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Battery Charger

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Highly-Efficient Battery Chargers with ParallelLoaded Resonant Converters
Ying-Chun Chuang Yu-Lung Ke Shun-Yi Chang

Department of Electrical Engineering, Kun Shan University, Tainan Hsien 71003, Taiwan, R.O.C.

Abstract—The well established advantages of resonant converters for battery chargers, including fast response, low switching losses, easy of the control scheme, simplicity of circuit configuration, and low electromagnetic interference (EMI), among others, have led to their increasing attraction. This work develops a highly efficient battery charger with a parallel-loaded resonant converter for battery charging applications to improve the performance of traditional switching-mode charger circuits. The charging voltage can be regulated by varying the switching frequency. The switching frequency of the parallel-loaded resonant battery charger was set at continuous conduction mode (CCM). Circuit operation modes are determined from the conduction profiles. Operating equations and operating theory are also developed. This study utilizes the fundamental wave approximation with a battery equivalent circuit to simplify the charger circuit analyses and presents an efficient, small-sized, and cost-effective switched-mode converter for battery chargers. A prototype charger with parallel-loaded resonant converter designed for a 12V-48Ah battery is built and tested to verify the analytical predictions. The maximum charging efficiency of the proposed battery charger topology is as high as 90.9%. Satisfactory performance is obtained from the experimental results. Keywords- battery charger, parallel-loaded resonant converter, softswitching converter.



Batteries are commonly used in renewable generation systems, electrical vehicles, communications systems and computer systems as electrical energy storage elements [1]– [7]. Although there are many kinds of batteries that can be used, the lead-acid battery can afford to store a reasonable amount of electrical energy and is adopted widely in the industrial field [8]-[11]. As the chemical reaction of the charging and discharging processes of the lead-acid battery will agitate the electrolyte and produce hydrogen gas, this will lead to reduction of the electrolyte and the stored-energy capability. Furthermore, the allowable usable life of the battery can also be reduced significantly. Therefore, a delicate designed battery charging system must be used to store the electrical energy of the battery. How to maintain the maximum capacity of lead-acid battery and extend its usable life is an important design problem for a charger, so many

charging schemes have been proposed to improve this problem. Hence, we need to develop a high performance charger circuit in a battery energy storage system (BESS) [12]-[16]. Traditionally, the charger can be classified in two categories: the linear-mode converters and the switch-mode converters [17]-[19]. The linear-mode converters offer the designer three advantages: simplicity in design, no electrical noise in the output, and low cost. While the linear-mode converter may be a simple way of converting a dc source to a lower dc voltage and charging a battery, the low efficiency of this charger circuit is a serious drawback for battery charging applications. An alternative method to improve the aforementioned problems is to employ a switch-mode converter that has the merits of high efficiency, small size and low cost. However, the switching devices consume power when they are turned on or off if they go through a transition when both voltage and current are nonzero. As the switching frequency increases, these transitions happen more often and the power loss in the device increases. To solve this problem, a new class of switch-mode converters known as softswitching resonant converter, has been thoroughly investigated in recent years [20]. The advantages of the resonant converter include the soft switching of power switches, leading to low switching losses, which in turn result in greater charger efficiency and higher switching and operating frequency. Consequently, the size and weight of the charger are reduced. Another benefit of soft-switching resonant converters over conventional switch-mode converters is the decrease in the harmonic content in the converter voltage and current waveforms. Therefore, when the resonant converters and conventional switch-mode converters are operated at the same power level and frequency, the resonant converters can be expected to have lower EMI problems. Accordingly, resonant converters have become the crucial technology for the majority of converters to improve power density, efficiency, reliability, and other performance characteristics. The life and capacity of the batteries depend on several factors, such as charge mode, maintenance, temperature, and age. Among these factors, the charge mode has a great impact on battery life and capacity. The batteries should be charged with current and voltage levels with low ripple. Therefore, a

978-1-4244-3476-3/09/$25.00 ©2009 IEEE

high performance battery charger is necessary in a BESS. In order to minimize the power losses, it is essential not to waste energy in the conversion process. In relation to the power electronics and associated control schemes, the main requirement is to guarantee that the charging system is efficient. Therefore, topologies with high frequencies and soft switching technique are used to reduce the charging current ripple and extend battery life. Among these existing soft switching converters, class D resonant converters is the most popular one because of its simplicity of circuit configuration, easy realization of the control scheme, low switching losses, and high flexibility for charging current regulation [21]-[22]. The class D resonant converters can be classified into three types, depending on the manner by which energy is extracted from the resonant tank. These three types are the series resonant converter, parallel resonant converter, and seriesparallel converter. Generally, the series-resonant charger is formed by an inductor, a capacitor, and a bridge rectifier. The alternating current (ac) through the resonant tank is rectified at the output terminals, then, the output direct current (dc) charges the battery. The series resonant converter seems to be suitable for the battery charger applications but it shows a low voltage variation with the switching frequency. Another shortcoming of the series-resonant charger is that the current carried by the power switches and resonant components is relatively loaded independently. The input impedance of the resonant topology is very low at the resonant frequency; this impedance equals to the sum of the parasitic resistances. As a result, a very high current will flow through the resonant circuit and the switches, causing large conduction losses in the equivalent series resistance and ripple voltage. In contrast to the series resonant converter, the parallel-loaded resonant converter is able to control the output voltage at no load by running at a frequency above resonance. The parallel-loaded resonant converter contains an inductive output filter and, thereby, the output current through the capacitor is low, reducing the conduction losses and the ripple voltage of the converter. Furthermore, the parallel-loaded resonant converter is inherently short circuit protected. Hence, the parallel-loaded resonant converter is very suitable for battery charger applications. Note also that the output voltage at resonance is a function of load and can rise to very high values at no load if the operating frequency is not raised by the regulator. On the other hand, the seriesparallel converter combines the best characteristics of the series resonant converters and parallel resonant converters. The resonant tank of this converter is the same as that of the parallel-loaded resonant inverter, except for an additional capacitor in series with the resonant inductor. The seriesparallel converter output can run over a wider input voltage and load ranges from no-load to full load. For the seriesparallel converter with capacitive output filter, the analysis of converter operation and the design of circuit parameters are complex because the capacitive output stage is decoupled from the resonant stage for a significant period during the switching cycle. Besides, the series-parallel converter cannot operate safely with a short circuit at switching frequency close

to the resonant frequency. Therefore, the charging stage of the series-parallel converter has not been minimized and simplified, resulting in bulky size and high cost in the applications of battery chargers. Comparing the pre-mentioned three different class D resonant converter topologies, it appears that the parallel-loaded resonant converter is the best topology for battery charging applications because of its many merits. In addition, for battery charging applications, the parallel-loaded resonant converter is generally recommended as energy conversion stage due to its simple circuitry and typical input characteristics. The parallel-loaded resonant converter can be operated either below resonance or above resonance. The operation of parallel-loaded resonant converter below resonance has many disadvantages, such as use of RC snubbers and dildt limiting inductances needed for fast recovery diodes across the switches, etc. All these disadvantages can be overcome by operating the parallelloaded resonant converter above resonance. Consequently, the work carried out here is for operation above resonance. This paper is organized as follows. Section II summarizes the circuit description and operation principles of the proposed parallel-loaded resonant converter for battery charger. In Section III, the operating characteristics are introduced. Section IV shows the electronic implementation of the parallel-loaded resonant converter for battery charger. Finally, conclusions of this work are given in Section V.

A. Circuit Description Among the different charging topologies, the softswitching scheme is the most attractive in recent years. Use of the soft-switching method has the advantages of reducing switching losses and extending the used life of the battery. In this paper, the proposed battery charger with parallel-loaded resonant converter is shown in Fig. 1. The two capacitors, C1 and C2, on the input are large and split the voltage of the input source. The elements Lr and Cr form the resonant tank. To facilitate the analysis, we assume that the power switching devices can be represented by a pair of bidirectional switches operated at a 50% duty ratio over a switching period T. For the half-bridge topology, each bidirectional power switch has an active power switch and an anti-parallel diode. The active power switches are driven by non-overlapping rectangularwave trigger signals vGS1 and vGS2 with dead time. Thus, we may represent the effect of the power switches by means of an equivalent square-wave voltage source with an amplitude equal to + Vs/2. The resonant capacitor voltage is rectified to obtain a dc bus. The dc bus voltage can be varied and closely regulated by controlling the switching frequency. Because the ac-to-dc power conversion, in this case, is achieved by rectifying the voltage across capacitor Cr, a large filtering inductance L is needed to minimize the loading effect of the output circuit and to ensure that the current through it is mostly dc. Consequently, the current input to the bridge

rectifier has constant amplitudes +Io and - Io, depending on whether the voltage vcr(t) is positive or negative, respectively. The frequency of this current waveform is the same as that of the switching frequency. With these observations, the parallelresonant converter can be modeled as a series LC circuit and a square-wave current source +Io in parallel with the resonant capacitor. The simplified equivalent circuit for the battery charger with parallel-loaded resonant converter is given in Fig. 2. iS ic1
v GS1


io ≈ I o iCo

S1 D1 vDS1


L i DR3

3) The characteristics of passive components are assumed to be linear, time-invariant and frequencyindependent. 4) The filter inductor L at the output terminal of the fullbridge rectifier is usually very large, and therefore the output current through the inductor L can be treated as a dc current in each switching cycle. 5) Active power switches S1 and S2 are on and off alternately, applying a square-wave voltage across the parallel-resonant circuit. If the load quality factor of the class-D half-bridge parallel-loaded resonant converter is sufficiently high, the resonant current, iLr, is sinusoidal.

+ +


vDR1 vcr +

ib +

DR1 v DR3

vGS1 ωO tO ωO tO
Vs 2

V S ic2

va is2 S2 D2 v


Cr vb i DR4 iDR2



o v Battery V Co



ωO t ωO t



DR4 v DR2



Fig.1 Parallel-loaded resonant converter for battery charger

ωO tO
Vs 2

ωO t

i Lr
Lr Cr v cr Io

iLr ωO t α β

ωO tO

Vs 2

vCr ωO tO ωO t

Fig.2 Simplified equivalent circuit of parallel-loaded resonant converter for battery charger

iS1 ωO tO ωO t

B. Circuit Operation Principles Figure 3 displays the idealized steady-state voltage and current waveforms in the class-D half-bridge parallel-loaded resonant converter for a switching frequency fs that exceeds the resonant frequency fo. Operation above resonance is preferred because the power switches turn on at zero current and zero voltage; thus, the freewheeling diodes do not need to have very fast reverse-recovery characteristics. During the positive half-cycle of the voltage across the resonant capacitor, the power is supplied to the battery through diodes Dr1and Dr2. During the negative half-cycle of the voltage across the resonant capacitor, the power is fed to the battery through diodes Dr3 and Dr4. Class-D half-bridge parallel-loaded resonant converter for battery charger is analyzed based on the following assumptions: 1) Switching elements of the converter are ideal, such that the decline in forward voltage in the on-state resistance of the switch is negligible. 2) The equivalent series resistance of the capacitance and stray capacitances is negligible.

iS2 ωO tO ωO t

iDR1 ωO tO ωO t

iDR3 ωO tO

ib ωO t2 ωO t5

ωO t

ωO t
D1 S1 D




ωO tO

ωO t1

T ωO t3


ωO t4 ωO ( T+tO )

Fig. 3 Idealized voltage and current waveforms

The steady-state operation of the parallel-load resonant charging circuit in one switching period can be divided into four modes.

Mode I: (between ωot0 and ωot2) The periodic switching of the resonant energy tank voltage between +Vs/2 and - Vs /2 generates a square-wave voltage across the input terminal. Since the output voltage is assumed to be a constant current Io, the input current to the full-bridge rectifier is +Io when vcr is positive and is -Io when vcr is negative. Hence, Fig. 4 presents the equivalent circuit of class-D half-bridge parallel-loaded resonant converter for the battery charger circuit in Fig. 2. This time interval ends when vcr reaches zero at ωot2. i Lr
Lr Cr vcr Io

Mode II: (between ωot2 and ωot3) This cycle starts at ωot2 when capacitor voltage vcr resonates from negative values to zero. At ωot3, before the half-cycle of the resonant current iLr oscillation ends, the switch S1 is forced to turn off, forcing the positive current to flow through the bottom freewheeling diode D2. Figure 5 displays the equivalent circuit. i Lr
Lr Cr vcr Io

Vs 2

Vs 2

Fig. 5 Equivalent circuit of Mode II

Fig. 4 Equivalent circuit of Mode I

Before ωot0, the active power switch S2 is excited, and conducts a current that equals the resonant tank current iLr. The active power switch S1 is turned on at ωot0. However, the resonant tank current iLr is negative and flows through the freewheeling diode D1. At the instant ωot1, the resonant tank current iLr reverses and naturally commutates from freewheeling diode D1 to the power switch S1. In this mode, the power switches are turned on naturally at zero voltage and at zero current. Accordingly, the active power switch is negative after turn-on and positive before turn-off. The initial condition of the capacitor Cr is Vco. Then, the instantaneous resonant inductor current and the voltage across Cr can be evaluated, where the angular resonance frequency 1 ωo = 2πf o = and the characteristic Lr Cr

The positive dc input voltage applied across the resonant tank causes the resonant current that flows through the power switch to go quickly to zero at ωot2. During this interval, the inductor current iLr is expressed as follows, where IL1 is the initial current in the inductor iLr. i Lr (t ) = I o + (I L1 − I o ) cos ω o (t − t 3 )
⎛ Vs ⎞ − Vc1 ⎟ ⎜ 2 ⎟ sin ωo (t − t3 ) +⎜ ⎜ Zo ⎟ ⎜ ⎟ ⎝ ⎠


impedance Z o =

Lr , respectively. Cr i Lr (t ) = − I o + (I o + I L0 ) cos ω o (t − t 0 )
⎛ Vs ⎞ − Vc0 ⎟ ⎜ 2 ⎟ sin ωo (t − t0 ) +⎜ ⎜ Zo ⎟ ⎜ ⎟ ⎝ ⎠

⎞ ⎛ Vs − Vc0 ⎟ ⎜ 2 ⎟ sin α I L1 = iLr (t = t 2 ) = − I o + (I o + I L0 ) cos α + ⎜ ⎟ ⎜ Zo ⎟ ⎜ ⎠ ⎝ The voltage vcr across the resonant capacitor Cr is given by Eq. (4), where Vc1 is the initial voltage across the capacitor Cr. V V ⎞ ⎛ ⎟ ⎜ v cr (t ) = s + ⎜Vc1 − s ⎟ cos ω o (t − t 3 ) 2 ⎝ 2 ⎠ (4) + Z o (I L1 − I o )sin ωo (t − t3 ) V V ⎞ ⎛ Vc1 = vcr (t = t 2 ) = s + ⎜Vc0 − s ⎟ cos α + Z o (I o + I L0 ) sin α 2 ⎝ 2 ⎠


Mode III: (between ωot3 and ωot5)

V V ⎛ v cr (t ) = s + ⎜Vc0 − s ⎜ 2 ⎝ 2

⎞ ⎟ cos ω o (t − t 0 ) ⎟ ⎠

+ Z o (I o + I L0 )sin ωo (t − t0 )


The current in the switches is turned on at zero voltage and zero current to eliminate turn-on losses, but the switches are forced to turn off a finite current, so turn-off losses may exit. Fortunately, small capacitors can be placed across the switches to act as snubbers to eliminate turn-off losses.

A turn-off trigger signal is applied to the gate of the active power switch S1. Then, the inductor current naturally commutates from the active power switch S1 to the freewheeling diode D2. Mode III begins at ωot3, when the diode D2 is turned on as displayed in Fig. 6, producing a resonant stage between inductor Lr and capacitor Cr. The inductor Lr and capacitor Cr resonate. Then, the inductor current iLr and the capacitor voltage vcr of the resonant circuit are given as Eq.(5) and Eq,(6), where Vc2 is the initial voltage across the resonant

capacitor Cr and IL2is the initial current of the resonant inductor, respectively. i Lr (t ) = I o + (I L 2 − I o ) cos ω o (t − t 3 )
⎞ ⎛ Vs + Vc2 ⎟ ⎜ ⎟ sin ωo (t − t3 ) ⎜ 2 + ⎟ ⎜ Zo ⎟ ⎜ ⎠ ⎝

V ⎛V ⎞ vcr (t ) = − s + ⎜ s + Vc3 ⎟ cos ωo (t − t5 ) 2 ⎝ 2 ⎠
+ Z o (I o + I L3 )sin ωo (t − t5 )



Then, the initial inductor current of this mode can be written as follows. I L3 = iLr (t = t5 ) = I o + (I L 2 − I o ) cos ωo (t5 − t3 )

V ⎞ ⎛V v cr (t ) = − s + ⎜ s + Vc 2 ⎟ cos ω o (t − t 3 ) ⎟ 2 ⎜ 2 ⎠ ⎝
+ Z o (I L 2 − I o )sin ωo (t − t3 )


⎛ Vs ⎞ ⎜ − Vc1 ⎟ 2 ⎟ sin β I L 2 = i Lr (t = t 2 ) = I o + (I L1 − I o ) cos β + ⎜ ⎜ Zo ⎟ ⎜ ⎟ ⎝ ⎠
V V ⎛ Vc 2 = v cr (t = t 2 ) = s + ⎜Vc1 − s ⎜ 2 ⎝ 2 ⎞ ⎟ cos β + Z o (I L1 − I o ) sin β ⎟ ⎠

Before ωot4, the trigger signal vgs2 excites the active power switch S2. When the capacitor voltage vCr changes direction, the rectifier diodes Dr1 and Dr2 are turned off at the instant ωot5 and Mode III ends. Figure 6 shows the equivalent circuit. i Lr
Lr Cr vcr Io

⎛ Vs ⎞ + Vc 2 ⎟ ⎜ 2 ⎟ sin ω o (t 5 − t 3 ) −⎜ ⎜ ⎟ Zo ⎜ ⎟ ⎝ ⎠ The following equation yields the initial value Vc 3 in the previous mode, to yield the following equation. V ⎛V ⎞ Vc3 = vcr (t = t5 ) = − s + ⎜ s + Vc 2 ⎟ cos ω o (t5 − t3 ) 2 ⎝ 2 ⎠ + Z o (I L 2 − I o ) sin ω o (t5 − t3 ) The inductor current and the capacitor voltage at t=t6 can be calculated as follows. I L 4 = iLr (t = t6 ) = − I o + (I o + I L3 ) cos ωo (t6 − t5 ) ⎛ Vs ⎞ + Vc3 ⎟ ⎜ 2 ⎟ sin ω o (t 6 − t 5 ) −⎜ ⎜ ⎟ Zo ⎜ ⎟ ⎝ ⎠ V ⎞ ⎛V Vc 4 = vcr (t = t6 ) = − s + ⎜ s + Vc3 ⎟ cos ωo (t6 − t5 ) 2 ⎝ 2 ⎠ + Z o (I o + I L3 ) sin ωo (t6 − t5 ) When the driving signal Vgs1 again excites the active power switch S1, this mode ends and the operation returns to mode I in the subsequent cycle. During the positive half-cycle of the capacitor voltage, the power is supplied to the battery through the output rectifier diodes DR1 and DR2. During the negative half-cycle of the inductor current, the power is supplied to the battery through the output rectifier diodes DR3 and DR4.

Vs 2

Fig. 6 Equivalent circuit of Mode III

Mode IV: (between ωot5 and ωot6) When the capacitor voltage vCr is negative, the rectifier diodes Dr3 and Dr4 are turned on with zero-voltage condition at the instant ωot5. Figure 7 depicts the equivalent circuit. i Lr
Lr Cr vcr Io

Vs 2

Figure 8 presents the rectifier stage of the class-D halfbridge parallel-loaded resonant converter for battery charger. The switching frequency of the active power switches is assumed to exceed the resonant frequency such that the resonant current is continuous. Given a large inductor filter at the output terminal, the charging current may be assumed to be constant. The charger circuit in Fig. 2 can be simplified to the schematic circuit shown in Fig. 8 to facilitate the analysis of the operation of the class-D half-bridge parallel-loaded resonant converter. In the full-bridge rectifier, when vcr is positive, diodes DR1 and DR2 conduct and vbo=vb and io=Io. When vcr goes negative, diodes DR3 and DR4 conduct,

Fig. 7 Equivalent circuit of Mode IV

Applying Kirchhoff’s law to Fig. 7 yields the inductor current iLr as Eq.(7) i Lr (t ) = − I o + (I o + I L3 ) cos ω o (t − t 5 )
⎛ Vs ⎞ + Vc3 ⎟ ⎜ 2 ⎟ sin ωo (t − t5 ) −⎜ ⎜ Zo ⎟ ⎜ ⎟ ⎠ ⎝


Equation (8) gives the voltage vcr of the resonant capacitor.

therefore, vbo=-vb and io=-Io. Accordingly, at any time, the dc-side output voltage of the full-bridge rectifier can be expressed as

ib (t ) =

∞ 4Io sin(nω t) ∑ n =1,3,5.... nπ


vbo = vb (9) = vb1m sin ω t Since the output current is assumed to be a constant Io, then the input current to the output full-bridge rectifier, vb, is Io/2 when vCr is positive and is –Io/2 when vCr is negative. vb1m iDR1 iDR3 DR3
+ + +

Equation (14) gives the peak value of the fundamental component of current ib. ib1 = 4I o


sin (ω t)



io ≈ I o iCo



The output resistance in this equivalent circuit of the parallel-loaded resonant converter is determined from the ratio of voltage to current at the input terminal of the full-bridge rectifier. Equation (15) thus defines resistance.
V π 2 Vo Re = b1m = ⋅ I b1 8 Io (15)

i b1

vDR1 Io ib +

DR1 vDR3


Re iDR4

v bo iDR2 DR2


vCo Battery Vo


DR4 vDR2

The relationship between input and output is approximated by ac circuit analysis using the fundamental frequencies of the voltage and current equations. Figure 9 plots the equivalent ac circuit. i Lr
Lr Cr Io

Fig. 8 Simplified equivalent output stage of the class-D half-bridge parallel-loaded resonant converter for battery charger

The class-D half-bridge parallel-loaded resonant converter for battery charger is analyzed based on the fundamental frequency of the Fourier series of the voltages and currents. Then, the output voltage vb of the full-bridge rectifier can be obtained by assigning an arbitrary time origin t=0 in Fig. 8 and then integrating vb(t)=vb1msinω t over onehalf period.
Vo =

Vs 2


vcr vb


Fig.9 Equivalent ac circuit of class-D half-bridge parallel-loaded resonant converter for battery charger

To achieve resonant operation, the resonant circuit must be underdamped. That is Re ≥ 2 Lr Cr (13)

1 π sin ωt ⋅d (ωt ) ∫ V π 0 b1m
2Vb1m (10)


Equation (11) gives the amplitude of the voltage vb and charging voltage vo Vb1m =


⋅ Vo


The ac-side current of the full-bridge rectifier can be expressed as if vcr > 0 ⎧+I ib (t ) = ⎨ o (12) −Io if vcr < 0 ⎩ and the transition between the two values is instantaneous due to the assumption of large filter inductor L. The error due to this approximation is very small when the switching frequency is higher than the resonant frequency. In the case of the square-wave current ib, the Fourier series contains the odd harmonics and can be represented as Eq. (13).

The input part of the class-D half-bridge parallel-loaded resonant converter for battery charger has a dc input voltage source Vs and a set of bidirectional power switches. The active power switches are controlled to generate a square-wave voltage va. Since a resonant circuit forces a sinusoidal current, only the power of the fundamental component is transferred form the input source to the resonant circuit. Therefore, only the fundamental component of this converter need be considered. Equation (14) defines a voltage transfer function of the parallel-loaded resonant converter. Vo = Vs 4 2 2 ⎛ ⎛X ⎞ X ⎞ π 2 ⎜1 − L ⎟ + ⎜ L ⎟ ⎜ ⎜ R ⎟ Xc ⎟ ⎝ ⎠ ⎝ e ⎠ (14)

The reactance XL and XC depend on the switching frequency. Accordingly, the output voltage can be regulated by changing the switching frequency of the converter. The normalized output voltage Vo/Vs is plotted as a function of fs/fo

at various loaded quality factors Q. This figure indicates that the half-bridge parallel-loaded resonant converter output voltage can be larger than the input voltage [21]. Therefore, the converter is quite appropriate for use in situations that require low input voltage and high output current, especially for middle power levels (as in this application, charging batteries), due to its simple circuitry and typical input characteristics.

which can be rewritten as
I V V ε L 2 = o { s β + 2Z o I o (cos β − 1) + ( s − Vco )[sin α − sin(α + β )] ωo 2 2 + Z o ( I o + I Lo )[cosα − cos(α + β )]} (19)

The following term is defined.
V V B ≡ { s β + 2 Z o I o (cos β − 1) + ( s − Vco )[sin α − sin(α + β )] 2 2

+ Z o ( I o + I Lo )[cos α − cos(α + β )]}



Q=5 Q=4 Q=3

Hence, the total energy that flows into the battery during the interval ωot0≦ ωot≦ ωot2 is determined by Eq. (21). I ε L = ε L1 + ε L 2 = o (B − A) ωo (21)



The energy from the input dc source during the interval


ωot0≦ ωot≦ ωot2 is given by Eq. (22).
V t −t ε S1 = s ∫ 02 0 i Lr (t )dt 2 =
1 1.2 1.4 1.6 1.8 2



f ωS = S ωO fO Fig 10 Normalized output voltage at various switching frequencies u =






Vs 2ω o

⎡ ⎛ Vs − Vc 0 ⎢− I oα + (I o + I Lo )sin α + ⎜ ⎜ Z ⎢ o ⎝ ⎣

⎤ ⎞ ⎟(1 − cos α )⎥ ⎟ ⎥ ⎠ ⎦


The following term is defined.
⎡ ⎤ ⎛ V − Vc0 ⎞ ⎟(1 − cos α )⎥ C ≡ ⎢− I oα + (I o + I Lo ) sin α + ⎜ s ⎟ ⎜ Z ⎢ ⎥ o ⎠ ⎝ ⎣ ⎦


ωot0≦ ωot≦ ωot2 is given by Eq. (15). t 2 −t ε L1 = ∫ 0 0 − I o vcr (t )dt

The energy that flows into the battery during the interval

The energy from the input dc source during the interval

ωot2≦ ωot≦ ωot3 is given by Eq. (24).
V t -t ε S2 = s ∫ 03 2 i Lr (t ) ⋅ dt 2

⎤ V ⎞ I ⎡V ⎛ = − o ⎢ s α + ⎜Vc0 − s ⎟ sin α + Z o (I o + I L0 )(1 − cos α )⎥ ωo ⎣ 2 2 ⎠ ⎝ ⎦

I =− o A ωo The following term is defined.


Vs − Vco Vs {I o β + [−2 I o + ( I o + I Lo ) cos α + ( 2 ) sin α ] sin β = 2ω Zo Vs − Vco (24) + [( 2 ) cosα − ( I o + I Lo ) sin α ](1 − cos β )} Zo The following term is defined. D ≡ {I o ( β − 2 sin β ) + ( I o + I Lo )[sin(α + β ) − sin α ] Vs − Vco +( 2 )[cos α − cos(α + β )]} (25) Zo Accordingly, the energy that is generated by the input dc source is given by Eq. (26). V (26) WS = WS1 + WS 2 = S (C + D ) 2ωo For a lossless system, these two energies are equal in the steady state. Therefore, Eq.(27) gives the output voltage. V C+D (27) Vo = S 2 B− A The ac sinusoidal wave on the load side of the charger filtered by the resonant tank is rectified by the full-bridge rectifier, which is then regulated by the L-C low-pass filter at

⎡V ⎤ V ⎞ ⎛ A ≡ ⎢ s α + ⎜Vc0 − s ⎟ sin α + Z o (I o + I L0 )(1 − cos α )⎥ (16) 2 ⎠ ⎝ ⎣2 ⎦

The energy that flows into the battery during the interval ωot2≦ ωot≦ ωot3 is given by Eq. (17).
3 ε L2 = ∫ 0 t −t 2 I o vcr (t ) dt

⎤ V ⎞ I ⎡V ⎛ = o ⎢ s β + ⎜Vc1 − s ⎟ sin β + Z o (I L1 − I o )(1 − cos β )⎥ (17) ωo ⎣ 2 2 ⎠ ⎝ ⎦

Substituting Eqs. (3) and (4) into the above equation yields Eq.(18).
⎡⎛ ⎤ I ⎧V V ⎞ ε L2 = o ⎨ s β + ⎢⎜Vco − s ⎟ cos α + Z o (I o + I Lo )sin α ⎥ sin β ωo ⎩ 2 2 ⎠ ⎣⎝ ⎦

⎛ Vs ⎞ − Vco ⎟ ⎜ 2 ⎟ sin α ](i − cos β )} (18) + Zo[− 2 I o + (I o + I Lo ) cos α ] + ⎜ ⎜ Zo ⎟ ⎜ ⎟ ⎝ ⎠

the output terminal. The regulated voltage and current charge the battery after they are filtered. The ripple following highfrequency filtering is smaller than that at low-frequency. Hence, a voltage and current more like pure dc are more useful for charging a battery. The parallel-load resonant charger is a charging device with a constant current as determined by the judgment of filtering type at output terminal. The most important advantage of the parallel-loaded resonant converter is that the maximum charging efficiency for the proposed converter operating above resonance can be obtained. This advantage makes the parallel-loaded resonant converter preferred configuration for battery charger applications.



CH1:10V/div CH2:10V /div Time:2.5μs /div Fig. 11 Trigger signals of power switches

The input of the proposed parallel-loaded resonant converter was connected to a system that comprised a dc source with an output voltage of 30V. A prototype of the battery charger with parallel-loaded resonant topology was established in a laboratory to verify the functional operations. The developed charger circuit is applied to a 12V, 48Ah leadacid battery. The conditions of the experiment were as follows: switching frequency fs=82 kHz, resonant frequency fo=80 kHz, charging current Io = 6.5A, charging voltage VBA = 15.5V, and the open circuit voltage of battery Voc = 11V. Under these operating conditions, the two parameters of the parallel-loaded resonant converter are as follows. Cr=1μF Lr=4μH The waveforms were measured using a digital multi-meter. Figure 11 plots the waveforms of the trigger signals VGS1, and VGS2. Figure 12 displays the voltage and current waveforms of the active power switch S1. Figure 13 depicts the voltage and current waveforms of the input terminal of resonant tank. Fig. 14 sketches the voltage waveform of resonant capacitor vcr and the current waveform of resonant inductor iLr. Figure 15 shows the input voltage and output voltage waveforms of the resonant tank terminals. Figure 16 illustrates the output voltage waveform of the resonant tank terminals and the input current waveform of the full-bridge rectifier. Figure 17 displays the voltage and current waveforms of the rectifier diodes DR1 and DR2. Figure 18 shows the charging voltage and current waveforms of battery terminal. From this figure we can see that the output is a smooth dc voltage and current, which is the ideal circuit for a battery charger. Figure 19 depicts the voltage variation curve of the battery. The terminal voltage of the battery rises from 10.5V to 15.5V in 400 minutes. Figures 20 and 21 plot the charging current and the charging efficiency, respectively. The charging current takes 400 minutes to maintain around 6.4A. The minimal and maximal efficiencies of the battery charging circuit are about 86.7% and 90.9%, respectively, and the average charging efficiency of the battery charger is 88.8%. vDS1 iS1

CH1:20V/div CH2:10A /div Time:2.5μs /div Fig. 12 Voltage and current waveforms of active power switch S1



CH1:20V/div CH2:10A /div Time:2.5μs /div Fig. 13 Voltage and current waveforms of the input terminal of resonant tank

v cr


CH1:20V/div CH2:10A /div Time:2.5μs /div Fig. 14 Voltage waveform of resonant capacitor and current waveform of resonant inductor

v a

15.5 14.5 13.5 12.5 11.5








400 (minutes)

Fig. 19 Battery voltage during charging period CH1:20V/div CH2: 20V /div Time:2.5μs /div Fig. 15 Input and output voltage waveforms of resonant tank
(A) 7.0 6.5


6.0 5.5







400 (minutes)

Fig. 20 Charging current during charging period
(%) 95 90 85 80 75 0 100 200 300 400 (minutes)

CH1:20V/div CH2: 10V /div Time:2.5μs /div Figure 16 The output voltage waveform of the resonant tank terminals and the input current waveform of the fullbridge rectifier

vDR1 ,vDR2

iDR1, i DR2

Fig. 21 Charging efficiency during charging period

CH1:20V/div CH2:10A /div Time:2.5μs /div Fig. 17 Voltage and current waveforms of rectifier diodes DR1 and DR2


V o


CH1:10V/div CH2:5A /div Time:2.5μs /div Fig. 18 Charging voltage and current waveforms of battery terminal

This work designed a parallel-loaded resonant converter with full-bridge rectifier for battery charger. The circuit structure is simpler and cheaper than other control mechanisms which require many components. The developed charger offers the advantages of zero-voltage switching, reduced switching losses, and increased charging efficiency. The charging current can be determined from the characteristic impedance of the resonant tank by the adjustable switching frequency of the converter, whereas the parallel-load resonant converter is applied to battery charger to yield the required charging conditions. The experimental results demonstrate the effectiveness of the developed charger. The maximum charging efficiency is 90. 9%, which is quite satisfactory when the highfrequency parallel-loaded resonant circuit is applied to a battery charger. Compared with conventional battery chargers, charging efficiency can be improved using the parallel-loaded resonant converter with full-bridge rectifier topology. Favorable performance is obtained at lower cost and with fewer circuit components.

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