Review

An Overview of Resonant Circuits for Wireless Power

Transfer
Chaoqiang Jiang 1,*, K. T. Chau 1, Chunhua Liu 2 and Christopher H. T. Lee 3
1 Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China;
ktchau@eee.hku.hk
2 School of Energy and Environment, City University of Hong Kong, Hong Kong, China; chualiu@eee.hku.hk

3 Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;

chtlee@mit.edu
* Correspondence: cqjiang@eee.hku.hk; Tel.: +852-28578617

Academic Editor: William Holderbaum

Received: 1 April 2017; Accepted: 27 June 2017; Published: 30 June 2017

Abstract: With ever-increasing concerns for the safety and convenience of the power supply, there
is a fast growing interest in wireless power transfer (WPT) for industrial devices, consumer
electronics, and electric vehicles (EVs). As the resonant circuit is one of the cores of both the
near-field and far-field WPT systems, it is a pressing need for researchers to develop a
high-efficiency high-frequency resonant circuit, especially for the mid-range near-field WPT
system. In this paper, an overview of resonant circuits for the near-field WPT system is presented,
with emphasis on the non-resonant converters with a resonant tank and resonant inverters with a
resonant tank as well as compensation networks and selective resonant circuits. Moreover, some
key issues including the zero-voltage switching, zero-voltage derivative switching and total
harmonic distortion are addressed. With the increasing usage of wireless charging for EVs,
bidirectional resonant inverters for WPT based vehicle-to-grid systems are elaborated.

Keywords: magnetic resonance; wireless power transfer; non-resonant converters; resonant

inverters; compensation networks; selective resonant circuits

1. Introduction
With the objectives to achieve no power cables, no sparking hazards, better convenience and
high flexibility, wireless power transfer (WPT) has attracted considerable attention in many
industrial applications and interdisciplinary areas [1–3]. As one of the most prominent technologies,
the WPT is changing the conventional usage of energy in daily life for human being. In addition, it
shows great potential for various applications, such as portable electronic devices [4], medical
instruments [5], non-accessible electronics [6], heating [7], electric vehicles (EVs) [8–10] including the
stationary charging [11], dynamic move-and-charge [12] and in-wheel motor drive [13].
Regarding to the power transmission distance, the WPT could be categorized into two major
groups, namely the far-field and the near-field transmission. The far-field transmission should be
mainly designed for low-power applications with lower priority of transmission efficiency. In
general, the far-field transmission is implemented with microwave or laser through a direct
line-of-sight transmission path [14]. Taking the efficiency and the human exposure safety into
consideration [15], the far-field transmission should not be a good option for power transmission in
our daily lives.
Due to the high efficiency and less radiofrequency exposure safety limit, near-field transmission
is a better option as compared to microwave or laser transmission [16]. In particular, the inductive
power transfer (IPT), capacitive power transfer (CPT) and permanent magnet coupling (PMC) are

Energies 2017, 10, 894; doi:10.3390/en10070894 www.mdpi.com/journal/energies

Energies 2017, 10, 894 2 of 20

the most popular near-field WPT technologies [17–19]. Moreover, based on the resonance of
magnetic and electric fields in the LC circuit, the use of magnetic resonant coupling (MRC) for IPT
has become dominant in the WPT system [20,21]. For the near-field transmission, it could be further
divided as two sub-groups, namely the short-range and mid-range transmissions. In general, the
short-range near-field WPT indicates that the transmitter and receiver are at a distance of a few
centimeters based on the two-coil approach. For these short-range applications, the operating
frequency of the resonant circuit is usually in the range of 10 kHz to several megahertz [22].
Normally, the energy dissipation in the power inverter increases with the operating frequency.
With the increase of the air-gap in the mid-range near-field transmission, less magnetic flux
linkage can be captured by the receiver coil [23]. By inserting intermediate resonators with the same
resonant frequency at the transmitter coil and the receiver coil, wide air-gap power transmission can
be facilitated efficiently [24,25]. Moreover, the structure of such coil arrays has been investigated to
strengthen the efficiency via stronger resonant coupling in the mid-range near-field applications [26].
Using a high operating frequency in excess of 10 MHz can improve the system quality factor, which
leads to higher transmission efficiency in the mid-range WPT system. However, such
high-frequency operation will substantially increase the switching losses in the driving circuits.
In previous review papers on WPT, they were focused on describing the historical development
of WPT from the late 1890s, from far field to near field and from the challenges to the advances
[16,27]. For better utilization of WPT in the mid-range transmission, the impedance matching issues,
relay and domino resonators topologies were summarized [28,29]. Due to the emerging market of
EVs, the wireless charging of EVs, including roadway powered EVs (RPEVs) and stationary
charging EVs (SCEVs), was placed in the spotlight to deal with green transportation [30]. Specifically,
several generations of the RPEVs, also dubbed as online EVs, were reviewed, with emphasis on their
core types, coil structures, and switching techniques [31]. For the SCEVs, different WPT systems,
including the IPT, CPT, and PMC, were also discussed [32]. However, a review of power electronic
circuitry for WPT is absent in literature. As the circuitry is one of the core technologies for WPT and
has undergone an active development in past decades, a comprehensive overview of this technology
is highly desirable.
The purpose of this paper is to give an overview of resonant circuits for the near-field WPT
system. The state-of-the-art technology of these resonant circuits, including the non-resonant
converters with a resonant tank and resonant inverters, will be reviewed and discussed. In the
meantime, the compensation networks and selective power transfer will also be presented.
In Section 2, the non-resonant converters with a resonant tank will be discussed. Then, various
resonant inverters including their topologies and operations will be discussed in Section 3. In Section
4, four basic compensation networks and two advanced compensation networks, namely the LCC
and LCL, will be presented. In Section 5, based on selective resonant circuits, typical selective WPT
applications will be discussed. The development trends of resonant circuits will also be revealed in
Section 6. Finally, a conclusion will be drawn in Section 7.

2. Non-Resonant Converters with Resonant Tank

There are numerous WPT applications as shown in Figure 1. Among them, the AC-DC-AC
power conversion is widely used in the primary side which involves an AC-DC converter in series
with a DC-AC converter (commonly called an inverter). The AC-DC converter serves to convert the
AC power from the grid to stable DC power. Then, the inverter produces high-frequency AC power
to feed the resonant circuit where it is classified as the resonant inverter as shown in Figure 2.
Obviously, this two-stage topology shows some drawbacks such as the costly and bulky DC-link,
and higher switching losses. In order to eliminate the DC-link, the direct one-stage AC-AC converter
is a good option for providing the desired high-frequency AC power.
Energies 2017, 10, 894 3 of 20

Wind Solar Fossil-fuel Hydro Nuclear

Power grid

DC-AC DC supply AC-DC

WPT system design WPT applications

 Human issues  Stationary EV charging
 Coil topologies  Roadway-powered EVs
 Resonant inverters  Implantable medical
 Magnetic materials  Smart home devices
 Flux flow directions  Portable devices
 Control methodologies  Flight UAV charging
 Wireless sensor networks
 Power flow dimensions
 Wireless heating
 Compensation networks  Wireless actuators
... ...

Figure 1. Typical applications of WPT.

Resonant circuits

Non-resonant converters with Resonant inverters with

resonant tank resonant tank

Single-phase AC- Three-phase AC- DC fed energy Class E Class D Class DE Class EF n Current fed Bidirectional
AC converter AC converter injection converter push-pull inverter
Parallel Cascaded

Figure 2. Classification of resonant circuits.

2.1. Single-Phase AC-AC Converter

The single-phase AC-AC converter is shown in Figure 3a, which is based on free oscillation and
energy-injection control. This one-stage converter can simplify the controller design with a low
switching frequency without reverse power flow [33]. The switches S1 and S2 are mainly used to
control the power flow, and the S3 and S4 operate to constitute the resonant loop during the S1 and S2
OFF.
The number of oscillations can be controlled by the switching frequency of S1 and S2. In the
meantime, the ratio of the nominal resonant frequency to the switching frequency can be used to
control the power flowing into the resonant circuit. A variable-frequency method can be applied to
follow the circuit resonance, which makes the switching operation achieve zero-current switching
(ZCS) easily [34]. This topology takes the definite advantage that the DC link and its bulky
energy-storage element can be eliminated [35]. However, current sags around the zero-crossing
points of the AC source are inevitable.

D1
CP CS
M
S1 D3
S3 RL
VAC
VP
LP LS
S4
S2 D4
Resonant Receiver
One-stage tank
D2
converter

(a)
Energies 2017, 10, 894 4 of 20

M
SA1 SB1 SC1 CP

LP LS RL

CS
SA2 SB2 SC2

AC-AC matrix converter with Resonant Receiver

reverse-blocking switches tank

(b)

CP CS
M
LD
RL
VDC CD
S1
D1 LP LS

Energy injection converter Resonant tank Receiver

(c)

Figure 3. Non-resonant converters with resonant tank for WPT. (a) Single-phase AC-AC converter;
(b) Three-phase AC-AC converter; and (c) DC fed energy injection converter.

2.2. Three-Phase AC-AC Converter

Normally, the single-phase AC-AC converter suffers from great current sags around the AC
source zero-crossings, especially under a high ratio of the nominal resonant frequency to the
switching frequency. For some three-phase AC source applications, a similar one-stage AC-AC
converter can be structured based on the same principle of free oscillation and energy injection
control.
The three-phase AC-AC converter as shown in Figure 3b incorporates a matrix converter with
six reverse-blocking switches and one regular MOSFET or IGBT. The operation includes eight modes
with six energy-injection modes and two free oscillation modes [36,37]. Basically, the energy
injection control is the same as that of the single-phase AC-AC converter. Aiming to avoid the
voltage zero-crossing, the LC tank terminals are altered between the most positive and the most
negative input phases.
Significantly, by controlling the energy injected into the LC tank accumulated in each half-cycle
of the resonant current until reaching the reference value, the output current, voltage and power
regulation control can be realized [38]. Naturally, this converter inherits the advantages of the
single-phase AC-AC converter, but with better current sags and higher power capability. Since the
number of power switches increases, the control difficulty rises inevitably.

2.3. DC Fed Energy Injection Converter

Another non-resonant converter, the DC fed energy injection converter, is depicted in Figure 3c
where the resonant circuit is used as an intermediate energy storage element [39]. The energy is
injected into the LC tank when the switch S1 is turned off. At the beginning, the switch S1 is turned
on to charge the inductor LD with the current increasing at the rate of VDC/LD for several cycles of the
LC resonance [40]. After the S1 is turned off, the energy is injected into the CD so that the LC tank
performs oscillations via the CP, LP and D1.
Unlike the conventional inverter, the operating frequency of the LC tank is no longer
determined by the switching frequency. This topology takes the advantage that the switching
frequency can be lower than the nominal resonant frequency of the LC tank, which helps reduce the
switching losses. However, the overall transmission efficiency and power level are limited by the
energy reflow during the damping oscillation; consequently, the output voltage is unstable.
The three mentioned non-resonant converters boost the resonant frequency equivalently with a
lower switching frequency for some switches. A comparison of these three non-resonant inverters is
Energies 2017, 10, 894 5 of 20

shown in Table 1. However, they suffer from a common drawback that high current ripples in the
resonant tank are inevitable during the energy oscillation.

Table 1. Comparison of non-resonant converters with resonant tank for WPT system.

Single-Phase Three-Phase DC Fed Energy

Title?
AC-AC Converter AC-AC Converter Injection Converter
 Reverse blocking switches  Energy injection
 Structure of matrix converter
 Switching synchronization  Energy oscillation
 Switching synchronization
 Zero current switching operation  Switching technique at
 Energy injection control
 Free oscillation time high-Q regimes
 Zero current switching operation
 Current sags  Energy reflow problems
 Free oscillation time
Factors  Input voltage variation  Zero voltage switching
 Current sags
 Switching frequency turn-off control
 Input voltage variation
 Output voltage ripple (around  Output voltage ripple
 Switching frequency
input AC voltage zero crossings) (determined by switching
 Output voltage ripple (around
 Current, voltage and power time)
input AC voltage zero crossings)
regulation control  Transient response analysis
 Three-phase AC supply  DC power supply
 Single-phase AC supply  No DC link  Only one switch
 No DC link  Medium power level  Low power level
 Less bulky energy storage  Less bulky energy storage  1 switching mode
Features
 4 modes of operation  More switches  Low control difficulty
 Low power level  8 modes of operation  Eliminating the impact of
 Medium control difficulty  Lower electromagnetic interference loading in the transmitter
 High control difficulty circuit

3. Resonant Inverters with Resonant Tank

For most WPT applications, the one-stage AC-AC converter with resonant tank is not suitable
mainly due to its high control difficulty and unstable output. Thus, the DC-link buffer is necessary to
improve the system’s power level, stable output, and flexibility. With the help of DC-link, the
resonant circuit can be driven at the resonant frequency by using resonant inverters.

3.1. Class E Resonant Inverter

The Class E resonant inverter topology is the same as the DC fed energy injection converter but
employing a special switching technique as shown in Figure 3c. Normally, the Class E resonant
inverter is driven at the nominal resonant frequency of LC tank without DC energy injection. The
simplified single switch structure is famous for the high efficiency at high operating frequency and
high power level to several kilowatts [41]. By optimizing the circuit parameters properly, it is
guaranteed that the transistor S1 is switched ON with zero-voltage switching (ZVS) and zero-voltage
derivative switching (ZVDS), and therefore the switching losses and stresses are reduced
significantly [42,43].
For high power level WPT applications, this topology can control the output power via
manipulating the duty cycle control or varying the switching frequency with an efficiency sacrifice
[44]. However, the main disadvantage of the Class E resonant inverter is its high peak voltage across
the switch, reaching up to 3.5 times DC voltage at a duty cycle of 0.5. Consequently, less power will
be produced by the Class E inverter than other resonant inverters with the same voltage and current
stresses. For some high DC power supply occasions, the high peak voltage may result in efficiency
drop or permanent damage to the inverter

3.2. Class D and Class DE Resonant Inverters

Due to easy system parameter design, the Class D and full-bridge Class D resonant inverters are
most popular for practical WPT systems [45], as shown in Figure 4a,b respectively. The Class D
inverter employs two switches and a series-resonant LC tank, which results in lower switching
frequency than the Class E inverter. It should be noted that the peak voltage across the switch in the
full-bridge Class D is as twice higher as the DC supply voltage. Thus, this topology can output twice
Energies 2017, 10, 894 6 of 20

the voltage to feed the LC resonant circuit, especially suitable for low DC supply WPT applications.
Obviously, the Class D resonant inverter with two switches has lower voltage stress across the
switch since the peak voltage is as high as the DC supply.
By combining the lower switching stress of Class D and high efficiency of Class E [46], the Class
DE topology is created as shown in Figure 4c. The Class DE inverter is quite similar to the Class D
inverter, only with two additional parallel-connected capacitors [47]. Thus, the Class DE inverter
realizes low switching voltage within the DC supply to reduce the switching losses. Furthermore,
the shunt capacitors enable high-frequency operation with ZVS and ZVDS.

S1

VDC CD CP CS
M
RL
S2
LP LS

Class D Resonant Receiver

half-bridge tank

(a)

S3 CP CS
S1 M
RL
CD
VDC LP LS

S2 S4
Resonant Receiver
tank

Class D
full-bridge

(b)

S1 CP1

CD CP CS
VDC M
RL
CP2
S2
LP LS

Class DE Resonant Receiver

inverter tank

(c)

CP
LD
CS
M
VDC RL
S1 C2
C1 LP LS
L2
Receiver

Class EFn inverter Resonant tank

(d)
Energies 2017, 10, 894 7 of 20

Figure 4. Resonant inverters with resonant tank for WPT. (a) Class D resonant inverter; (b)
Full-bridge Class D resonant inverter; (c) Class DE resonant inverter; and (d) Class EFn resonant
inverter.

3.3. Class EFn Resonant Inverter

In order to inherit the advantages of the Class E inverter and reduce the number of switches, an
inverter topology called the Class EFn was proposed as shown in Figure 4d. It consists of a choke
inductor LD, shunt capacitor C1, and two parallel-connected LC resonant tanks, where the L2C2
resonant tank is tuned to n times the operating resonant frequency f0 of LPCP [48]. Typically, the
subscript n is set to two, namely the EF2 resonant inverter. Hence, the peak voltage stress across the
switch can be reduced to 2 times the input DC supply. Besides, the class EF2 inverter has a higher
power output capability and efficiency than the Class E and other EFn inverters with the same
voltage stresses on their switches.
Comparing with the Class D inverter or full-bridge Class D inverter, the Class EF2 inverter can
be designed to achieve ZVS and ZVDS, which makes the single switch operate efficiently up to the
megahertz range [49]. Other two benefits of this topology are that the switch’s drain voltage and the
output current do not contain a second harmonic component, and has an improved electromagnetic
interference performance. However, the corresponding feasibility is limited by the requirement of
additional resonant tank.
A detailed design method of Class EF2 inverter for WPT has been presented in [50]. Both the
primary inverter and the secondary rectifier adopt the Class EF2 inverter topology and operate at 6.78
MHz and 27.12 MHz respectively, hence offering improved efficiency and lower total harmonic
distortion (THD).

3.4. Parallel and Cascaded Inverters

In order to provide higher and more flexible output levels for WPT, the parallel inverter with
two full-bridge Class D inverters was proposed as shown in Figure 5a. Each full-bridge Class D
inverter is controlled by the clamped-mode switching technique, which results in controllable
output voltage, rather than by the duty cycle control [51]. By taking the advantage that power is
distributed evenly by the parallel inverters, the heat dissipation becomes easier than the single
inverter topology. Moreover, active research is being investigated on the conduction angle and
phase delay of the two full-bridge Class D inverters to improve the system stability. Furthermore,
this topology has high fault-tolerant ability. When one of the parallel bridge is in the open circuit
fault, another bridge can still make the system work properly [52]. However, if the fault type is short
circuit, there is no option for the LC resonant operating properly except shutting down the whole
system.
By the same token, the output power can be enhanced under the same switching capacity by the
cascaded inverter [53] as shown in Figure 5b. The cascaded structure has saliency preponderance in
terms of reducing the voltage stress and alleviating the harmonic contamination of the output
voltage, namely, with a lower THD. Furthermore, more operating modes can be achieved with
higher flexibility in the cascaded structure; therefore the switching losses can be reduced effectively
[54].
So far, the topology combining the parallel and cascaded topologies has yet not been
investigated. The fault-tolerant ability will be further improved with more complicated switching
control technique and higher cost.
Energies 2017, 10, 894 8 of 20

CP CS
S1A S3A S1B S3B M
RL
CD
VDC LP LS

S2A S4A S2B S4B

Resonant tank Receiver

H-bridge A H-bridge B

(a)

H-bridge A

S1A S3A
CD
VDC
CP CS
S2A S4A M
RL

LP LS
S1B S3B
CD Resonant Receiver
VDC tank

S2B S4B

H-bridge B

(b)

LDC1 LDC2
CP CS
M
RL
VDC
D1 CS2 D2 LP LS
CS1

Resonant Receiver
S1 S2 tank
R1 R2
Current-fed push-pull topology

(c)

CP CS
M
VDC CD
Battery

LP LS CB

Resonant Receiver
Primary of tank Secondary of
bidirectional inverter bidirectional inverter

(d)

Figure 5. Parallel and cascaded inverters. (a) Parallel full-bridge Class D resonant inverter; (b)
Cascaded full-bridge Class D resonant inverter; (c) Current-fed push-pull resonant inverter; and (d)
Bidirectional resonant inverter.

3.5. Other Resonant Inverters

(1) Current-fed push-pull resonant inverter: In general, the switches in the inverter should be
driven by externally controlled signal for WPT applications. Recently, an autonomous current-fed
push-pull resonant inverter with ZVS operation was proposed in which the driving signal was
generated automatically without external gate control and kept running at the steady state [55], as
shown in Figure 5c. In this topology, the startup should be analyzed, since the two switches S1 and S2
tend to turn ON simultaneously once the DC power supply is turned ON. In a practical system, the
Energies 2017, 10, 894 9 of 20

two switches would not act at the identical speed due to some parameter differences, hence once a
switch is ON first, the other one will be turned OFF. However, it is hard to control which switch
should be ON first in the startup process. Moreover, the RC circuit with CSi and Ri should be
calculated carefully to make sure that the requirements of switching frequency and circuit losses are
fulfilled. By using two or more autonomous push-pull resonant inverters with various phase shifts, a
rotating magnetic field can be generated for rotary WPT applications [56].
(2) Bidirectional resonant inverter: With the EV wireless charging becoming more and more
popular, combining the vehicle-to-grid (V2G) or vehicle-to-home (V2H) technology [57] and the
WPT technique is a viable solution for shaving the peak demand in the power grid. In order to
charge or discharge EVs in the V2G or V2H system, a current-source bidirectional resonant inverter
was developed in [58]. A typical bidirectional resonant inverter for WPT is shown in Figure 5d, and
the corresponding wireless charging scheme for V2G and V2H operations is shown in Figure 6. In
order to improve the power level and the fault tolerant ability, a bidirectional WPT system
consisting of two resonant inverters was also proposed with optimized control method [59,60]. Such
structure makes it more effective and suitable to modify the power flow direction.

Wind Solar Fossil-fuel Hydro Nuclear

Power grid

V2G V2H

Residential Office House House

areas buildings building building

Bidirectional Bidirectional Bidirectional

inverter inverter inverter

Compensation Compensation Compensation

network network network

EV EV charging/ EV charging/
charging/discharging discharging discharging

Figure 6. Wireless charging scheme for V2G and V2H operations.

3.6. Comparison of Resonant Circuits

The aforementioned resonant circuits including the non-resonant converters with resonant tank
and the resonant inverters with resonant tank are qualitatively compared as shown in Table 2. This
comparison focuses on assessing some key features for WPT, namely the voltage stress, power level,
high frequency operation, control difficulty, switching loss, and effective cost.

Table 2. Comparison of resonant circuits for WPT.

High
Voltage Control Switching Effective
Type Power Level 2 Frequency
Stress 1 Difficulty Loss Cost
Operation 3
Single-phase AC-AC
Low Low Medium Medium Low Medium
converter
Three-phase AC-AC
Medium Medium Medium High Medium Medium
converter
DC fed energy
Low Low High Medium Low Low
injection converter
Class E resonant
High High High Low Low Low
inverter
Energies 2017, 10, 894 10 of 20

Medium Low
Class D resonant (half-bridge) (half-bridge)
Medium Medium Medium 4 Low
inverter High Medium
(full-bridge) (full-bridge)
Class DE resonant
Low Medium High Medium Low Medium
inverter
Class EF2 resonant
Low Medium High Low Low Low
inverter
Current-fed
push-pull resonant Medium Medium Medium NA Low Low
inverter
Parallel resonant
Medium High Medium High High High
inverter
Cascaded resonant
Medium High Medium High High High
inverter
1 Voltage stress can range from 1 to 3.5 times voltage supply. 2 Power level can range from 50 W to
20 kW. Generally, medium power level represents power higher than 300 W but lower than several
kilowatts, and high power level represents power higher than several kilowatts. 3 Generally, the
switching frequency for wireless power transfer is above several dozen kHz, which is in the
medium frequency range. In addition, the high frequency can reach several megahertz for some low
power applications and far field transmission. 4 Normally, the switching loss with series resonant
tank is higher when compared with a parallel resonant tank.

4. Compensation Networks
Considering the relationship between the mutual inductance and the coil leakage inductance
both in the primary and secondary resonant circuits, various compensation networks are required to
optimize the system performance. There are four basic compensation networks, namely the
series-series (SS), series-parallel (SP), parallel-series (PS) and parallel-parallel (PP) topologies [61–63]
as shown in Figure 7. Moreover, the LCC-compensation and LCL-compensation topologies are
developed, as shown in Figure 8, aiming to improve the system performance.

M M
CP CS CP
CS
VS RL VS RL
LP LS LP LS

SS topology SP topology

(a) (b)

M M CS

CP CS CP
VS RL VS RL
LP LS LP LS

PP topology PS topology

(c) (d)

Figure 7. Basic compensation networks.

Energies 2017, 10, 894 11 of 20

S1 S2 CS
M
VDC LSP CP
CPP
RL
LP LS
S3 S4
SP LCC topology

Inverter

(a)

S1 S2 CPP
M
VDC CSS
CP CSP RL
LP LS
S3 S4
PP LCC topology

Inverter

(b)

S1 S2
LR M
VDC RL
CP CS
LP LS
S3 S4
PP LCL topology

Inverter

(c)

Figure 8. LCC and LCL compensation networks. (a) SS LCC topology; (b) PP LCC; and (c) PP LCL
topology.

4.1. Compensation Topologies in Secondary

The equivalent resonant circuits of the secondary side are shown in Figure 7a,b with series and
parallel compensa-tions, respectively, where LP, CP represent the primary coil and primary
compensated capacitor, LS, CS represent the secondary coil and secondary compensated capacitor,
and RL is the load resistor. The series equivalent resistances of coils and capacitors are neglected to
facilitate the analytical derivation. When the current in the secondary coil is IS and in the primary
coil is IP, the reflected impedance from the secondary to the primary can be expressed:
 jMI S  2 M 2
Zr   (1)
IP ZS

where M is the mutual inductance related to the magnetic coupling coefficient k,

M  k LP LS (2)
The impedance of the secondary side ZS depends on the compensation topology, which can be
expressed as:
 1
 jLS  jC  RL (for series)

ZS  
S

1
(3)
 jL  (for parallel)


S
j  C S  1 / RL

Normally, the operating frequency is equal to the resonant frequency of the secondary side
given by 0  1 / LS CS .
Energies 2017, 10, 894 12 of 20

According to (1), the reflected impedance is written as the reflected resistance and reactance as
listed below:
 0 2 M 2
For series-secondary Re (Z r ) 
 RL (4)
Im (Z )  0
 r

 R M2
Re (Z r )  L 2
For parallel-secondary  LS
 (5)
Im (Z )   0 M
2

 r
 LS

Generally, the power transferred from the primary side to the secondary side can be regarded
as the power consumed by the real component of the reflected impedance, it yields:
P  Re (Z r )I P
2
(6)
From (6), it can be observed that the energy received by the secondary side will decrease
quadratically with the mutual inductance; equivalently, the increase of transmission distance.

4.2. Compensation Topologies in Primary

The series- and parallel-compensated primary networks are shown in Figure 7a,c, respectively.
The equivalent load impedance regarded by the AC power source is determined by various
combinations of the primary and secondary topologies. For the series-compensated primary system,
the load impedance ZP can be expressed as:
1
Z P  jLP   Zr (7)
jCP

For the parallel-compensated primary system, the load impedance ZP can be expressed as:
1
ZP  (8)
jCP  1 /( jLP  Z r )

In order to minimize the VA rating of the power supply, normally, the resonant circuits work at
the resonant state, where the real component of the load impedance ZP should be zero.
Consequently, the zero-phase-angle (ZPA) between the output voltage and current can be achieved.
Meanwhile, the ZPA operation will cause more switching loss in the inverter using the
hard-switching technique. Practically, the primary side often shifts away from the nominal resonant
frequency slightly to realize a small portion of reactive power, which makes the inverter switches
operate in ZVS or ZCS.
A comparison of four basic topologies is shown in Table 3. It should be noted that the reflected
impedance of the series-compensated secondary includes no reactance. As a result, the nominal
resonant frequency in the series-compensated primary will not be affected by the mutual inductance
and load variations [63]. In the SP and PP compensated topologies, the mutual inductance variation
will shift the nominal resonant frequency of the primary. The high tolerance of SS compensated
topology with the system parameters is the main reason for being the most popular choice [64].

Table 3. Comparison of four basic topologies.

Topology Reflected Resistance Re (Z r ) Reflected Reactance Im (Z r ) Secondary Quality Factor (QS)

0 M
2 2
0 LS
SS 0 RL
RL
RL M 2
0 M 2
RL
SP -
LS
2
LS 0 LS

0 2 M 2 0 LS
PS 0 RL
RL
Energies 2017, 10, 894 13 of 20

RL M 2 0 M 2 RL
PP -
LS
2
LS 0 LS

0 2 M 2 0 LS
LCC-S * 0 RL
RL
RL M 2 0 M 2 RL
LCL-P * -
LS
2
LS 0 LS

* The compensated capacitor CPP and LSP should be calculated depending on the load and output
voltage of inverter. Normally, the primary is operated at or near the resonant frequency of the
secondary.

Based on the scattering parameter, the transmission efficiency can be calculated as ƞ = |S21|2,
where the network is matching at both ports [65]. According to this expression, the transmission
efficiency declines rapidly with the increasing distance. The selection of various compensations was
analyzed in details in [66], demonstrating that the SS topology is preferred when ω2M2/RL<M2RL/LS2
whereas PP topology is preferred when ω2M2/RL>M2RL/LS2. The features of different topologies are
listed in Table 4.

Table 4. Comparison of various compensation topologies for WPT.

Topology Features Topology Features

 High tolerance of system parameters
 No reflected reactance  Reflected reactance relating to
SS SP
 Most popular topology for practical operating frequency
topology topology
applications  Be able to supply a stable current
 Preferred at ω2M2/RL < M2 RL/LS2
 Reflected reactance relating to
PS  No reflected reactance PP
operating frequency
topology  Be able to supply a stable voltage topology
 Preferred at ω2M2/RL > M2 RL/LS2
 Constant high frequency currents flowing into  Reflected reactance can be tuned
the primary coil regardless of the existence of out by series connected inductor
secondary  Continuous or discontinuous
 Lower power transfer efficiency current operation
 Better misalignment tolerance with appropriate  Remain high efficiency at
LCC matched parameters LCL low-quality factor Q
topology  Highly sensitive to capacitor and inductor topology  Variable frequency control to
parameters close to UPF
 Can achieve ZCS and ZPA operation at the  Eliminate VAR loading for high
same time power applications
 LCC SP compensation topology typically for  Low tolerance ability of
multi-load WPT misalignment

4.3. LCC-Compensation Topology

In order to achieve more flexible operations, such as ZVS, ZCS and ZPA, the LCC compensation
was proposed as shown in Figure 8a,b by tuning the compensation network parameters. In the LCC
symmetrical T-type compensation network, shown in the primary side of Figure 8a, constant current
or constant voltage can be achieved practically regardless of the impedance of the load [67].
The LCC compensation topology is typically designed for a multi-load WPT system, such as the
RPEV system [68]. In order to achieve lower turn-off losses and switching stresses, the near ZCS
with ZPA was derived for the LCC compensation topology by inserting the series-connected
inductor LSP and parallel-connected capacitor CPP [69]. The parameters design procedure with ZCS
operation is unlike the conventional topology. First, the nominal primary power PP and resonant
frequency ɷ0 of the secondary side should be determined. Then, the primary coil current IP and the
parallel compensation capacitor CPP can be calculated as:
Energies 2017, 10, 894 14 of 20

PP
IP  (9)
RF
IP
CPP  (10)
w0Vinverter

where RF is the reflected resistance from the secondary, Vinverter is output voltage of the inverter.
Consequently, the series-connected inductor LSP and the resonant capacitor CP can be expressed
as:
1
LSP  (11)
0 2C PP

CPP
CP =
LP / LSP - p 2 / 8 (12)

The PP LCC topology was proposed to improve the transmission distance [70]. The maximum
transmission efficiency can be harvested within a certain distance by changing the ratio of series-
and parallel-connected compensation capacitors. Nevertheless, the main drawback is that the system
performance is sensitive to parameter changes.

4.4. LCL-Compensation Topology

Moreover, the reflected capacitive reactance in the PP topology can be tuned out by the
series-connected inductor as shown in Figure 8c. There are several advantages for the LCL
compensation networks. One is that the converter for LCL only supplies the active power required
by the load when the system is under the resonant frequency. The LCL resonant tank is supplied by
a DC voltage source, it leads to a major advantage that the output current is directly related to the
input voltage supply and independent of the load variation. These make the controller design more
simplified and easy to regulate the output power. Besides, the LCL topology can be operated with
continuous and discontinuous current [71]. Furthermore, inverter working close to unity power
factor (UPF) can be achieved by variable frequency control method.
As the LCL topology remains high transmission efficiency at low-quality factor Q, it is more
preferred in high-power applications. In order to achieve operation closer to the UPF, normally, an
additional series compensation capacitor can be added in series with LR as shown in Figure 8c to
compose the LCLC topology, which help the circuit block DC current from flowing in the inductor.
However, the inductor saturation is easy to occur in high power applications due to heavy and high
frequency current [72]. A comparison of efficiency versus Q with various topologies is shown in
Figure 9. It can be observed that the efficiencies of LCL and LCLC topologies are higher than the LC
topology. In this LCL topology, the major concern is that the receiver coil should be fixed relative to
the transmitter coil, namely, the system has low tolerance ability of position variations.

100

90
Efficiency (%)

80

70 LC
LCL
LCLC
60
0 0.4 0.8 1.2 1.6 2
Quality factor

Figure 9. Comparison of efficiencies of LC, LCL and LCLC topologies.

Energies 2017, 10, 894 15 of 20

5. Selective Resonant Circuits

Based on the variation of the compensation capacitor, different resonant frequencies can be
tuned or controlled in a real-time mode. Thus, the resulting selective resonant circuits can be utilized
for some specific applications such as the targeted WPT.

5.1. Selective Wireless Power Transfer

Currently, the WPT system for multiple receivers has been widely used to power all devices
simultaneously [73]. However, for some practical applications, the selective wireless power transfer
is required to feed the targeted receiver [74,75]. In the LC resonant circuit, if the operating frequency
deviates from the nominal resonant frequency, there will be an obvious great impedance presented
in the circuit. Thus, the transmission efficiency will be very low. By using this characteristic, the
power flow path can be diverted to the desired receiver, where distinct resonant frequencies are
designed for multiple receivers.
As shown in Figure 10, the primary circuit has a transmitter (Tx) coil in series with a capacitor
array which includes various compensation capacitors while each receiver circuit has a receiver (Rx)
coil in series with a proper compensation capacitor. After the targeted receiver is predetermined
with a certain resonant frequency, the primary circuit calculates the corresponding capacitance to
suit the resonant frequency of the targeted receiver. Thus, the targeted receiver has the strongest
coupling with the primary to pick up the energy [76].

Capacitor array CS1

CP0
RL1
Rx coil
RP CP1 M

AC CP2 CS2
Tx coil
power
CPn RL2
Rx coil
M

Figure 10. Selective WPT system.

5.2. Energy Encryption

Based on the principle of selective WPT, the transmitted energy can be encrypted to facilitate
targeted WPT. In public WPT applications, especially for EV charging, the energy security issue is
extremely important to the electricity provider. No matter what the charging type is, the stationary
or dynamic charging, the energy transferred to the unauthorized receiver should be eliminated.
Figure 11 shows a recently developed energy encrypted WPT system, which consists of the
primary, resonant and secondary coils [77]. The capacitor arrays are used to adjust the resonant
frequency dynamically. Consequently, the energy can be delivered to the authorized receiver
effectively while avoiding the energy transferred to the unauthorized receiver. In order to avoid
code-breaking, chaotic encryption has been developed [78]. When several receivers are coupled to a
single transmitter, the bifurcation phenomena might occur due to the varying reflected impedance
in the primary. Under different compensation topologies, the bifurcation behaves different
characteristics. Thus, an appropriate resonant converter should be determined to satisfy the desired
performance. According to various requirements on power level, loss, cost and operation frequency,
the corresponding resonant converter should adopt an appropriate control strategy. For some
practical applications, jitter control and hysteric control methods were developed to regulate the
power flow [79]. Nevertheless, this energy encryption technique suffers from discontinuous
resonant frequency variations due to discrete capacitances of the capacitor array. Also, there are
slight power variations in the presence of frequency variations, which need additional control for
power regulation.
Energies 2017, 10, 894 16 of 20

Primary coil Resonant coil Secondary coil

CP3 CR3 CS6

CS5
CP2 CR2
CS4
CP1 CR1
CS3
CS2
Power
supply
Load CS1

Figure 11. Energy encrypted WPT system.

5.3. Online Load Identification

Another application based on switching resonant capacitors is the steady-state load
identification online [80]. For some practical applications such as battery charging, the condition of
load changes with the charging process. Being aware of the real-time load is the precondition to
adjust the operation frequency or other system parameters for achieving the maximum efficiency or
power. The online load identification circuit is shown in Figure 12, where the CP1 is the main
resonant capacitor series-connected with the coil LP, and the CP2 series-connected with switches S1
and S2 is a dynamic capacitor [81]. The CP1 and LP are to determine the nominal resonant frequency
ɷ0 at the normal mode of operation. The CP2 is to shift the nominal resonant frequency to ɷ2 at the
load identification mode of operation. Based on these two modes of operation, the online
measurable parameters can be used to calculate the load and mutual inductance:
(VP  I P 2 RP )(1 / (2 CS )  2 LS )
RL  (13)
Im Z r 2 I P 2

Im Z r 2  (RL  RS )2  (1 / (ω2 CS )  ω2 LS )2 
M (14)
ω2 2 (1 / (ω2 CS )  ω2 LS )

where Zr2 and IP2 are the reflected impedance and the primary coil current in the identification mode,
respectively.

CP2 CS
S1 S2 M
VP
Controller CP1
LP LS RL

RP RS

Figure 12. Online load identification circuit.

6. Development Trends
Although fruitful achievements have been made on the development of resonant circuits,
resonant inverter topologies and control techniques of the WPT system, there are still many research
topics worth being studied:
(1) To develop targeted WPT for electric machines without requiring any energy storage, power
electronic circuitry or sensory circuitry in the machine side.
(2) To devise optimized compensation networks or auxiliary circuits, aiming to suppress the power
crosstalk between the targeted and nontargeted receivers.
(3) To utilize the parasitic capacitance in the coil to realize the resonant circuit, hence achieving
high resonant frequencies for long-distance WPT.
Energies 2017, 10, 894 17 of 20

(4) To design high-frequency inverters up to the MHz range while retaining low switching loss,
simple gate-driving requirement and reasonable cost.
(5) To develop high-power high-efficiency bidirectional inverters for WPT, hence realizing V2G
operation without physical contacts.
(6) To integrate wireless power transfer and wireless information transfer into the same channel to
form the wireless power and information transfer (WPIT), hence manipulating power and
control simultaneously.

7. Conclusions
In this paper, an overview of the resonant circuits for WPT has been presented, with emphasis
on non-resonant converters, resonant inverters, compensation networks and the selective resonant
circuits. Their characteristics and key features, such as the operation frequency, power level,
fault-tolerant ability, ZVS, ZCS and ZVDS are summarized with advantages and drawbacks. It is
anticipated that the high frequency and high power level inverters for WPT system will be the major
research direction such as in the long-distance targeted WPT or the emerging WPT for EV charging.

Acknowledgments: This work was supported by a grant (Project No. 201511159096) from The University of
Hong Kong, Hong Kong Special Administrative Region, China.

Author Contributions: Chaoqiang Jiang and K. T. Chau carried out the analysis and wrote this paper. Chunhua
Liu and Christopher H. T. Lee helped obtain the literatures and made important suggestions.

Conflicts of Interest: The authors declare no conflict of interest.

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