Electromagnetic analysis of different geometry of transmitting coils for wireless power transmission applications

Abstract

Inductive power transfer is recently a common method for transferring power. This technology is developing as the modern technologies need to get more efficient and updated. The power transfer efficiency has potential to get better. There are different ways to achieve a desirable efficiency. In this paper, a suitable geometry of a coil for transferring power as a transmitting coil is examined. In this work, three types of geometries are designed. Frequency analysis at frequency range (10 kHz-50 kHz) is done to investigate behaviour of various geometries. Magnetic field, electric field, magnetic flux density, and current density for various geometries are presented and compared. Magnetic flux density is measured via an experimental setup and is compared to simulated one to verify the validity of simulation results.

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Electromagnetic Analysis of Different Geometry of Transmitting
Coils for Wireless Power Transmission Applications
Mohammad Haerinia1, *, Ali Mosallanejad2, and Ebrahim S. Afjei2
Abstract—Inductive power transfer is recently a common method for transferring power. As the
modern technologies need to get more efficient and updated, this technology is developing. The power
transfer efficiency has potential to get better. There are different ways to achieve a desirable efficiency.
In this paper, the suitable geometry of a coil for transferring power as a transmitting coil is examined.
In this work, three type of geometries are designed. Frequency analysis at frequency range (10 kHz–
50 kHz) is done to investigate behaviour of various geometries. Magnetic field, electric field, magnetic
flux density, and current density for various geometries are presented and compared. Magnetic flux
density is measured via an experimental setup and is compared to simulated one to verify the validity
of simulation results.
1. INTRODUCTION
Transferring power wirelessly is well known due to its reliability and related applications. The technology
of wireless power transfer has been used for various applications in which power is transferred without
any physical contact. This technology is popular among consumers [1]. There are various forms of
wireless power transmission, including; inductive, capacitive, laser, microwave, etc. Among the listed
methods, inductive power transfer is very popular and has been used for various applications [2]. This
method is well-known and the method has been well applied for decades [3]. The mentioned technology
has been applied to charge electric vehicles, electric toothbrushes and mobile devices. It has been applied
to implanted devices applications [4, 5]. The advantages of inductive-based wireless power transfer are
its safety and high efficiency at short distances. One disadvantage of this technology is the fact that
the transmitter and receiver need to be aligned [6]. An inductive system can include parts like coil,
core, and coupling capacitances [7]. The operation of such a system can be compared to an air core
transformer [8]. The transmitting coil, which is excited by means of an alternating current, generates an
electromagnetic field which is dependent on dimensions of the coil, drive current and frequency [9]. There
is an inductive coupling between transmitting and receiving coils [10]. Inductive-based wireless power
transmission is dependent on different parameters such as air gap between the transmitter and receiver,
frequency, and current excitation [11]. The power quality is dependent on geometry of coil [12]. Many
of the coils are designed based on the classic theories, and this method does not work for the complex
shape of coils [13]. The objective of this paper is to present an obvious understanding of the various
geometric forms coils take when being used as a transmitter. This objective is achieved by the analysis
and comparison of various coils via electromagnetic results. This paper can provide a useful perspective
for designing innovative coils. The different geometries of coils are accessible and reasonable. Diameter
of a wire is standard as used in [14]. The designing process of coils and its dimensions are presented
in detail. 2D-tools of COMSOL Multiphasic 5.1 software has been used to simulate problems [15].
Magnetic field, electric field, magnetic flux density, and current density are presented and compared.
The behavior of various geometries of coils versus changing frequency is illustrated. The experimental
results are added to verify the validity of simulation results.
Received 5 July 2016
* Corresponding author: Mohammad Haerinia (M.haerinia@mail.sbu.ac.ir).
1Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran. 2Faculty of Electrical Engineering, Shahid
Beheshti University, Tehran, Iran.

2 Haerinia, Mosallanejad, and Afjei
2. FUNDAMENTAL THEORY OF ELECTROMAGNETIC
According to Ampere’s law, the integral of magnetic field intensity is proportional to current in the
closed path.
IH·ds =I(1)
where His magnetic field intensity, in Amperes per Meter (A/m). Iand ds are electric current and the
vector area of an infinitesimal element of surface S, respectively.
In practice, the relationship between magnetic flux density and magnetic field intensity can be
expressed:
B=f(H) (2)
where Bis magnetic flux density in Tesla (T).
The following linear model states relationship between magnetic flux density and magnetic field
intensity with this assumption that the magnetic field in the coil is homogeneous:
H=B
µ(3)
where µis magnetic permeability, in Henries per Meter (H/m).
According to Faraday’s law, the induced voltage is proportional to the changes of external magnetic
field:
e=−Ndϕ
dt (4)
where Nis the number of turns, eand ϕare induced voltage and magnetic flux, in Volt (V) and Weber
(Wb), respectively.
Lenz’s law states that induced current in the coil generates a magnetic field which tends to
counteract the external magnetic field [16]. The similarity of magnetic flux to electric current is useful.
As the electric resistant opposes electric current, the reluctance opposes magnetic flux [16].
The Equations (5) and (6) are presented to evaluate the stored magnetic and electric energy in free
space, respectively:
WE=∫∫∫ 1
2ε0|E|2dv (5)
WH=∫∫∫ 1
2µ0|H|2dv (6)
where WEand WHare the stored electric and magnetic energy in free space. E,H,ε0and µ0are
electric field intensity, magnetic field intensity, vacuum permittivity and magnetic permeability of free
space, respectively [17].
3. MODELLING OF A DIFFERENT GEOMETRY OF COILS FOR FINITE
ELEMENT ANALYSIS
Finite element method (FEM) can be used to solve different physical problems. This method makes
differential equations solvable. This method approaches the problem by reducing errors [18]. FEM is
used in different researches for various purposes such as modeling and parameter identification [19–25].
An acceptable solution from Maxwells equations for most practical cases is neither possible nor accurate.
Thus FEM is often used to calculate physics quantities [26]. 2D-tools of COMSOL Multiphysics 5.1
software has been used to solve problems via finite element method. In this work diameter of a wire
is considered as used in [14]. New geometries of coils are designed. These models are shown in Fig. 1.
Design values of proposed coils are presented in Table 1.

EM analysis of different geometry of transmitting coils for wireless power transmission applications 3
(a) (b)
(c)
Figure 1. Geometry of coils. (a) Helical. (b) Conical. (c) Circular.
Table 1. Design values of proposed coils.
Parameter Value
Diameter (d) 2 (mm)
Space (S) 5 (mm)
Turns 4
Voltage source (p-p) 20 (V)
4. ASSESSMENT OF SIMULATION AND EXPERIMENTAL RESULTS
4.1. Simulation Results
For all type of coils 4 turns are considered. The coils are connected to a signal generator as shown in
Fig. 2.
Figure 2. Inductive coupling system.
To analyse the behavior of the coils, a transmitting coil, connected to a source is assumed. Figs. 3–6
illustrate magnetic field, electric field, magnetic flux density, and current density at frequency 10kHz,
respectively.
In most models, the effect of high frequency is ignored while this effect is an important source of
losses [27].

4 Haerinia, Mosallanejad, and Afjei
(c)(a) (b)
Figure 3. Magnetic field norm at 10 kHz (A/mm) in (a) Helical. (b) Conical. (c) Circular.
(c)(a) (b)
Figure 4. Electric field norm at 10 kHz (V/m) in (a) Helical. (b) Conical. (c) Circular.
(c)(a) (b)
Figure 5. Magnetic flux density norm at 10 kHz (µT) in (a) Helical. (b) Conical. (c) Circular.
(c)(a) (b)
Figure 6. Current density norm at 10 kHz (mA/mm2) in (a) Helical. (b) Conical. (c) Circular.
4.2. Skin Effect at High Frequencies
Behavior of the coil changes at high frequencies. The skin and proximity effects lead to reduction of coil
inductance. The parasitic capacitors are not negligible at high frequencies [28]. The skin effect leads to
an internal magnetic field in a conductive wire. This internal field pushes electric current to external

EM analysis of different geometry of transmitting coils for wireless power transmission applications 5
surface of conductor. There is an expression to calculate skin depth (δ) [29]:
δ=1
√πσµf (7)
In the above equation, (σ) is medium conductivity and (µ) is permeability. The skin effect is
illustrated in Fig. 7.
Figure 7. Skin effect [29].
4.3. Verification of Simulation Results
To verify the validity of simulation results, magnetic flux density is measured practically and compared
to simulated values. Experimental setup is shown in Fig. 8.
Figure 8. Experimental setup.
Figure 9 presents comparison of magnetic flux density norm was calculated experimentally, as well
as through simulation. This figure illustrates magnetic flux density versus changing frequency from
5 kHz to 15 kHz.
The error occurs when comparing the experimental results of magnetic flux density with simulations
ones. It increases as the frequency goes high and that is due to the measuring instrument. Fig. 10

6 Haerinia, Mosallanejad, and Afjei
Figure 9. Comparison of magnetic flux density
was calculated experimentally, as well as through
simulation.
Figure 10. Comparison of measured voltage and
current.
shows comparison of measured current and voltage versus changing frequency from 10 kHz to 50 kHz
for a various geometry of coils.
To calculate the current density practically, it is assumed that the electric current is distributed
within the cross section uniformly. The comparison of simulation via calculated values are presented in
Table 2.
Table 2. Comparison of simulation via calculated values.
Current density (J)
Type Maximum point-Simulation (mA/mm2)
at 10 kHz
Uniform-Measured (mA/mm2)
at 10 kHz
Helical 108 103.95
Conical 107 105.61
Circular 108 105.73
About 3% error occurs at frequency 10 kHz when comparing the experimental results of current
density with simulations ones. The design of inductive power transfer systems is based on an accurate
understanding of spatial distribution of magnetic field that is produced by a certain geometry of coil [26].
Table 3. Comparison of maximum electromagnetic characteristics at 10 kHz.
Type Magnetic Field
(A/mm)
Magnetic Energy Density
(J/m3)
Electric Field
(V/m)
Electric Energy Density
(J/m3)
Helical 3.05 ×10−23.24 ×10−46.18 ×10−31.05 ×10−16
Circular 2.92 ×10−22.92 ×10−45.17 ×10−37.36 ×10−17
Conical 2.88 ×10−22.87 ×10−44.92 ×10−36.67 ×10−17
Magnetic and electric field have been compared to evaluate the stored magnetic and electric energy
produced by the coils. According to (5) and (6) and assuming an equal volume around each coil, the one
with higher magnetic and electric field has the larger magnetic and electric energy [17]. According to
the values presented in Table 3, the stored electric energy is negligible compare to the stored magnetic
energy. Storing the most magnetic energy is an important factor in all wireless transfer systems based on
inductive technique because storing more magnetic energy leads to higher power transmission efficiency.
The above table shows that helical coil can be recognized as an efficient geometry among proposed coils,
based on storing magnetic energy.

EM analysis of different geometry of transmitting coils for wireless power transmission applications 7
5. CONCLUSION
In this paper, various geometries of coils for inductive power transfer applications are analysed. A
set of simulation results; Magnetic field, electric field, magnetic flux density, and current density are
presented. The COMSOL multiphasic software has been used to simulate results. The simulation have
been verified with empirical results. This work has presented an efficient perspective to coil designers.
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