15th Brazilian Power Electronics Conference and 5th IEEE Southern Power Electronics Conference

Distance Detection System for Digital Transmitter
Coil Achieving Distance-Variation-Tolerant
Wireless Power Transfer
Hao Qiu
The University of Tokyo
Tokyo, Japan
hqiu@iis.u-tokyo.ac.jp

Yoshiaki Narusue
The University of Tokyo
Tokyo, Japannarusue@akg.t.u-tokyo.ac.jp

Takayasu Sakurai
The University of Tokyo
Tokyo, Japantsakurai@iis.u-tokyo.ac.jp

Makoto Takamiya
The University of Tokyo
Tokyo, Japanmtaka@iis.u-tokyo.ac.jp

Abstract— In this paper, a distance detection system that
only processes the information in the transmitter (TX) side is
proposed. By using the distance detection system, the radius of
the digital TX coil can change automatically depending on the
distance and thus achieve the maximum efficiency tracking. A
wireless power transfer (WPT) prototype is fabricated andexperimental results demonstrate that, compared with using theconventional TX coil with a constant radius, the efficiency isimproved from 12% to 20% at the distance of 4 times the RX
coil radius.
Keywords—Coil-to-coil efficiency, coil design, distancevariation, distance detection, impedance measurement, magnetic
resonance coupling, mutual inductance, optimal radius, wirelesspower transfer.

I. INTRODUCTION
Wireless power transfer (WPT) using magnetic resonancecoupling has been applied in a wide range of applications
such as electric vehicles (EVs), portable electronics andbiomedical implanted devices [1]–[4]. The distance (d)variation between the transmitter (TX) and receiver (RX)coils is a common problem. For example, EVs with different
ground clearances [2] can have a different d. In portableelectronics [3], it is preferred that these devices are not put on
the wireless charging pad but can be held in hand andoperated during wireless charging. Thus, d can change during
operations. In biomedical implanted devices [4], the different
body postures of the patients can also change d and affect thesystem’s efficiency. Thus, a d-variation-tolerant WPT
method is required for practical applications.
The efficiency of a WPT system is determined by both thecoil-to-coil efficiency (η) and the impedance matchingThis work was partially supported by JST ERATO Grant Number
JPMJER1501, Japan.

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

Yoshihiro Kawahara
The University of Tokyo
Tokyo, Japankawahara@akg.t.u-tokyo.ac.jp

condition [1]. When d changes, the coupling between the TX
and RX coils varies and then affects η. In addition, thecoupling variation changes the input impedance of the TX
coil and there will be an impedance mismatch with the source
impedance. Therefore, the maximum system efficiency
cannot be achieved when d varies.
Several adaptive impedance matching methods withrespect to d have been proposed. The first method uses theadaptive frequency tracking [5]. The optimal frequency istracked to overcome the frequency-splitting phenomenon
even when the coupling between TX and RX coils enters theover-coupling region. However, it can be problematic since
the industrial, scientific, and medical (ISM) bands are very
narrow. The second method has the same operating frequency
but uses the adaptive impedance matching network [1], [6]–[7], which requires complex control and affects the system’s
reliability. The third method uses coil repeaters between the
TX and RX coils [8]–[12], in which a large number of
repeaters adds the system’s complexity. In addition, theimpedance matching condition in [8]–[9] is adjusted
manually, which makes the system impractical.
Though the above methods can achieve the impedance
matching condition with respect to d, η cannot be improved
since the coil design is not discussed. In [13], the optimal
design of the RX coil was discussed. From a practical pointof view, however, a TX-only tuning is preferred since the RX
coil should be as simple as possible. On the other hand, [14]shows the optimal layout of the TX coil, but how toadaptively change the coil’s radius is not discussed.
In [15], the topology of digital TX coil that consists ofseveral sub-coils connected in parallel is proposed and its
radius can be changed by selectively turning on one of these830

15th Brazilian Power Electronics Conference and 5th IEEE Southern Power Electronics Conference

Fig. 1. (a) Conventional TX coil with constant rTX and the proposed TX coil with adaptive rTX depending on d. (b) Schematic of d dependence of η.

sub-coils. However, its radius is changed manually, which isfar from practical applications. In this paper, we propose a ddetection system that only processes the information in the
TX side. Based on the d detection system, the digital TX coilcan change its radius automatically and realize the trackingof the maximum η at different d. The rest of the paper isorganized as follows. Section II discusses the optimal radiusof the TX coil for the maximum η. In Section III, the digital
TX coil integrated with the d detection system is proposed.
Experimental results are presented in Section IV. Finally,
conclusions are given in Section V.
II. OPTIMAL TRANSMITTER COIL RADIUS
FOR MAXIMUM EFFICIENCY
In this paper, as shown in Fig. 1, it is assumed that the RX
coil is perfectly aligned with the TX coil and changes its
position along the central axis. The radii of the TX and RX
coils are rTX and rRX, respectively. In a conventional (CON)design, the TX coil has a constant radius, whereas in the
proposed (PPSD) design, the TX coil has an adaptive rTX that
depends on d. As d increases to d’, ηPPSD’ using the PPSD TX
coil is higher than ηCON’ using the CON TX coil.
In a WPT system, η is defined as the ratio of the power
delivered to the load (RL) to the power input into the TX coil.
Under the condition that RL is the optimal value, η can be
expressed as [16]η=

(1 + 1 + k Q Q )
TX

2

,

k2QTXQRX, on the other hand, is correlated with thephysical parameters of the coils. Firstly, we discuss thecalculation of the coils’ resistances. For loosely wounded
coils, the proximity effect is negligible, so RTX and RRX canbe simplified to [14]
=
RTX

as
2

(2)

σϖδ

(3)

σϖδ

Secondly, under the condition that rRX << rTX, M can beobtained as [17]RX

( 2π f 0 M ) .
k 2QTX QRX =RTX RRX

2mrTX
2nrRX
.
, RRX
=

Here, σ is the conductivity of copper (5.96×107 S/m), ϖ isthe diameter of the copper wire (1 mm). The skin depth (δ)
can be calculated as (πμ0f0σ)-1/2, where μ0 is the vacuum
permeability (4π×10-7 H/m). m and n are the number of turnsof the TX and RX coils, respectively.

(1)

where

831

Thus, η can be optimized by maximizing k2QTXQRX.

M=

k 2QTX QRX
2Here, f0 is the resonance frequency. M is the mutual
inductance between the TX and RX coils. RTX, RRX are theparasitic resistances of the TX and RX coils, respectively. k
is the coupling coefficient between the TX and RX coils. QTX
and QRX are the quality factors of the TX and RX coils,
respectively.

µ0π
2

mn

rTX 2 rRX 2(d + r )
2

TX

2 3/2

.

(4)

By substituting (3) and (4) into (2), k2QTXQRX is expressedk 2QTX QRX = (π 2 µ0σϖδ f 0 2
2

) mn

rRX 3

(r + d / r )
TX

2

TX

3

. (5)

15th Brazilian Power Electronics Conference and 5th IEEE Southern Power Electronics Conference

RL

Distance detection system

RX coil

CRX

Labview control

d=d1
d=d2

SW1

VS (f0)RS

Distance
detection system

C1

Oscilloscope

d=d3

SW control

Magnitude
output

d=d4

SW3
SW2
C2 C3 C4

SW4

SW control

TX1 (rTX1)
TX2 (rTX2)
TX3 (rTX3)
TX4 (rTX4)
d=0

Phase
outputTX1Gain and phasedetector

VS (f0)RS

Incident
wave

RX coil

C1

Reflected
wave

Bi-directional coupler

CRX

k
L1

LRX

R1

RRX

RL

Zin

Fig. 3. Block diagram of d detection system in Fig. 2. TX1 in the digital TX
coil is used. d can be detected by measuring Zin.

Digital TX coilFig. 2. A WPT system consisting of the proposed digital TX coil, the RX
coil, and the d detection system.

It can be derived that when f0, m, n, and rRX are constants,
k2QTXQRX reaches the maximum when rTX equals its optimalvalue (rTX, OPT) which is obtained as

rTX, OPT = d .

(6)Equation (6) means, under the condition that rRX << rTX,
using the TX coil with rTX that equals d, we can achieve themaximum η.
III.
DIGITAL TRANSMITTER COIL
WITH PROPOSED DISTANCE DETETION SYSTEM
A.

communication channel between the TX and RX coils isnecessary, the d detection system here only processes theinformation of the TX side and makes the whole systemeasier and more reliable. In this paper, TX1 in the digital TX
coil is used for d detection. The details are given as follows.
Using a bidirectional coupler and a gain phase detector, Zin
can be measured from the ratio of the amplitude of thereflected and incident waves, namely, the reflection
coefficient (Γ).
Z in = Z 0

1+ Γ
,
1− Γ

(7)

where Z0 is the characteristic impedance of thetransmission line and equals 50 Ω.

Digital Transmitter Coil Topology
M is correlated with Zin and expressed by [16]Fig. 2 shows a WPT system consisting of a voltage source(VS) with a source resistance (RS), the digital TX coil, the RX
coil, and the proposed d detection system followed by a
( Z in − R1 )( RL + RRX ).
(8)M=
switch (SW) control unit. In this paper, we assume the RX
2π f 0coil has four positions, namely, d1, d2, d3, and d4. The digital
TX coil consists of four concentric sub-coils (TX1, TX2, TX3,
Thus, by combining (4), (7), and (8), d can be detected as
and TX4). For TXp (p = 1, 2, 3, and 4), its radius (rTXp) is
determined according to (6). Its number of turns, inductance
1/3
and parasitic resistance are represented by mp, Lp, and Rp, ( µ π 2 f m nr 2 r 2 )2 
0 1 TX1 RX
 0
 −r 2 .
respectively. The compensation capacitor has the capacitance
(9)
d
=
TX1


(
Z
R
)(
R
R
)
−
+
in
1
L
RX
of Cp. For the RX coil, the inductance and compensation
capacitance are represented by LRX and CRX, respectively. f0
of each sub-coil in the digital TX coil is the same as that ofWith the developed d detection system, the algorithm of
the RX coil. With respect to dp detected by the d detection
selecting the corresponding sub-coil in the digital TX coil issystem, the corresponding TXp is selected.
given. Firstly, SW1 is turned on and dp is detected, followedby turning off SW1 and then turning on the corresponding
B.
Proposed Distance Detection System
SWp. Here, p = 1, 2, 3, and 4. Thus, in an electronical way,
Fig. 3 shows the block diagram of the proposed d detection
theradius of the digital TX coil can be automaticallysystem in Fig. 2. According to (4), d is correlated with M. At
controlled
to the optimal value for the maximum η at each d.
the same time, M can be known by measuring the input
impedance (Zin) of the TX coil [16]. Thus, d can be detectedby measuring Zin. Different from [10] and [11], where the832

15th Brazilian Power Electronics Conference and 5th IEEE Southern Power Electronics Conference

Digital waveformgenerator

TX1
TX2
TX3
TX4

Signal source

Oscilloscope

AD8302

SW1

Bidirectional coupler

SW3

SW2

Digital TX coil
RX coilSW4

RX coilFig. 5. Photograph of the WPT prototype consisting of digital TX coil withthe developed d detection system and the RX coil. RL = 50 Ω.
Digital TX coil

20 mm

Fig. 4. Photograph of fabricated digital TX coil and RX coil.

TABLE IMEASURED PARAMETERS OF DIGITAL TX COIL AND RX COIL
Digital TX Coil
TX1

TX2

Inductance

TX4

RX Coil13.6 MHzf0
RadiusTX3

rTX1 = 80 mm rTX2 = 70 mm rTX3 = 45 mm rTX4 = 35 mm
L1 = 15.3 μH

L2 = 12.4 μH

L3 = 4.77 μH

L4 = 2.73 μH

rRX = 20 mm
LRX = 0.554 μH

Parasitic
resistance

R1 = 2.6 Ω

R2 = 2.3 Ω

R3 = 1.0 Ω

R4 = 0.70 Ω

RRX = 0.18 Ω

Capacitance

C1 = 11 pF

C2 = 13 pF

C3 = 32 pF

C4 = 52 pF

CRX = 247 pF

Qualityfactor

503

461

408

333

263

Note: Number of turns of the digital TX and RX coils are 5 and 3,
respectively. Thicknesses of the digital TX and RX coils are 15 mm and 7mm, respectively.

IV.

MEASUREMENT RESULTS

In order to verify the effectiveness of the proposed d
detection system in the digital TX coil, a WPT prototype isfabricated, and experimental results are presented.
A.

WPT Prototype Implementation
In this paper, it is assumed that the RX coil has 4 known
positions, namely, d1 = 80 mm, d2 = 65 mm, d3 = 50 mm, andd4 = 35 mm. The RX coil and digital TX coil consisting offour concentric sub-coils were fabricated, as shown in Fig.4.
Four relays (TQ2-L2-4.5, Panasonic Electric Works) with anon resistance of less than 50 mΩ were used as SWs. rRX is 20mm, and all radii of the sub-coils in the digital TX coil are
determined by the electromagnetic simulation results in [15].
The difference from (6) is analyzed in [15] and mainly
ascribed to the approximation made in (4). Table I lists themeasured parameters of each coil. Considering the coils’
thicknesses, d is defined as the distance between the833geometrical center points of the digital TX coil and the RX
coil.
Fig. 5 shows the photograph of the WPT prototype
consisting of the digital TX coil with the proposed d detection
system and the RX coil. A signal source (AFG3252,
Tektronix) is used to generate a sinusoidal wave signal witha peak-to-peak value of 5 V at 13.6 MHz. RS is 50 Ω. A
bidirectional coupler (ZFBDC20-61HP+, Mini-Circuits) anda gain phase detector (AD8302, Analog Devices) perform Zin
measurement. The output waveforms are measured by an
oscilloscope (D5054A, Agilent Technologies). A labview
control program is run to perform the d detection and thengenerate the control voltages for the SWs through a digital
waveform generator (PXIe-6555, National Instruments).
B.

Evaluation of WPT Prototype
Firstly, the d detection system was evaluated, in whichmeasured M according to (8) and calculated M according to(4) are compared in Fig. 6. In addition, the calculated M byincluding the coils’ thicknesses is also shown for comparison.
It is shown that the difference between measured andcalculated M becomes smaller when the coils’ thicknesses areincluded. The percentage error is estimated as 14% at d = 35mm and decreases to 2.7% at d = 80 mm. The remaining
difference is mainly ascribed to the fact that no impedance
calibration is performed in Zin measurement. To guarantee thecorrect d detection, the measured M is calibrated using the
calculated M at d = 65 mm as a reference. After M calibration,
the detected d (ddet) is calculated according to (4). Fig. 7
shows the relationship between ddet and d. Their strong
correlation guarantees the correct operation of SW control
unit.
In addition, a network analyzer (E5061B, KeysightTechnologies) was used to measure the S parameters between
the TX and RX coils, and η is calculated as |S21|2/(1-|S11|2).
Fig. 8 shows the measured d dependence of η. Compared withthe conventional TX coil with a constant radius, the proposed15th Brazilian Power Electronics Conference and 5th IEEE Southern Power Electronics Conference

digital TX coil with an adaptive radius achieves the
maximum η at different d. For example, at d = 80 mm, η is
improved from 12% to 20% (almost doubled) by turning on
TX1 rather than TX4. Similarly, for d = 35 mm, η is improved
from 51% to 75% by turning on TX4 rather than TX1.

Mutual inductance (M) (µH)

0.16

0.12

V.

0.08

0.04

Measurement
Calculation
Calculation: including coils' thicknesses

0.00

35

50

65

80

Distance (d) (mm)Fig. 6. d dependence of measured and calculated M.

Detected distance (ddet) (mm)One-point calibration
at d = 65 mm

[1]

60

40

20

0

20

40

60

80

Distance (d) (mm)Fig. 7. Correlation between ddet and d.

100

Efficiency (η) (%)

TX1

80

TX2

75%

20
0

Conventional

TX3

TX4
Digital TX (Proposed)60
40

A distance detection system that only processes
information in the TX side is proposed and implemented in
the digital TX coil for wireless power transfer robust against
distance variation. Experimental results demonstrate that,based on the proposed distance detection system, the radiusof the digital TX coil can adjust automatically depending on
the distance. Compared with the conventional TX coil with aconstant radius, the WPT efficiency is improved from 12% to20% (almost doubled) at the distance of 4 times the RX coilradius.
REFERENCES

80

0

CONCLUSIONS

51%
20%

Measurement
rRX=20mm

35

12%

50

65

80

Distance (d) (mm)Fig. 8. Measured d dependence of η using the proposed digital TX coil,compared with the conventional TX coil with a constant rTX.

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