Finite Element Analysis of Contactless Power Transmission
System Using Meander Antennas
Yuki Sato, Hajime Igarashi

Graduate School of Information Science and Technology, Hokkaido University, Japan
1Introduction

In recent years, contactless power transmission techniques havebeen used for electric vehicles and battery charger of phone andso on. The contactless power transmission techniques areclassified into four types: electromagnetic induction,electromagnetic resonance, microwave transmission and lasertransmission. In the electromagnetic induction type, whose
operating frequency is some kHz, coils must be located at a very
short distance, which is, for example, about 10cm when using
coils of 1m radius. One of the drawbacks of this type is that theenergy transmission efficiency rapidly reduces when theposition difference in the coil centers increases. The microwave
transmission and laser transmission types can have longer
transmission distance up to several kilometres aselectromagnetic waves are used. The operating frequency of thistype ranges from MHz and GHz. The drawbacks of this type
would be that the efficiency is not high, and effects on humanhealth have not been clarified.
On the other hand, the electromagnetic resonance type hasintermediate communication distance, some meters, and theefficiency can be more than 90% when the distance oftransmission is less than 1m. The electromagnetic resonancetype is based on either electric coupling or magnetic coupling.
In the electromagnetic coupling, the transmission power
becomes the maximum at the resonant frequency of the systemcomposed of transmission and receiver antennas. Because theoperating frequency of the electromagnetic resonance type ishigher than that of the induction type, the former has higher Q
values and also lower power losses.
In recent studies, the contactless power transmission based on
the electromagnetic resonance has been analysed using
equivalent circuits which approximate the characteristics of thetransmission and receiver antennas. Moreover, this system has
been analyzed using the moment method [1].
In this paper, the electric coupling analysis using FEM ispresented. The present method would be useful for, e.g., theanalysis of bio-magnetic effects of the contactless powertransmission, because complicated media can be modeled withease. In order to realize the electric coupling, transmission andreceiver antenna generically are used meander line antenna(MLA).
22.1

Electric coupling analysis using FEM
Meander line antenna

Let us consider the contactless power transmission system using
the meander line antennas (MLA) shown by Fig. 1, which has
been discussed in [2]. The transmission antenna is excited by a
voltage source v, which is connected to the antenna through thetransmission line with characteristic impedance Z0, as shown in
Fig.2. The receiver antenna is also connected to Z0. The
structure parameters of MLA are antenna length l (mm), antenna
width w (mm) and distance of conductor wire d (mm). To know
the resonant frequency, the input impedance Z of thewdlgx

receiver antennayzgtransmission antennax

Fig.1 Geometry of contactless power transfer

ir

it

Z0vr

vt

Z0v

transmission antenna

receiver antenna

Fig. 2 Circuit of transmission and receiver antennatransmission antenna is calculated by FEM. The input
impedance Z is computed fromV(1)
Z 0I0where V0 and I0 are induced voltage and current at the feeding
point of MLA. At resonance, the imaginary part of inputimpedance is equal to zero.
2.2

Finite element analysis

The circuit equation for transmission antenna is given byvt  Z 0it  v(2)where vt and it are induced voltage and current at the feeding
point of transmission antenna. Also, the circuit equation forreceiver antenna part is given byvr  Z 0ir

80

where vr and ir are induced voltage and current at the feeding
point of receiver antenna. In order to perform the electric
coupling analysis using FEM, we must simultaneously solve thecircuit equations (2)-(3) and the Maxwell equations

70  (  A)   2A  j  J(4)   2A  0(5)power transmission rate (%)(3)

where A is vector potential, φ scalar potential and J current
density. To couple the Maxwell equations (4), (5) to the circuit
equation (2), (3), the current density J in (4) is expressed interms of the induced current it and ir. In the FE analysis, theperfect matched layer is used on the open boundaries. The
discretized equations derived from (2)-(5) are solved using theconjugate gradient method preconditioned by the incompleteCholesky factorization (ICCG).
3x=400mm60x=500mm

50403020100
2.00E+07

2.40E+07

2.80E+07

3.20E+07

frequency (Hz)Fig. 4 Power transmission rate

Numerical Results

3.1

Input impedance

In the analysis, the structure parameters of MLA are set as
follows: l=840mm, w=840mm, g=20mm and d=40mm and thedriving frequency ranges from15MHz to 35MHz. The resultant
input impedance of MLA is shown in Fig. 3, from which we cansee that the resonant frequency is about 26MHz.
400300input impedance (Ω)

200

Fig.5 Electric field around MLA100

40

In this paper, we have presented FE analysis of a contactless
power transmission system using MLAs. The powertransmission rate η can be about 60% when x/l is about 0.5. The
dependence of η on the number of fold in MLA will be
discussed, and optimization of the shape of MLA will bepresented in the final paper.

-100-200

real part
imagenary part

-300
-400
1.50E+07

2.00E+07

2.50E+07

3.00E+07

3.50E+07

References

frequency (Hz)[1]
Fig.3 Input impedance characteristic of MLA

3.2

Power transmission rate

We analyze the power transmission rate between the MLAs
shown in Figs.1 and 2, which is defined byv r *i r
vt *it2

 100(%) .

Conclusion(6)

The distance x between transmission and receiver antennas is set
to 400 and 500 mm. The results are shown in Fig.4, from which
we can see that the peaks in η are at 26MHz and their maximum
values are about 60 and 40 %, respectively. The profiles in Fig.4
are slightly unsymmetric. This would come from thediscretization errors. It is observed that this non-symmetry
becomes more remarkable when x decreases. Hence the numberof finite elements must be increased to obtain sufficiently
accurate results especially when x is small. The electric field
distribution around MLA is shown in Fig. 5. We can see in Fig.5
that there are concentrations of the electric field near the gaps ofMLA.

[2]

T. Imura, H. Okabe, T. Uchida, and Y. Hori, “Study of Magneticand Electric Coupling for Contactless Power Transfer Using
Equivalent Circuits,” (in Japanese) IEEJ Trans. IA, vol. 130, no.1
pp,84-92, 2010.
T. Imura, H. Okabe, T. Uchida, and Y. Hori, “Wireless Power
Transfer during Displacement Using Electromagnetic Coupling inResonance,” (in Japanese) IEEJ Trans. IA, vol. 130, no.1 pp,76-83,
2010.