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Resonant Converter with Coupling and Load Independent Resonance for
Omnidirectional Wireless Power Transfer Application
Junjie Feng, Minfan Fu, Qiang Li and Fred C. Lee
Center for Power Electronics Systems
The Bradley Department of Electrical and Computer Engineering
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061 USA
Abstract—Omnidirectional wireless power transfer (WPT)
system has been studied recently due to its better user
experience compared with directional WPT system. And this
paper focus on resonant converter study in omnidirectional
WPT system. At first, three challenges of resonant converter
design are identified: I. moving resonant frequency under
variable coupling condition; II. voltage controllability under
load change; III. complicated system control with coupling
between multiple coils. CLCL-LC resonant converter is
proposed to solve all the challenges and provide zero voltage
switching (ZVS) operation for primary device at resonant
frequency. A 6.78MHz CLCL-LC resonant converter for
omnidirectional WPT system is built and tested.
I. INTRODUCTION
Starting from Nicolas Tesla [1], wireless power transfer
(WPT) technology has been studied intensely in the past
century [2-8]. Up to now, the majority of near field inductive
coupling platforms are planar structure [2, 3]. In planar
directional WPT system, exact alignment between transmitter
coil and receiver coil is required. This characteristics is not
user-friendly. Therefore, a well-designed WPT system with
omnidirectional power transfer capability is highly attractive
in consumer electronics application [4-6]. The focus of these
work is how to utilize three dimensional (3D) transmitter coil
structure and modulation current to induce omnidirectional
magnetic field. Resonant converter study in omnidirectional
WPT system is lacked. In this paper, resonant converter
design for omnidirectional WPT system is studied.
One crucial challenge of resonant converter design in WPT
application is variable coupling between transmitter coil and
receiver coil. There is no physical connection between
transmitter and receiver coil. The position of receiver coil is
dependent on users, therefore, coupling coefficient between
transmitter coil and receiver coil is not fixed as conventional
transformer case. The most efficient operating point of
resonant converter is normally at the system resonant
frequency. And if the resonant frequency is dependent on
coupling, it’s difficult to operate at optimal point when
coupling between transmitter and receiver is variable.
Therefore, resonant converter with coupling independent
resonance is highly attractive in WPT application.
This work was supported primarily by the Power Management
Consortium (PMC) of Center for Power Electronics System.
The second challenge of resonant converter design in
wireless charging is voltage controllability under load
change. The lithium-ion battery in receiver device can be
equivalent to different load at different charging stage in its
charging profile. Therefore, extra control circuit is normally
needed to keep constant output voltage under load change. To
cope with this disadvantage, resonant converter with load
independent output voltage characteristics is preferred to
achieve good controllability [7,8].
The third challenge in omnidirectional WPT system design
is how to decouple multiple transmitter coils from control
point of view. In omnidirectional WPT system, multiple
transmitter coils structure is always needed to induce
magnetic field in different direction [4-6]. And coupling
between different transmitter coils makes the system control
much more complicated than single transmitter coil case.
Therefore, resonant converter, which can decouple electrical
information of different transmitter coils to some degree, is
advantageous in omnidirectional WPT system.
With these three challenges, series-series resonant
converter, which is very popular in wireless power transfer
research society, is first evaluated in section II [2,5,7,11].
And it cannot satisfy all these requirements simultaneously.
Then LLC resonant converter, the popular resonant converter
in power electronics society, is also evaluated in this section
[9]. In section III, CLCL-LC resonant converter is derived by
modifying traditional CLL resonant converter [10]. And
CLCL-LC resonant converter can solve all three challenges at
the same time. A 6.78MHz CLCL-LC resonant converter is
built and tested in section IV. Finally, conclusion is drawn in
section V.
II. SERIES-SERIES RESONANT CONVERTER AND LLC
RESONANT CONVERTER
Series-series resonant converter, which is named as seriesseries compensation topology in previous literature, is shown
in Fig. 1 [2,5,7,11]. Lp and Ls are the self-inductance of
transmitter coil and receiver coil respectively. Cp and Cs are
resonant capacitor and they are designed to resonate with Lp
and Ls respectively at same frequency. The equivalent circuit
of series-series resonant converter is shown in Fig. 2.
Transformer T model is utilized to represent coupled coil and
equivalent resistor Rrec represents diode bridge with
capacitive filter and load resistor. The voltage gain
characteristics in different coupling condition with variable
load resistance is shown in Fig. 3, with only fundamental
component of input voltage source considered.
Fig. 4 LLC resonant Converter
Fig.1 Series-series resonant converter
(a). k=0.4
(b).k=0.2
Fig.5 LLC voltage gain curve in different coupling
There is two resonant frequency
characteristics as shown in Fig.5.
Fig.2 Equivalent Circuit of SS resonant converter
(a). k=0.4
(b).k=0.2
Fig.3 Voltage gain curve of SS resonant converter in different coupling
There is three resonant frequency fo, f1, and f2 in gain
characteristics as shown in Fig.3:
f1=
1
2π (1 + k ) L p C p
(1)
f2=
1
2π (1 − k ) L p C p
(2)
1
1
=
2π L pC p 2π LsCs
(3)
fo=
As illustrated by Fig.3, resonant frequency f1 and f2 is
dependent of coupling condition and constant voltage
characteristics can be achieved at these frequency. Resonant
frequency fo is independent of coupling condition, but voltage
gain at fo fluctuates a lot under load change.
Therefore, series-series resonant converter cannot achieve
coupling independent resonance and load independent
voltage output characteristics simultaneously.
Other than series-series resonant converter, LLC resonant
converter, which is very popular in power electronics society,
is also evaluated in this section [9]. The coupled coil is
represented by cantilever model in LLC circuit diagram as
shown in Fig. 4 [12]. LLC voltage gain characteristics in
different coupling condition with variable load resistance is
shown in Fig. 5, with only fundamental component of input
voltage source considered.
f1
in
gain
1
2π Lk C p
(4)
1
2π ( L p + Lm )C p
(5)
fo=
f1=
f o,
In LLC resonant converter, resonant frequency fo is the
most efficient operation point with zero voltage switching in
wide load range [9]. In WPT application, this optimal point is
sensitive to coupling change because it’s determined by
leakage inductance. Therefore, it’s difficult to operate at this
point in variable coupling case. As for resonant frequency f1,
there is no constant voltage output characteristics although it
is independent of coupling. Therefore, LLC resonant
converter cannot satisfy all the requirement either. New
resonant converter topology is preferred to solve all the
challenges mentioned in introduction section.
III. CLCL-LC RESONANT CONVERTER
CLL resonant converter, which is LLC-like resonant
converter, is first evaluated in this section [10]. The circuit
diagram of CLL resonant converter is shown in Fig. 6, and
coupled coils is represented by transformer T model. In order
to identify the resonant frequency with voltage source output
characteristics in CLL resonant converter, equivalent circuit
with one branch in series with load is derived with
Thevenin’s theorem and Norton’s theorem as shown in Fig.
7[13].
Fig. 6 CLL resonant Converter
Fig. 9 CLL-LC resonant Converter
Fig. 7 Equivalent Circuit of CLL resonant Converter
In the equivalent circuit, the impedance of resonant
network in series with load is zero at resonant frequency with
voltage source output characteristics. According to this
criteria, the resonant frequency fo can be calculated as:
1
fo=
2
2π ( Lr //
2
N Lsk Lm + N Lsk L pk + Lm L pk
N 2 Lsk + Lm
)Cr
(6)
The voltage source resonant frequency fo is still related to
leakage inductance and magnetizing inductance, which is
dependent on coupling condition. Therefore, resonant
frequency with voltage source output characteristics in CLL
is also dependent of coupling. The voltage gain
characteristics in different coupling condition with variable
load of CLL resonant converter is shown in Fig. 8. Compared
with LLC resonant converter, resonant frequency fo in CLL is
less sensitive to coupling change.
(a). k=0.4
Fig. 10 Equivalent Circuit of CLL-LC resonant Converter
(b).k=0.2
Fig.8 CLL voltage gain curve in different coupling
In the equivalent circuit of CLL resonant converter, there
are only Lm and Lsk between input source and load at resonant
frequency of Lr, Cr due to their high impedance. Lm and Lsk in
series is equivalent to self-inductance (Ls) of receiver coil,
which is independent of coupling. Then if another capacitor
Cs is added to resonate with Ls at this frequency, a series
resonant frequency can be formed.
With Cs added in receiver side, CLL-LC resonant converter
is formed as illustrated in Fig.9. The equivalent circuit and
voltage gain characteristics in different coupling condition is
shown in Fig. 10 and Fig. 11. In Fig. 10, the power will go
through Lm, Lsk and Cs as the blue arrow due to high
impedance formed by Lr and Cr at their resonant frequency. If
Cs is designed to resonate with self-inductance Ls at this
frequency, then coupling independent fo with voltage source
output characteristics can be obtained. This can be verified in
Fig. 11, the resonant frequency fo is fixed at 6.78MHz in
different coupling condition.
1
1
fo=
=
(7)
2π Lr Cr 2π Ls Cs
(a). k=0.4
(b).k=0.2
Fig.11 CLL-LC voltage gain curve in different coupling
In the gain characteristics of CLL-LC resonant converter,
resonant frequency fo is in positive slope region. Therefore,
zero voltage switching (ZVS) operation of primary device
would be a great concern. To ensure ZVS operation,
inductive input impedance is necessary to let input current lag
switching node voltage [11]. The phase of input impedance
with different load in k=0.4 is plotted in Fig.12. As
demonstrated by Fig. 12, the phase of input impedance of
CLL-LC is negative, which means capacitive input
impedance. Therefore, there is no ZVS operation at fo in
CLL-LC resonant converter. This is detrimental for switching
device when operating at 6.78MHz. The system performance
also suffers due to large switching loss and EMI problem
associated with hard switching.
Fig. 12 CLL-LC’s Input impedance
To achieve ZVS operation, another capacitor Cp, is added
in CLL-LC resonant converter as shown in Fig. 13. The
criteria for designing Cp is making sure input impedance of
CLCL-LC resonant converter is inductive. One example
design is shown in Fig.14. The input impedance is always
inductive at fo with different load condition to achieve ZVS
operation in CLCL-LC resonant converter.
Fig.16 Current source mechanism of CLCL-LC resonant converter
Fig. 13. CLCL-LC resonant converter
Fig. 14 CLCL-LC’s Input impedance
The voltage gain characteristics of CLCL-LC resonant
converter in different coupling is shown in Fig. 15. As shown
in this figure, a coupling independent resonant frequency fo
with voltage source output characteristics is achieved with
ZVS operation. Therefore, the first two challenge mentioned
in section I is solved with CLCL-LC resonant converter.
In summary, CLCL-LC resonant converter can solve all
the challenges mentioned before:
1: coupling independent resonance frequency fo;
2: voltage source output characteristics at fo;
3: decoupled system control variable at fo.
Besides, ZVS operation can also be achieved in CLCL-LC
resonant converter at fo. Therefore, CLCL-LC resonant
converter is very promising circuit topology for
omnidirectional WPT application.
Other than CLCL-LC resonant converter, LCCL-LC
resonant converter as shown in Fig. 17, has very similar
characteristics. In the future, more resonant converter
topologies with similar characteristics will be studied in
systematic way.
Fig.17 LCCL-LC Resonant converter
(a). k=0.4
(b).k=0.2
Fig.15 CLCL-LC voltage gain curve in different coupling
In WPT application, the power received by receiver coil is
determined by transmitter coil current and coupling condition
between them [14-15]. Therefore, transmitter coil current is
important control variable in system control. And there are
multiple transmitter coils in omnidirectional WPT system.
The system control will be much complicated if transmitter
coil current is impacted by each other due to some
unintentional coupling. In CLCL-LC resonant converter, the
transmitter coil current has current source output
characteristics due to resonance of Lr and Cr. The mechanism
of constant transmitter coil current is explained by Fig. 16. In
Fig. 16, square wave voltage source in series with capacitor
can be equivalent to input current source in parallel with
capacitor. Due to Lr and Cr at resonant frequency fo, the
transmitter coil current is determined by this current source.
Since the transmitter coil current is decoupled between
different coils, the system control will be much simpler.
IV. EXPERIMENT RESULT
The experiment setup of our omnidirectional WPT system
is shown in Fig.18. There are multiple transmitter coils in our
platform. In transmitter side circuit, EPC 8009 half bridge
demo board is utilized to provide square voltage source for
resonant tank. In receiver side, diode bridge with capacitor
rectifies 6.78MHz AC power to DC power. The resonant tank
parameter of CLCL-LC converter is provided in Table I.
Fig.18 Experiment setup
The experiment waveform of CLCL-LC converter is
shown in Fig. 19. The pink waveform is 6.78MHz switching
node voltage waveform of half bridge, red waveform is the
input current waveform and blue curve is the output voltage
waveform after diode bridge. The waveform is very clear,
benefit from ZVS operation of primary device. Output
voltage is 5V, which can be directly connect to cell phone for
charging. The system efficiency from input to output is
around 60% with coupling coefficient of 0.15.
TABLE I
Switching frequency fs
Lr
Cr
Cp
Lp
Ls
Cs
R
6.78MHz
1uH
550pF
120pF
5.6uH
5uH
110pF
10Ω
Fig. 19 CLLC-LC’s Experiment waveform
IV. CONCLUSION
First, three challenges in resonant converter design for
omnidirectional WPT system are identified in section I. Then
series-series resonant converter and LLC resonant converter
are evaluated in section II. Both of them cannot solve all
three challenges at the same time. Starting from CLL
resonant converter, CLCL-LC resonant converter is proposed
to satisfy all the requirement. And more resonant topologies
with similar characteristics can be derived with our
methodology. Finally, a 6.78MHz CLCL-LC resonant
converter is built. ZVS operation at resonant frequency is
achieved and the system efficiency is around 60%.
ACKNOWLEDGMENT
This work was supported by the Power Management
Consortium in CPES, Virginia Tech.
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