1. Study on Frequency-tracking Wireless Power Transfer
System by Resonant Coupling
Wenzhen Fu, Bo Zhang Member IEEE, Dongyuan Qiu Member IEEE
College of Electric Engineering South China University of Technology Guangzhou, P. R. China, 510641
Abstract-Detuning is the application barrier of resonant
coupling wireless power transfer. This paper analyzes the effects
about inductance variations of launch coil and receiving coil to
wireless transmission efficiency from its transmission mechanism
and model, and also analyzes detuning mechanism. And thus, it
reveals that transmission efficiency has a great affection with
inductance of launch coil changing. In order to make sure that
wireless power transfer by resonant coupling operates without
detuning, a new method of frequency tracking control is came up
with, which is, making frequency of transmitting power source
tracking with the nature frequency of launch resonant circuit
automaticllly. Hence, it avoids detuning and improves
transmission efficiency greatly. Finally, a prototype of 1 MHz
wireless power transfer system by resonant coupling was made.
Experimental results prove this method very well.
I. INTRODUCTION
Wireless power transfer has been a dream of human
beings. Many scientists have researched it uninterruptedly but
little progress has been made. Untill now,there two kinds of
wireless power transfer that one is non-contact
electromagnetic induction and another is radio waves
transceiver[1-4].They have been studied deeply and usde in
daily life, such as electric toothbrushes, cordless home phones
and so on[5-7]. Efficiency of non-contact electromagnetic
induction can reach to 80% but in a very short distance, just in
1cm. Radio waves can transfer energy in 10m with very low
efficiency and only 1mW 100mW power can be transferred.
Due to the conflict between transfer efficiency and distance,
they are used not in a very wide range. And more,low
efficiency results in serious heat problems[8]. Comparatively
speaking, wireless power transfer of resonant coupling can
transfer energy in 5m and its efficiency can
Project Supported by National Natural Science Foundation of China
(NSFC)(50877028) Science Foundation of Guangdong Province
(8251064101000014) Hi-tech research and development program of China(863)
(2007AA05Z200).
to 40%, which will be a new technology with wider using
range[9]. In addition, comparing with the contactless
electromagnetic induction, resonance coupling uses weak
magnetic field but can transfer farther;And comparing with
the radio waves, resonance coupling has less dissipated
energy during transfering process[10].
However, resonance coupling wireless power transfer is
still in its infancy, whose theoretics and experimental analysis
are in lacks,especially for efficiency analysis [11-12]. During
the wireless power transfer process, resonant frequency
maybe change because resonant inductance changes with
obstacles (such as magnetic objects,etc.), parasitical
parameters,impacts of receiving loop,temperature rising in
circuit and so on. Once detuning happens,the efficiency will
drop rapidly. Technologies of frequency tracking focusing on
CD4046 and all digital PLL have been more mature[13-14],
but they can not meet fast tracking in higher than 1MHz.
In order to overcome these problems, focusing on
transmission mechanism and model of wireless power transfer
by resonant coupling, this paper analyzed its efficiency and
detuning mechanism. On this basis, frequency-tracking
wireless power transfer system of resonant coupling basing on
phase-locked loop 74HC4046 is came up with.Lastly,1MHz
frequency-tracking wireless power transfer system by
resonant coupling was made and got better results, which
would be a very good guide to the future study on wireless
power transfer system by resonance coupling.
II. DETUNING MECHANISM AND EFFICIENCY ANALYSIS
A.Detuning mechanism of resonant coupling wireless
Electromagnetic field decayes rapidly with transmission
distance increasing,which is very undesirable. Resonant
coupling just catches this decayed electromagnetic fields by
two resonant loops. When resonance occurred between launch
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2. loop and receiving loop, most of energy will be transfered
from transmitting power source to receiving load[12].
Resonant coupling wireless power transfer system
includes not only two LC resonant circuits but also a high
frequency transmitting power source and a receiving load. In
order to simplify analysis, ignoring high frequency source,
transceiver circuits are used as studyed objects directly. Model
of resonant coupling is shown in Fig.1, where Vi is
high-frequency power source; R1 R2 are parasitical resistances
of coils L1,L2; C1, C2 are series resonant capacitors;RL is load;
L1, L2 are coils inductance; M is mutual inductance and D is
transmission distance.
Vi
R1 R2
C2C1
L1 L2
D
M
I1
I2
.
..
.
RL
Fig.1 Model of resonant coupling circuit
From Fig.1, when frequency of Vi equals to natural
resonant frequency of transceiver circuits,their impedance are
at least.Thereby, currents of the loops will be at the most and
energy can be deliveryed mostly to receiving loop. On the
other hand, energy of transmitting power source will be
consumed in the launch circuit itself and its efficiency is very
low. That is to say, keeping the frequencies in synchronism
without detuning happening is the key point to achieve
resonant coupling wireless power transfer.
coil. At the moment, if another coil is put aside it, the
magnetic field will also appear around the other coil, which is
the reason that the wireless energy transmission is set up
between those two coils. Like that, resonance coupling is a
special circumstance of non-contectless wireless energy
transmission, where the special is: all coils used for resonance
coupling operate in resonant state. Resonance occurs when
the self-resonant frequency of coils equal to the frequency of
AC power supply, when the equivalent circuits of coils in high
frequency have the minimum impedance. Then, the most
energy will be transferred from the resonant path.
The schematic of resonance coupling wireless energy
transmission system was showed in fig.1.It includes two
spatial isolated hollow coils: one is LS, which sends the
energy inducted from the high frequency power supply; the
other is LD, which receives energy from LS. These two coils
have the same sizes and operate at the resonant state.
B. Efficiency analysis of resonant coupling
By Fig.1, resonant coupling model of wireless power
transfer can be expressed by the following state equation.
1 1
1 1
2
2 L 2
2
1
( )
10 ( )
R j L j M
V C Ii
I
j M R R j L
C
ω ω
ω
ω ω
ω
ª º
+ − −« »ª º ª º« »=« » « »« » ¬ ¼« »¬ ¼ − + + −« »
¬ ¼
(1)
To simplify analysis, the transceiver loops impedance are
written as Z1 and Z2, namely,
1 1 1
1
1
( )Z R j L
C
ω
ω
= + − , 2 2 L 2
2
1
( )Z R R j L
C
ω
ω
= + + − ,
By (1), currents of this two loops can be obtained as follows
1 2
2
2 11 2
j1
j 0( )
iI Z M V
I M ZZ Z M
ω
ωω
−ª º ª º ª º
=« » « » « »−+ ¬ ¼¬ ¼ ¬ ¼
(2)
Then, input power Pin of launch circuit and output power
Pout on the receiving load RL can be expressed as
2
2
2
1 2 ( )
i
in
V Z
P
Z Z Mω
=
+
(3)
2 2
L
2 2
1 2
( M)
[ ( ) ]
i
out
V R
P
Z Z M
ω
ω
=
+
(4)
Transmission efficiency is
2
L
2
2 1 2
( )
100%
[ ( ) ]
M R
Z Z Z M
ω
η
ω
= ×
+
(5)
Taking specific formulas of Z1, Z2 and mutual inductanc
1 2kM L L= (k is coupling coefficients) (5), (5) can be
changed as
2
1 2 L 2 L 2
2
1 1 2 L 2
1 2
2
1 2
1
[( k ) ]/{[ ( )]
1 1
{[ ( )] [ ( )]
( k ) }} 100%
L L R R R j L
C
R j L R R j L
C C
L L
η ω ω
ω
ω ω
ω ω
ω
= + + − ⋅
+ − ⋅ + + −
+ ×
(6)
From(6),transmission efficiency relates to many factors.
If resonant parameters are determinded,resonant capacitor
does not change any more, but Ȧ, R1 and R2 will change with
resonant inductance changing. So resonant inductance is of
the most important,which maybe change with its operation
environment and some other factors in this system besides
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3. making errors. So it is too difficult to make actual value of
coil inductance equaling to its calculated value exactly,which
easily results in detuning. Once detuning happens, resonant
coupling efficiency will drop. Therefore, the impact about
coil inductance change to efficiency will be mainly analyzed
in this paper.
When the frequency is 1MHz, basing on the theory
formulas about dual-tube LLC resonant inverter of class E in
reference[13], resonant coupling parameters of picture.1 are
calculated as:L1=2.35μH,C1=12nF,L2=25μH,C2=1.0nF.
Due to high frequency, hollow coil parasitic resistance
included ohm resistance Ro and radiation resistance Rr [10].
0 0
o
2 2ʌ 2
l nr
R
a a
ωμ ωμ
σ σ
= = (7)
[ ]2 4 20
r 3
0
ʌ 2
( ) ( )
12 3ʌ
r h
R n
c c
μ ω ω
ε
= + (8)
Where ȝ is the space permeability; a is the wire radius; r
is the coil radius; n is the coil turns ;σ is the conductivity l is
the wire length; 0ε is the dielectric constant; h is the coil
length; c is the light velocity. For middle distance resonance
coupling system, the optimum frequency range is 1 50MHz,
then usually Rr RO from (7) and (8). Coil parasitic resistance
is ohm loss Ro mostly. In order to decrease parasitic resistance,
the size parameters of hollow coils L1 and L2 are designed
as :a1=0.725mm, a2=0.362mm; n1=2, n2=10; r1= r2=5cm. And
then, from (7), the parasitical resistances of L1 and L2 are
calculated as: R1=0.014ȍ R2=0.139ȍ In order to analyze the
immpacts of coils inductance change to efficiency, coupling
coefficient k and load RL are fixed firstly(k=0.02 RL=10ȍ).
Then, taking parasitic resistance R1, R2 and resonant
parameters into (6), relation curves is got in Fig.2, where coil
inductance L1 and L2 are independent variables and
transmission efficiency is dependent variable.
(a) launch coil (b) receiving coil
Fig.2 Curves of efficiency vs. coil inductance
III. FREQUENCY-TRACKING SYSTEM
A. Principle of tracking control
Frequency-tracking resonant coupling system is shown in
Fig.3,where it includes three parts, high frequency inverter,
LC resonant couling and frequency-tracking control.
Dual-tube LLC resonant inverter of class E is selected as
high-frequency inverter. Characters of this inverter are as
follows: firstly, high-frequency transformer is instead by
resonant inductance directly, which will reduce transformer
loss and increase transmission distance.Secondly,the
efficiency of this topology is very high because switches
operate on ZVS and ZCS states. Finally but not last, two
switches operate without dead time so that it is very fit for
high frequency.
Eenergy is delivered from high-frequency inverter to
receiving load by LC resonant coulping circuit. Frequency-
tracking control includes currrent detection,differential
amplifier,phase compensator and phase-locked loop, which
are shown in Fig.3.
Fig.3 System principle diagram of frequency tracking
Control principles are as follows: current transformer has
a real-time detection to the launch resonant loop, where
detection signal is converted into a signal voltage VD. And
then VD is converted into another signal Vp through
differential amplifier.Lastly,Vp will be used to compare with
a DC bias voltage that is abtained by rectifyingVp. After
that,a pulse signal VC is got, which is the input of
phase-locked loop and has the same frequency with the
detection current. Herence, frequency-tracking control to
launch resonant loop is realized.
B. Method of frequency tracking
(1) High-frequency current detection
Real-time current detection is needed in frequency-
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4. tracking system. In the article, frequency of wireless power
transfer system is 1MHz, so it must use high-frequency
performance core for making current transformer to avoid
high frequency saturation. Due to launch resonant circuit is
not connected to the ground directly, detected current is a
differential signal, which can not be sent into comparator
directly and differential amplifier is need. High-frequency
current detection is shown in Fig.4. According to principle of
differential amplifier, there are R3=R4, R5=R6.
Fig.4 Circuit of high frequency current detection
(2) Method of phase compensation
In actual circuit, some time delay exists in the process of
current detection, MOSFET on/off and so on,which will make
resoant voltage delaying a phase to the resonant current and
then resonant inveter operates in capacitive state. So phase
compensation is needed in this system, which will make sure
that high frequency inverter of class E always operates on
quasi-resonant states to improve its efficiency.That is, most
energy in transmitting power source will be delivered to
receiving load. Schematic diagram and waveforms of phase
compensation are shown in Fig.5.
(a) Compensation circuit
(b) waveforms
Fig.5 Phase compensation circuit and its waveforms
VP is the ouput voltage of differential ampilifier.
Reference voltage Vref has been got through rectifying VP and
then Vref will fluctuate with VP, which will make sure that
compensated phase ǻt does not change with detection current.
Regulating adjustable resistance RP, Vref can be changed so
that ǻt will vary flexibly with Vref changing. So,phase
compensation is realized.
(3) Method of phase-locked control
Phase-locked loop is compose of phase detector (PC1,
PC2, PC3), external RC passive filter and voltage-controlled
oscillators(VCO), which are seen in the phase-locked circuit
of 74HC4046 in Fig.6. Its center frequency of VCO depends
on the resistance of pin 11 and capacitance C3; Shifted
frequency is determined by the resistance of pin 12,which is,
when resistance decreaseing, shifted frequency will increase.
In the conditions of frequency1MHz and frequency-tracking
range 0.99MHz~1.1MHz, basing on the typical operation
curves of 74HC4046, resistance values of pin11,12 and value
of capacitor C3 are designed in Fig.6. Output pulse VCOout of
phase-locked loop and its input VC are sent into phase detector
PC2 to compare.When phase difference exists, a voltage
signal is created by PC2, which will control the input of pin 9.
And then make the frequency of VCO changing untill the
phase difference does not exist.
Fig.6 Control circuit of phase-locked loop
when main circuit comes into operation, coil current can
not be established immediately. PWM driveras also does not
generate, which results in that whole system can not self-start.
In order to solve this problem, it uses the features
of74HC4046 for system self-starting, seeing in Fig.6. It is
composed of R11, R12, C5 and D1. At the moment of
phase-locked loop powered on, capacitorC5 will be short.
Then,voltage of pin 9 is in its maximum and will decline from
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5. this value. At this time, frequency of VCOout falls down from
the maximum fmax to the minimum fmin. As long as the natural
resonant frequency of LC circuit is in this range, system will
enter into be locked automatically.
IV. EXPERIMENTAL VERIFICATION
Basing on the parameters in section B of part II, a
prototype of 1MHz frequency-tracking wireless power
transfer system by resonant coupling was produced.Power of
high frequency dual-tube LLC resonant inverter of class E is
about 30W. IRF840 is switches with smaller junction
capacitance. High speed integrated PWM driver UCC27325 is
used to driving MOSFET, whose driving ability is 4A. A lamp
with 25W/110V is used as receiving load. Differential
amplifier and comparator use LM318 and LM311 respectively,
both of which have high speed characters.High-speed
optocoupler 6N137 is used for isolating main circuit and
control circuit.
To verify frequency-tracking circuit, regulates size of
launch resonant inductance L1, making resonant frequency of
launch circuit changing in the trace range of phase-locked
loop. In difference frequency, comparator output pulseVC and
phase-locked loop output VCOout were measured as in
Fig.7.From the picture, it can be seen that VCOout has a good
accordance with VC in the trace range designed in this paper.
(a) f=0.993MHz (b) f=1.001MHz
(c) f=1.047MHz (d) f=1.103MHz
Fig.7 Effects of frequency-tracking at different frequencies
VD, VP, VC were also measured as shown in Fig.8, where it
can be seen that they are consistent with theory analysis.
Fig.8 Output voltages of detection,amplifier and comparator
At the same parameters, output voltages of load in
frequency tracking and no frequency tracking were seen in
Fig.9, where transmission distances are all 3cm and DC input
of inverter is 30V/1.0 A. In frequency tracking, from Fig.9(a),
output voltage is a sine wave,which effective value is 106.8V
and frequency was measured as 995.392kHz; In no frquency
tracking, from Fig.9(b),it has a little distortion,
where effective value is 68.7V and frequency is 1.000MHz.
From that, experimental result with frequency tracking is
better than that of no frequency tracking.
(a) Frequency tracking (b) No frequency tracking
Fig.9 Output voltage waveforms of receiving load
In addition, when transmission distance are 3cm, 5cm,
10cm, 15cm, 20cm respectively, their transmission
efficiency curves are shown in Fig.10 basing on the output
voltages measured in frequency tracking and no frequency
tracking. From Fig.10, it can be seen that efficiencies of
frequency tracking are all better than those of no frequency
tracking at the same transmission distance. It proves the
effectiveness of frequency tracking to avoid detuning once
again and follows up the theory analysis.
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6. Frequency tracking
No frequency
tracking
0
20
40
60
80
100
3 5 10 15 20
Distance(cm)
Efficiency(%)
Fig.10 Efficiency curves in different distance
V. CONCLUSIONS
This paper focuses on the theory analysis of resonant
coupling wireless power transfer, finding that efficiency has a
big drop when launch coil inductance changes a little but
varys smally when the receiving coil inductance changes the
same ratio. Based on this, frequency-tracking technology is
implemented on resonant coupling wireless power transfer
system. Experimental results verified that transmission
efficiency of frequency tracking is higher than that of no
frequency tracking, which sloved the problem of efficiency
droping when detuning. It is propitious to popularize and
apply this kind of technology furtherly.
ACKNOWLEDGEMENT
The authors wish to thank all of the reviewers for their
constructive comments, based on which the passage has been
improved.
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