Revista de Ciencias Tecnológicas (RECIT). Volumen 3 (1): 10-22
Revista de Ciencias Tecnológicas (RECIT). Universidad Autónoma de Baja California ISSN 2594-192
Volumen 4 (4): 314-328. Octubre-Diciembre, 2021 https://doi.org/10.37636/recit.v44314328.
ISSN: 2594-1925
314
Solid state resonant circuits and wireless electrical power
propagation for mobile devices applications
Circuitos resonantes de estado sólido y propagación de energía
eléctrica inalámbrica para aplicaciones de dispositivos móviles
Sergio Orendain-Castro 1, Eduardo Murillo-Bracamontes 2, Oscar Edel Contreras-López2,
Alberto Hernández-Maldonado 1
1Facultad de Ciencias de la Ingeniería y Tecnología, Universidad Autónoma de Baja California, Unidad Valle de
las Palmas, Tijuana, Baja California, México
2Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México. Ensenada, Baja
California, México
Corresponding author: Alberto Hernández Maldonado, Facultad de Ciencias de la Ingeniería y Tecnología,
Universidad Autónoma de Baja California. Unidad Valle de las Palmas, Tijuana, Baja California, México. E-mail:
hernandez.alberto@uabc.edu.mx, ORCID: 0000-0002-9768-4060.
Received: August 20, 2021 Accepted: October 19, 2021 Published: November 1, 2021
Abstract. -. In this work, theoretical and experimental results of solid-state resonant circuits for the
transmission and reception of wireless electrical energy, for applications in mobile devices are presented.
Analytical expressions are found to calculate the voltage range as a function of the distance between the
emitter and the load, as well as the current at the front end of an electromagnetic wave receiver. These
expressions show the parameters to be varied to achieve a greater range in the transmission of wireless
electrical energy. The transmitted voltage and current are measured by an electromagnetic wave receiver
and compared with theoretical values, finding an excellent correspondence between the two.
Keywords: Wireless energy; Resonant circuits; Power propagation.
Resumen. - En el presente trabajo se presentan resultados teóricos y experimentales de circuitos
resonantes de estado sólido para la transmisión y recepción de energía eléctrica inalámbrica, para
aplicaciones en dispositivos móviles. Se encuentran expresiones analíticas para calcular el alcance de
voltaje en función de la distancia entre el emisor y la carga, así como la corriente en el extremo frontal de
un receptor de ondas electromagnéticas. Estas expresiones muestran los parámetros a variar para lograr
un mayor alcance en la transmisión de energía eléctrica inalámbrica. La tensión y la corriente transmitidas
se miden mediante un receptor de ondas electromagnéticas y se comparan con valores teóricos,
encontrando una excelente correspondencia entre ambos.
Palabras clave: Energía inalámbrica; Circuitos resonantes; Propagación de energía.
315 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
1. Introducción
As is well known, the transmission of electrical
energy is carried out through the use of electrical
wiring, however, recent technological advances
in the area of communications have motivated
people to look for different ways of transmitting
energy [1]. An example of this, are the cellular
charging systems by magnetic induction [2, 3].
The transfer of electrical energy by magnetic
induction through radio waves, was a problem
initially raised by Nikola Tesla [4]. He worked
on this problem, with the purpose of achieving a
distribution of electricity wirelessly, over long
distances.
We can classify wireless energy transfer systems
into two types, inductive power transfer and
magnetic resonance coupling and Near Field [5].
The inductive power transfer system uses a pair
of coupled coils, at the transmitting side, an
alternating current flow through the coil,
generating a magnetic field, a second coil is used
to receive the magnetic field and generate a
current for energy storage. A magnetic resonant
coupling system uses a pair of coupled coils with
additional capacitance, which makes that the
transmitter and the receiver have the same
resonant frequency, which increases the
efficiency and the transmission distance [6, 7].
Near Field Communication (NFC) is a
technology that uses an inductive coupling
technique oriented for mobile smart phone and
operates at 13.56 MHz; it works via magnetic
field induction and can transmit information in
short distances up to a maximum rate of 424 Kbit
per second. NFC systems are oriented to data
exchange applications and usually used in mobile
phones [8].
Some research from the Massachusetts Institute
of Technology have worked in wireless power
transfer because power cables reduce and limit
the mobility of electronic devices. These
investigations are based on magnetic induction
techniques using new ring-shaped solenoid
geometries. In these studies, it is possible to
transfer electricity wirelessly, turning on a 60
Watts bulb, located 2 meters away, with an
efficiency of 40% [9].
Some works have focused on the wireless
transmission of electrical energy, using
magnetically coupled aluminum and copper
rings, achieving an efficiency of between 7% and
10% [10]. In these studies, the energy is used in
the form of electromagnetic waves, using an
emitter and receiver ring with resistive loads.
A related work demonstrated that the energy
range of a wireless transmitter can be increased,
by using a system of rings located at a distance of
0.4 meters between them, achieving a power of
18 watts when a lamp is connected at 2.1 m of the
transmitter ring system [11]. The system has an
efficiency of 14.43% at 10 mm of distance.
A method of wireless power transfer technique is
called Strongly Coupled Magnetic Resonance
(SCMR) which take the advantage of
electromagnetic resonance to efficiently transfer
power over mid-range distances. A novel
approach is the use of a wideband SCMR to
mitigate the drop of efficiency caused by the shift
of the resonance frequency [12]. However, most
of the research in SCMR is at the simulation
stage with a limited number of experimental
results [13]. Although with these devices great
range in the transmission of electric energy is
achieved, they are macroscopic devices and are
not viable, for example, to be used to charge
mobile devices.
316 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
In this work, a magnetic resonant coupling
system using high frequency energy is presented.
The system was designed to increase the signal
range by reducing the receiver energy losses and
use commercial electronic components to reduce
the size of the circuit and allow its
implementation in a mobile device. Resonant
circuits applied to the transmission and reception
of wireless electrical energy are analyzed
theoretically and experimentally. The
implemented circuit has the advantage of use
commercial components that can be
implemented in a printed circuit board in SMT
package. Figure 1 shows the scheme of wireless
power transfer system with magnetic coupling.
Figure 1. Scheme of wireless power transfer with magnetic coupling.
This article is structured as follows. In section 2,
the resonant solid-state device is presented. In
section 3, the design of an electromagnetic wave
receiver is shown. In section 4, a relationship of
the voltage received by the receiver and the
transmitting range of the emitter is presented. In
section 5, an analysis of the current is presented
and, finally, the conclusions are shown in section
6.
2. Resonant solid state device
2.1. Primary winding analysis
In this section, a resonant solid-state device is
analyzed. Some results and simulations
corresponding to its operation are presented.
Figure 2 shows a schematic diagram of the
device. Its operation is based on the transistor, in
switch configuration, working as a high
frequency function generator, which transforms
the primary winding (PW) and secondary
winding (SW) in an RLC circuit, with a
resonance frequency tuned to the corresponding
transistor resonance.
The circuit of Figure 2 is a resonant circuit. When
the circuit is powered up, current flow to the base
terminal of the transistor through R1. In this
condition the transistor is activated and the
current start to flow to the PW, producing a
magnetic flux which causes a high voltage in the
SW since it has more turns than the PW. As the
current in the PW increases, the transistor gets
into saturated region and due to both the PW and
R1 are connected to the +12V, all the current
flow through PW causing a current drop through
R1 and this condition turn off the transistor. The
current start to flow again to the base terminal of
the transistor and this cycle is repeated.
The SW, as well as the PW, when a high-
frequency signal is applied, shows a parasitic
capacitance. Due to the geometry of the winding,
the PW and SW have a parasitic capacitance C1
and C2 respectively.
317 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
Figure 2. Resonant solid-state device.
The coil on the left side of the device corresponds
to the PW, with a winding length l = 0.556 m.
The height h of the primary winding is 6.6
m and the number of turns is 5.
The wire diameter of the winding is 6.438
m. It should be noted that this diameter does not
include insulation. With insulation, its diameter
is 1.32 m.
The radius r1 of the PW core is 1.27 m.
On the other hand, the Wheeler formula,
provides a way to calculate the inductance in
windings with air core and circular geometry
[14]. This formula is given by,
Figure 3. Physical model of a coil
318 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
, (1)
where L represents the inductance of the coil, r
corresponds to the radius of the coil, l represents
the length and N is the number of turns of the
winding. These parameters are represented in
figure 3.
Using the Wheeler formula, Eq. (1), the
inductance corresponding to the PW is 0.88
.
The PW shows a resonance by itself, and
implicitly presents a capacitance when a high
frequency is applied. This parasitic capacitance
C1 corresponds to a value of 2.71 nF.
On the other hand, the impedance Z for our
RLC circuit, is defined by,
(2)
With = and .
The value minimum of Z, is obtained when =
.
By matching the reactances as a function of the
frequencies, the following expression results,
, (3)
where corresponds to the resonant frequency
in rad/s, and , resulting the following
relation
(4)
From the previous results, and through Eq. (4),
the resonance frequency of PW is. This frequency was confirmed by measuring it
with an oscilloscope as shown in figure 4.
319 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
Figure 4. Measurement of the resonance frequency using an oscilloscope.
2.2 Secondary winding analysis
The winding shown on the right side of the
device of Figure 2, corresponds to the SW. This
winding has a radius of m, a cross
section of and a winding length
of 18.04 m. Its resistance is 6.0506 Ω, and the
height is, 5.8 m.
On the other hand, the number of turns of the SW
is 212. With the previous data and using the Eq.
(1), we calculate the inductance of SW,
yielding a value of .
Through Eq. (4) and using the resonance
frequency , as well as the inductance the
calculated parasitic capacitance is .
2.3 Potential energy and maximum voltage
of secondary winding
The SW has a capacitance at high frequency
(parasitic capacitance) and also a capacitance
between each turn (intrinsic capacitance). Using
the model of a cylindrical solenoid, and the
equation of Medhurst [12], which gives a
capacitance per unit of length. We can calculate
the capacitance for the SW.
. (5)
Substituting the corresponding values in the
previous equation, gives a value of
The total capacitance of the SW can be obtained
as the difference of the capacitance and ,
which is called or real capacitance. is
present even when no current is flowing in SW.
The capacitance per unit length without load, is
as follow,
320 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
. (6)
When a load is placed on the SW, the resulting
capacitance per unit of length , can be
calculate with the following equation.
. (7)
The winding diameters of the core of PW and SW
are and = 0.01 respectively.
Using the Eq (7), is 0.31 pF. When the load is
placed on the SW, a discharge occurs on
capacitor CD, and the capacitance decreases,
while the voltage increases.
In order to know the maximum voltage on the
extreme of the SW, it is necessary to know the
stored energy in the winding, so the input voltage
in the PW is also required.
The equation that defines the energy with respect
to voltage and capacitance, for the PW, is written
as follows,
. (8)
Substituting the corresponding values in Eq. (8),
the resulting energy in the PW corresponds to
. Assuming there is no loss of
energy transfer between the PW and the SW, we
can say that , where is the energy
of the SW.
As the load resistance of cooper makes contact
with the tip of the SW, the open circuit voltage
increases. To calculate this voltage, we can
use the Eq (8) for the SW, resulting,
. (9)
The real voltage of the SW without load, can
be calculated, using the real capacitance,
which is equal to 290.7 V.
3. Electromagnetic wave receiver
A good receiver design is crucial to improve the
system energy transfer. Figure 4 shows an
electromagnetic wave receiver (EMWR),
designed to measure the resonance frequency and
the voltage , at a distance r from the extreme of
the SW, as well as the power in that distance.
Also, the EMWR receive the electromagnetic
waves emitted by the SW, which go through a
process of amplification and decoding, to convert
the resulting electric field , into a potential .
The EMWR includes a PSoC microcontroller,
which is a device with a CPU core and mixed-
signal arrays of configurable integrated analog
and digital peripherals.
This PSoC microcontroller was configured to
acquire the transmitted signal. An analog to
digital converter was used to measure the
receiver voltage. Also, a comparator was
configured to measure the frequency of the
signal. An ultrasonic sensor was used to measure
automatically the distance between the
transmitter and receiver. A display was
configured to show the received voltage in SW,
the range r and the frequency. The PSoC
microcontroller was also configured to send the
received information to a PC with Matlab
software to save the data in a log file and plot the
corresponding curves. Figure 6 shows the
diagram of the PSoC microcontroller and the
receiver circuit.
321 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
Figure 5. Electromagnetic wave receiver (EMWR).
Figure 6. Circuit diagram of the receiver.
322 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
4. Secondary winding
In order to perform a quantitative study to know
the variation of the voltage corresponding to the
SW, as a function of the distance regard to the
detector.
Using the Gauss theorem, expressed as,
. (10)
The cylindrical Gaussian surface is represented
in figure 7, where corresponds to the radius of
the SW, and corresponds to the radius of the
Gaussian surface. We can calculate the electric
field , at a distance from SW.
Let ds be a differential element of surface, where
the electric field E and this ds are parallel in the
lateral surface, whereas in the upper and lower
surfaces, they are perpendicular.
Figure 7. Gaussian surface around the SW.
The angles and in the cylinder caps that form
E and ds are perpendicular, while ,
corresponding to the angle between E and ds of
the lateral surface of the cylinder, is zero degrees.
According to Gauss's theorem, for the lower and
upper surface, we find that,
. (11)
Therefore, it is shown that the electric field on the
upper and lower surface is zero.
On the other hand, for the lateral Gaussian
surface
. (12)
Since the electric field is uniform throughout the
lateral periphery of the Gaussian surface,
323 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
, (13)
Where, L corresponds to the height of
the cylindrical surface, s, represents the lateral
surface of the cylinder. Thus
. (14)
From eq. (10) results,
, (15)
where Q is the total charge of the cylinder.
The SW is formed by a winding that contains
multiple turns. These capacitors are in parallel,
forming a cylindrical capacitor with a total
capacitance C, which stores a charge that will be
proportional to the voltage in the secondary
winding . Using the model to calculate the
electric field in a cylindrical capacitor [15].
, (16)
where and , are the permittivity of the
insulator and the height the cylinder respectively.
Using the capacitance in the equation that
defines the charge (and the result in
eq. (15), the equation that defines the electric
field as a function of distance is,
, (17)
where is the electric permittivity in vacuum,
On the other hand, to obtain an expression for V2,
which is the voltage measured by the
electromagnetic wave receiver (EMWR), as a
function of the distance r, we use the knowledge
the electric field E, is expressed as the voltage V
divided by the distance r. In our case, r expresses
the electric field reaching E in terms of voltage
V2, processed by the receiver placed at the
distance r of the SW. From the above, and the Eq.
(17), the voltage can be expressed as,
. (18)
From Eq. (18) we can obtain an expression to
calculate the reaching as a function of the
transmitting voltage and the receiving
voltage .
, (19)
where =/.
The figure 8, is a block diagram that represents
the SW voltage and EMWR.
Figure 8. Block diagram of SW and EMWR
To increase the reaching range , it is necessary
to increase the radius R of the ES, as well the as
the electrical permittivity in the insulator and the
number of windings. The Eq. (19) provides us
with a nice relation of the relevant parameters of
the system to obtain a greater range r of voltage
324 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
V2. And corresponds to a one of the principal
results of this paper.
From Eq. (19) we note that if the voltage tends
to 0, then tends to infinity as is shown in Fig. 8.
On the other hand, if tends to infinity, tends
to , which is an expected result, since the
maximum voltage occurs at the minimum
distance, when .
It is important to highlight that all the parameters
of Eq. (18) can be measured, and gives the
effective voltage drop V2, as a function of
distance r.
Figure 9. Voltage V2 as function of the range r. The red dotted line corresponds to experimental data. The blue continuous line is obtained
theoretically from Eq. (14).
In figure 9, the experimental voltage was obtained in a real-time interface that communicates a PSoC
microcontroller and a Matlab script. We can see both experimental and theorical (Eq. (18)) curves show
the same behavior.
Figure 10. From left to right, is shown multimeter, SW and EMWR
325 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
In figure 10, is observed that the maximum
voltage measured in the EMWR is 1.217 V.
This is close to theoretical value given by Eq.
(18).
5. Electrical current analysis
Knowing that the resonance frequency F0 of the
ES, corresponds to 3.25 MHz, the coil and
capacitor of the EMWR are 411.3 H and 5.8 pF
respectively, and that these form a resonant LC
circuit, we can obtain the current in the LC
circuit.
In resonance, it can be calculated the parameters
of a free LC oscillator, without using a power
supply, using the simple equation,
. (20)
It is found that the charge on the capacitor is,
. (21)
While the current in the LC oscillator
corresponds to,
. (22)
In this way, the amplitude of the maximum
current of the LC circuit it is obtained,
. (23)
We know that the capacitance is given by the
reason of the charge and the voltage, the current
of the LC circuit as function of the ES voltage is
obtained, replacing L and C by and
, leads to,
. (24)
Substituting the values of CEMWR, V2 and ,
in the previous equation, we obtain the value of
A, which is the maximum rms
current that goes through LEMWR or CEMWR. To
enhance the current in the EMWR, is necessary
to increase V2 and , nevertheless, by
varying , the ES will no longer be in
resonance with the EMWR, unless in both
systems increase the capacitance proportionally.
In figure 11, the measured current is plotted
as function of the range r. We can see a
maximum initial value of A, which is near
than the calculated value.
Figure 11. Total current passing through the coil and the capacitor of the electromagnetic wave receiver
326 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
Unlike the measurement presented in figure 10,
the current measurement is carried out using a
high resolution miltimeter, this because the
current received by the EMWR is in the order of
micro-Ampere. If you want to measurement the
current with a low-resolution multimeter you will
not be able measure it. The measuring instrument
used was the Fluke 87. The measurement is
shown in figure 11.
Figure 11. Measurement of current in the EMWR.
The value of 150.06 A is close to the theoretical
result obtained in the Eq. (24).
6. Conclusions
In this work, a theoretical framework was
implemented to analyze a solid-state resonant
circuit, based on a designed device for
transmitting and receiving wireless electrical
energy. Both, theoretical and experimental
results were obtained for the energy transmission
and reception of energy. Also, analytical
expression was obtained to calculate the effective
voltage as a function of the distance from the
secondary coil to the receiver. This expression
allows us to explore the parameter necessary to
achieve a greater range V2.
Using the PSoC microcontroller coupled to the
electromagnetic waves receiver to acquire the
received voltage and distance. A visual interface
was designed in real time to plot the behavior of
the effective voltage that the SW emits, with
respect to the distance of the receiver, observing
a concordance between the theoretical and
experimental value. It was demonstrated, that the
voltage at the receiver, decreases exponentially
as function of the range.
The current in the front end of the
electromagnetic wave receiver was calculated, it
also shows an exponential decay as a function of
the range.
We obtained that for increase the range, it is
necessary to increase the radius R, as well as the
electrical permittivity in the insulator and the
number of windings, by varying both parameters,
it is observed experimentally that the range
increases exponentially.
It was shown that the resonance frequency of the
secondary winding is constant, regardless of a
load.
327 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
The advantage of our results compared to others
reported in the, is that although exist devices
great range in the transmission of electric energy
is achieved, they are macroscopic devices and are
not viable, for example, to be used to charge
mobile devices.
While the system presented here was designed to
increase the signal range by reducing the receiver
energy losses and use commercial electronic
components to reduce the size of the circuit and
allow its implementation in a mobile device, as is
the case of the device shown here, which is small
in size and can be used in recharging this
purpose.
7. Acknowledgments
The authors acknowledge Salvador Fierro for his
support in the design of Fig. 7. Also, Alberto
Hernández thanks the Center for Nanosciences
and Nanotechnology for their support during his
sabbatical stay in this institution.
8. Authorship acknowledgment
Sergo Orendain castro: Conceptualización;
Recursos; Ideas; Metodología; Análisis formal;
Investigación; Recursos; Análisis de datos;
Borrador original. Eduardo Murillo
Bracamontes: Conceptualización; Ideas;
Investigación; Análisis de datos; Escritura.
Oscar Edel Contreras López: Adquisición de
fondos y Administración de proyecto. Alberto
Hernández Maldonado: Conceptualización;
Ideas; Metodología; Análisis formal;
Investigación; Análisis de datos; Escritura;
Borrador original; Revisión y edición;
Administración de proyecto.
References
[1] X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z.
Han, "Wireless Charging Technologies:
Fundamentals, Standards, and Network
Applications," IEEE Commun. Surv. Tutorials,
vol. 18, no. 2, pp. 1413-1452, 2016.
https://doi.org/10.1109/COMST.2015.2499783.
[2] K. H. Yi, "Output voltage analysis of
inductive wireless power transfer with series lc
and llc resonance operations depending on
coupling condition," Electron., vol. 9, no. 4,
2020.
https://doi.org/10.3390/electronics9040592.
[3] P.S. Riehl et al., "Wireless power systems for
mobile devices supporting inductive and
resonant operating modes," IEEE Trans. Microw.
Theory Tech., vol. 63, no. 3, pp. 780-790, 2015.
https://doi.org/10.1109/TMTT.2015.2398413.
[4] N. Tesla, "Experiments with altrnate current
of very high frequency and their application to
methods of artificial illumination," Columbia
Coll., pp. 267-319, 1891.
https://doi.org/10.1109/T-AIEE.1891.5570149.
[5] S. K. Oruganti and F. Bien, "Investigation of
Near-Field Wireless Energy Transfer for
Through Metal-Wall Applications," 2014 IEEE
Wirel. Power Transf. Conf., pp. 247-250, 2014.
https://doi.org/10.1109/WPT.2014.6839573
[6] S. Kim, Y. Lim, and S. Lee, "Magnetic
Resonant Coupling Based Wireless Power
Transfer System with In-Band Communication,"
no. May 2015, 2013.
https://doi.org/10.5573/JSTS.2013.13.6.562
[7] R. Kerid and H. Bourouina, "Analysis of
Wireless Power Transfer System with New
Resonant Circuit for High Efficiency Using
Perforated Capacitors," Arab. J. Sci. Eng., vol.
328 ISSN: 2594-1925
Revista de Ciencias Tecnológicas (RECIT). Volumen 4 (4): 314-328
44, no. 3, pp. 2445-2451, 2019.
https://doi.org/10.1007/s13369-018-3579-2.
[8] P. Sittithai, K. Phaebua, T. Lertwiriyaprapa,
and P. Akkaraekthalin, "Magnetic field shaping
technique for HF-RFID and NFC systems,"
Radioengineering, vol. 27, no. 1, pp. 121-128,
2019. https://doi.org/10.13164/re.2019.0121
[9] R. A. Moffatt, "Wireless Transfer of Electric
Power," Massachusetts Institute of Technology,
2009.
[10] T. Supriyanto, A. Wulandari, and T.
Firmansyah, "Design and Comparison Wireless
Power Transfer Base on Copper (Cu) and
Aluminium (Al) Rings Loop Magnetic
Coupling," no. January 2016, pp. 6-10, 2017.
https://doi.org/10.18178/IJIEE.2016.6.2.605
[11] C. K. Lee, W. X. Zhong, and S. Y. R. Hui,
"Effects of Magnetic Coupling of Nonadjacent
Resonators on Wireless Power Domino-
Resonator Systems," vol. 27, no. 4, pp. 1905-
1916, 2012.
https://doi.org/10.1109/TPEL.2011.2169460
[12] W. Zhou, S. Sandeep, P. Wu, P. Yang, W.
Yu, and S. Y. Huang, "A wideband strongly
coupled magnetic resonance wireless power
transfer system and its circuit analysis," IEEE
Microw. Wirel. Components Lett., vol. 28, no.
12, pp. 1152-1154, 2018.
https://doi.org/10.1109/LMWC.2018.2876767
[13] C. M. W. Basnayaka, D. N. K. Jayakody, A.
Sharma, H.-C. Wang, and P.
Muthuchidambaranathan, "Performance Study of
Strongly Coupled Magnetic Resonance," 2019,
[Online]. Available:
http://arxiv.org/abs/1908.02541.
[14] D. Knight, The self-resonance and self-
capacitance of solenoid coils: applicable theory,
models and calculation methods, no. May. 2016.
[15] P. Azimi and H. Golnabi, "Precise
Formulation of Electrical capacitance for a
Cylindrical Capacitive Sensor," J. Appl. Sci., vol.
9, no. 8, pp. 1556-1561, 2009.
https://doi.org/10.3923/jas.2009.1556.1561
[16] H. Wheeler, "Formulas the Skin Effect,"
Proc. IRE, pp. 412-424, 1942.
https://doi.org/10.1109/JRPROC.1942.232015
Este texto está protegido por una licencia Creative Commons 4.0
Usted es libre para Compartir —copiar y redistribuir el material en cualquier medio o formato — y
Adaptar el documento —remezclar, transformar y crear a partir del material— para cualquier propósito,
incluso para fines comerciales, siempre que cumpla la condición de:
Atribución: Usted debe dar crédito a la obra original de manera adecuada, proporcionar un enlace a la
licencia, e indicar si se han realizado cambios. Puede hacerlo en cualquier forma razonable, pero no de
forma tal que sugiera que tiene el apoyo del licenciante o lo recibe por el uso que hace de la obra.
Resumen de licencia - Texto completo de la licencia
