Bidirectional DC Converter with Frequency Control: Analysis and Implementation

: In this paper, a direct current (dc) converter with the abilities of bidirectional power transfer and soft switching characteristics is studied and implemented. The circuit schematic of the developed dc converter is built by a half-bridge converter and a center-tapped rectifier with synchronous rectifier. Under forward power transfer, a half-bridge circuit is controlled to regulate the low-voltage side at a stable value. For backward power transfer, a center-tapped rectifier with synchronous rectifier is regulated to control the high-voltage side at the desired voltage value, and the half-bridge circuit is operated as a voltage doubler rectifier. Active power devices are operated at zero-voltage switching using a series resonant technique on the high-voltage side with frequency modulation and inductive load operation. The practicability of the developed converter is established from experiments with a laboratory prototype circuit.


Introduction
To reduce air pollution and climate change, renewable energy sources with power electronic conversion have been demanded and developed in recent years. Bidirectional power converters [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] have been developed for alternating current (ac) to direct current (dc) conversion and dc-dc conversion. In references [1][2][3][4][5][6][7], ac-dc bidirectional power converters are employed between an ac power source and dc bus voltage, and dc-ac bidirectional power converters are widely employed in ac drive systems. Direct current to dc bidirectional power converters [8][9][10][11][12][13] are demanded for battery-based storage systems. Bidirectional power flow dc converters with dual full-bridge circuit topology or half-bridge circuit topology were proposed to deliver power between high-voltage side dc bus and low-voltage side storage devices. Duty cycle control is normally used in dual full-bridge converters to control load voltage and attain soft switching characteristics. The main drawbacks of dual full-bridge converters are complicated control scheme and high conduction losses under low effective duty cycle case with high circulating current. Resonant techniques with a frequency-control scheme have been developed in modern power converters with high circuit efficiency due to wide load range of soft switching characteristics. The dual full-bridge resonant converter in reference [14] achieves soft switching characteristics in forward power transfer. However, the soft switching characteristics were lost in this circuit topology in backward power transfer due to the non-symmetric circuits in both power flow operations. The circuit topologies of dual full-bridge resonant converters in references [15][16][17] are symmetric for both forward and backward power transfer. Therefore, active switches can achieve soft switching at turn-on instant to eliminate switching loss. However, one parallel inductor is used on the high-voltage side. The circulating current in this parallel inductor will result in additional power loss when the circuit is operated under forward power transfer.
A soft switching resonant converter is studied and implemented in this paper to have the benefits of bidirectional power transfer ability, soft switching characteristics and less power devices.
The proposed circuit is constructed by a half-bridge circuit on the primary-side and a center-tapped rectifier on the secondary-side. The LLC resonant circuit with frequency control is used on high-voltage side to control secondary-side voltage, reach soft switching turn-on for main power devices. To achieve same LLC resonant characteristics for both forward and backward power transfer, a parallel inductor is connected between half-bridge leg and split input capacitors on the high-voltage side. Under forward power transfer, power switches on half-bridge circuit are controlled by frequency-modulation to generate a square voltage input to the resonant tank and regulate low-side voltage V L . Power switches on a center-tapped rectifier with synchronous switches are operated as synchronous rectifiers for reducing the conduction losses on the low-voltage side. Under forward power flow, the parallel inductor on the high-voltage side is disconnected (ac power switch is off) to reduce the power loss on this parallel inductor. When the proposed circuit is worked under backward power transfer, the parallel inductor is used on the high-voltage side to achieve LLC resonant characteristics. Power switches on the center-tapped rectifier are controlled to create a square voltage waveform on the primary-side of the isolated transformer and regulate high-side voltage V H . Finally, experimental results are presented to verify the feasibility of the proposed circuit. Figure 1a shows the circuit schematic of a conventional resonant converter with s center-tapped rectifier on the secondary side. The main drawback in Figure 1a is high conduction loss on secondary-side rectifier diodes for high current output. In order to reduce conduction loss on secondary-side diodes, synchronous switches instead of fast recovery diodes are used on the secondary-side as shown in Figure 1b. For achieving bidirectional power control, Figure 2a demonstrates the circuit structure of the developed bidirectional dc converter. The circuit differences between the proposed converter and conventional unidirectional half-bridge resonant converter shown in Figure 1b are one ac switch S and inductor L m1 used in the proposed circuit to achieve LLC resonant behavior for both forward and backward power transfer. Therefore, the advantages of a conventional unidirectional LLC resonant converter all exist in the proposed circuit. Half-bridge circuit is employed on the high voltage side to clamp voltage ratings of power semiconductor devices Q 1 and Q 2 at V H . A center-tapped circuit topology with synchronous rectifier is employed on the secondary-side to reduce the conduction loss on the low-voltage side. An ac switch S is adopted on the primary-side to achieve resonant behavior when the adopted circuit is operated at backward power transfer. Figure 2b demonstrates the equivalent circuit of the developed circuit operated at forward power transfer from V H to V L . AC switch S is turned off. C r , L r and L m2 are operated to achieve soft switching turn-on of Q 1 and Q 2 . Power devices Q 3 and Q 4 on the low-voltage side operate as the synchronous switches. Therefore, the conduction losses on Q 3 and Q 4 are reduced at the low-voltage and high-current sides. Figure 2c illustrates circuit structure of the studied circuit operated at backward power transfer from V L to V H . At backward power transfer condition, power switch S is closed and Q 1 and Q 2 are turned off. L m1 , C r and L r are resonant. Thus, main switches Q 3 and Q 4 are turned on under zero-voltage switching. Table 1 gives the basic comparison between the proposed circuit and the conventional bidirectional dc-dc converters. It can be observed that the proposed converter has less component counts. A soft switching resonant converter is studied and implemented in this paper to have the benefits of bidirectional power transfer ability, soft switching characteristics and less power devices. The proposed circuit is constructed by a half-bridge circuit on the primary-side and a center-tapped rectifier on the secondary-side. The LLC resonant circuit with frequency control is used on highvoltage side to control secondary-side voltage, reach soft switching turn-on for main power devices. To achieve same LLC resonant characteristics for both forward and backward power transfer, a parallel inductor is connected between half-bridge leg and split input capacitors on the high-voltage side. Under forward power transfer, power switches on half-bridge circuit are controlled by frequency-modulation to generate a square voltage input to the resonant tank and regulate low-side voltage VL. Power switches on a center-tapped rectifier with synchronous switches are operated as synchronous rectifiers for reducing the conduction losses on the low-voltage side. Under forward power flow, the parallel inductor on the high-voltage side is disconnected (ac power switch is off) to reduce the power loss on this parallel inductor. When the proposed circuit is worked under backward power transfer, the parallel inductor is used on the high-voltage side to achieve LLC resonant characteristics. Power switches on the center-tapped rectifier are controlled to create a square voltage waveform on the primary-side of the isolated transformer and regulate high-side voltage VH. Finally, experimental results are presented to verify the feasibility of the proposed circuit. Figure 1a shows the circuit schematic of a conventional resonant converter with s center-tapped rectifier on the secondary side. The main drawback in Figure 1a is high conduction loss on secondaryside rectifier diodes for high current output. In order to reduce conduction loss on secondary-side diodes, synchronous switches instead of fast recovery diodes are used on the secondary-side as shown in Figure 1b. For achieving bidirectional power control, Figure 2a demonstrates the circuit structure of the developed bidirectional dc converter. The circuit differences between the proposed converter and conventional unidirectional half-bridge resonant converter shown in Figure 1b are one ac switch S and inductor Lm1 used in the proposed circuit to achieve LLC resonant behavior for both forward and backward power transfer. Therefore, the advantages of a conventional unidirectional LLC resonant converter all exist in the proposed circuit. Half-bridge circuit is employed on the high voltage side to clamp voltage ratings of power semiconductor devices Q1 and Q2 at VH. A centertapped circuit topology with synchronous rectifier is employed on the secondary-side to reduce the conduction loss on the low-voltage side. An ac switch S is adopted on the primary-side to achieve resonant behavior when the adopted circuit is operated at backward power transfer. Figure 2b demonstrates the equivalent circuit of the developed circuit operated at forward power transfer from VH to VL. AC switch S is turned off. Cr, Lr and Lm2 are operated to achieve soft switching turn-on of Q1 and Q2. Power devices Q3 and Q4 on the low-voltage side operate as the synchronous switches. Therefore, the conduction losses on Q3 and Q4 are reduced at the low-voltage and high-current sides. Figure 2c illustrates circuit structure of the studied circuit operated at backward power transfer from VL to VH. At backward power transfer condition, power switch S is closed and Q1 and Q2 are turned off. Lm1, Cr and Lr are resonant. Thus, main switches Q3 and Q4 are turned on under zero-voltage switching. Table 1 gives the basic comparison between the proposed circuit and the conventional bidirectional dc-dc converters. It can be observed that the proposed converter has less component counts.

Forward Power Flow
If the converter is operated at forward power transfer as shown in Figure 2a, the power flow is from VH terminal to VL terminal. Power device S is controlled at the OFF state. Power switches Q1 and Q2 are regulated with frequency control to create a square voltage vab on the high-voltage side. Power switches Q3 and Q4 are operated as the synchronous switches to decrease conduction loss compared

Forward Power Flow
If the converter is operated at forward power transfer as shown in Figure 2a, the power flow is from V H terminal to V L terminal. Power device S is controlled at the OFF state. Power switches Q 1 and Q 2 are regulated with frequency control to create a square voltage v ab on the high-voltage side. Power switches Q 3 and Q 4 are operated as the synchronous switches to decrease conduction loss compared to the rectifier diodes with high voltage drop when diodes are conducting. The ON/OFF state of the synchronous switches are based on the current direction on the low-voltage side. Then a square voltage waveform can be created on the primary-side of the isolated transformer. L m2 , L r and C r are the magnetizing inductance, series resonant inductance and series resonant capacitance, respectively. Due to the inductive impedance of the resonant tank on the high-voltage side, as shown in Figure 3a, the soft switching characteristics of main switches Q 1 and Q 2 are achieved. The basic pulse-width to the rectifier diodes with high voltage drop when diodes are conducting. The ON/OFF state of the synchronous switches are based on the current direction on the low-voltage side. Then a square voltage waveform can be created on the primary-side of the isolated transformer. Lm2, Lr and Cr are the magnetizing inductance, series resonant inductance and series resonant capacitance, respectively. Due to the inductive impedance of the resonant tank on the high-voltage side, as shown in Figure 3a, the soft switching characteristics of main switches Q1 and Q2 are achieved. The basic pulse-width modulation signals for forward power transfer operation are illustrated in Figure 3a. There are six operation modes under fr (series resonant frequency) > fsw (switching frequency). On the other hand, four operation modes per switching cycle can be observed if fsw > fr. Figure 4 illustrates the equivalent topological circuits for each mode of operation under forward power transfer. The principles of operation are discussed in what follows.

v ab
Thus, Q1 is turned on under zero voltage after t0. In mode 1, iLr > iLm2 so that iQ3 < 0 and DQ3 conducts. Thus, Q3 is forced to turn on. Due to low turn-on resistance Ron, the conduction losses on Q3 are reduced. In this mode, the voltage vab = VCH1 = VH/2 and vLm2 = nVL. The magnetizing current iLm2 will increase with the current slope nVL/Lm2. In mode 1, the current variation on Lm2 is calculated as ΔiLm2,1 = nVLΔt10/Lm2 where Δt10 is time duration in this mode. Cr and Lr are resonant under vab = VH/2, vLm2 = nVL and the series resonant frequency conducts. Thus, Q 1 is turned on under zero voltage after t 0 . In mode 1, i Lr > i Lm2 so that i Q3 < 0 and D Q3 conducts. Thus, Q 3 is forced to turn on. Due to low turn-on resistance R on , the conduction losses on Q 3 are reduced. In this mode, the voltage v ab = V CH1 = V H /2 and v Lm2 = nV L . The magnetizing current i Lm2 will increase with the current slope nV L /L m2 . In mode 1, the current variation on L m2 is calculated as ∆i Lm2,1 = nV L ∆t 10 /L m2 where ∆t 10 is time duration in this mode. C r and L r are resonant under v ab = V H /2, v Lm2 = nV L and the series resonant frequency f r = 1/2π √ C r L r . If f r > f sw , then i DQ3 will fall to zero. Thus, the next mode will go to mode 2. On the other hand, the circuit operation will go to mode 3 if f r < f sw .
Mode 2 [t 1~t2 ]: At time t 1 , i Q3 falls to zero. Then Q 3 is forced to turn off. i Lr will flow through Q 1 , C r , L r , L m2 and C H1 . Due to C H1 > C r , L r , C r and L m2 are resonant in mode 2 with v ab = V H /2 and resonant frequency f p = 1/2π C r (L r + L m2 ). Mode 2 ends at the half of the switching frequency t = T sw /2.
is charged (discharged) by the resonant current i Lr . The zero-voltage switching condition of power device Q 2 is derived as.
where C eq = C Q1 = C Q2 . Based on the switching frequency, magnetizing inductance and turn-ratio, the maximum magnetizing current can be calculated as: From the given dead time, switching frequency, and input and output voltages, the magnetizing inductance L m2 is obtained as: Mode 4 [t 3~t4 ]: At t 3 , v CQ2 = 0. Since i Lr (t 3 ) > 0, the antiparallel diode D Q2 is forward biased. Thus, Q 2 will turn on at zero voltage switching. Due to i Q4 (t 3 ) < 0, Q 4 turns on to reduce the conduction loss on Q 4 . In this mode, v ab = −V H /2, v Lm2 = −nV L /2, and i Lm2 decreases. The current variation on L m2 is ∆i Lm2,4 = nV L ∆t 34 /L m2 where ∆t 34 is the time duration in mode 4. L r and C r are resonant with If f r > f sw , the next step of the circuit operation will go to mode 5. Otherwise, the circuit operation will go to mode 6.
Mode 5 [t 4~t5 ]: At time t 4 , i Q4 = 0 and synchronous switch Q 4 turns off. The resonant inductor current i Lr will flow through Q 2 , C r , L r , L m2 and C H2 . L r , C r and L m2 are resonant with input voltage v ab = −V H /2. Mode 6 [t 5~Tsw + t 0 ]: At t 5 , power device Q 2 turns off. Due to i Lr (t 5 ) < 0, capacitor C Q1 (C Q2 ) is discharged (charged). The soft switching condition of power device Q 1 is the same as power device Q 2 . The charge (discharge) time of C Q2 (C Q1 ) is sufficiently quick and can be ignored. At time T sw + t 0 , v CQ1 = 0 and the circuit operations of the developed converter are completed.
other hand, the circuit operation will go to mode 3 if fr < fsw.
Mode 2 [t1 ~ t2]: At time t1, iQ3 falls to zero. Then Q3 is forced to turn off. iLr will flow through Q1, Cr, Lr, Lm2 and CH1. Due to CH1 > Cr, Lr, Cr and Lm2 are resonant in mode 2 with vab = VH/2 and resonant where Ceq = CQ1 = CQ2. Based on the switching frequency, magnetizing inductance and turn-ratio, the maximum magnetizing current can be calculated as: From the given dead time, switching frequency, and input and output voltages, the magnetizing inductance Lm2 is obtained as: Mode 4 [t3 ~ t4]: At t3, vCQ2 = 0. Since iLr(t3) > 0, the antiparallel diode DQ2 is forward biased. Thus, Q2 will turn on at zero voltage switching. Due to iQ4(t3) < 0, Q4 turns on to reduce the conduction loss on Q4. In this mode, vab = −VH/2, vLm2 = −nVL/2, and iLm2 decreases. The current variation on Lm2 is ΔiLm2,4 = nVLΔt34/Lm2 where Δt34 is the time duration in mode 4. Lr and Cr are resonant with vab = −VH/2, vLm2 = −nVL and If fr > fsw, the next step of the circuit operation will go to mode 5.
Otherwise, the circuit operation will go to mode 6.   Although there are several approaches [18][19][20][21] to generate square voltage waveforms on the ac side of the converter leg, fundamental frequency analysis [22] is the most useful approach to obtain voltage gain of the proposed circuit under different switching frequency. Based on the switching states of power devices, two square voltage signals are observed on high-voltage side vab and vLm2. Cr, Lr and Lm2 work as a circuit filter to eliminate harmonic signals. Therefore, vab and vLm2 can be treated as ac voltage's only fundamental frequency to simplify the circuit analysis. The fundamental root mean square (rms) voltages vab,rms and vLm2,rms are calculated as 2 / H V π and 2 2 / L V n π . The primary-side fundamental resistance is obtained as   . Based on (5), the switching frequency is derived with the given high voltage value VH, low voltage value VL, inductor ratio K1 = Lm2/Lr and equivalent load resistance Rac2.

Reverse Power Flow
When the proposed converter is worked as backward power transfer to transfer power from VL to VH (Figure 3b), power devices Q3 and Q4 on the low-voltage side work as active switches to control primary-side voltage VH. For having the circuit characteristics of LLC resonant converter, ac switch S is ON so that Lm1 is connected between points a and b. Based on the amplitude of |iLr| and |iLm1|, the anti-parallel diodes DQ1 and DQ2 are ON or OFF and the quasi-square voltage waveform is generated on voltage vab. Likewise, a square waveform is also generated on the primary-side voltage vLm2 based on the ON/OFF state of Q3 and Q4. Under reverse power transfer operation, Lr, Cr and Lm1 are resonant and the input impedance from the low-voltage side should be an inductive load. Then, Q3 and Q4 can be operated under zero-voltage condition such that the switching loss is lessened. The key pulsewidth modulation signals under backward power transfer operation are demonstrated in Figure 3b. The equivalent topological circuits corresponding to mode operations are demonstrated in Figure 5.
Mode 1 [t0 ~ t1]: The voltage on CQ3 is decreased to zero voltage at time t0. Since iQ3 < 0 and iLr > 0, the body diode DQ3 of MOSFET Q3 conducts so that MOSFET Q3 turns on after t0 to realize soft switching. In this mode,  Although there are several approaches [18][19][20][21] to generate square voltage waveforms on the ac side of the converter leg, fundamental frequency analysis [22] is the most useful approach to obtain voltage gain of the proposed circuit under different switching frequency. Based on the switching states of power devices, two square voltage signals are observed on high-voltage side v ab and v Lm2 . C r , L r and L m2 work as a circuit filter to eliminate harmonic signals. Therefore, v ab and v Lm2 can be treated as ac voltage's only fundamental frequency to simplify the circuit analysis. The fundamental root mean square (rms) voltages v ab,rms and v Lm2,rms are calculated as √ 2V H /π and 2 √ 2V L n/π. The primary-side fundamental resistance is obtained as R ac2 = 8n 2 R o,L /π 2 where R o,L is load resistance on the low-voltage side. The equivalent circuit at the fundamental switching frequency under forward power transfer is shown in Figure 3a. Based on a resonant tank consisting of C r , L r , L m2 and R ac2 , the voltage gain G H2L (s) and |G H2L (s)| under different switching frequency are obtained as: where Q 1 = √ L r /C r /R ac2 , K 1 =L m2 /L r , F = f sw /f r and f r = 1/(2π √ L r C r ). Based on (5), the switching frequency is derived with the given high voltage value V H , low voltage value V L , inductor ratio K 1 = L m2 /L r and equivalent load resistance R ac2 .

Reverse Power Flow
When the proposed converter is worked as backward power transfer to transfer power from V L to V H (Figure 3b), power devices Q 3 and Q 4 on the low-voltage side work as active switches to control primary-side voltage V H . For having the circuit characteristics of LLC resonant converter, ac switch S is ON so that L m1 is connected between points a and b. Based on the amplitude of |i Lr | and |i Lm1 |, the anti-parallel diodes D Q1 and D Q2 are ON or OFF and the quasi-square voltage waveform is generated on voltage v ab . Likewise, a square waveform is also generated on the primary-side voltage v Lm2 based on the ON/OFF state of Q 3 and Q 4 . Under reverse power transfer operation, L r , C r and L m1 are resonant and the input impedance from the low-voltage side should be an inductive load. Then, Q 3 and Q 4 can be operated under zero-voltage condition such that the switching loss is lessened. The key pulse-width modulation signals under backward power transfer operation are demonstrated in Figure 3b. The equivalent topological circuits corresponding to mode operations are demonstrated in Figure 5.
Mode 1 [t 0~t1 ]: The voltage on C Q3 is decreased to zero voltage at time t 0 . Since i Q3 < 0 and i Lr > 0, the body diode D Q3 of MOSFET Q 3 conducts so that MOSFET Q 3 turns on after t 0 to realize soft switching. In this mode, i Lr (t 0 ) + i Lm1 (t 0 ) < 0, D Q1 is conducting, C H1 is charged by i DQ1 , v ab = V CH1 = V H /2, v Lm2 = nV L , i Lm2 increases with the slope nV L /L m2 and i Lm1 increases with the slope V H /(2L m1 ). L r and C r are resonant. Power transfer is from V L to V H in this mode through components Q 3 , T, L r , C r and D Q1 . If f sw < f r , the circuit action will go to mode 2. However, the circuit action will go to mode 3. are resonant. Power transfer is from VL to VH in this mode through components Q3, T, Lr, Cr and DQ1.
If fsw < fr, the circuit action will go to mode 2. However, the circuit action will go to mode 3. Mode 3 [t2 ~ t3]: At t2, power device Q3 turns off. Since iQ3 > 0 and iQ4 < 0, CQ3 is charged and CQ4 is discharged. The zero-voltage switching condition of Q4 is obtained as: where CQ,s = CQ3 = CQ4, where td is a dead time.
Mode 4 [t3 ~ t4]: At time t3, vCQ4 = 0. Then, DQ4 becomes forward biased. Since iQ4(t3) is negative, Q4 can be turned on at this instant without turn-on switching loss. In this mode, DQ2 is forward biased, Q4 is turned on, vab = vLm1 = −VH/2, vLm2 = −nVL, and Cr and Lr are resonant. If fsw < fr, the next operating mode will go to mode 5. Otherwise, the next operating mode is mode 6.
Mode 2 [t 1~t2 ]: If i DQ1 (t 1 ) = 0, then diode D Q1 is off. The resonant current i Lr flows through components S, C r , L r , T and L m2 , the components C r , L r and L m1 are resonant with v Lm2 = nV L , and the resonant frequency is f p = 1/2π C r (L r + L m1 ) << f r . Mode 3 [t 2~t3 ]: At t 2 , power device Q 3 turns off. Since i Q3 > 0 and i Q4 < 0, C Q3 is charged and C Q4 is discharged. The zero-voltage switching condition of Q 4 is obtained as: where C Q,s = C Q3 = C Q4 , i Lm2,peak ≈ nV L /(4L m2 f sw ) and i Lm1,peak ≈ V H /(8L m1 f sw ). The time duration in this mode is calculated when v CQ4 is decreased to zero voltage.
where t d is a dead time. Mode 4 [t 3~t4 ]: At time t 3 , v CQ4 = 0. Then, D Q4 becomes forward biased. Since i Q4 (t 3 ) is negative, Q 4 can be turned on at this instant without turn-on switching loss. In this mode, D Q2 is forward biased, Q 4 is turned on, v ab = v Lm1 = −V H /2, v Lm2 = −nV L , and C r and L r are resonant. If f sw < f r , the next operating mode will go to mode 5. Otherwise, the next operating mode is mode 6.
Mode 5 [t 4~t5 ]: If f sw < f r , i DQ2 = 0 before active device Q 4 turns off. At time t 4 , i DQ2 = 0 and D Q2 is reverse biased. Therefore, the resonant inductor current i Lr flows through L m1 , C r , L r and T. L m1 , C r and L r are resonant under v Lm2 = −nV L . Mode 6 [t 5~Tsw + t 0 ]: Q 4 is turned off at t 5 . Then, C Q3 and C Q4 are discharged and charged, respectively. At time T sw + t 0 , v CQ3 = 0. Then the circuit operation will go to mode 1 for next switching period.
The operation of the proposed converter at reverse power transfer is like the forward power transfer. Q 3 and Q 4 are controlled by frequency-mode operation. The resonant tank included L r , C r and L m1 and is operated as a band-pass filter to eliminate harmonics. In Figure 3b, the input fundamental rms voltage v Lm2,rms = 2 √ 2nV L /π. The resonant tank includes R ac1 , L m1 , C r and L r . The equivalent resistance R ac1 = 2R o,H /π 2 . The voltage gains G L2H (s) and |G L2H (s)| under reverse power transfer are calculated as: where f r = 1/(2π √ L r C r ), Q 2 = √ L r /C r /R ac1 , K 2 = L m1 /L r and F = f sw /f r . Based on Equation (9), the necessary switching frequency f sw is calculated from the given parameters V H , V L , K 2 = L m1 /L r and R ac1 .

Experimental Waveforms
In this section, a design procedure of the studied circuit is discussed and the experiments are demonstrated. For forward power operation, the high-side voltage V H = 350 V~400 V and the low-side voltage V L = 48 V. For reverse power transfer, the low-voltage V L varies from 38 V to 52 V and V H = 400 V. The power rating P o,rated = 480 W. Based on Equations (5) and (9), the voltage transfer functions for both forward power operation and reverse power operation are alike. To simplify the circuit design, only the forward power transfer is discussed. The voltage gain |G H2L (s)| under V H = 400 V is set to one. Then, the turn-ratio n of power transformer T is calculated as n = |G H2L | × V H,max 2V L,max = 1 × 400 2×52 ≈ 3.85. In this prototype, the selected primary turns and secondary turns are 23 and 6, respectively. According to turn-ratio n, the dc gains are derived under 48 V output voltage.
|G H2L | dc,max = 2nV L,nom V H,min Since the maximum gain of |G H2L (s)| is 1.05, the select inductor ratio K 1 and quality factor Q 1 should be selected under the full load and minimum input voltage case. The larger K 1 can reduce circulating current loss and the smaller K 1 can increase voltage gain. Since the maximum voltage gain of |G H2L (s)| is 1.05, K 1 = 13 is selected in the prototype to lessen the circulating current loss. The maximum gain of |G H2L (s)| under K 1 = 13 and Q 1 = 0.35 is close to 1.18. Since n = 23/6, R ac2 at rated power can be obtained as: Since f r is selected as 100 kHz, C r and L r are calculated as C r = 1/2πQ 1 f r R ac2 ≈ 79.5 nF and L r = 1/(2π f r ) 2 C r ≈ 31.86 µH. The selected components are C r = 78 nF, L r = 32 µH and L m2 = K 1 L r = 13 × 32 = 416 µH. The secondary-side rms current reflected to the primary-side is obtained as I rms,p = π I o 2 √ 2n ≈ 2.9 A. The minimum switching frequency of the prototype circuit is obtained as f sw,min = 1/2π C r (L r + L m2 ) ≈ 27 kHz. The maximum rms magnetizing current occurs at minimum switching frequency f sw,min and can be expressed as I Lm2,rms = 1 2 √ 3 nV L 4 f sw,min L m2 ≈ 1.18 A. The rms current of L r is obtained as I Lr,rms = I 2 Lm2,rms + I 2 rms,p ≈ 3.13 A. The maximum peak voltage on capacitor C r is derived as v Cr,peak = √ 2I Lr,rms 2π f sw,min C r ≈ 334.5V. The theoretical voltage ratings of Q 1~Q4 are v Q1,stress = v Q2,stress = 400 V and v Q3,stress = v Q4,stress = 104V. The rms switch currents are I Q1,rms = I Q2,rms = I Lr,rms / √ 2 ≈ 2.21 A and I Q3,rms = I Q4,rms = nI sec,p / √ 2 ≈ 7.85 A. Power devices Q 1 and Q 2 are implemented using IRG4PC40W with 600 V/20 A rating, and power devices Q 3 and Q 4 are implemented using IRFB4321PbF with 150 V/85 A rating. Two SiHG20N50C with 500 V/20 A rating with back-to-back connection is adopted to implement ac switch S. The selected inductor L m1 = 224 µH means the inductor ratio K 2 = L m1 /L r = 7 at reverse power transfer condition. In the prototype circuit, the input and output capacitances are C H1 = C H2 = 180 µF/400 V and C L = 2200 µF/100 V.
Based on the circuit values calculated in design procedure, a prototype circuit was implemented, and the experiments are provided to verify the effectiveness of the developed circuit. Figure 6 gives the photograph of the proposed prototype. The test results of the developed converter operated at forward power transfer are shown in Figures 7-10. Likewise, Figures 11-14 show the test results under backward power transfer. Figure 7 gives the test results of the developed circuit under 100% load and V H = 350 V case. Since f sw is less than f r , the secondary-side currents are decreased to zero before active device is turned off. Similarly, Figure 8 illustrates the experimental results under 100% rated power and V H = 400 V case. It is clear that f sw (switching frequency) is close to f r (resonant frequency) so that i Lr and v Cr are close to sinusoidal waveforms. Figures 9 and 10 demonstrate the test waveforms of the power devices Q 1 and Q 2 under different input voltage and load situations. It is observed that zero-voltage turn-on switching of Q 1 and Q 2 are achieved from 20 to 100% of rated power. The switching frequency at V H = 350 V case is less than the switching frequency at V H = 400 V case. For forward power transfer, the circuit efficiencies are 94.73% (90%), 94.8% (93.2%) and 93.9% (92.3%) at 20%, 50% and 100% rated power, respectively, under 400 V (350 V) input. The measured switching frequencies are 151.3 kHz (67.4 kHz), 114.3 kHz (60 kHz) and 97.6 kHz (52.85 kHz) at 20%, 50% and 100% rated power, respectively, under 400 V (350 V) input. Figures 11 and 12 give the test results of main voltage and current waveforms under backward power transfer at input voltage V L = 38 V and 52 V cases. Based on test results, the switching frequencies f sw under these cases are all less than f r (resonant frequency). Therefore, the reverse recovery current loss on D Q1 and D Q2 is improved. Figures 13 and 14 demonstrate the measured waveforms of power devices Q 3 and Q 4 at different load and voltage cases. The soft switching characteristics of Q 3 and Q 4 are realized from 20% of rated power. Based on test results shown in Figures 7-14, the experimental waveforms are agreed with the theoretical waveforms in the system analysis. For backward power transfer, the circuit efficiencies are 88.2% (87.1%), 91.1% (90.4%) and 90.2% (90.1%) at 20%, 50% and 100% rated power, respectively, under 52V (38V) input. The measured switching frequencies are 72.5 kHz (62.8 kHz), 60.2 kHz (53.4 kHz) and 53.5 kHz (48.8 kHz) at 20%, 50% and 100% rated power, respectively, under 52 V (38 V) input. Because of low voltage and high current input at the low voltage side under backward power transfer, more conduction loss will be introduced on power switches at the low voltage side. Thus, the circuit efficiency under backward power operation is less than the circuit efficiency under forward power operation.       Figure 11. Test results under backward power transfer and full load with V L = 38 V (a) v Q3,g , v Q4,g and i Lm1 [v Q3, g , v Q4, g : 10 V/div; i Lm1 : 5 A/div; time: 4 µs/div] (b) v Q3,g , V H , v Cr and −i Lr [v Q3,g : 10 V/div; V H , v Cr : 500 V/div; −i Lr : 10 A/div; time: 4 µs/div] (c) v Q3,g , i DQ1 and i DQ2 [v Q3,g : 10 V/div; i DQ1 , i DQ2 : 5 A/div; time: 4 µs/div].

Conclusions
A bidirectional resonant converter is studied and implemented to achieve bidirectional power transfer capability. To achieve the dual symmetric resonant behavior for both forward power operation and backward power operation and reduce the circulating current loss under forward

Conclusions
A bidirectional resonant converter is studied and implemented to achieve bidirectional power transfer capability. To achieve the dual symmetric resonant behavior for both forward power operation and backward power operation and reduce the circulating current loss under forward power transfer, an ac switch and a parallel inductor is used on the high voltage side. The input impedance of the proposed circuit is regulated with the frequency-modulation scheme. The soft switching of active devices is realized. The forward and backward power transfers have the same LLC circuit characteristics. The parallel inductor on the primary-side is disconnected under forward power transfer in order to improve the circulating current loss. Finally, experimental waveforms are provided to demonstrate the achievability of the developed converter. The main drawback of the proposed converter is more conduction loss on magnetizing inductor during the backward power transfer, because the low-side voltage will introduce a magnetizing current, and this is an additional power loss on low-side power devices and transformers. Therefore, the circuit efficiency at the backward power transfer is less than forward power transfer. In order to overcome low circuit efficiency at backward power flow in the proposed converter, the symmetric resonant circuit, such as CLLLC or CLLC, instead of using half-bridge or full-bridge circuit topology, may be researched and studied in future work.
Author Contributions: B.-R.L. designed the main parts of the project and was also responsible for writing the paper. Y.-C.H. built the prototype circuit and measured experimental waveforms.