of signal exiting at an output port to a signal
incident at an input port. This parameter is really

important because a power gain, the critical factor
determining of power transfer efficiency, is given by
[|S21|*|S21|], the squared magnitude of S21. The
parameter of S21 is calculated by (9) [7].
(9)
Thus, combining with
derived from (8), the S21 parameter is given as
(10)
The system equation indicated in (10) is expanded in
terms of quality factor which appreciates how well the
resonator can oscillate. The quality factor is presented in a
formula as given below
(11)
Where i and Ri are respectively the self-resonant
frequency and equivalent resistance of each resonant
circuit. In the power coil, for instance, Ri is a sum of RS
and R1. Actually, i of each coil is defined to be the
same. When the resonance takes place, the total
impedance of each coil is presented as following
Z1 = RS + R1 ≈ RS, Z2 = R2, Z3 = R3,
Z1 = RL + R4 ≈ RL
For simplicity, it is common to set RS equal to RL. At the
resonant frequency, 0 = 1 / LiCi, from (10), the
magnitude of S21 can be written as
(12)
The coupling coefficient k12 and k34 would be constant.
There is only k23 varying with medium conditions. To
find the range between the resonators at which |S21| or the
efficiency is certainly at maximum, a derivative of S21
with respect to k23 is taken and then setting the result to
zero, yielding
(13)
(14)
This value of * k23 is equivalent to the maximum range
that the transmitter is able to effectively transfer power to
the receiver at the given resonant frequency (before the
resonant frequency breaking in two peaks). Note that *
k23 ≤ 1. With the purpose of finding out the maximum
efficiency of the system in terms of |S21|, it is feasible to
substitute k23, which is derived above, into (13)
(15)
It is clear that |S21|max un-proportionally depends on *
k23. It means for the sake of a higher efficiency, the
extent that the highest efficiency can be achievable is
shortened. In order to get a greater value of |S21|max, *
k23 is supposed to decrease. From (14), increasing Q2
and Q3 is able to reduce the * k23. In general, making the
very high-Q transmitting and receiving coils is very
crucial so as to achieve high transfer performance.
F. Wheeler's formula
The classic formula for single-layer inductance (air core)
is called Wheeler's formula is given as:
Figure 6 Coil antenna
(16)
Where,
L = inductance in micro-Henries
N = number of turns of wire
R = radius of coil in cm
H = height of coil in cm
3. WPT SYSTEM DESIGN CALCULATIONS
A. Block Diagram of Proposed System
The paper will be based on the principle of resonant
inductive coupling. Magnetic coupling is an old and well
understood method in the field of wireless power transfer.
But as magnetic fields decay very quickly, it’s effective
only at a very short distance. By applying resonance
within magnetic coupling, the power transfer at a greater
distance can be obtained. For near field wireless power
transfer, Magnetic resonant coupling can be more
effective than any other methods available. The structure
of the whole system is shown below.
Figure 7: Structure of the WPT System

Here, I assume:
Object A represents high frequency oscillator.
Object B is representative of signal amplifier.
Object C is a source coil.
Object F is a load coil.
Object G is a resistive load.
Object D and E are transmitter and receiver antenna
respectively.
By including a signal amplifier in the system, it will be
able to amplify the amount of power that is transmitted.
This is crucial for conduction tests at high power. From
the amplifier the signal is then dumped into object C. This
is located at the top of object D. This allows for the
resonate frequency to pass from the object C to D. When
the transmitting antenna begins to resonate it generates
the evanescent resonate waves. Object E will pick up
these waves. From the receiving antenna, the signal is
then passed to object F. The load coil will then pass the
signal on to the load G.
Figure 8: Block Diagram of the whole system
The intermediate coils D and E are placed between object
C and F, which is tuned at the same frequency as C and F.
The coil D, being in the area of the magnetic field
generated by coil C, receives power. Similarly, coil E,
being in the area of the magnetic field generated by coil
D, receives power. Not having any resistive load, the coil
in turn generates its own oscillating magnetic field. The
advantage of using these intermediate coils is that these
coils are completely separated from the source internal
resistance. This increases the Q-factor, allowing greater
power to be radiated.
The block diagram of the whole system is shown in figure
8. For the dc source, the simple full wave bridge model is
used just for the simplicity of the project. At the same
time the capacitor is used for smoothing the output curve.
The PSPICE circuit diagram is given below.
The main advantages of a full-wave bridge rectifier is that
it has a smaller AC ripple value for a given load and a
smaller reservoir or smoothing capacitor than an
equivalent half-wave rectifier. The full-wave bridge
rectifier is designed on the Cadence, PSPICE Simulator as
shown in Figure 9 and the result is shown in Figure 10.
Figure 9: Rectifier
Figure 10: Input and Output curves of Rectifier
The following oscillator circuit is used. This oscillator
uses PSPICE VPULSE that generates square wave in
combination with H bridge amplifier.
When MOSFET M1 and M4 are turned on we have a
positive voltage, when all 4 MOSFETs are off we have 0
voltage, and when MOSFETs M2 and M3 are turned on
we get what appears to be a negative voltage because of
the direction the current flows. For this reason, an h-
bridge amplifier creates a more efficient amplifier
because we get both positive and negative voltage from a
single power supply. The designed h-bridge amplifier is
shown in Figure 11.
Figure 11: H-Bridge Amplifier

The transient analysis of the designed h-bridge amplifier
through PSPICE simulation is done. The oscillator
generates 13.56MHz frequency and can be verified with
simulation result given below in Figure 12.
Figure 12: Output of H Bridge Amplifier
For the rectifying purpose at the receiver, the simple full
wave bridge model is used.
B. Parameter Identification of Proposed System
We have from (16),
Where,
L = inductance in micro-Henries
N = number of turns of wire
R = radius of coil in cm
H = height of coil in cm
For Power Coil,
N = 2, R = 5 cm, H = 3.3 cm, Then, L ≈ 0.5 uH
Also we have from (1),
C = 275.518 Pf
The design parameters for all the antennas are listed in the
table below:
Table 1: Parameters of coil antennas
Coil
(antenna)
N
(turns)
R
(cm)
H
(cm)
L
(uH)
F
(MHz)
C
(Pf)
Power 2 5 3.3 0.5 13.56 275.518
Transmitter 3 6 4.4 1.3 13.56 105.968
Receiver 1.67 6 4.4 0.4 13.56 344.398
Load 1 3.7 2 0.1 13.56 1.377nf
From (14) and (15), with the value given in Table I,
quality factors, coupling coefficient and the maximum
value of magnitude of S21 parameter are calculated as
follows
From (1),
From (3), assuming RS=RL=50 Ohm and R1=R2=R3=R4
=0.015 Ohm,
It is assumed that the distance between power coil and
transmitter coil antenna is fixed, so the coupling
coefficient (k12) is fixed and assumed k12= 0.1. Also it is
assumed that the distance between load coil and receiver
antenna is fixed, so the coupling coefficient (k34) is also
fixed and assumed k34= 0.01.The varying distance is
between transmitter coil antenna and receiver coil
antenna, so the coupling coefficient (k23) is a varying
parameter. When the distance between Tx and Rx
increases, the coupling between them decreases.
From (14), the coupling coefficient is calculated as,
From (15), the maximum value of magnitude of S21
parameter is calculated as follows
Power Transfer Efficiency of the WPT system is
calculated as,
4. DESIGN VERIFICATION THROUGH
SIMULATION
The equivalent circuit model of whole WPT system is
simulated by using an advanced design system (ADS), a
popular electric automation tool in RF engineering of
Agilent Technologies with the circuit setup illustrated in
Figure 13.

Figure 13: Equivalent circuit of WPT system on ADS
The parameters’ values are taken from the Table I. The
radius of power coil is 5 cm, the radius of load coil is 3.7
cm, radius of transmitter and receiver coil is 6cm. The
power coil has two turns, load coil has one turn,
transmitter coil has three turns and receiver coil has 1.67
turns.
The parameter S11 is the power reflection, which is the
ratio of the receiving power at the transmitter divided by
the transmitting power at the same transmitter and the S21
is the power transfer, which is the ratio of the receiving
power at the receiver divided by the transmitting power at
the transmitter. The result of the magnitude of S21 and
S11 is obtained as shown in Figure 14.
Figure 14: Simulation result showing │S11│ and │S21│
It can be seen from the above plot, the parameter │S21│
has maximum value 0.884 which is very much close to
theoretically calculated value 0.882 at operating
frequency of 13.56 MHz at a distance that corresponds to
the coupling coefficient k23=0.00429.
The smith chart plot of Input Reflection Coefficient (S11)
and Output Reflection Coefficient (S22) is shown in
Figure 15.
Figure 15: Input and Output Reflection Coefficient
It can be seen from the above plot that the S11 and S22 lie
on the real axis at operating frequency 13.56 MHz. The
value of input port source impedance is Zo*(0.977 – j
4.939E-4) ohms and the value of output port load
impedance is Zo*(0.664 – j 3.193E-4) where Z0 =ZL=50
Ohm.
The equivalent circuit model to calculate the maximum
power transfer efficiency ( ) is shown
in Figure 16.
Figure 16: Simulation setup for Power transfer efficiency
The result of power transfer efficiency of the designed
WPT system is shown in Figure 17.
Figure 17: Power transfer efficiency of WPT system
The maximum power transfer efficiency of the WPT
system as seen from the above result is equal to 78.176%
which is very close to the theoretically calculated
maximum power transfer efficiency 77.79%.The above
results can be tabulated as shown in Table 2.
Table II: Theoretical and simulated efficiency of WPT system
Parameter Theoretical Simulation
Maximum Power Transfer 0.882 0.884
Power transfer efficiency 77.79% 78.18%
The value of magnitude of S21 of designed WPT System
for three different coupling coefficients which is a
function of distance between transmitter and receiver is

shown in Figure 18. The coupling coefficient decreases as
the distance increases or vice versa.
Figure 18: Simulation result showing │S21│ at different k23
5. COMPARISON WITH OTHER WPT SYSTEMS
The simulations in this section are based on the similar
conditions as in Section IV. The parameters’ values used
here are taken from Table I.
A. Traditional Two Coil System
The circuit setup of traditional two coil (Power coil as
transmitter antenna and load coil as receiver antenna)
WPT system on ADS at a distance equivalent to coupling
coefficient k=0.5 is shown in Figure 19.
Figure 19: Simulation setup of two coil WPT System
The result of the magnitude of S21 and S11 can be
obtained as shown in Figure 20.
The value of magnitude of S11 and S21 of traditional 2
coil WPT System for coupling coefficient, k=0.5 which is
a function of distance between transmitter and receiver is
shown in Figure 20. The coupling coefficient decreases as
the distance increases or vice versa.
B. Three Coil System
The circuit setup of three coil (Power coil as transmitter
antenna and load coil as receiver antenna and an
intermediate coil as relay antenna at transmitter side)
WPT system on ADS at a distance equivalent to coupling
coefficient k=0.5 is shown in Figure 21.
Figure 21: Simulation setup of three coil WPT System
The result of the magnitude of S21 and S11 can be
obtained as shown in Figure 22.
C. Designed Vs Two Coil Vs Three Coil WPT
System
The Simulation results of│S11│ and │S21│ of designed
WPT System, Traditional two coil system and three coil
systems at operating frequency of 13.56 MHz are shown
in Figure 23 in a single plot.
Figure 23: Simulation result showing │S11│ and │S21│ of
designed WPT System, Two coil system and three coil system
The above results can be tabulated as shown in Table 3.

Table 3: Efficiency of two coil system, three coil system and
designed WPT system
Systems k │S11│ │S21│ Efficiency
Two coil system 0.5 0.929 0.367 13.46%
Three coil system 0.5 0.667 0.743 55.20%
Designed system 0.00429 0.012 0.884 78.18%
It is very clear from the above results that the advantage
of the four coil system over the two coil and three coil
system is a high efficiency at a greater distance
(k=0.00429).
6. CONCLUSION AND FUTURE ENHANCEMENT
The goal of this paper was to design a wireless power
transfer system via magnetic resonant coupling at
13.56MHz. After analyzing the whole system step by step
for optimization, a WPT system was designed. The
designed WPT system has power transfer efficiency
78.18% at a coupling coefficient 0.00429. Simulation
results showed that significant improvements in terms of
power-transfer efficiency have been achieved. Simulated
results are in good agreement with the theoretical models.
It is described that magnetic resonant coupling can be
used to deliver power wirelessly from a source coil to a
load coil with two intermediate coils placed between the
power (source) and load coil and with capacitors at the
coil terminals providing a simple means to match resonant
frequencies for the coils. This mechanism is a potentially
robust means for delivering wireless power to a receiver
from a power (source) coil at a fixed distance.
From the Figure 18, it is clear that the magnitude of S21
is highest at operating frequency 13.56 MHz at a distance
corresponding to coupling coefficient 0.00429. As the
distance between transmitter and receiver increases or
decreases, the value of S21 decreases. In fact, the transfer
efficiency significantly decreases with distance variations
between the transmitter and the receiver. So, the designed
WPT System is very efficient at a fixed distance
corresponding to k=0.00429 but deteriorates its efficiency
at other distance that does not correspond to designed
coupling coefficient.
The distance at which the system has coupling coefficient
0.00429 and maximum efficiency of 78.18% can be found
by designing the prototype of the system and using Vector
Network Analyzer (VNA).
Figure 18 clarifies that when the coupling coefficient k23
decreases, there is the frequency splitting issue which
substantially reduces the system efficiency. Moreover, as
k23 increases, the resonant frequency also changes from
the operating frequency of 13.56 MHz. Therefore, an
optimal control mechanism is needed to maintain the
optimal resonant condition and to realize the maximum
wireless power transfer efficiency as well.
REFERENCES
[1] Sabuj Das Gupta, Md. Shahinur Islam, Kawser Md. Nuronnabi,
Mohammad Sakib Hossain, Md. Zahid Hasan - Design &
Implementation of Cost Effective Wireless Power Transmission
Model: GOOD BYE Wires – published at: “International Journal
of Scientific and Research Publications(IJSRP), Volume 2, Issue
12, December 2012 Edition” .
[2] William C. Brown, "The history of wireless power transmission,"
Solar Energy, vol.56, no.1, pp. 3-21, Jan. 1996
[3] Sanghoon Cheon, Yong-Hae Kim, Seung-Youl Kang, Myung Lae
Lee, and Taehyoung Zyung “Wireless Energy Transfer System
with Multiple Coils via Coupled Magnetic Resonances” ETRI
Journal, Volume 34, Number 4, August 2012
[4] Mandip Jung Sibakoti, Professor Derin Sherman and Joey
Hambleton “Wireless Power Transmission Using Magnetic
Resonance” Cornell College PHY312, December 2011.
[5] Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, M.
Soijacic, “Wireless Power Transfer via Strongly Coupled Magnetic
Resonances”, Massachusetts Institute of Technology, 2007
Science, Vol. 317. no. 5834, pp. 83— 86, 2007.
[6] Kawamura, Atsuo, and Tae-Woong Kim. "Proposed Equivalent
Circuit and Parameter Identification Method for Electro-Magnetic
Resonance Based Wireless Power Transfer.” April 2013.
[7] Hoang, Huy, and Franklin Bien. "Maximizing Efficiency of
Electromagnetic Resonance Wireless Power Transmission Systems
with Adaptive Circuits."Wireless Power Transfer–Principles and
Engineering Explorations: K. Y. Kim, ed., InTech, 2012. Print.
[8] Jordan, Edward C., and K. G. Balmain. Electromagnetic Waves
and Radiating Systems. Second ed. New Dehli: Prentice-Hall of
India, 2006. Print.
[9] Nilsson, James William., and Susan A. Riedel. Electric Circuits.
Boston: Prentice Hall, 2011. Print.

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Design of wireless power transfer system via magnetic resonant coupling at 13.56 m hz