alysis of Wireless Power Transfer
Yoon Goo Kim
School of Electrical Engineering and Computer Science,
gu Seoul Korea
Recently, wireless power transfer using near
field is receiving much attenti
on and is being studied
Several analysis models for the
wireless power transfer have been proposed. These
include an a
nalysis by coupled mode theory
is using an equivalent circuit
analysis using filter theory
. Another analysis method involves the use of spherical modes [
paper we investigate characteristics of wireless power transfer using spherical modes.
In order to use
a wireless power transfer in practice the effect of wireless power transfer on the
human body and electronic devices must be investigated. In addition, such systems
it is needed to calculate
near wireless power
In this paper, we calculate electromagnetic fields near two coupled antennas
ANALYSIS OF ANTENNA COUPLING USING SPHERICAL MODES
In order to derive
antennas, we f
an antenna as a
in terms of spherical modes
b T S a
receiving and scattering properties of an antenna are contained in this matrix equation.
on the origin of coo
rdinate 1 (
) and antenna
on the origin of
), as shown in Fig. 1.
oordinate 2 (
) is obtained
and coordinate 3 is obtained by rotating coordinate 2. It is assumed tha
t two spheres
enclosing each antenna do not overlap.
The coupling of two antennas can be considered as the
cascading of a transmitting antenna network, a space network, and a receiving antenna network, as
shown in Fig. 2.
Here, the antenna networks are exp
scattering matrix and the space
network is expressed
2, left side p
in the space network
the mode ports for coordinate 1 and
right side ports
the mode ports of coordinate 3.
ic impedance of antennas be Z
and the characteristic impedance of the space network be 1.
For simplicity, we assume that antennas are canonical minimum scattering
generate only fundamental modes.
The canonical minimum scattering antenn
a is one which does not
scatter electromagnetic fields when its local port is open
Antennas that are small
compared with wavelength can be modeled as a minimum scattering antenna [
matrix of the space network was derived in
 using the addition theorem.
two identical CMS antennas generating only fundamental mode is presented in [
]. Once the Z
, the maximum power transfer efficiency and optimum load impedance can be
determined by th
e formula in [
]. According to [
], the radiation efficiency of an antenna is
parameter in wireless power transfer. Fig
3 shows maximum power transfer efficiency of the antennas
) mode for different radiation efficiencies.
It can be seen in Fig.
maximum power transfer efficiency increases
ELECTROMAGNETIC FIELDS NEAR
WIRELESS POWER TRANSFER SYSTEMS
If we know the voltages and currents of
ports in the space network, we can calc
electromagnetic fields near wireless power transfer systems and far
field that wireless power transfer
The region where electromagnetic fields are calculated is divided into two regions
and the method for calculating fields in
ch region is different
This is because
of the addition theorem are different in the two regions. In region 1 (blue region), both incoming and
outgoing spherical waves exist. In region 2, only outgoing spherical waves exist. If we kno
voltages and currents of ports
the space network, we can determine the spherical mode coefficients
in both regions. From the spherical mode coefficients, we can calculate electromagnetic fields near
wireless power transfer system and far
t the system radiates.
s of the space
are as follow:
1 1 1
2 2 2
modal transmitting pattern (
) of antenna j
current at the
local port of antenna
is currents at the mode ports of
coordinate 1 and
oltages can be determined from the impedance matrix of the
and the currents.
To verify the theory, we simulated
romagnetic fields near
two coupled helix coils with FEKO.
, the radius is 30cm, the height is 20cm, and
number of turn is
radius is 20cm, the height is 20cm, and
number of turn is 6
All the antennas are made out
copper wire with a diameter of
Two helices are
load of 3
on the port of helix 2 and excite 10V at the port of helix 1.
We calculated electric fields on the sphere
radius is 2m
r component of
electric fields against
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Fig. 1. Coordinate systems and antennas
Fig. 2. Network representation of two coupled antennas
Fig. 3. Maximum power transfer efficiencies of antennas for different radiation efficiencies at
Two regions where electromagnetic fields are calculated
the sphere where electromagnetic fields are calculated.
component of electric fields against
. Frequency=13.56MHz. r = 2.
= 0. (a) real part. (b) imaginary part.