Patent Publication Number: US-11641164-B2

Title: Power conversion circuit and power conversion apparatus with same

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a Continuation application of U.S. patent application Ser. No. 17/115,605 filed on Dec. 8, 2020 and entitled “POWER CONVERSION CIRCUIT AND POWER CONVERSION APPARATUS WITH SAME”, which claims priority to China Patent Application No. 201911268267.8, filed on Dec. 11, 2019. The entire contents of the above-mentioned patent application are incorporated herein by reference for all purposes. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to a power conversion circuit and a power conversion apparatus, and more particularly to a power conversion circuit with an adjustable voltage gain and a power conversion apparatus. 
     BACKGROUND OF THE INVENTION 
     Nowadays, the resonant power conversion circuit having a non-isolated circuit topology with extended duty cycle is widely used in the application of high current. The resonant power conversion circuits are usually divided into a symmetrical type and an asymmetrical type. In the prior power conversion circuit, regardless of the type, the voltage gain is set to be fixed, which means the ratio of the output voltage to the input voltage is fixed. That is, the voltage gain cannot be determined and adjusted according to the practical requirements. However, the fixed voltage gain may limit the applications of the resonant power conversion circuit. 
     SUMMARY OF THE INVENTION 
     An object of the present invention provides a power conversion circuit with an adjustable voltage gain. Since the voltage gain is adjustable, the applications of the power conversion circuit are expanded. 
     Another object of the present invention provides a power conversion apparatus with a power conversion circuit. 
     In accordance with an aspect of the present invention, a power conversion circuit is provided. The power conversion circuit includes a first terminal, a second terminal, a first switching conversion unit, a second switching conversion unit, a flying capacitor and a magnetic element. The first terminal includes a first positive electrode and a first negative electrode. The second terminal includes a second positive electrode and a second negative electrode. The second negative electrode is electrically connected with the first negative electrode. The first switching conversion unit includes a first switch and a third switch, which are electrically connected with each other in series. The second switching conversion unit includes a second switch and a fourth switch, which are electrically connected with each other in series. A first terminal of the first switch is electrically connected with a first terminal of the second switch. A second terminal of the first switch is electrically connected with the first positive electrode. The third switch is serially connected with the first switch. The fourth switch is serially connected with the second switch. A first terminal of the third switch and a first terminal of the fourth switch are electrically connected with the first negative electrode. A second terminal of the fourth switch is electrically connected with a second terminal of the second switch. The first switch, the second switch, the third switch and the fourth switch are periodically operated at a switching cycle. The switching cycle has a duty cycle. The magnetic element includes two first windings and a second winding. The two first windings and the second winding interact with each other to result in an electromagnetic coupling effect. The second terminals of the two first windings are opposite-polarity terminals and electrically connected with the second positive electrode. A first terminal of a first one of the two first windings is electrically connected with a second terminal of the third switch. A first terminal of a second one of the two first windings is electrically connected with the second terminal of the fourth switch and the second terminal of the second switch. The second winding and the flying capacitor are serially connected between the first terminal of the first switch and the first terminal of the first one of the two first windings. Moreover, a turn ratio between the second winding, the first one of the two first windings and the second one of the two first windings is N:1:1, and N is a positive value. The switching cycle comprises a first working period and a second working period. A current flowing through the second winding is equal to a current flowing through the first one of the two first windings during the first working period. The current flowing through the second winding is equal to a current flowing through the second one of the two first windings during the second working period. 
     In accordance with another aspect of the present invention, power conversion apparatus is provided. The power conversion apparatus includes M power conversion circuits. Each power conversion circuit has the above circuitry structure. The first terminals of the M power conversion circuits are electrically connected with each other. The second terminals of the M power conversion circuits are electrically connected with each other. 
     In accordance with another aspect of the present invention, a power conversion circuit is provided. The power conversion circuit includes a first terminal, a second terminal, a first flying capacitor, a second flying capacitor, a first switching conversion unit, a second switching conversion unit and a magnetic element. The first terminal includes a first positive electrode and a first negative electrode. The second terminal includes a second positive electrode and a second negative electrode. The second negative electrode is electrically connected with the first negative electrode. The first switching conversion unit includes a first switch, a second switch and a third switch. A first terminal of the first switch is electrically connected with the first positive electrode. A second terminal of the second switch is electrically connected with a first terminal of the third switch. A second terminal of the third switch is electrically connected with the second negative electrode. The second switching conversion unit includes a fourth switch, a fifth switch and a sixth switch. A first terminal of the fourth switch is electrically connected with the first positive electrode. A second terminal of the fifth switch is electrically connected with a first terminal of the sixth switch. A second terminal of the sixth switch is electrically connected with the second negative electrode. A second terminal of the fourth switch is electrically connected with a first terminal of the second switch. A first terminal of the fifth switch is electrically connected with the second terminal of the first switch. The first switch, the second switch, the third switch, the fourth switch, the fifth switch and the sixth switch are periodically operated at a switching cycle. The switching cycle has a duty cycle. The magnetic element includes two first windings and two second windings. The two first windings and the two second windings interact with each other to result in an electromagnetic coupling effect. The second terminals of the two first windings are opposite-polarity terminals and electrically connected with the second positive electrode. A first terminal of a first one of the two first windings is electrically connected with the second terminal of the fifth switch and the first terminal of the sixth switch. A first terminal of a second one of the two first winding is electrically connected with the second terminal of the second switch and the first terminal of the third switch. A first one of the two second windings and the second flying capacitor are serially connected between the second terminal of the fourth switch and the second terminal of the fifth switch. A second one of the two second windings and the first flying capacitor are serially connected between the second terminal of the first switch and the second terminal of the second switch. Moreover, a turn ratio between the first one of the two second windings, the second one of the two second windings, the first one of the two first windings and the second one of the two first windings is N:N:1:1, and N is a positive value. The switching cycle comprises a first working period and a second working period. A total current flowing through the two second windings is equal to a current flowing through the first one of the two first windings during the first working period. The total current flowing through the two second windings is equal to a current flowing through the second one of the two first windings during the second working period. 
     In accordance with another aspect of the present invention, power conversion apparatus is provided. The power conversion apparatus includes M power conversion circuits. Each power conversion circuit has the above circuitry structure. The first terminals of the M power conversion circuits are electrically connected with each other. The second terminals of the M power conversion circuits are electrically connected with each other. 
     The above contents of the present invention will become more readily apparent to those ordinarily skilled in the art after reviewing the following detailed description and accompanying drawings, in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1 A  is a schematic circuit diagram illustrating a power conversion circuit according to a first embodiment of the present invention; 
         FIG.  1 B  is a schematic timing waveform diagram illustrating the on/off states of associated switches in the power conversion circuit as shown in  FIG.  1 A  and associated voltage signals and current signals; 
         FIG.  1 C  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  1 A  in the time interval between the time point t 0  and the time point t 1  as shown in  FIG.  1 B ; 
         FIG.  1 D  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  1 A  in the time interval between the time point t 2  and the time point t 3  as shown in  FIG.  1 B ; 
         FIG.  1 E  is a schematic circuit diagram illustrating a power conversion circuit according to a second embodiment of the present invention; 
         FIG.  2 A  is a schematic circuit diagram illustrating a power conversion circuit according to a third embodiment of the present invention; 
         FIG.  2 B  is a schematic timing waveform diagram illustrating the on/off states of associated switches in the power conversion circuit as shown in  FIG.  2 A  and associated voltage signals and current signals; 
         FIG.  2 C  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  2 A  in the time interval between the time point t 0  and the time point t 1  as shown in  FIG.  2 B ; 
         FIG.  2 D  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  2 A  in the time interval between the time point t 2  and the time point t 3  as shown in  FIG.  2 B ; 
         FIG.  2 E  is a schematic circuit diagram illustrating a power conversion circuit according to a fourth embodiment of the present invention; 
         FIG.  3    is a schematic circuit diagram illustrating a power conversion apparatus according to a first embodiment of the present invention; and 
         FIG.  4    is a schematic circuit diagram illustrating a power conversion apparatus according to a second embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention will now be described more specifically with reference to the following embodiments. It is to be noted that the following descriptions of preferred embodiments of this invention are presented herein for purpose of illustration and description only. It is not intended to be exhaustive or to be limited to the precise form disclosed. 
       FIG.  1 A  is a schematic circuit diagram illustrating a power conversion circuit according to a first embodiment of the present invention.  FIG.  1 B  is a schematic timing waveform diagram illustrating the on/off states of associated switches in the power conversion circuit as shown in  FIG.  1 A  and associated voltage signals and current signals.  FIG.  1 C  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  1 A  in the time interval between the time point t 0  and the time point t 1  as shown in  FIG.  1 B .  FIG.  1 D  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  1 A  in the time interval between the time point t 2  and the time point t 3  as shown in  FIG.  1 B . 
     The power conversion circuit of the present invention has the function of converting the electric power in a bidirectional manner. In case that a first terminal of the power conversion circuit is an input terminal, a second terminal of the power conversion circuit is an output terminal. In case that the first terminal of the power conversion circuit is the output terminal, the second terminal of the power conversion circuit is the input terminal. Moreover, the power conversion circuit is a resonant power conversion circuit with extended duty cycle. 
     As shown in  FIG.  1 A , the circuit topology of the power conversion circuit has an asymmetrical configuration. The power conversion circuit  1  includes a first terminal (including a first positive electrode V 1 + and a first negative electrode V 1 −), a second terminal (including a second positive electrode V 2 + and a second negative electrode V 2 −), a first switching conversion unit, a second switching conversion unit, a first capacitor C 1 , a second capacitor C 2 , a flying capacitor Cb 11  and a magnetic element T- 1 . The first negative electrode V 1 − and the second negative electrode V 2 − are connected to a ground terminal. The first switching conversion unit includes a first switch S 11  and a third switch Sr 11 , which are electrically connected in series. The second switching conversion unit includes a second switch S 12  and a fourth switch Sr 12 , which are electrically connected in series. The first switch S 11 , the second switch S 12 , the third switch Sr 11  and the fourth switch Sr 12  are periodically operated at a switching cycle Ts. The switching cycle has a duty cycle. 
     The first terminal of the first switch S 11  is electrically connected with the first terminal of the second switch S 12 . The second terminal of the first switch S 11  is electrically connected with the first positive electrode V 1 +. The second terminal of the fourth switch Sr 12  is electrically connected with the second terminal of the second switch S 12 . The first terminal of the third switch Sr 11  and the first terminal of the fourth switch Sr 12  are connected with the first negative electrode V 1 −. The on/off states of the first switch S 11  and the fourth switch Sr 12  are identical. The on/off states of the second switch S 12  and the third switch Sr 11  are identical. The phase difference between a control signal of the first switch S 11  and a control signal of the second switch S 12  is 180 degrees. The ON time durations of the first switch S 11  and the second switch S 12  are less than or equal to 0.5×Ts and greater than or equal to 0.4×Ts. The first capacitor C 1  is electrically connected between the first positive electrode V 1 + and the first negative electrode V 1 −. The second capacitor C 2  is electrically connected between the second positive electrode V 2 + and the second negative electrode V 2 −. 
     The magnetic element T- 1  includes two first windings T 11 , T 12  and a second winding T 13 . These windings are wound around the same pillar of a magnetic core of the magnetic element to result in an electromagnetic coupling effect. The second terminals of the two first windings T 11  and T 12  are electrically connected with the second positive electrode V 2 +. The second terminals of the two first windings T 11  and T 12  are opposite-polarity terminals. The first terminal of the first winding T 11  is electrically connected with the second terminal of the third switch Sr 11 . The first terminal of the first winding T 12  is electrically connected with the second terminal of the fourth switch Sr 12  and the second terminal of the second switch S 12 . The second winding T 13  and the flying capacitor Cb 11  are connected with each other in series to form a serially-connected branch. The first end of the serially-connected branch is connected with the first terminal of the first switch S 11 . The second end of the serially-connected branch is connected with the second terminal of the third switch Sr 11  and the first terminal of the first winding T 11 . The turn ratio between the second winding T 13 , the first winding T 11  and the first winding T 12  is N:1:1, wherein N is a positive value, and preferably a positive integer. 
     In the serially-connected branch, the positions and sequence of the second winding T 13  and the flying capacitor Cb 11  are not restricted. In an embodiment, the first terminal of the second winding T 13  is electrically connected with the first terminal of the first winding T 11 . The first terminal of the second winding T 13  and the first terminal of the first winding T 11  are opposite-polarity terminals. The second terminal of the second winding T 13  is electrically connected with the flying capacitor Cb 11 . In another embodiment, a terminal of the flying capacitor Cb 11  is electrically connected with the first terminal of the first winding T 11 , and the other terminal of the flying capacitor Cb 11  is electrically connected with the first terminal of the second winding T 13 . The first terminal of the second winding T 13  and the first terminal of the first winding T 11  are opposite-polarity terminals. 
     The working principle of the power conversion circuit  1  will be described as follows. For illustration, taking the first terminal of the power conversion circuit  1  as the input terminal, and the second terminal of the power conversion circuit  1  as the output terminal for example. 
     Please refer to  FIGS.  1 B,  1 C and  1 D  again. When the power conversion circuit  1  is in a steady state, the time interval between the time point t 0  and the time point t 4  is equal to the switching cycle Ts. 
     In the time interval between the time point t 0  and the time point t 1 , the first switch S 11  and the fourth switch Sr 12  are in the on state. This time interval is also referred as a first working period. The flying capacitor Cb 11  is charged by the input voltage V 1  through the first switch S 11 . The electric energy is transmitted from the input terminal to the output terminal through the second winding T 13  and the first winding T 11 . The first winding T 12  is in a freewheeling state through the fourth switch Sr 12 . Meanwhile, the current flowing through the second winding T 13  is equal to the current flowing through the first winding T 11 . The equivalent circuit diagram is shown in  FIG.  1 C . In  FIG.  1 C , T 11 ′, T 12 ′ and T 13 ′ are the ideal windings corresponding to the windings T 11 , T 12  and T 13 , Lr 11 , Lr 12  and Lr 13  are equivalent leakage inductors corresponding to the windings, and Lm 1  is an equivalent magnetized inductor of the magnetic element T- 1 . Due to the resonant effect between the equivalent resonant inductor of the power conversion circuit  1  (i.e., the equivalent resonant inductor resulted by the equivalent leakage inductors Lr 11 , Lr 12  and Lr 13 ) and the flying capacitor Cb 11 , the resonant currents iLr 11  and iLr 12  are generated. The equivalent magnetized current generated by the magnetic element T- 1  is iLm 1 . 
     The associated voltages of the power conversion circuit  1  can be seen in  FIG.  1 C . The voltage between the two terminals of the ideal first winding T 12 ′ is equal to the voltage V 2  of the second terminal of the power conversion circuit  1 . As mentioned above, the turn ratio between the second winding T 13 , the first winding T 11  and the first winding T 12  is N:1:1. Consequently, the voltage between the two terminals of the ideal first winding T 11 ′ is also equal to the voltage V 2 , and the voltage between the two terminals of the ideal second winding T 13 ′ is equal to N×V 2 . 
     Consequently, the voltage V 1  of the first terminal of the power conversion circuit  1  may be expressed by the following mathematical formula:
 
 V 1= Vc 11+(2+ N )× V 2  (1)
 
     In the above mathematic formula, Vc 11  is the terminal voltage of the flying capacitor Cb 11 . 
     At the time point t 1 , the resonant currents iLr 11  and iLr 12  are equal to the magnetized currents iLm 1  and −iLm 1 , respectively. Meanwhile, the first switch S 11  and the fourth switch Sr 12  are turned off. Since the zero current switching (ZCS) function is achieved, the switching loss is decreased and the energy transfer efficiency of the power conversion circuit  1  is enhanced. 
     In the time interval between the time point t 1  and the time point t 2 , all switches are turned off. The magnetized current iLm 1  flowing through the magnetic element T- 1  is in the freewheeling state. In addition, the charges on the parasitic capacitors of the second switch S 12  and the third switch Sr 11  are extracted. Consequently, the terminal voltages of the second switch S 12  and the third switch Sr 11  are decreased. In an embodiment, the second switch S 12  and the third switch Sr 11  are turned on when the terminal voltages of the second switch S 12  and the third switch Sr 11  are decreased to 50% of the respective initial voltages (i.e., the terminal voltages at the time point t 1 ). Consequently, the switching loss is decreased, and the energy transfer efficiency and the power density of the power conversion circuit  1  are enhanced. 
     In another embodiment, the inductance of the magnetic element T- 1  is controlled. Consequently, the inductance of the equivalent magnetized inductor Lm 1  of the magnetic element T- 1  is low enough, and the magnetized current iLm 1  flowing through the equivalent magnetized inductor Lm 1  is high enough. Since the charges on the parasitic capacitors of the second switch S 12  and the third switch Sr 11  are extracted completely, the terminal voltages of the second switch S 12  and the third switch Sr 11  are decreased to zero. At this time, the second switch S 12  and the third switch Sr 11  are turned on. Consequently, the zero voltage switching (ZVS) function is achieved. In such way, the switching loss is further decreased, and the energy transfer efficiency and the power density of the power conversion circuit  1  are further enhanced. 
     In the time interval between the time point t 2  and the time point t 3 , the second switch S 12  and the third switch Sr 11  are in the on state. This time interval is also referred as a second working period. The energy stored in the flying capacitor Cb 11  is transmitted to the output terminal through the second switch S 12 , the first winding T 12 , the third switch Sr 11  and the second winding T 13 . The first winding T 11  is in the freewheeling state through the third switch Sr 11 . Meanwhile, the current flowing through the second winding T 13  is equal to the current flowing through the first winding T 12 . The equivalent circuit diagram is shown in  FIG.  1 D . Due to the resonant effect between the of the power conversion circuit  1  (i.e., the equivalent resonant inductor resulted by the leakage inductors Lr 11 , Lr 12  and Lr 13 ) and the flying capacitor Cb 11 , the resonant currents iLr 11  and iLr 12  are generated. The equivalent magnetized current generated by the magnetic element T- 1  is iLm 1 . 
     The associated voltages of the power conversion circuit  1  can be seen in  FIG.  1 D . The voltage between the two terminals of the ideal first winding T 11 ′ is equal to the voltage V 2  of the second terminal of the power conversion circuit  1 . As mentioned above, the turn ratio between the second winding T 13 , the first winding T 11  and the first winding T 12  is N:1:1. Consequently, the voltage between the two terminals of the ideal first winding T 12 ′ is also equal to the voltage V 2 , and the voltage between the two terminals of the ideal second winding T 13 ′ is equal to N×V 2 . 
     Consequently, the voltage Vc 11  of the flying capacitor Cb 11  may be expressed by the following mathematical formula:
 
 Vc 11=(2+ N )× V 2  (2)
 
     The energy stored in the flying capacitor Cb 11  in the time interval between the time point t 0  and the time point t 1  is transmitted to the output terminal in the time interval between the time point t 2  and the time point t 3 . Consequently, after the formula (2) is introduced into the formula (1), the voltage V 1  of the first terminal of the power conversion circuit  1  may be deduced as: V 1 =(4+2N)×V 2 . 
     At the time point t 3 , the resonant currents iLr 11  and iLr 12  are equal to the magnetized currents iLm 1  and −iLm 1 , respectively. Meanwhile, the second switch S 12  and the third switch Sr 11  are turned off. Since the zero current switching (ZCS) function is achieved, the switching loss is decreased and the energy transfer efficiency of the power conversion circuit  1  is enhanced. 
     In the time interval between the time point t 3  and the time point t 4 , all switches are turned off. The magnetized current iLm 1  flowing through the first windings T 11  and T 12  is in the freewheeling state. In addition, the charges on the parasitic capacitors of the first switch S 11  and the fourth switch Sr 12  are extracted. Consequently, the terminal voltages of the first switch Si  1  and the fourth switch Sr 12  are decreased. In an embodiment, the first switch S 11  and the fourth switch Sr 12  are turned on when the terminal voltages of the first switch S 11  and the fourth switch Sr 12  are decreased to 50% of the respective initial voltages (i.e., the terminal voltages at the time point t 1 ). Consequently, the switching loss is decreased, and the energy transfer efficiency and the power density of the power conversion circuit  1  are enhanced. 
     In another embodiment, the inductance of the magnetic element T- 1  is controlled. Consequently, the inductance of the equivalent magnetized inductor Lm 1  of the magnetic element T- 1  is low enough, and the magnetized current iLm 1  flowing through the equivalent magnetized inductor Lm 1  is high enough. Since the charges on the parasitic capacitors of the first switch S 11  and the fourth switch Sr 12  are extracted completely, the terminal voltages of the first switch S 11  and the fourth switch Sr 12  are decreased to zero. At this time, the first switch S 11  and the fourth switch Sr 12  are turned on. Consequently, the zero voltage switching (ZVS) function is achieved. In such way, the switching loss is further decreased, and the energy transfer efficiency and the power density of the power conversion circuit  1  are further enhanced. 
     In the time interval between the time point t 0  and the time point t 1  and in the time interval between the time point t 2  and the time point t 3 , the resonant current iLr 11  flows through the first winding T 11  and the resonant current iLr 12  flows through the first winding T 12 . In addition, the frequency of each of the resonant current iLr 11  and the resonant current iLr 12  is equal to the switching frequency. In this embodiment, the resonant cycle and the switching cycle are nearly equal. 
     In some other embodiments, the capacitance of the flying capacitor Cb 11  is larger, and the inductance of the equivalent resonant inductor is smaller. Consequently, if the resonant currents iLr 11  and iLr 12  are respectively greater than the magnetized currents iLm 1  and −iLm 1  in the time interval between the time point t 0  and the time point t 1 , the corresponding switches are turned off. If the resonant currents iLr 11  and iLr 12  are respectively greater than −iLm 1  and iLm 1  in the time interval between the time point t 2  and the time point t 3 , the corresponding switches are turned off. The turn-off current is greater than zero. However, since the inductance of the equivalent resonant inductor is low, the power loss caused by the non-zero current turning-off action may be neglected. In other words, the switching cycle of the power conversion circuit  1  is less than or equal to the resonant cycle of the resonant current. For reducing the power loss and increasing the energy transfer efficiency, it is preferred that the switching cycle Ts is greater than or equal to a half of the resonant cycle. 
     In an embodiment, the ratio of the input voltage V 1  to the output voltage V 2  of the power conversion circuit  1  is (4+2N):1. That is, the ratio of the input voltage V 1  to the output voltage V 2  may be adjusted according to the change of N. In this embodiment, the magnetic element T- 1  includes the two first windings T 11 , T 12  and the second winding T 13 . These windings interact with each other to result in the electromagnetic coupling effect. Moreover, the turn ratio between the second winding T 13 , the first winding T 11  and the first winding T 12  is N:1:1. The second winding T 13  is disposed on a specific position of the power conversion circuit  1 . Since the voltage gain of the power conversion circuit  1  is adjustable according to the turn number of the second winding T 13 , the applications of the power conversion circuit  1  are expanded. 
     In the embodiment, as shown in  FIGS.  1 C and  1 D , the equivalent leakage inductors corresponding to the first windings T 11 , T 12  and the second winding T 13  are Lr 11 , Lr 12  and Lr 13 , respectively. For clearly analyzing the relationship between the resonant currents, the magnetized current iLm 1  and the magnetized voltage VLm 1  of the equivalent magnetized inductor Lm 1  are neglected in the following example. In the time interval between the time point t 0  and the time point t 1  and the time interval between the time point t 2  and the time point t 3 , the resonant effect between the flying capacitor Cb 11  and the equivalent leakage inductors Lr 11 , Lr 12  and Lr 13  is generated. In this embodiment, the resonant capacitor of the power conversion circuit  1  is the flying capacitor Cb 11 , and the equivalent resonant inductance is the sum of the inductances of the equivalent leakage inductors Lr 11 , Lr 12  and Lr 13 . If the magnetized current iLm 1  is neglected, the output current io of the power conversion circuit  1  may be expressed by the following mathematic formula:
 
 io=iLr 11+ iLr 12  (3)
 
     In the above mathematic formula, iLr 11  is the resonant current flowing through the equivalent leakage inductor Lr 11 , and iLr 12  is the resonant current flowing through the equivalent leakage inductor Lr 12 . 
     In the time interval between the time point t 0  and the time point t 1 , the resonant current iLr 13  flowing through the equivalent leakage inductor Lr 13  is equal to the resonant current iLr 11  flowing through the equivalent leakage inductor Lr 11 . That is,
 
 iLr 13= iLr 11  (4)
 
     According to the magnetic potential balance principle, the following mathematic formula is obtained.
 
 N×iLr 13+ iLr 11= iLr 12  (5)
 
     According to the above mathematic formulae (3), (4) and (5), the resonant current iLr 12  is equal to (N+1)×io/(N+2), and the resonant current iLr 11  is equal to io/(N+2). 
     In the time interval between the time point t 2  and the time point t 3 , the resonant current iLr 13  flowing through the equivalent leakage inductor Lr 13  is equal to the resonant current iLr 12  flowing through the equivalent leakage inductor Lr 12 . That is,
 
 iLr 13= iLr 12  (6)
 
     According to the magnetic potential balance principle, the following mathematic formula is obtained.
 
 N×iLr 13+ iLr 12= iLr 11  (7)
 
     According to the above mathematic formulae (3), (6) and (7), the resonant current iLr 11  is equal to (N+1)×io/(N+2), and the resonant current iLr 12  is equal to io/(N+2). 
     From the above descriptions, the voltage gain of the power conversion circuit  1  is adjustable according to the turn number of the second winding T 13  of the magnetic element T- 1 . The sum of the resonant currents iLr 11  and iLr 12  in the time interval between the time point t 0  and the time point t 1  and the sum of the resonant currents iLr 11  and iLr 12  in the time interval between the time point t 2  and the time point t 3  are equal. In other words, the resonant effect of the power conversion circuit  1  is not influenced by the second winding T 13 . The terminal voltage Vc 11  of the flying capacitor is obtained by superimposing a DC voltage with an AC resonant voltage. Typically, the DC voltage is equal to Vin/2, and thus the ratio of the DC voltage to the input voltage is 0.5. When the device parameter distribution and other factors are taken into consideration, the ratio of the DC voltage to the input voltage (i.e., the terminal voltage of the first terminal of the power conversion circuit  1 ) is in the range between 0.4 and 0.6. The amplitude of the AC resonant voltage of the terminal voltage Vc 11  is determined according to the inductance of the equivalent resonant inductor, the capacitance of the equivalent resonant capacitor, the switching frequency of the power conversion circuit and the size of the load. 
     In the above embodiment, the equivalent resonant inductor comprises the leakage inductance caused by the coupling effect of the first windings T 11 , T 12  and the second winding T 13  and the parasitic inductance of the wiring structure. When the resonant cycle, the switching cycle and the capacitance of the flying capacitor Cb 11  are taken into consideration, the coupling efficiency between every two of the first windings T 11 , T 12  and the second winding T 13  is preferably greater than 0.9, but it is not limited thereto. 
       FIG.  1 E  is a schematic circuit diagram illustrating a power conversion circuit according to a second embodiment of the present invention. In comparison with the first embodiment, the power conversion circuit of this embodiment further includes at least one external inductor (not shown). The position of the at least one external inductor may be determined according to the practical requirements. In an example, one external inductor is serially connected between the second terminal of the first windings T 11  or T 12  and the second positive electrode V 2 +. That is, the external inductor is located at the position A. In another embodiment, two external inductors with the same inductance are serially connected with two first windings T 11  and T 12 . That is, the two external inductors are located at the positions B 1  or/and B 2 . In an example, at least one external inductor is serially connected to the flying capacitor Cb 11  and the second winding T 13  in the serially-connected branch. For example, one external inductor is located at the position C 1 , C 2  or C 3 , two external inductors are respectively located at two of the positions C 1 , C 2  and C 3 , or three external inductors are respectively located at the positions C 1 , C 2  and C 3 . Consequently, a suitable resonant cycle is acquired. Nevertheless, the at least one external inductor is serially connected between the first terminal of the first switch S 11  and the second positive electrode V 2 +. 
     In some embodiments, the third switch Sr 11  and the fourth switch Sr 12  are replaced by diodes. The diodes are used as freewheeling diodes. The switching cycle of the power conversion circuit is less than or equal to the resonant cycle. The equivalent circuit and the current waveform are similar to those of the above embodiment, and not redundantly described herein. For example, the switches are controllable switches such as MOS switches, SiC switches or GaN switches. 
     As mentioned above, the power conversion circuit  1  of the present invention has the function of converting the electric power in the bidirectional manner. Consequently, in case that the first terminal of the power conversion circuit  1  is the output terminal, the second terminal of the power conversion circuit  1  is the input terminal. The operations are similar to those of the first embodiment, and are not redundantly described herein. Under this circumstance, the ratio of the input voltage to the output voltage of the power conversion circuit  1  is 1:(4+2N). 
       FIG.  2 A  is a schematic circuit diagram illustrating a power conversion circuit according to a third embodiment of the present invention.  FIG.  2 B  is a schematic timing waveform diagram illustrating the on/off states of associated switches in the power conversion circuit as shown in  FIG.  2 A  and associated voltage signals and current signals.  FIG.  2 C  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  2 A  in the time interval between the time point t 0  and the time point t 1  as shown in  FIG.  2 B .  FIG.  2 D  is a schematic equivalent circuit diagram of the power conversion circuit as shown in  FIG.  2 A  in the time interval between the time point t 2  and the time point t 3  as shown in  FIG.  2 B . As shown in  FIG.  2 A , the circuit topology of the power conversion circuit  2  has a symmetrical configuration. The power conversion circuit  2  includes a first terminal (including a first positive electrode V 1 + and a first negative electrode V 1 −), a second terminal (including a second positive electrode V 2 + and a second negative electrode V 2 −), a first capacitor C 1 , a second capacitor C 2 , a first flying capacitor Cb 21 , a second flying capacitor Cb 22 , a first switching conversion unit, a second switching conversion unit and a resonant circuit T- 2 . The first negative electrode V 1 − and the second negative electrode V 2 − are connected to a ground terminal. 
     The first switching conversion unit includes a first switch S 21 , a second switch S 24  and a third switch Sr 22 . The second switching conversion unit includes a fourth switch S 23 , a fifth switch S 22  and a sixth switch Sr 21 . The circuitry structure of the second switching conversion unit is similar to the circuitry structure of the first switching conversion unit. The first terminal of the first switch S 21  is electrically connected with the first positive electrode V 1 +. The second terminal of the first switch S 21  is electrically connected with the first terminal of the fifth switch S 22 . The second terminal of the fifth switch S 22  is electrically connected with the first terminal of the sixth switch Sr 21 . The second terminal of the sixth switch Sr 21  is electrically connected with the second negative electrode V 2 −. The first terminal of the fourth switch S 23  is electrically connected with the first positive electrode V 1 +, and the fourth switch S 23  and the first switch S 21  are connected in parallel. The second terminal of the fourth switch S 23  is electrically connected with the first terminal of the second switch S 24 . The second terminal of the second switch S 24  is electrically connected with the first terminal of the third switch Sr 22 . The second terminal of the third switch Sr 22  is electrically connected with the second negative electrode V 2 −. The first terminal of the first flying capacitor Cb 21  is electrically connected with the second terminal of the first switch S 21  and the first terminal of the fifth switch S 22 . The second terminal of the first flying capacitor Cb 21  is electrically connected with the second terminal of the second switch S 24  and the first terminal of the third switch Sr 22 . The first terminal of the second flying capacitor Cb 22  is electrically connected with the second terminal of the fourth switch S 23  and the first terminal of the second switch S 24 . The second terminal of the second flying capacitor Cb 22  is electrically connected with the second terminal of the fifth switch S 22  and the first terminal of the sixth switch Sr 21 . The first switch S 21 , the second switch S 24 , the third switch Sr 22 , the fourth switch S 23 , the fifth switch S 22  and the sixth switch Sr 21  are periodically operated at a switching cycle Ts. The switching cycle has a duty cycle. 
     The on/off states of the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are identical. The on/off states of the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are identical. The phase difference between the control signal of the first switch S 21  and the control signal of the fourth switch S 23  is 180 degrees. The time durations of the first switch S 21  and the fourth switch S 23  are less than or equal to 0.5×Ts and greater than or equal to 0.4×Ts. The first capacitor C 1  is electrically connected between the first positive electrode V 1 + and the first negative electrode V 1 −. The second capacitor C 2  is electrically connected between the second positive electrode V 2 + and the second negative electrode V 2 −. 
     The magnetic element T- 2  includes two first windings T 21 , T 22  and two second windings T 23 , T 24 . These windings are wound around the same pillar of a magnetic core of the magnetic element to result in an electromagnetic coupling effect. The second terminals of the two first windings T 21  and T 22  are electrically connected with the second positive electrode V 2 +. The second terminals of the two first windings T 21  and T 22  are opposite-polarity terminals. The first terminal of the first winding T 21  is electrically connected with the second terminal of the fifth switch S 22  and the first terminal of the sixth switch Sr 21 . The first terminal of the first winding T 22  is electrically connected with the second terminal of the second switch S 24  and the first terminal of the third switch Sr 22 . The second winding T 23  and the second flying capacitor Cb 22  are connected with each other in series to form a first serially-connected branch. The first serially-connected branch is connected between the second terminal of the fourth switch S 23  and the second terminal of the fifth switch S 22 . The second winding T 24  and the first flying capacitor Cb 21  are connected with each other in series to form a second serially-connected branch. The second serially-connected branch is connected between the second terminal of the first switch S 21  and the second terminal of the second switch S 24 . The turn ratio between the second winding T 23 , the second winding T 24 , the first winding T 21  and the first winding T 22  is N:N:1:1, wherein N is a positive value, and preferably a positive integer. 
     In the first serially-connected branch, the positions and sequence of the second winding T 23  and the second flying capacitor Cb 22  are not restricted. In an embodiment, the first terminal of the second winding T 23  is electrically connected with the first terminal of the first winding T 21 . The first terminal of the second winding T 23  and the first terminal of the first winding T 21  are opposite-polarity terminals. The second terminal of the second winding T 23  is electrically connected with the second flying capacitor Cb 22 . In another embodiment, a terminal of the second flying capacitor Cb 22  is electrically connected with the first terminal of the first winding T 21 , and the other terminal of the second flying capacitor Cb 22  is electrically connected with the first terminal of the second winding T 23 . The first terminal of the second winding T 23  and the first terminal of the first winding T 21  are opposite-polarity terminals. 
     In the second serially-connected branch, the positions and sequence of the second winding T 24  and the first flying capacitor Cb 21  are not restricted. In an embodiment, the first terminal of the second winding T 24  is electrically connected with the first terminal of the first winding T 22 . The first terminal of the second winding T 24  and the first terminal of the first winding T 22  are opposite-polarity terminals. The second terminal of the second winding T 24  is electrically connected with the first flying capacitor Cb 21 . In another embodiment, a terminal of the first flying capacitor Cb 21  is electrically connected with the first terminal of the first winding T 22 , and the other terminal of the first flying capacitor Cb 21  is electrically connected with the first terminal of the second winding T 24 . The first terminal of the second winding T 24  and the first terminal of the first winding T 22  are opposite-polarity terminals. 
     The working principle of the power conversion circuit  2  will be described as follows. For illustration, taking the first terminal of the power conversion circuit  2  as the input terminal, and the second terminal of the power conversion circuit  2  as the output terminal for example. 
     Please refer to  FIGS.  2 B,  2 C and  2 D  again. When the power conversion circuit  2  is in a steady state, the time interval between the time point t 0  and the time point t 4  is equal to the switching cycle Ts. 
     In the time interval between the time point t 0  and the time point t 1 , the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are in the on state. This time interval is also referred as a first working period. The first flying capacitor Cb 21  is charged by the input voltage V 1  through the first switch S 21 . The electric energy is transmitted from the input terminal to the output terminal through the second winding T 24  and the first winding T 22 . The energy stored in the second flying capacitor Cb 22  is transmitted to the output terminal through the second switch S 24 , the first winding T 22 , the sixth switch Sr 21  and the second winding T 23 . The first winding T 21  is in a freewheeling state through the sixth switch Sr 21 . Meanwhile, the sum of the current flowing through the second winding T 23  and the current flowing through the second winding T 24  is equal to the current flowing through the first winding T 22 . The equivalent circuit diagram is shown in  FIG.  2 C . In  FIG.  2 C , T 21 ′, T 22 ′, T 23 ′ and T 24 ′ are the ideal windings corresponding to the windings T 21 , T 22 , T 23  and T 24 , Lr 21 , Lr 22 , Lr 23  and Lr 24  are equivalent leakage inductors corresponding to the windings, and Lm 2  is an equivalent magnetized inductor of the magnetic element T- 2 . Due to the resonant effect between the power conversion circuit  2  (i.e., the equivalent resonant inductor resulted from the equivalent leakage inductors Lr 21 , Lr 22 , Lr 23  and Lr 24 ) and the flying capacitors Cb 21  and Cb 22 , the resonant currents iLr 21  and iLr 22  are generated. The equivalent magnetized current generated by the magnetic element T- 2  is iLm 2 . 
     The associated voltages of the power conversion circuit  2  can be seen in  FIG.  2 C . The voltage between the two terminals of the ideal first winding T 21 ′ is equal to the voltage V 2  of the second terminal of the power conversion circuit  2 . As mentioned above, the turn ratio between the second winding T 23 , the second winding T 24 , the first winding T 21  and the first winding T 22  is N:N:1:1. Consequently, the voltage between the two terminals of the ideal first winding T 22 ′ is also equal to the voltage V 2 , the voltage between the two terminals of the ideal second winding T 23 ′ is equal to N×V 2 , and the voltage between the two terminals of the ideal second winding T 24 ′ is equal to N×V 2 . 
     Consequently, the voltage V 1  of the first terminal of the power conversion circuit  2  and the voltage Vc 22  of the second flying capacitor Cb 22  may be expressed by the following mathematical formula:
 
 V 1= Vc 21+(2+ N )× V 2  (8); and
 
 Vc 22=(2+ N )× V 2  (9)
 
     In the above mathematic formula, Vc 21  is the terminal voltage of the first flying capacitor Cb 21 , and Vc 22  is the terminal voltage of the second flying capacitor Cb 22 . At the time point t 1 , the resonant currents iLr 21  and iLr 22  are equal to the magnetized currents iLm 1  and −iLm 1 , respectively. Meanwhile, the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are turned off. Since the zero current switching (ZCS) function is achieved, the switching loss is decreased and the energy transfer efficiency of the power conversion circuit  2  is enhanced. 
     In the time interval between the time point t 1  and the time point t 2 , all switches are turned off. The magnetized current iLm 2  flowing through the magnetic element T- 2  is in the freewheeling state. In addition, the charges on the parasitic capacitors of the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are extracted. Consequently, the terminal voltages of the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are decreased. In an embodiment, the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are turned on when the terminal voltages of the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are decreased to 50% of the respective initial voltages (i.e., the terminal voltages at the time point t 1 ). Consequently, the switching loss is decreased, and the energy transfer efficiency and the power density of the power conversion circuit  2  are enhanced. 
     In another embodiment, the inductance of the magnetic element T- 2  is controlled. Consequently, the inductance of the equivalent magnetized inductor Lm 2  of the magnetic element T- 2  is low enough, and the magnetized current iLm 2  flowing through the equivalent magnetized inductor Lm 2  is high enough. Since the charges on the parasitic capacitors of the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are extracted completely, the terminal voltages of the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are decreased to zero. At this time, the fifth switch S 22  and the third switch Sr 22  are turned on, the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are turned on. Consequently, the zero voltage switching (ZVS) function is achieved. In such way, the switching loss is further decreased, and the energy transfer efficiency and the power density of the power conversion circuit  2  are further enhanced. 
     In the time interval between the time point t 2  and the time point t 3 , the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are in the on state. This time interval is also referred as a second working period. The voltage V 1  of the input terminal is transmitted to the second flying capacitor Cb 22  through the fourth switch S 23  so as to charge the second flying capacitor Cb 22 . In addition, the energy stored in the second flying capacitor Cb 22  is transmitted to the output terminal through the second winding T 23  and the first winding T 21 . The energy stored in the first flying capacitor Cb 21  is transmitted to the output terminal through the fifth switch S 22 , the first winding T 21 , the third switch Sr 22  and the second winding T 24 . The first winding T 22  is in the freewheeling state through the third switch Sr 22 . Meanwhile, the sum of the current flowing through the second winding T 23  and the current flowing through the second winding T 24  is equal to the current flowing through the first winding T 21 . The equivalent circuit diagram is shown in  FIG.  2 D . Due to the resonant effect between the power conversion circuit  2  (i.e., the equivalent resonant inductor resulted from the equivalent leakage inductors Lr 21 , Lr 22 , Lr 23  and Lr 24 ) and the flying capacitors Cb 21  and Cb 22 , the resonant currents iLr 21  and iLr 22  are generated. The equivalent magnetized current generated by the magnetic element T- 2  is iLm 2 . 
     The associated voltages of the power conversion circuit  2  can be seen in  FIG.  2 D . The voltage between the two terminals of the ideal first winding T 22 ′ is equal to the voltage V 2  of the second terminal of the power conversion circuit  2 . As mentioned above, the turn ratio between the second winding T 23 , the second winding T 24 , the first winding T 21  and the first winding T 22  is N:N:1:1. Consequently, the voltage between the two terminals of the ideal first winding T 21 ′ is also equal to the voltage V 2 , the voltage between the two terminals of the ideal second winding T 23 ′ is equal to N×V 2 , and the voltage between the two terminals of the ideal second winding T 24 ′ is equal to N×V 2 . 
     Consequently, the voltage V 1  of the first terminal of the power conversion circuit  2  and the voltage Vc 21  of the first flying capacitor Cb 21  may be expressed by the following mathematical formula:
 
 V 1= Vc 22+(2+ N )× V 2  (10); and
 
 Vc 21=(2+ N )× V 2  (11)
 
     The energy stored in the first flying capacitor Cb 21  in the time interval between the time point t 0  and the time point t 1  is transmitted to the output terminal in the time interval between the time point t 2  and the time point t 3 . The energy stored in the second flying capacitor Cb 22  in the time interval between the time point t 2  and the time point t 3  is transmitted to the output terminal in the time interval between the time point t 0  and the time point t 1 . According to the formulae (8), (9), (10) and (11), the voltage V 1  of the first terminal of the power conversion circuit  2  may be deduced as: V 1 =(4+2N)×V 2 . 
     At the time point t 3 , the resonant currents iLr 21  and iLr 22  are equal to the magnetized currents iLm 2  and -iLm 2 , respectively. Meanwhile, the fourth switch S 23 , the fifth switch S 22  and the third switch Sr 22  are turned off. Since the zero current switching (ZCS) function is achieved, the switching loss is decreased and the energy transfer efficiency of the power conversion circuit  2  is enhanced. 
     In the time interval between the time point t 3  and the time point t 4 , all switches are turned off. The magnetized current iLm 2  flowing through the magnetic element T- 2  is in the freewheeling state. In addition, the charges on the parasitic capacitors of the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are extracted. Consequently, the terminal voltages of the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are decreased. In an embodiment, the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are turned on when the terminal voltages of the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are decreased to 50% of the respective initial voltages (i.e., the terminal voltages at the time point t 1 ). Consequently, the switching loss is decreased, and the energy transfer efficiency and the power density of the power conversion circuit  2  are enhanced. 
     In another embodiment, the inductance of the magnetic element T- 2  is controlled. Consequently, the inductance of the equivalent magnetized inductor Lm 2  of the magnetic element T- 2  is low enough, and the magnetized current iLm 2  flowing through the equivalent magnetized inductor Lm 2  is high enough. Since the charges on the parasitic capacitors of the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are extracted completely, the terminal voltages of the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are decreased to zero. At this time, the second switch S 24  and the sixth switch Sr 21  are turned on, the first switch S 21 , the second switch S 24  and the sixth switch Sr 21  are turned on. Consequently, the zero voltage switching (ZVS) function is achieved. In such way, the switching loss is further decreased, and the energy transfer efficiency and the power density of the power conversion circuit  2  are further enhanced. 
     In the time interval between the time point t 0  and the time point t 1  and in the time interval between the time point t 2  and the time point t 3 , the resonant current iLr 21  flows through the first winding T 21  and the resonant current iLr 22  flows through the first winding T 22 . In addition, the frequency of each of the resonant current iLr 21  and the resonant current iLr 22  is equal to the switching frequency. In this embodiment, the resonant cycle and the switching cycle are nearly equal. 
     In some other embodiments, the capacitances of the flying capacitors Cb 21  and Cb 22  are larger, and the inductance of the equivalent resonant inductor is smaller. Consequently, if the resonant currents iLr 22  and iLr 21  are respectively greater than the magnetized currents iLm 1  and −iLm 1  in the time interval between the time point t 0  and the time point t 1 , the corresponding switches are turned off. If the resonant currents iLr 22  and iLr 21  are respectively greater than the magnetized currents −iLm 2  and iLm 2  in the time interval between the time point t 2  and the time point t 3 , the corresponding switches are turned off. The turn-off current is greater than zero. However, since the inductance of the equivalent resonant inductor is low, the power loss caused by the non-zero current turning-off action may be neglected. In other words, the switching cycle of the power conversion circuit  2  is less than or equal to the resonant cycle of the resonant current. For reducing the power loss and increasing the energy transfer efficiency, it is preferred that the switching cycle Ts is greater than or equal to a half of the resonant cycle. 
     In an embodiment, the ratio of the input voltage V 1  to the output voltage V 2  is (4+2N):1. That is, the ratio of the input voltage V 1  to the output voltage V 2  may be adjusted according to the change of N. In this embodiment, the magnetic element T- 2  includes the two first windings T 21 , T 22  and the two second windings T 23  and T 24 . These windings interact with each other to result in the electromagnetic coupling effect. Moreover, the turn ratio between the second winding T 23 , the second winding T 24 , the first winding T 21  and the first winding T 22  is N:N:1:1. Since the voltage gain of the power conversion circuit  2  is adjustable according to the turn numbers of the second winding T 23  and T 24 , the applications of the power conversion circuit  2  are expanded. 
     In the embodiment, as shown in  FIGS.  2 C and  2 D , the equivalent leakage inductors corresponding to the windings T 21 , T 22 , T 23  and T 24  are Lr 21 , Lr 22 , Lr 23  and Lr 24 , respectively. For clearly analyzing the relationship between the resonant currents, the magnetized current iLm 2  and the magnetized voltage VLm 2  of the equivalent magnetized inductor Lm 2  are neglected in the following example. In the time interval between the time point t 0  and the time point t 1  and the time interval between the time point t 2  and the time point t 3 , the resonant effect between the flying capacitors Cb 21 , Cb 22  and the equivalent leakage inductors Lr 21 , Lr 22 , Lr 23  and Lr 24  is generated. In this embodiment, the resonant capacitance of the power conversion circuit  2  is the sum of the capacitances of the flying capacitors Cb 21  and Cb 22 , and the equivalent resonant inductance is equal to the parallel conductance of the equivalent leakage inductances Lr 23  and Lr 24  plus the equivalent leakage inductances Lr 21  and Lr 22  (i.e., the resonant capacitance of the power conversion circuit  2  is Lr 23 ∥Lr 24 +Lr 21 +Lr 22 ). If the magnetized current iLm 2  is neglected, the output current io of the power conversion circuit  2  may be expressed by the following mathematic formula:
 
 io=iLr 21+ iLr 22  (12)
 
     In the above mathematic formula, iLr 21  is the resonant current flowing through the equivalent leakage inductor Lr 21 , and iLr 22  is the resonant current flowing through the equivalent leakage inductor Lr 22 . 
     In the time interval between the time point t 0  and the time point t 1 , the resonant current iLr 23  flowing through the equivalent leakage inductor Lr 23  is equal to the resonant current iLr 23  flowing through the equivalent leakage inductor Lr 24 . That is,
 
 iLr 23= iLr 24  (13)
 
     The sum of the resonant current flowing through the equivalent leakage inductor Lr 23  and the resonant current flowing through the equivalent leakage inductor Lr 24  is equal to the resonant current iLr 22  flowing through the equivalent leakage inductor Lr 22 . That is,
 
 iLr 23+ iLr 24= iLr 22  (14)
 
     According to the magnetic potential balance principle, the following mathematic formula is obtained.
 
 N×iLr 23+ N×iLr 24+ iLr 22= iLr 21  (15)
 
     According to the above mathematic formulae (13), (14) and (15), the resonant current iLr 12  is equal to io/(N+2), and the resonant current iLr 21  is equal to (N+1)×io/(N+2). 
     In the time interval between the time point t 2  and the time point t 3 , the resonant current iLr 23  flowing through the equivalent leakage inductor Lr 23  is equal to the resonant current iLr 24  flowing through the equivalent leakage inductor Lr 24  (e.g., the formula (13)), and the sum of the resonant current flowing through the equivalent leakage inductor Lr 23  and the resonant current flowing through the equivalent leakage inductor Lr 24  is equal to the resonant current iLr 22  flowing through the equivalent leakage inductor Lr 22  (e.g., the formula (14)). 
     According to the magnetic potential balance principle, the following mathematic formula is obtained.
 
 N×iLr 23+ N×iLr 24+ iLr 21= iLr 22  (16)
 
     According to the above mathematic formulae (13), (14) and (16), the resonant current iLr 21  is equal to io/(N+2), and the resonant current iLr 22  is equal to (N+1)×io/(N+2). 
     From the above descriptions, the voltage gain of the power conversion circuit  2  is adjustable according to the turn numbers of the second winding T 23  and T 24  of the magnetic element T- 2 . The sum of the resonant currents iLr 21  and iLr 22  in the time interval between the time point t 0  and the time point t 1  and the sum of the resonant currents iLr 21  and iLr 22  in the time interval between the time point t 2  and the time point t 3  are equal. In other words, the resonant effect of the power conversion circuit  2  is not influenced by the second windings T 23  and T 24 . The terminal voltage Vc 21  of the first flying capacitor Cb 21  is obtained by superimposing a DC voltage with an AC resonant voltage. Similarly, the terminal voltage Vc 22  of the second flying capacitor Cb 22  is obtained by superimposing a DC voltage with an AC resonant voltage. Typically, the DC voltage is equal to Vin/2, and thus the ratio of the DC voltage to the input voltage (e.g., the voltage of the first terminal of the power conversion circuit  2 ) is 0.5. However, when the device parameter distribution and other factors are taken into consideration, the ratio of the DC voltage to the input voltage is in the range between 0.4 and 0.6. The amplitudes of the AC resonant voltage of the terminal voltages Vc 21  and Vc 22  are determined according to the inductance of the equivalent resonant inductor, the capacitance of the equivalent resonant capacitor, the switching frequency of the power conversion circuit and the size of the load. 
     In the above embodiment, the equivalent resonant inductor comprises the leakage inductance caused by the coupling effect of the windings T 21 , T 22 , T 23  and T 24  and the parasitic inductance of the wiring structure. When the resonant cycle, the switching cycle and the capacitances of the flying capacitors Cb 21  and Cb 22  are taken into consideration, the coupling efficiency between every two of the windings T 21 , T 22 , T 23  and T 24  is preferably greater than 0.9. 
       FIG.  2 E  is a schematic circuit diagram illustrating a power conversion circuit according to a fourth embodiment of the present invention. In comparison with the third embodiment, the power conversion circuit of this embodiment further includes at least one external inductor (not shown). 
     The position of the at least one external inductor may be determined according to the practical requirements. In an example, one external inductor is serially connected between the second terminals of the first winding T 21  or T 22  and the second positive electrode V 2 +. That is, the external inductor is located at the position D. In another embodiment, two external inductors with the same inductance are serially connected with two first windings T 21  and T 22 . That is, the two external inductors are located at the positions E 1  or E 2 . In an example, at least one external inductor is serially connected to the first/second serially-connected branch. For example, one external inductor is located at the position F 1 , F 2  or F 3  two external inductors are respectively located at two of the positions F 1 , F 2  or F 3 , or three external inductors are respectively located at the positions F 1 , F 2  or F 3 . Consequently, a suitable resonant cycle is acquired. Nevertheless, the at least one external inductor is serially connected between the first terminal of the first switch S 21  and the second positive electrode V 2 +. 
     In some embodiments, the third switch Sr 22  and the sixth switch Sr 21  are replaced by diodes. The diodes are used as freewheeling diodes. The switching cycle of the power conversion circuit is less than or equal to the resonant cycle. The equivalent circuit and the current waveform are similar to those of the above embodiment, and not redundantly described herein. For example, the switches are controllable switches such as MOS switches, SiC switches or GaN switches. 
     As mentioned above, the power conversion circuit  2  of the present invention has the function of converting the electric power in the bidirectional manner. Consequently, in case that the first terminal of the power conversion circuit  2  is the output terminal, the second terminal of the power conversion circuit  2  is the input terminal. The operations are similar to those of the first embodiment, and are not redundantly described herein. Under this circumstance, the ratio of the input voltage to the output voltage of the power conversion circuit  2  is 1:(4+2N). 
     The present invention further provides a power conversion apparatus. The power conversion apparatus includes M power conversion circuits, M is an integer greater than 1. The M power conversion circuits are connected with each other in an interleaving manner. Consequently, the carrying capability of the power conversion system is enhanced. The first terminals of the M power conversion circuits are connected with each other. The second terminals of the M power conversion circuits are connected with each other. The circuitry structures and the circuitry parameters of the M power conversion circuits are identical. 
     In an embodiment, each power conversion circuit has the circuit topology as shown in  FIG.  1 A . In case that M is an odd value, the M power conversion circuits are controlled according to M control signals. Each power conversion circuit is controlled according to one corresponding control signal. The phase difference between the control signals for controlling every two adjacent power conversion circuits is in the range between (360/M−20) degree and (360/M+20) degree. In case that M is an even value, the M power conversion circuits are controlled according to M/2 control signals. Every two power conversion circuits are controlled according to one corresponding control signal. For example, the m-th power conversion circuit and the (M/2+m)-th power conversion circuit are controlled according to the m-th control signal. The phase difference between the control signals for controlling every two adjacent power conversion circuits is in the range between (360/M−20) degree and (360/M+20) degree, wherein m is an integer smaller than M. 
     In another embodiment, each power conversion circuit has the circuit topology as shown in  FIG.  2 A . The M power conversion circuits are controlled according to M control signals. Each power conversion circuit is controlled according to one corresponding control signal. The phase difference between the control signals for controlling every two adjacent power conversion circuits is in the range between (360/2M−20) degree and (360/2M+20) degree. 
     In the following embodiments, taking the power conversion apparatus including two power conversion circuits as an example to illustrate the embodiments, where the two power conversion circuits are connected with each other in an interleaving manner. 
       FIG.  3    is a schematic circuit diagram illustrating a power conversion apparatus according to a first embodiment of the present invention. As shown in  FIG.  3   , the power conversion apparatus  100  includes two power conversion circuits  1 . Each power conversion circuit  1  has the circuitry structure as shown in  FIG.  1 A . The first terminals of the two power conversion circuits  1  are electrically connected with each other. The second terminals of the two power conversion circuits  1  are electrically connected with each other. 
     In the embodiment as shown in  FIG.  3   , each power conversion circuit  1  of the power conversion apparatus  100  includes a first capacitor C 1  and a second capacitor C 2 . In a variant example, one first capacitor C 1  is shared by the first terminals of the power conversion circuits  1 , and one second capacitor C 2  is shared by the second terminals of the power conversion circuits  1 . 
       FIG.  4    is a schematic circuit diagram illustrating a power conversion apparatus according to a second embodiment of the present invention. As shown in  FIG.  4   , the power conversion apparatus  110  includes two power conversion circuits  2 . Each power conversion circuit  2  has the circuitry structure as shown in  FIG.  2 A . The first terminals of the two power conversion circuits  2  are electrically connected with each other. The second terminals of the two power conversion circuits  2  are electrically connected with each other. 
     In the embodiment as shown in  FIG.  4   , each power conversion circuit  2  of the power conversion apparatus  110  includes a first capacitor C 1  and a second capacitor C 2 . In a variant example, one first capacitor C 1  is shared by the first terminals of the power conversion circuits  2 , and one second capacitor C 2  is shared by the second terminals of the power conversion circuit  2 . 
     From the above descriptions, the present invention provides a power conversion circuit and a power conversion apparatus. The magnetic element of the power conversion circuit includes two first winding and at least one second winding. These windings interact with each other to result in the electromagnetic coupling effect. The turn ratio between the second winding and the first winding is N:1. Since the voltage gain of the power conversion circuit is adjustable according to the turn number of the second winding, the applications of the power conversion circuit are expanded. 
     While the invention has been described in terms of what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention needs not be limited to the disclosed embodiment. On the contrary, it is intended to cover various modifications and similar arrangements included within the spirit and scope of the appended claims which are to be accorded with the broadest interpretation so as to encompass all such modifications and similar structures.