Patent Publication Number: US-11652396-B2

Title: DC-DC resonant converter and control method thereof

Description:
RELATED APPLICATION 
     This application claims the benefit of priority to U.S. Provisional Application No. 63/046,158, filed Jun. 30, 2020, the entire contents of which are incorporated herein by reference for all purposes. 
    
    
     TECHNICAL FIELD 
     This present disclosure relates to a DC-DC resonant converter and a control method thereof. More particularly, the present disclosure relates to a stacked-bridge resonant converter with switching frequency control and voltage balancing strategies. 
     BACKGROUND 
     The resonant converter, which employ a resonant-tank circuit to shape the switch voltage and/or current waveforms to minimize switching losses and allow high-frequency operation, has been widely employed as an isolated DC/DC converter, due to its high efficiency, simple structure achieved by magnetic integration, soft switching on both primary and secondary switches, and capability suitable for applications with wide voltage ranges. 
     For example, U.S. Pat. No. 6,344,979 to Huang et al, entitled “LLC Series Resonant DC-to-DC Converter”, issued Feb. 5, 2002, discloses an LLC resonant converter and its basic operation principles.  FIGS.  1 A and  1 B  respectively show a conventional full-bridge LLC resonant converter under closed-loop voltage control and the timing diagrams of control signals for switches S 1  to S 4  and a primary-side full-bridge output voltage V AB . Output voltage V AB  may be regulated by controlling the switching frequency of these primary-side switches. Highest efficiency is attained when the LLC resonant converter operates at resonant frequency f r , determined by resonant inductor L r  and resonant capacitor Cr, and when DC voltage gain M equals the transformer&#39;s turns ratio N P /N S . DC voltage gain M diminishes when switching frequency f sw  is greater than resonant frequency f r . Conversely, gain M becomes greater when switching frequency f sw  is less than resonant frequency f r . Efficiency, however, always diminishes as switching frequency f sw  moves away from resonant frequency f r . To achieve desired output voltage range, the LLC resonant converter should operate at its corresponding frequency range. 
     As shown in  FIGS.  1 A and  1 B , the resonant tank includes inductor L r  and capacitors Cr connected in series, and the circuit can be referred to as a series-resonant converter. If the magnetizing inductance L m  of transformer TR is relatively small, i.e., if it is only several times of resonant inductance L r , the converter can operate as an LLC series-resonant converter. It should be noted that the secondary-side diode rectifier (including diodes D 1 , D 2 , D 3 , and D 4 ) can be implemented by a synchronous rectifier (e.g., using low on-resistance MOSFETs) to improve the efficiency. This implementation also makes the converter bidirectional, because controllable switches on both sides of the transformer allow power to flow in both directions. It should also be noted that the secondary-side of the isolated resonant converter can be implemented with a center-tapped secondary side winding instead of employing a full-wave rectifier as shown in  FIG.  1 A . 
     Generally, resonant converters are controlled by variable switching-frequency control. During above-resonant-frequency operations, the resonant converters operate with zero-voltage-switching (ZVS) of the primary switches, while during below-resonant-frequency operations, the resonant converters operate with zero-current switching (ZCS). More details about resonant converter topologies and control thereof can be found in Ref. [1]. 
     Typical timing diagrams of switch-control signals for the series-resonant converter in  FIG.  1 A  operating with ZVS are shown in  FIG.  1 B . As shown in  FIG.  1 B , all switches S 1 , S 2 , S 3 , and S 4  operate with the same duty ratio of 50%. The primary side switches in the same leg (i.e., switches S 1  and S 2  in leg A and switches S 3  and S 4  in leg B) operate in a complementary fashion to avoid cross-conduction. The frequency of the primary side switches is determined by a feedback control loop that is employed to regulate the output. To achieve ZVS in practical implementations, the duty ratios of the primary switches are set to a value slightly less than 50% by introducing a short delay (or dead time) between the turn-off and the turn on of the complementary operated same-leg switches. During this dead time, the current is commutated from the switch of the device that is being turned off to the antiparallel diode of the other device which creates a condition for its subsequent ZVS turn on. 
     The full bridge structure is normally used in less than 800V DC input voltage applications when 1.2 kV devices are applied. In high input voltage applications, three-level topology in Ref. [2] is more attractive, because of the fact that each switching device needs to block only one half of the input voltage. Three-level topology is applied to LLC converters in Ref [3], in which the proposed converters achieve ZVS for the switches without additional auxiliary circuit. In Ref. [4], a three-level serial half bridge (SHB) topology, also known as stacked buck topology, is proposed for the first time. This topology removes the two clamping diodes in comparison with the conventional three-level topology from Ref. [2]. 
       FIGS.  2 A and  2 B  respectively illustrate an exemplary serial half bridge resonant converter and its timing diagrams of control signals for switches S 1  to S 4  and a primary-side full-bridge output voltage V AB  The serial half bridge resonant converter is also controlled by variable switching-frequency control. As shown in  FIG.  2 A , all switches S 1 , S 2 , S 3 , and S 4  operate with the same duty ratio of 50%. The primary side switches in the same leg (i.e., switches S 1  and S 2  in leg A and switches S 3  and S 4  in leg B) operate in a complementary fashion to avoid cross-conduction. Switches S 1  and S 4  have the same switch control signals, while switches S 2  and S 3  have the same switch control signals. The frequency of the primary side switches is determined by a feedback control loop that is employed to regulate the output. 
     Generally, the power of a full bridge resonant converter based on a discrete device is limited to a few kilowatts because of the device&#39;s power rating. A three-phase LLC resonant converter is proposed in Ref. [5] to further increase the converter power by adding another half bridge phase leg in parallel to the existing legs on the primary side and another half bridge phase leg in parallel to the existing legs on the secondary side. The three-phase converter can have either three separated transformers or a single integrated transformer. The topology of a typical three phase LLC converter and its timing diagrams of switch-control are shown in  FIGS.  3 A and  3 B . The switch-control signals of each primary half bridge are usually interleaved with each other with a 120-degree phase shift. This implementation can reduce the current and voltage ripple, thus reducing the stress on the components. 
     Recently, high input voltage (&gt;2 kV) power supplies are more and more attractive in high power applications, such as a solid-stage-transformer, because they can deliver more power for the same amount of input current. A multi-phase multi-level LLC resonant converter with a star connection of transformers is proposed in Ref. [6] to satisfy the requirement for high-voltage and high-power applications. The topology of a multi-phase multi-level LLC resonant converter with three modules and its timing diagrams of switch-control shown in  FIGS.  4 A and  4 B . The switch-control signals of each primary side half bridge are usually interleaved with each other with a 120-degree phase shift. However, the resonant capacitors in each phase leg suffer DC voltage bias due to the stacking structure and the star connection of the transformers. The bias voltage further increases when the input voltage increases. In addition, the voltage imbalance issue of the stacked capacitors and the bidirectional operation are not addressed in Ref. [6]. Therefore, there is a need to develop a DC/DC bidirectional resonant converter that is capable of operating in high input voltage and high-power applications, as well as reserving the merit of conventional resonant converters. There is also a need to develop a voltage balancing control strategy applied in multi-phase multi-level LLC resonant converters. 
     REFERENCES 
     
         
         [1] B. Yang, F. C. Lee, A. J. Zhang and G. Huang, “LLC resonant converter for front end DC/DC conversion,” APEC. Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition (Cat. No. 02CH37335), Dallas, Tex., USA, 2002. 
         [2] J. R. Pinheiro and I. Barbi, “The three-level ZVS PWM converter—a new concept in high voltage DC-to-DC conversion,” Proceedings of the 1992 International Conference on Industrial Electronics, Control, Instrumentation, and Automation, 1992. 
         [3] Y. Gu, Z. Lu, L. Hang, Z. Qian and G. Huang, “Three-level LLC series resonant DC/DC converter,” IEEE Transactions on Power Electronics, vol. 20, no. 4, pp. 781-789, July 2005. 
         [4] I. Barbi, R. Gules, R. Redl and N. O. Sokal, “DC-DC converter: four switches V/sub pk/=V/sub in//2, capacitive turn-off snubbing, ZV turn-on,” IEEE Transactions on Power Electronics, vol. 19, no. 4, pp. 918-927, July 2004. 
         [5] T. Jin and K. Smedley, “Multiphase LLC Series Resonant Converter for Microprocessor Voltage Regulation,” Conference Record of the 2006 IEEE Industry Applications Conference Forty-First IAS Annual Meeting, Tampa, Fla., 2006, pp. 2136-2143. 
         [6] F. Jin, F. Liu, X. Ruan and X. Meng, “Multi-phase multi-level LLC resonant converter with low voltage stress on the primary-side switches,” 2014 IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, Pa., 2014, pp. 4704-4710. 
       
    
     SUMMARY 
     In one embodiment of the present disclosure, a DC-DC resonant converter with improved performance is disclosed. Specifically, the resonant converter of the embodiment of the present disclosure can be used in high power and high voltage applications by stacking a plurality of circuit elements in series. 
     In one aspect, one embodiment of the present disclosure provides a DC-DC converter including: a primary side including a serial stack of at least two half-bridge inverter cells, each including two active switches in series in one leg and two input capacitors in series in a parallel leg together forming a loop wherein each inverter cell is connected from a point between the switches to a resonant tank circuit to a primary side winding wound on a transformer core, and to a point between the two capacitors, wherein one end of the loop connecting the legs of one inverter cell is directly connected to the opposite end of the corresponding loop in an inverter cell on which it is stacked and a primary side voltage is applied or produced between the two ends of the loops of the serial stack of inverter cells that are not directly connected to another inverter cell and wherein the transformer core is sharable with other inverter cells; a secondary side including at least two sets of rectifier circuit elements each coupled to a secondary side winding wound on a transformer core shared with a corresponding primary side winding and is configured to rectify current induced at the secondary stage by current flowing in the corresponding primary side winding, and wherein a secondary side voltage is produced or applied; and control circuitry that activates switches in the converter to vary the pulse frequency or width or phase shift angle of voltage or current through inverter cells or rectifier circuits. 
     In one embodiment, the rectifier circuit elements are each a half-bridge rectifier cell including in a leg two diodes in series and oriented in the same direction between which is a connection to the corresponding secondary side winding to a common star connection of the corresponding ends of all the rectifiers, wherein corresponding ends of the diode legs form common connections with a parallel capacitor legs such that the secondary side voltage is produced between the two ends of the parallel legs. 
     In one embodiment, the rectifier circuit elements are each an active half-bridge rectifier including in a leg two active switches in series, each controlled by the control circuitry, between which switches is a connection to the corresponding secondary side winding to a common star connection of the corresponding ends of all the rectifier cells, wherein corresponding ends of the switch legs form common connections with a parallel capacitor leg such that the secondary side voltage is produced or applied between the two ends of the parallel legs. 
     In one embodiment, the rectifier circuit elements are each a full-bridge rectifier cell including two parallel legs of two diodes in series oriented in the same direction wherein each rectifier cell is connected from a point between the diodes of one leg to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the diodes of the other leg, wherein corresponding ends of the diode legs form common connections with a parallel capacitor leg such that the secondary side voltage is produced between the two ends of the parallel legs. 
     In one embodiment, the rectifier circuit elements are each a full-bridge rectifier cell including two parallel legs of two active switches in series, each controlled by the control circuitry, between which switches in a leg is a connection to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the switches of the other leg, wherein corresponding ends of the switch legs form common connections with a parallel capacitor leg such that the secondary side voltage is produced or applied between the two ends of the parallel legs. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two diodes in series oriented in the same direction in one leg and two capacitors in series in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the diodes to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the two capacitors, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two active switches in series in one leg, each controlled by the control circuitry, and two capacitors in series in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the switches to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the two capacitors, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two diodes in series oriented in the same direction in one leg and a capacitor in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the diodes through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a common star connection of the corresponding ends of all the rectifier cells, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two active switches in series in one leg, each controlled by the control circuitry, and a capacitors in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the switches through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a common star connection of the corresponding ends of all the rectifier cells, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of full-bridge rectifier cells, each including two legs of two diodes in series oriented in the same direction and a capacitor leg in parallel connected at each end of the respective legs wherein each rectifier cell is connected from a point between the diodes of one leg to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the diodes of the other leg, wherein one connection of the parallel legs of one rectifier cell is directly connected to the opposite side connection of the parallel legs of a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two connections of parallel legs of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of full-bridge rectifier cells, each including two legs of two active switches in series, each controlled by the control circuitry, and a capacitor leg in parallel connected at each end of the respective legs wherein each rectifier cell is connected from a point between the switches of one leg to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the switches of the other leg, wherein one connection of the parallel legs of one rectifier cell is directly connected to the opposite side connection of the parallel legs of a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two connections of parallel legs of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of serial-half-bridge rectifier cells, each including a first set of two diodes oriented in the same direction in a first series leg and a capacitor in a parallel leg connected at each end of the legs to form a first loop connecting at its reverse end to the forward end of a second loop of two diodes oriented in the same direction in a second series leg and a capacitor in a parallel leg, wherein each rectifier cell is connected from a point between the diodes of the first series leg through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the diodes of the second series leg, wherein the reverse end of the stacked loops of one rectifier cell is directly connected to the forward end of the stacked loops of a rectifier cell on which it is stacked and a secondary side voltage is produced between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another loop. 
     In one embodiment, the rectifier circuit elements form a serial stack of serial-half-bridge rectifier cells, each including a first set of two active switches, each controlled by the control circuitry, in a first series leg and a capacitor in a parallel leg connected at each end of the legs to form a first loop connecting at a reverse end to a forward end of a second loop of two active switches, each controlled by the control circuitry, in a second series leg and a capacitor in a parallel leg, wherein each rectifier cell is connected from a point between the switches of the first series leg through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the switches of the second series leg, wherein the reverse end of the stacked loops of one rectifier cell is directly connected to the forward end of the stacked loops of a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another loop. 
     In one embodiment, the control circuitry determines whether the average of voltages detected across the two input capacitors of an inverter cell is greater than a reference voltage and, if so, adjusts the inverter cell duty cycles through the two switches to balance the capacitor voltages. 
     In one embodiment, the control circuitry determines whether any of the average voltages across the two input capacitors of each inverter cell minus a reference voltage is greater than a threshold voltage and, if so, determines the greatest difference among the cells and adjusts the phase shift angle to each phase leg through the two switches to balance the capacitor voltages. 
     In another aspect, one embodiment of the present disclosure provides a DC-DC converter including: a primary side including sets of at least two serial half-bridge inverter cells, each including a first half-bridge of two active switches in a first series leg and an input capacitor in a parallel leg connected at each end of the legs to form a first loop connecting at a reverse end to a forward end of a second half-bridge loop of two active switches in a second series leg and a capacitor in a parallel leg, wherein each inverter cell is connected from a point between the switches of the first series leg through a resonant tank circuit, through the primary side winding wound on a transformer core to a point between the switches of the second series leg, wherein the reverse end of the stacked loops of one inverter cell is directly connected to the forward end of the stacked loops of an inverter cell on which it is stacked and a primary side voltage is applied or produced between the two ends of the loops of the serial stack of inverter cells that are not directly connected to another loop and wherein the transformer core is shared with other inverter cells; a secondary side including at least two sets of rectifier circuit elements each coupled to a secondary side winding wound on the transformer core shared with a corresponding primary side winding and is configured to rectify current induced at the secondary stage by current flowing in the corresponding primary side winding, and wherein a secondary side voltage is produced or applied; and control circuitry that activates switches in the converter to vary the pulse frequency or width or phase shift angle of voltage or current through inverter or rectifier circuits. 
     In one embodiment, the rectifier circuit elements are each a half-bridge rectifier including in a leg two diodes in series and oriented in the same direction between which is a connection to the corresponding secondary side winding to a common star connection of the corresponding ends of all the rectifier cells, wherein corresponding ends of the diode legs form common connections with a parallel capacitor legs such that the secondary side voltage is produced between the two ends of the parallel legs. 
     In one embodiment, the secondary circuit elements are each an active half-bridge rectifier cell including in a leg two active switches in series, each controlled by the control circuitry, between which switches is a connection to the corresponding secondary side winding to a common star connection of the corresponding ends of all the rectifier cells, wherein corresponding ends of the switch legs form common connections with a parallel capacitor leg such that the secondary side voltage is produced or applied between the two ends of the parallel legs. 
     In one embodiment, the rectifier circuit elements are each a full-bridge rectifier including two parallel legs of two diodes in series oriented in the same direction wherein each rectifier cell is connected from a point between the diodes of one leg to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the diodes of the other leg, wherein corresponding ends of the diode legs form common connections with a parallel capacitor leg such that the secondary side voltage is produced between the two ends of the parallel legs. 
     In one embodiment, the rectifier circuit elements are each a full-bridge rectifier including two parallel legs of two active switches in series, each controlled by the control circuitry, between which switches in a leg is a connection to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the switches of the other leg, wherein corresponding ends of the switch legs form common connections with a parallel capacitor leg such that the secondary side voltage is produced or applied between the two ends of the parallel legs. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two diodes in series oriented in the same direction in one leg and two capacitors in series in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the diodes to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the two capacitors, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two active switches in series in one leg, each controlled by the control circuitry, and two capacitors in series in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the switches to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the two capacitors, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two diodes in series oriented in the same direction in one leg and a capacitor in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the diodes through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a common star connection of the corresponding ends of all the rectifier cells, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of half-bridge rectifier cells, each including two active switches in series in one leg, each controlled by the control circuitry, and a capacitors in a parallel leg together forming a loop wherein each rectifier cell is connected from a point between the switches through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a common star connection of the corresponding ends of all the rectifier cells, wherein one end of the loop connecting the parallel legs of one rectifier cell is directly connected to the opposite end of the corresponding loop in a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of full-bridge rectifier cells, each including two legs of two diodes in series oriented in the same direction and a capacitor leg in parallel connected at each end of the respective legs wherein each rectifier cell is connected from a point between the diodes of one leg to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the diodes of the other leg, wherein one connection of the parallel legs of one rectifier cell is directly connected to the opposite side connection of the parallel legs of a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two connections of parallel legs of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of full-bridge rectifier cells, each including two legs of two active switches in series, each controlled by the control circuitry, and a capacitor leg in parallel connected at each end of the respective legs wherein each rectifier cell is connected from a point between the switches of one leg to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the switches of the other leg, wherein one connection of the parallel legs of one rectifier cell is directly connected to the opposite side connection of the parallel legs of a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two connections of parallel legs of the serial stack of rectifier cells that are not directly connected to another rectifier cell. 
     In one embodiment, the rectifier circuit elements form a serial stack of serial-half-bridge rectifier cells, each including a first set of two diodes oriented in the same direction in a first series leg and a capacitor in a parallel leg connected at each end of the legs to form a first loop connecting at its reverse end to the forward end of a second loop of two diodes oriented in the same direction in a second series leg and a capacitor in a parallel leg, wherein each rectifier cell is connected from a point between the diodes of the first series leg through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the diodes of the second series leg, wherein the reverse end of the stacked loops of one rectifier cell is directly connected to the forward end of the stacked loops of a rectifier cell on which it is stacked and a secondary side voltage is produced between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another loop. 
     In one embodiment, the rectifier circuit elements form a serial stack of serial-half-bridge rectifier cells, each including a first set of two active switches, each controlled by the control circuitry, in a first series leg and a capacitor in a parallel leg connected at each end of the legs to form a first loop connecting at a reverse end to a forward end of a second loop of two active switches, each controlled by the control circuitry, in a second series leg and a capacitor in a parallel leg, wherein each rectifier cell is connected from a point between the switches of the first series leg through a blocking capacitor to one end of the corresponding secondary side winding wound on the transformer core and through the other end of the winding to a point between the switches of the second series leg, wherein the reverse end of the stacked loops of one rectifier cell is directly connected to the forward end of the stacked loops of a rectifier cell on which it is stacked and a secondary side voltage is produced or applied between the two ends of the loops of the serial stack of rectifier cells that are not directly connected to another loop. 
     In one embodiment, the control circuitry determines for each inverter cell whether a detected voltage difference across the two input capacitors is greater than a threshold voltage, and if so, adjusts the phase shift angle through the four switches in the corresponding cell; and determines for each inverter cell whether the average voltage across the two input capacitors is greater than a reference voltage, and if so, generates an extra duty cycle through the four switches in the corresponding cell. 
     The use of the word “a” or “an” when used in conjunction with the term “comprising/including” in the claims and/or the specification may mean “one,” but it is also consistent with the meaning of “one or more,” “at least one,” and “one or more than one.” 
     The use of the term “or” in the claims is used to mean “and/or” unless explicitly indicated to refer to alternatives only or the alternative are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and/or.” 
     Other objects, features and advantages of the present invention will become apparent from the following detailed description. It should be understood, however, that the detailed description and the specific examples, while indicating specific embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure is better understood upon consideration of the following detailed description and the accompanying drawings. 
         FIGS.  1 A and  1 B  respectively show a conventional full-bridge LLC resonant converter under closed-loop voltage control and the timing diagrams of control signals for switches S 1  to S 4  and a primary-side full-bridge output voltage V AB . 
         FIGS.  2 A and  2 B  respectively illustrate an exemplary serial half bridge resonant converter and its timing diagrams of control signals for switches S 1  to S 4  and primary-side full-bridge output voltage V AB . 
         FIGS.  3 A and  3 B  respectively illustrate the topology of a typical three phase LLC converter and its timing diagrams of switch-control. 
         FIGS.  4 A and  4 B  respectively illustrate the topology of a multi-phase multi-level LLC resonant converter with three modules and its timing diagrams of switch-control. 
         FIG.  5 A  illustrates a three-stacked half bridge LLC resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  5 B  illustrates the timing diagrams for the converter in  FIG.  5 A  under variable frequency control for switch control signals GS 1  to GS 6 , resonant tank input voltages V AB  V CD , and V EF , resonant capacitor voltages V cr1 , V cr2 , and V cr3 , and resonant currents i r1 , i r2 , and i r3 , in accordance with an embodiment of the present disclosure. 
         FIG.  5 C  illustrates the timing diagrams for the converter in  FIG.  5 A  under variable duty cycle control for switch control signals GS 1  to GS 6 , resonant capacitor voltages V cr1  to V cr3 , and resonant currents i r1  to i r3 , in accordance with an embodiment of the present disclosure. 
         FIG.  6 A  illustrates a three-stacked half bridge LLC resonant converter with active switches on the secondary side for bidirectional operation, in accordance with an embodiment of the present disclosure. 
         FIG.  6 B  illustrates the timing diagrams for the converter in  FIG.  6 A  under variable frequency control and phase shift control for switch control signals GS 1  to GS 12 , resonant capacitor voltages V cr1  to V cr3 , and resonant currents i r1  to i r3 , in accordance with an embodiment of the present disclosure. 
         FIG.  7 A  illustrates an n-stacked half bridge resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  7 B  illustrates an n-stacked half bridge resonant converter with an integrated transformer. 
         FIG.  7 C  illustrates an n-stacked half bridge resonant converter with active switches on the secondary side for synchronous rectification and bidirectional operation. 
         FIG.  8 A  illustrates a three-stacked serial half bridge resonant converter with a three-phase diode bridge rectifier, in accordance with an embodiment of the present disclosure. 
         FIG.  8 B  illustrates the timing diagrams for the converter in  FIG.  8 A  under variable frequency control for switch control signals GS 1  to GS 6 , full bridge output voltage V AB  to V EF , resonant capacitor voltage V cr1  to V cr3 , and resonant current i r1  to i r3 . 
         FIG.  8 C  illustrates a three-stacked serial half bridge resonant converter with three full-wave diode bridges in parallel for rectification, in accordance with an embodiment of the present disclosure. 
         FIG.  9 A  illustrates an n-stacked serial half bridge resonant converter with total n half-wave diode bridges in parallel for rectification, in accordance with an embodiment of the present disclosure. 
         FIG.  9 B  illustrates an n-stacked serial half bridge resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
         FIG.  9 C  illustrates an n serial half bridge resonant converter with active switches on the secondary side for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. 
         FIG.  9 D  illustrates an n-stacked serial half bridge resonant converter with total n full-wave diode bridges in parallel for rectification, in accordance with an embodiment of the present disclosure. 
         FIG.  10 A  illustrates a voltage balancing control diagram based on duty cycle method for a stacked half bridge resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  10 B  illustrates a voltage balancing control diagram based on duty cycle method for a stacked half bridge resonant converter with star connection of transformers, in accordance with an embodiment of the present disclosure. 
         FIG.  10 C  illustrates a voltage balancing control flow chart based on phase shift method for a three-stacked half bridge resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  10 D  illustrates a voltage balancing control flow chart based on phase shift method for a three-stacked half bridge resonant converter with star connection of transformers, in accordance with an embodiment of the present disclosure. 
         FIG.  10 E  illustrates a voltage balancing control diagram based on a hybrid method for a stacked serial half bridge resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  11 A  illustrates a three stacked full bridge resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  11 B  illustrates the timing diagrams for the converter in  FIG.  11 A  under variable frequency control for switch control signals GS 1  to  12  full bridge output voltage V AB  to V EF , resonant capacitor voltage V cr1  to V cr3 , and resonant current i r1  to i r3 . 
         FIG.  11 C  illustrates an n-stacked full bridge resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  11 D  illustrates an n-stacked full bridge resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
         FIG.  11 E  illustrates an n-stacked full bridge resonant converter with active switches on the secondary side for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. 
         FIG.  12 A  illustrates a three stacked half bridge rectifier with transformer star connection applied in a three-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  12 B  illustrates the timing diagrams for the converter in  FIG.  12 A  under variable frequency control for switch control signals GS 1  to GS 6 , primary resonant current i r1  to i r3  secondary current i s1  to i s3 , secondary blocking capacitor voltage V cs1  to V cs3 , output capacitor voltage V CO1  to V CO3  and output voltage V o . 
         FIG.  12 C  illustrates an n-stacked half bridge rectifier with transformer star connection applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  12 D  illustrates an n-stacked half bridge rectifier with transformer star connection applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
         FIG.  12 E  illustrates an n-stacked active half bridge rectifier with transformer star connection applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. 
         FIG.  13 A  illustrates a three stacked half bridge rectifier applied in a three-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  13 B  illustrates the timing diagrams for the converter in  FIG.  13 A  under variable frequency control for switch control signals GS 1  to GS 6 , primary resonant current i r1  to i r3  secondary current i s1  to i s3 , output capacitor voltage V CO1  to V CO6  and output voltage V O . 
         FIG.  13 C  illustrates an n-stacked half bridge rectifier applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  13 D  illustrates an n-stacked half bridge rectifier applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
         FIG.  13 E  illustrates an n-stacked active half bridge rectifier applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. 
         FIG.  14 A  illustrates a three stacked full bridge rectifier applied in a three-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  14 B  illustrates an n-stacked full bridge rectifier applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  14 C  illustrates an n-stacked full bridge rectifier applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
         FIG.  14 D  illustrates an n-stacked active full bridge rectifier applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. 
         FIG.  15 A  illustrates a three-stacked serial-half-bridge rectifier applied in a three-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  15 B  illustrates an n-stacked serial-half-bridge rectifier applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  15 C  illustrates an n-stacked serial-half-bridge rectifier applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
         FIG.  15 D  illustrates an n-stacked serial-half-bridge rectifier applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. 
         FIG.  16    illustrates a generalized stacked resonant converter, in accordance with an embodiment of the present disclosure. 
         FIG.  17    illustrates a generalized stacked resonant converter including multiple circuits in parallel on both the primary and secondary sides, in accordance with an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     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. For example, the formation of a first feature over or on a second feature in the description that follows may include embodiments in which the first and second features are formed in direct contact, and may also include embodiments in which additional features may be formed between the first and second features, such that the first and second features may not be in direct contact. In addition, the present disclosure may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. Further, spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. The apparatus may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein may likewise be interpreted accordingly. When an element is referred to as being “connected,” or “coupled,” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. Although the wide numerical ranges and parameters of the present disclosure are approximations, numerical values are set forth in the specific examples as precisely as possible. In addition, although the “first,” “second,” “third,” and the like terms in the claims be used to describe the various elements can be appreciated, these elements should not be limited by these terms, and these elements are described in the respective embodiments are used to express the different reference numerals, these terms are only used to distinguish one element from another element. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of example embodiments. Besides, “and/or” and the like may be used herein for including any or all combinations of one or more of the associated listed items. While the numerical ranges and parameters set forth for the broad scope of the present invention are approximations, the numerical value reported in the specific examples set forth as accurately as possible. However, any numerical values inherently contain certain errors necessarily the standard deviation found in the respective testing measurements caused. Also, as used herein, the term “about” generally means away from a given value or a range of 10%, 5%, 1% or 0.5%. Alternatively, the word “about” means within an acceptable standard error of ordinary skill in the art-recognized average. In addition to the operation/working examples, or unless otherwise specifically stated otherwise, in all cases, all of the numerical ranges, amounts, values and percentages, such as the number for the herein disclosed materials, time duration, temperature, operating conditions, the ratio of the amount, and the like, should be understood as the word “about” decorator. Accordingly, unless otherwise indicated, the numerical parameters of the present invention and scope of the appended patent proposed is to follow changes in the desired approximations. At least, the number of significant digits for each numerical parameter should at least be reported and explained by conventional rounding technique is applied. Herein, it can be expressed as a range between from one endpoint to the other or both endpoints. Unless otherwise specified, all ranges disclosed herein are inclusive. 
     A. Stacked Half Bridge Resonant Converter 
     Three Stacked Half Bridge Resonant Converter 
       FIG.  5 A  illustrates a stacked half bridge resonant converter  500 , in accordance with an embodiment of the present disclosure.  FIG.  5 B  illustrates the timing diagrams for converter  500  in  FIG.  5 A  under variable frequency control for switch control signals GS 1  to GS 6 , resonant tank input voltages V AB  V CD , and V EF , resonant capacitor voltages V cr1 , V cr2 , and V cr3 , and resonant currents i r2 , and i r3 , in accordance with an embodiment of the present disclosure.  FIG.  5 C  illustrates the timing diagrams for converter  500  in  FIG.  5 A  under variable duty cycle control for switch control signals GS 1  to GS 6 , resonant capacitor voltage V cr1  to V cr3 , and resonant current i r1  to i r3 , in accordance with an embodiment of the present disclosure. 
     In the embodiment, the DC-DC converter  500  includes a primary side, a secondary side, a control circuitry, a transformer stage electrically connected to the primary side and the secondary side, and at least one resonant tank circuit electrically connected between the primary side and the at least one transformer TR. The primary side includes a serial stack of at least two half-bridge inverter cells  501 ,  502 , and  503 . The inverter cells  501  includes two active switches S 1  and S 2  in series in one leg and two input capacitors C 1  and C 2  in series in a parallel leg. The inverter cells  502  includes two active switches S 3  and S 4  in series in one leg and two input capacitors C 3  and C 4  in series in a parallel leg. The inverter cells  503  includes two active switches S 5  and S 6  in series in one leg and two input capacitors C 5  and C 6  in series in a parallel leg. In the embodiment, the transformer stage includes a first transformer TR 1 , a second transformer TR 2 , and a third transformer TR 3 , and the at least one resonant tank circuit includes a first resonant tank circuit, a second resonant tank circuit, and a third resonant tank circuit. In the embodiment, each of the transformers TR 1 , TR 2 , and TR 3  includes a transformer core, a primary side winding wound on the transformer core, and a secondary side winding wound on the transformer core. The control circuitry is configured to activate the active switches S 1 , S 2 , S 3 , S 4 , S 5 , and S 6  to vary the pulse frequency or width or phase shift angle of voltage or current through the inverter cells or the rectifier circuit elements. 
     It should be noted that the terms “rectifier,” “rectifier circuit element,” “rectifier cell,” and the like in the disclosure may mean the same in some embodiments and may be used herein for ease of description to describe one element or feature utilized for providing rectification function. 
     Converter  500  employs three half bridges  501 ,  502 , and  503  in stack on the primary side including switches S 1  to S 6  and also includes six input capacitors C 1 , C 2 , C 3 , C 4 , C 5 , and C 6  in stack. As shown in  FIG.  5 A , first half bridge  501  includes switches S 1  and S 2  connected in series and input capacitors C 1  and C 2  connected in series. Switches S 1  and S 2  and input capacitors C 2  and C 1  are connected together in series to form a first circuit loop. Point A between switches S 1  and S 2  is connected to one end of a first resonant tank including a resonant capacitor C r1  and a resonant inductor L r1 . The other end of the first resonant tank is connected to one end of the primary side winding of transformer TR 1 . The other end of the primary side winding of transformer TR 1  is connected to point B between input capacitors C 1  and C 2 . 
     Likewise, as shown in  FIG.  5 A , second half bridge  502  includes switches S 3  and S 4  connected in series and input capacitors C 3  and C 4  connected in series. Switches S 3  and S 4  and input capacitors C 4  and C 3  are connected together in series to form a second circuit loop. Point C between switches S 3  and S 4  is connected to one end of a second resonant tank including a resonant capacitor C r2  and a resonant inductor L r2 . The other end of the second resonant tank is connected to one end of the primary side winding of transformer TR 2 . The other end of the primary side winding of transformer TR 2  is connected to point D between input capacitors C 3  and C 4 . It is appreciated that the first and second circuit loops are directly connected. 
     Further, as shown in  FIG.  5 A , third half bridge  503  includes switches S 5  and S 6  connected in series and input capacitors C 5  and C 6  connected in series. Switches S 5  and S 6  and input capacitors C 6  and C 5  are connected together in series to form a third circuit loop. Point E between switches S 5  and S 6  is connected to one end of a third resonant tank including a resonant capacitor C r3  and a resonant inductor L r3 . The other end of the second resonant tank is connected to one end of the primary side winding of transformer TR 3 . The other end of the primary side winding of transformer TR 3  is connected to point F between input capacitors C 5  and C 6 . It is appreciated that the second and third circuit loops are directly connected, but the first and third circuit loops are not directly connected. 
     In sum, in this embodiment, three separated transformers TR 1 , TR 2 , and TR 3  are used where one end of each transformer&#39;s primary side winding is connected to a resonant tank which in turn is connected to the middle point of the corresponding switches, while the other end of each transformer&#39;s primary side winding is coupled to the middle point of the corresponding input capacitors. 
     In one embodiment, a first terminal (between switch S 1  and input capacitor C 1 ) of first half bridge  501  is connected to a positive electrode of input voltage V in  and a second terminal (between switch S 2  and input capacitor C 2 ) of first half bridge  501  is connected to a first terminal (between switch S 3  and input capacitor C 3 ) of second half bridge  502 . A second terminal (between switch S 4  and input capacitor C 4 ) of second half bridge  502  is connected to a first terminal (between switch S 5  and input capacitor C 5 ) of third half bridge  503 . A second terminal (between switch S 6  and input capacitor C 6 ) of third half bridge  503  is connected to a negative electrode of input voltage V in . In other words, first, second, and third half bridges  501 ,  502 ,  503 , each forming a circuit loop, are “stacked” vertically to form a stacked half bridge. 
     In one embodiment, the secondary side includes at least two sets of rectifier circuit elements each coupled to a secondary side winding wound on the transformer core shared with a corresponding primary side winding and is configured to rectify current induced at the secondary side by current flowing in the corresponding primary side winding, and wherein a secondary side voltage V o  is produced or applied. In the embodiment, conventional three phase diode bridges (including diodes D 1 , D 2 , D 3 , D 4 , D 5 , and D 6 ) are used in secondary side to provide rectification function. 
     Variable Switching Frequency Control for Three Stacked Half Bridge Resonant Converter 
       FIG.  5 B  illustrates the timing diagrams for converter  500  in  FIG.  5 A  under variable frequency control for switch control signals GS 1  to GS 6 , resonant tank input voltages V AB  V CD , and V EF , resonant capacitor voltages V cr1 , V cr2 , and V cr3 , and resonant currents i r1 , i r2 , and i r3 , in accordance with an embodiment of the present disclosure. Switch control signals GS 1  to GS 6  are the respective control signals of switches S 1  to S 6 . In this embodiment, variable switching frequency control is used to regulate the output voltage and output power of stacked half bridge resonant converter  500 . 
     As shown in  FIG.  5 B , all switches operate with the same switching frequency (e.g., 100 kHz or greater than 20 kHz) and have identical duty cycles of approximately 50%. To achieve zero-voltage-switching of the complementary-operated primary side switches of the same leg, a small dead time is provided between the turn-on and turn-off instants of these complementary-operated switches. The switch control signals of each half bridge are interleaved with each other with a phase shift of 120°. For example, switch control signals GS 1  and GS 2  are phase shifted with respect to switch control signals GS 3  and GS 4  by 120 degrees. In this embodiment, the resonant tank input voltages V AB , V CD  and V EF  are in a square waveform with no DC bias voltage. For the same reason, resonant capacitor voltages V cr1 , V cr2 , and V cr3  are in a sinusoidal waveform with no DC bias voltage. Resonant currents i r1 , i r2 , and i r3  for all three resonant tanks are pure sinusoid, if the resonant converter operates at its resonant frequency and the magnetizing current is negligible. Each resonant current is interleaved with each other with a phase shift of 120° due to the interleaved switch control signals. The interleaved currents can provide minimal ripple on the components to further improve the converter performance. 
     Pulse Width Modulation (PWM) for Stacked Half Bridge Resonant Converter 
     If wide input and/or output voltage range is required in specific applications, such as in battery charging applications, implementing only the variable switching frequency control may not be able to achieve the required gain range. Pulse width modulation (PWM) or variable duty cycle control is proposed to regulate the gain of the resonant circuit in this situation, when switching frequency control reaches its upper limit. 
       FIG.  5 C  illustrates the timing diagrams for converter  500  in  FIG.  5 A  under variable duty cycle control for switch control signals GS 1  to GS 6 , resonant capacitor voltages V cr1  to V cr3 , and resonant currents i r1  to i r3 , in accordance with an embodiment of the present disclosure. Switch control signals GS 1  to GS 6  are the respective control signals of switches S 1  to S 6 . As shown in  FIG.  5 C , the switch control signals of each half bridge are interleaved with each other with a phase shift of 120°. For example, switch control signals GS 1  and GS 2  in the first leg are phase shifted with switch control signals GS 3  and GS 4  in the second leg by a phase shift angle of 120°. The duty cycle for switch control signals GS 1  to GS 6  are reduced from the nominal 50% to 40%, so as to further reduce the output voltage. The resonant currents i r1  to i r3  may become discontinuous in this modulation. 
     Phase Shift Modulation for Stacked Half Bridge Resonant Converter 
       FIG.  6 A  illustrates a stacked half bridge LLC resonant converter  600  with active switches S 7  to S 12  on the secondary side for bidirectional operation, in accordance with an embodiment of the present disclosure. Converter  600  in  FIG.  6 A  is substantially identical to converter  500  in  FIG.  5 A  on the primary side. However, instead of diodes, converter  600  in  FIG.  6 A  employs three active half bridges in parallel on the secondary side including switches S 7  to S 12  for bidirectional operation. 
       FIG.  6 B  illustrates the timing diagrams for converter  600  in  FIG.  6 A  under variable frequency control and phase shift control for switch control signals GS 1  to GS 12 , resonant capacitor voltages V cr1  to V cr3 , and resonant currents i r1  to i r3 , in accordance with an embodiment of the present disclosure. Switch control signals GS 1  to GS 12  are the control signals of switches S 1  to S 12 . 
     Variable switching frequency control is normally used to regulate the output voltage and output power in resonant converter. If wide input and/or output voltage range is required in specific applications, such as battery charging applications, implementing only the variable switching frequency control may not be able to achieve the required gain range. Phase shift modulation can be used to achieve wide input and/or output voltage range as well as bidirectional operation. As shown in  FIG.  6 B , all switches operate with the same switching frequency and have identical duty cycles of approximately 50%. To achieve zero-voltage-switching of the complementary-operated primary side switches of the same leg, a small dead time is provided between the turn-on and turn-off instants of these complementary-operated switches. 
     On the primary side, the switch control signals of each half bridge are interleaved with each other with a phase shift of about 120°. On the secondary side, the switch control signals of each half bridge are also interleaved with each other with a phase shift of about 120°. In addition, in one embodiment, the control signals of the first bridge on the primary side may be phase shifted with the control signals of the first bridge on the secondary side. Such a phase shift angle becomes another critical control variable besides the switching frequency. In other words, the output voltage and power are controlled by both the switching frequency and the phase shift angle. In this embodiment, resonant capacitor voltages V cr1  to V cr3  have no DC-bias voltage due to the primary side circuit structure. Resonant currents i r1  to i r3  are interleaved with each other for 120° due to the interleaved switch control signals. These interleaved currents can provide minimal ripple on the components to further improve the converter performance. 
     n-Stacked Half Bridge Resonant Converter 
       FIG.  7 A  illustrates an n-stacked half bridge resonant converter  700 , in accordance with an embodiment of the present disclosure. Converter  700  employs n “stacked” half bridges on the primary side, including 2n switches S 1  to S (2n)  and 2n input capacitors C 1  to C (2n) , where n is a natural number corresponding to the number of phases or resonant tanks in converter  700 . The middle point of each half bridge is connected to a resonant tank which includes a resonant capacitor and a resonant inductor. A total of n separated transformers may be used, and each transformer has a primary side winding and a secondary side winding. The first end of each transformer&#39;s primary side winding is connected to its corresponding middle point of the input capacitors and the second end of each transformer&#39;s primary side winding is connected to the other end of each resonant tank. A total of n half-wave diode bridges in parallel perform the secondary side rectification. 
     Variable switching frequency control can be used to regulate the output voltage and output power of resonant converter  700 . All switches S 1  to S (2n)  operate with the same switching frequency and have identical duty cycles of approximately 50%. To achieve zero-voltage-switching of the complementary-operated primary side switches of the same half bridge, a small dead time is provided between the turn-on and turn-off instants of these complementary-operated switches. The switch control signals of each half bridge are interleaved with each other with a phase shift of 360°/n, where n stands for the number of phases in converter  700 . The resonant currents for all resonant tanks are sinusoid if the magnetizing current is negligible when resonant converter  700  operates at its resonant frequency. Each resonant current is interleaved with each other with 360°/n phase shift angle due to the interleaved switch control signals. This interleaved current can provide the minimal ripple on the components to further improve the converter performance. 
     The total n number of the separated transformer can be integrated to less than n number of transformers. For example,  FIG.  7 B  shows an n-stacked half bridge resonant converter  700  that employs only one integrated transformer, which has total n windings on the primary side and n windings on the secondary side. 
       FIG.  7 C  illustrates an n-stacked half bridge resonant converter  700  with active switches on the secondary side for synchronous rectification and bidirectional operation. As shown in  FIG.  7 C , the 2n diodes on the secondary side as shown in  FIGS.  7 A and  7 B  are replaced by 2n active switches S O1  to S O(2n)  for synchronous rectification to improve the operation efficiency. In this matter, the resonant converter can also provide bidirectional power flow with the active switches. 
     All of the control methods disclosed herein can be implemented in the n-stacked half bridge resonant converter. 
     B. Stacked Serial-Half-Bridge Resonant Converter 
     Three-Stacked Serial-Half-Bridge Resonant Converter 
       FIG.  8 A  illustrates a three-stacked serial half bridge resonant converter  800  with a three-phase diode bridge rectifier, in accordance with an embodiment of the present disclosure. Instead of applying half bridge inverter cells  501 ,  502 , and  503  as basic elements in stacked half bridge resonant converter  500  as shown in  FIG.  5 A , resonant converter  800  employs three serial half bridge inverter cells  801 ,  802 , and  803  in stack, where each serial half bridge includes two half bridges (an upper half bridge and a lower half bridge) connected in series in a stacked structure. 
     As shown in  FIG.  8 A , first serial half bridge inverter cell  801  includes four active switches S 1a , S 1b , S 1c  and S 1d  and two input capacitors C 1a  and C 1b . Switches S 1a  and S 1b , which constitute an upper half bridge, are connected in parallel with input capacitor C 1a  to form a circuit loop. Switches S 1 , and S 1d , which constitute a lower half bridge, are connected in parallel with input capacitor C 1b  to form another circuit loop. Likewise, second serial half bridge inverter cell  802  includes four active switches S 2a , S 2b , S 2c  and S 2d  and two input capacitors C 2a  and C 2b . Switches S 2a  and S 2b , which constitute an upper half bridge, are connected in parallel with input capacitor C 2a  to form a circuit loop. Switches Sec and S 2d , which constitute a lower half bridge, are connected in parallel with input capacitor C 2b  to form another circuit loop. Moreover, third serial half bridge inverter cell  803  includes four active switches S 3a , S 3b , S 3c , and S 3d  and two input capacitors C 3a  and C 3b . Switches S 3a  and S 3b , which constitute an upper half bridge, are connected in parallel with input capacitor C 3a  to form a circuit loop. Switches S 2c  and S 2d , which constitute a lower half bridge, are connected in parallel with input capacitor C 2b  to form another circuit loop. 
     As shown in  FIG.  8 A , a middle point (point A) of the upper half bridges of first serial half bridge inverter cell  801  is connected to a resonant tank which includes a resonant capacitor C r1  and resonant inductor L r1  in series. A middle point (point C) of the upper half bridges of second serial half bridge inverter cell  802  is connected to a resonant tank which includes a resonant capacitor C r2  and resonant inductor L r2  in series. A middle point (point E) of the upper half bridges of third serial half bridge inverter cell  803  is connected to a resonant tank which includes a resonant capacitor C r3  and resonant inductor L r3  in series. 
     In this embodiment, three separated transformers TR 1 , TR 2 , and TR 3  are used. Each transformer has one primary side winding and one secondary side winding. A first end of each transformer&#39;s primary side winding is connected to a middle point (points B, D and F) of the lower half bridge of each serial-half-bridge. A second end of each transformer&#39;s primary side winding is coupled to the other side of each resonant tank. Three phase diode bridges  820  in parallel perform the secondary side rectification. 
     Variable switching frequency control can be used to regulate the output voltage and output power of the stacked serial half bridge resonant converter  800 .  FIG.  8 B  illustrates the timing diagrams for the converter in  FIG.  8 A  under variable frequency control for switch control signals GS 1  to GS 6 , full bridge output voltages V AB  to V EF , resonant capacitor voltage V cr1  to V cr3 , and resonant current i r1  to i r3 . As shown in  FIG.  8 B , all switches operate with the same switching frequency and have identical duty cycles of approximately 50%. To achieve zero-voltage-switching of the complementary-operated primary side switches of the same leg, a small dead time is provided between the turn-on and turn-off instants of these complementary-operated switches. The switch control signals of each serial half bridge are interleaved with each other with a phase shift angle of 120°. The peak-to-peak output voltage of each serial-half-bridge is ⅓ of the input voltage. The resonant capacitor voltages \Teri to vera have a DC bias voltage, which is equal to ⅙ of the input voltage. The resonant currents in three resonant tanks are sinusoid if the magnetizing current is negligible, when the resonant converter operates at its resonant frequency. Due to the interleaved switch control signals, the resonant currents are interleaved with each other with a phase shift angle of 120°. The interleaved currents provide the minimal ripple on the components to further improve the converter performance. 
       FIG.  8 C  illustrates a three-stacked serial half bridge resonant converter  800  with three full-wave diode bridges  830  in parallel for rectification, in accordance with an embodiment of the present disclosure. As shown in  FIG.  8 B , a total of three full-wave diode bridges are implemented on the secondary side in order to reduce the current stress of the secondary diodes in  FIG.  8 A . The control signals of the primary side switches are the same as those shown in  FIG.  8 B . 
     n-Stacked Serial-Half-Bridge Resonant Converter 
       FIG.  9 A  illustrates an n-stacked serial half bridge resonant converter  900  with a total of n half-wave diode bridges in parallel for rectification, in accordance with an embodiment of the present disclosure. Resonant converter  900  employs n serial half bridges in stack, where each serial half bridge includes two half bridge in series. The (m)th serial half bridge has four active switches S ma , S mb , S mc  and S md , together with two input capacitors C ma  and C mb , where m can be any positive integer not larger than n. One of the two middle points of the (m)th serial half bridge is connected to a resonant tank which includes a resonant capacitor C rm  and resonant inductor L rm  in series. A total of n separated transformers are used, and each transformer has one primary side winding and one secondary side winding. A first end of each transformer&#39;s primary side winding is connected to the other middle point of each serial half bridge and a second end of each transformer&#39;s primary side winding is connected to the other side of each resonant tank. A total of n half-wave diode bridges in parallel perform the secondary side rectification. 
     Variable switching frequency control can be used to regulate the output voltage and output power of the stacked serial half bridge resonant converter  900 . All switches operate with the same switching frequency and have identical duty cycles of approximately 50%. To achieve zero-voltage-switching of the complementary-operated primary side switches of the same leg, a small dead time is provided between the turn-on and turn-off instants of these complementary-operated switches. The switch control signals of each serial half bridge are interleaved with each other with a phase shift of 360°/n. For example, the four control signals of the first serial half bridge have 360°/n degree phase shift angle with the four control signals of the second serial half bridge. The resonant currents for all n resonant tanks are sinusoid if the magnetizing current is negligible, when the resonant converter operates at its resonant frequency. Due to the interleaved switch control signals, each resonant current is interleaved with each other with a phase shift angle of 360°/n. The interleaved currents provide the minimal ripple on the components to further improve the converter performance. 
     The total n number of separated transformers can be integrated to less than n transformers. For example,  FIG.  9 B  illustrates an n-stacked serial half bridge resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
     All of the secondary side diodes in  FIG.  9 B  can be replaced with active switches for synchronous rectification to improve the converter efficiency. Resonant converter  900  can provide bidirectional power flow with the active switches on both input and output sides.  FIG.  9 C  illustrates an n-stacked serial half bridge resonant converter with active switches on the secondary side for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. As shown in  FIG.  9 C , the 2n diodes on the secondary side in  FIG.  9 B  are replaced with 2n active switches. 
       FIG.  9 D  illustrates an n-stacked serial half bridge resonant converter with total n full-wave diode bridges in parallel for rectification, in accordance with an embodiment of the present disclosure. A total of n full-wave diode bridges (i.e., a total of 4n diodes) is implemented on the secondary side in order to reduce the current stress of the secondary side diodes in  FIG.  9 A . The control signals of the primary side switches are the same as those in  FIG.  9 A . The transformer integration and active switches on the secondary side can also be implemented in this structure. 
     C. Input Capacitor Voltage Balancing Control Method 
     Voltage Balancing Control Method for Stacked Half Bridge Resonant Converter 
     One challenge to operate a stacked half bridge resonant converter is to balance the input capacitor voltages when mismatches exist in the practical circuit, like capacitor equivalent series resistances (ESR) mismatch, timing mismatch of gate signals for the switches and the resonant parameters mismatch under practical tolerance. 
     Various approaches are possible to balance the input capacitor voltages for different primary stacking structures. The first one is to adjust the duty cycle of the control signals of the switches.  FIG.  10 A  illustrates a voltage balancing control diagram based on duty cycle method for the stacked half bridge resonant converter in  FIG.  7 A , in accordance with an embodiment of the present disclosure. The voltages of the two capacitors for the (m)th half bridge cell are sensed as V Cma  and V Cmb . Average values of the capacitor voltages of each half bridge cell is calculated and compared with a reference voltage V R . When the difference is greater than a predefined threshold voltage V th , a proper modified duty cycle is then generated by a dedicated controller and then implemented to balance the capacitor voltage. This approach can also be implemented in the converter in  FIG.  4    with a star connection of the transformers. Because each half bridge cell is coupled with only one input capacitor, the capacitor voltage is directly sensed and compared with the reference voltage.  FIG.  10 B  illustrates a voltage balancing control diagram based on duty cycle method for a stacked half bridge resonant converter with star connection of transformers, in accordance with an embodiment of the present disclosure. 
     Another approach is to adjust the phase shift angle between the control signals of each half bridge cell. Ideally, 360°/n phase shift angle is implemented between the control signals of each half bridge cell. When detected voltage imbalance by the sensing circuit is greater than a predefined threshold voltage Vth, a proper modified phase shift angle is then implemented to each phase leg to balance the capacitor voltage by changing the power delivered from each phase capacitor to the resonant tank. 
       FIG.  10 C  illustrates a voltage balancing control flow chart based on phase shift method for a three-stacked half bridge resonant converter, in accordance with an embodiment of the present disclosure. As shown in  FIG.  10 C , the voltages of a total of six input capacitors are sensed. Then, imbalance voltage for each phase ΔV A , ΔV B , and ΔV C , is calculated. If any of the imbalance voltage is greater than a threshold voltage Vth, proper modified phase shift angle is then implemented to each phase leg. 
       FIG.  10 D  illustrates a voltage balancing control flow chart based on phase shift method for a three-stacked half bridge resonant converter with star connection of transformers, in accordance with an embodiment of the present disclosure. As shown in  FIG.  10 D , the voltages of three input capacitors are sensed and imbalance voltage for each phase, ΔV A , ΔV B  and ΔV C , is then calculated. If any of the imbalance voltage is greater than a threshold voltage V th , proper modified phase shift angle is then implemented to each phase leg. 
     Voltage Balancing Control Method for Stacked Serial-Half-Bridge Resonant Converter 
     A hybrid control scheme including two control loops can balance the input capacitor voltages in stacked serial-half-bridge resonant converter.  FIG.  10 E  illustrates a voltage balancing control diagram based on a hybrid method for a stacked serial half bridge resonant converter, in accordance with an embodiment of the present disclosure. The first loop of the hybrid control scheme is the internal voltage balancing loop in each serial half bridge cell aiming to balance the two capacitor voltages inside each cell. The voltages of the two capacitors in each serial half bridge cell are sensed and compared with each other. If a voltage difference between these two capacitors is greater than a predefined threshold voltage Vth, a phase shift angle command is generated by a dedicated controller. The phase shift angle is then implemented between the switch control signals of the first half bridge and the second half bridge. In other words, each serial half bridge cell has its own internal phase shift angle between the switch signals of its first half bridge and its second half bridge, where the phase shift angle is calculated based on the voltage difference between its first input capacitor voltage and its second input capacitor voltage. 
     The second loop of the control scheme is the external voltage balancing loop between all serial-half-bridge cells aiming to balance the average capacitor voltage of each cell. The voltages of the two capacitors in each serial-half-bridge cell are sensed and the average voltage of each cell is then calculated. The average voltage in then compared with the reference voltage. If the voltage difference is greater than the predefined threshold voltage, an extra duty cycle is generated by a dedicated controller. The extra duty cycle is implemented to all four switch control signals in a corresponding serial-half-bridge cell. In other words, each-serial-half bridge cell has its own extra duty cycle, where the extra duty cycle is calculated based on the voltage difference between its average capacitor voltage and the reference voltage. It is appreciated that the extra duty cycle can have a positive value or negative value with respect to the original duty cycle. 
     D. Stacked Full Bridge Resonant Converter 
     Three Stacked Full Bridge Resonant Converter 
       FIG.  11 A  illustrates a three stacked full bridge resonant converter  1100 , in accordance with an embodiment of the present disclosure. Converter  1100  employs three full bridge inverter cells  1101 ,  1102 , and  1103  stacked together with three input capacitors C 1  to C 3  in series to block the DC input voltage. In this embodiment, three separated transformers TR 1 , TR 2 , and TR 3  are used, and each transformer has one primary side winding and one secondary side winding. 
     As shown in  FIG.  11 A , first full bridge inverter cell  1101  includes four switches S 1 , S 2 , S 3 , and S 4 . Point A between switches S 1  and S 3  is connected to one end of a resonant tank including a resonant capacitor C r1  and a resonant inductor L r1  in series. A first end of the primary side winding of transformer TR 1  is connected to the other side of the resonant tank. A second end of the primary side winding of transformer TR 1  is connected to point B between switches S 2  and S 4 . 
     Likewise, second full bridge inverter cell  1102  includes four switches S 5 , S 6 , S 7 , and S 8 . Point C between switches S 5  and S 7  is connected to one end of a resonant tank including a resonant capacitor C r2  and a resonant inductor L r2  in series. A first end of the primary side winding of transformer TR 2  is connected to the other side of the resonant tank. A second end of the primary side winding of transformer TR 2  is connected to point D between switches SG and S 8 . 
     Moreover, third full bridge inverter cell  1103  includes four switches S 9 , S 10 , S 11 , and S 12 . Point E between switches S 9  and S 11  is connected to one end of a resonant tank including a resonant capacitor C r3  and a resonant inductor L r3  in series. A first end of the primary side winding of transformer TR 3  is connected to the other side of the resonant tank. A second end of the primary side winding of transformer TR 3  is connected to point F between switches S 10  and S 12 . 
     Three phase diode bridges  1120  in parallel perform the secondary side rectification, which is coupled with the secondary side windings of the three transformers TR 1 , TR 2 , and TR 3 . 
     Variable switching frequency control can be used to regulate the output voltage and output power of three-stacked full bridge resonant converter.  FIG.  11 B  illustrates the timing diagrams for the converter in  FIG.  11 A  under variable frequency control for switch control signals GS 1  to GS 12  full bridge output voltage V AB  to V EF , resonant capacitor voltage V cr1  to V cr3 , and resonant current i r1  to i r3 . As shown in  FIG.  11 B , all switches operate with the same switching frequency and have identical duty cycles of approximately 50%. To achieve zero-voltage-switching of the complementary-operated primary side switches of the same leg, a small dead time is provided between the turn-on and turn-off instants of these complementary-operated switches. The switch control signals of each full bridge are interleaved with each other full bridge control signals with a phase shift of 120°. For example, GS 1  and GS 4  have 120° phase shift angle with respect to GS 5  and GS 8 . The resonant tank input voltage V AB , V CD , and V EF  do not have a DC bias because each transformer is connected directly to the resonant tank. Similarly, resonant capacitor voltages V cr1 , V cr2 , and V cr3  do not have a DC bias either. The resonant currents for all three resonant tanks are pure sinusoid if the resonant converter operates at its resonant frequency and the magnetizing current is negligible. Each resonant current is interleaved with each other for a phase shift of 120° due to the interleaved switch control signals. This interleaved current can provide the minimal ripple on the components to further improve the converter performance. 
     n-Stacked Full Bridge Resonant Converter 
       FIG.  11 C  illustrates an n-stacked full bridge resonant converter, in accordance with an embodiment of the present disclosure. The converter in  FIG.  11    employs n full bridge inverter cells in stack together with n input capacitors C 1  to C n  in series to block the DC input voltage. One of the two middle points of each full bridge is connected to a resonant tank which includes a resonant capacitor and resonant inductor in series. Total n separated transformers are used, and each transformer has one primary side winding and one secondary side winding. The first end of each transformer&#39;s primary side winding is connected to the other middle point of the full bridge and the second end of each transformer&#39;s primary side winding is connected to the other side of each resonant tank. Total n half-wave diode bridges in parallel perform the secondary side rectification. 
     Variable switching frequency control can be used to regulate the output voltage and output power of n-stacked full bridge resonant converter. All switches operate with the same switching frequency and have identical duty cycles of approximately 50%. To achieve zero-voltage-switching of the complementary-operated primary side switches of the same leg, a small dead time is provided between the turn-on and turn-off instants of these complementary-operated switches. The switches control signals of each full bridge are interleaved with each other full bridge control signals with a phase shift of 360°/n. The resonant currents for all n resonant tanks are sinusoid if the magnetizing current is negligible when the resonant converter operates at its resonant frequency. Each resonant current is interleaved with each other with a phase shift of 360°/n due to the interleaved switch control signals. The interleaved currents provide the minimal ripple on the components to further improve the converter performance. 
     The total n number of the separated transformer can be integrated to less than n number of transformers to reduce the complexity of the system. For example,  FIG.  11 D  illustrates an n-stacked full bridge resonant converter with a single integrated transformer, in accordance with an embodiment of the present disclosure. The single integrated transformer has total n windings on primary side and n windings on secondary side. 
       FIG.  11 E  illustrates an n-stacked full bridge resonant converter with active switches on the secondary side for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. As shown in  FIG.  11 E , 2n diodes are replaced with 2n active switches for synchronous rectification to improve the converter efficiency. The resonant converter is capable of providing bidirectional power flow with the active switches on both input and output side. 
     Stacked Half Bridge Rectifier with Transformer Star Connection 
       FIG.  12 A  illustrates a three stacked half bridge rectifier with transformer star connection applied in a three-phase resonant converter in accordance with an embodiment of the present disclosure. According to the embodiment, the three-phase resonant DC-DC converter includes a primary side, a secondary side, a transformer stage electrically coupled between the primary side and the secondary side, a control circuitry, and at least one resonant tank circuit electrically connected between the primary side and the transformer stage. In the embodiment, the transformer stage includes a first transformer TR 1 , a second transformer TR 2 , and a third transformer TR 3 , and the at least one resonant tank circuit includes a first resonant tank circuit, a second resonant tank circuit, and a third resonant tank circuit. In the embodiment, each of the transformers TR 1 , TR 2 , and TR 3  includes a transformer core, a primary side winding wound on the transformer core, and a secondary side winding wound on the transformer core. The primary side includes a serial stack of at least two half-bridge inverter cells, each including two active switches S 1  and S 2 , S 3  and S 4 , or S 5  and S 6  in series in one leg and an input capacitor C 1 , C 2  or C 3  in a parallel leg together forming a first loop, wherein each inverter cell is connected from a point between the two active switches thereof through a corresponding resonant tank circuit to a first end of the primary side winding of the corresponding transformer, and through a second end of the primary side winding to a common star connection as point O of the corresponding ends of all the inverter cells, wherein one end of the first loop connecting the legs of one inverter cell is directly connected to the opposite end of the corresponding loop in an inverter cell on which said one inverter cell is stacked, and a primary side voltage V in  is applied or produced between the two ends of the first loops of the serial stack of inverter cells that are not directly connected to another inverter cell, and wherein the transformer core is shareable with other inverter cells. In one embodiment, the transformer cores of the transformers TR 1 , TR 2 , and TR 3  is integrated as one and shareable with the inverter cells. The secondary side includes at least two sets of rectifier circuit elements each coupled to the secondary side winding of the corresponding transformer shared with the corresponding primary side winding and is configured to rectify current induced at the secondary side by current flowing in the corresponding primary side winding, and wherein a secondary side voltage V o  is produced or applied. 
     This resonant rectifier employs three half bridges D 1  to D 6  in stack in the secondary side. First diode bridge D 1  and D 2  is connected in parallel with a first output capacitor C O1 . Second diode bridge D 3  and D 4  is connected in parallel with a second output capacitor C O2 . Third diode bridge D 5  and D 6  is connected in parallel with a third output capacitor C O3 . Output capacitors C O1 , C O2 , and C O3  are connected in series to provide the output voltage V O  to a load R. The middle point of first diode bridge D 1  and D 2  is connected to one end of the secondary side winding of first transformer TR 2  through a DC-blocking capacitor C s1 . The middle point of second diode bridge D 3  and D 4  is connected to one end of the secondary side winding of second transformer TR 2  through a DC-blocking capacitor C s2 . The middle point of third diode bridge D 5  and D 6  is connected to one end of the secondary side winding of third transformer TR 3  through a DC-blocking capacitor C s3 . The other end of the secondary side winding of each transformer is connected together as point P, which is also defined as transformer star connection. The DC-blocking capacitors C s1 , C s2 , and C s3  establish the required DC bias voltage for the proper operation of the rectifier. 
     Variable switching frequency control may be applied to regulate the output voltage and output power of the stacked half bridge resonant converter with the three-stacked half bridge rectifier of one embodiment of the present disclosure.  FIG.  12 B  illustrates the timing diagrams for the converter in  FIG.  12 A  under variable frequency control for switch control signals GS 1  to GS 6 , primary resonant current i r1  to i r3 , secondary current i s1  to i s3 , secondary blocking capacitor voltage V cs1  to V cs3 , output capacitor voltage V CO1  to V CO3  and output voltage V O . The transformer secondary current i s1  to i s3  are sinusoid in phase with the primary resonant current i r1  to i r3 . The blocking capacitor C s1  has a positive DC bias voltage, the blocking capacitor C s3  has a negative DC bias voltage and the blocking capacitor C s2  has an almost zero DC voltage. The three output capacitor voltages V CO1  to V CO3  are self-balanced as shown in  FIG.  12 B . The output voltage is three times of each output capacitor voltage. 
       FIG.  12 C  illustrates an n-stacked half bridge rectifier with transformer star connection applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. In  FIG.  12 C , a total of n half bridge are stacked as the rectification stage of the n-stacked half bridge resonant converter. The output voltage is n times of each output capacitor voltage. 
     The total n number of the separated transformer can be integrated to less than n number of transformers. For example,  FIG.  12 D  illustrates an n-stacked half bridge rectifier with transformer star connection applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. As shown in  FIG.  12 D , only one integrated transformer is employed for an n-stacked half bridge rectifier. The integrated transformer has a total of n windings on the primary side and n windings on the secondary side. 
       FIG.  12 E  illustrates an n-stacked active half bridge rectifier with transformer star connection applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. In  FIG.  12 E , all diodes of the n-stacked half bridge rectifier are replaced with active switches for synchronous rectification. The resonant converter can provide bidirectional power flow. The phase shift modulation for stacked half bridge resonant converter can also be used in this topology. 
     Stacked Half Bridge Rectifier 
       FIG.  13 A  illustrates a three-stacked half bridge rectifier applied in a three-phase resonant converter, in accordance with an embodiment of the present disclosure. The resonant rectifier in  FIG.  13 A  employs three half bridges, D 1  through D 6 , in stack in the secondary side. First diode bridge D 1  and D 2  is connected in parallel with two output capacitors C O1  and C O2 . Second diode bridge D 3  and D 4  is connected in parallel with two output capacitors C O3  and C O4 . Third diode bridge D 5  and D 6  is connected in parallel with two output capacitors C O5  and C O6 . A total six output capacitors C O1 , C O2 , C O3 , C O4 , C O5 , and C O6  are connected in series to provide the output voltage V O  to a load R. 
     The middle point of first diode bridge D 1  and D 2  is connected to one end of the secondary side winding of first transformer TR 1 . The middle point of second diode bridge D 3  and D 4  is connected to one end of the secondary side winding of second transformer TR 2 . The middle point of third diode bridge D 5  and D 6  is connected to one end of the secondary side winding of third transformer TR 3 . The other end of the secondary side winding of first transformer TR 1  is connected to the middle point of output capacitors C O1  and C O2 . The other end of the secondary side winding of second transformer TR 2  is connected to the middle point of output capacitors C O3  and C O4 . The other end of the secondary side winding of third transformer TR 3  is connected to the middle point of output capacitors C O5  and C O6 . 
     Variable switching frequency control can be applied to regulate the output voltage and output power of the three phase resonant converter with the three-stacked half bridge rectifier of one embodiment of the present disclosure.  FIG.  13 B  illustrates the timing diagrams for the converter in  FIG.  13 A  under variable frequency control for switch control signals GS 1  to GS 6 , primary resonant current i r1  to i r3 , secondary current i s1  to i s3 , output capacitor voltage V CO1  to V CO6  and output voltage V O . The transformer secondary current i s1  to i s3  are sinusoid in phase with the primary resonant current i r1  to i r3 . The six output capacitor voltages V CO1  to V CO6  are self-balanced as shown in  FIG.  13 B . The output voltage is six times of each output capacitor voltage. 
       FIG.  13 C  illustrates an n-stacked half bridge rectifier applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. In  FIG.  13 C , a total of n number of half bridge are stacked as the rectification stage of the n-phase resonant converter. The output voltage is 2n times of each output capacitor voltage. 
     The total n number of the separated transformers as shown in  FIG.  13 C  can be integrated to less than n number of transformers. For example,  FIG.  13 D  illustrates an n-stacked half bridge rectifier applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. In  FIG.  13 D , only one integrated transformer for an n-stacked half bridge rectifier, which has a total of n windings on the primary side and n windings on the secondary side. 
       FIG.  13 E  illustrates an n-stacked active half bridge rectifier applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. In  FIG.  13 E , all diodes of the n-stacked half bridge rectifier are replaced with active switches for synchronous rectification. The resonant converter can provide bidirectional power flow. The phase shift modulation for stacked half bridge resonant converter can also be used in this topology. 
     Stacked Full Bridge Rectifier 
       FIG.  14 A  illustrates a three-stacked full bridge rectifier applied in a three-phase resonant converter, in accordance with an embodiment of the present disclosure. The resonant rectifier in  FIG.  14 A  employs three full bridges, including diodes D 1  through D 12 , in stack on the secondary side. First full bridge including diodes D 1  through D 4  is connected in parallel with first output capacitor C O1 . Second full bridge including diodes D 5  through D 8  is connected in parallel with second output capacitor C O2 . Third full bridge D 9  through D 12  is connected in parallel with third output capacitor C O3 . Output capacitors C O1 , C O2 , and C O3  are connected in series to provide output voltage V O  to a load R. 
     One end of the secondary side winding of first transformer TR 1  is connected to the middle point between diodes D 1  and D 3 , while the other end of the secondary side winding of first transformer TR 1  is connected to the middle point between diodes D 2  and D 4 . One end of the secondary side winding of second transformer TR 2  is connected to the middle point between diodes D 5  and D 7 , while the other end of the secondary side winding of second transformer TR 2  is connected to the middle point between diodes D 6  and D 8 . One end of the secondary side winding of third transformer TR 3  is connected to the middle point between diodes D 9  and D 11 , while the other end of the secondary side winding of third transformer TR 2  is connected to the middle point between diodes D 10  and D 12 . Variable switching frequency control can be applied to regulate the output voltage and output power of the stacked half bridge resonant converter with the proposed three-stacked full bridge rectifier. Blocking capacitors are not required in this rectifier. 
       FIG.  14 B  illustrates an n-stacked full bridge rectifier applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. In  FIG.  14 B , a total of n number of full bridges is stacked as the rectification stage of the n-stacked half bridge resonant converter. The output voltage is n times of each output capacitor voltage. 
     The total n number of the separated transformer can be integrated to less than n number of transformers.  FIG.  14 C  illustrates an n-stacked full bridge rectifier applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. As shown in  FIG.  14 C , an n-stacked full bridge rectifier employs only one integrated transformer, which has a total n windings on the primary side and n windings on the secondary side. 
       FIG.  14 D  illustrates an n-stacked active full bridge rectifier applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. In  FIG.  14 D , all diodes of the n-stacked full bridge rectifier are replaced with a total of 4n active switches for synchronous rectification. The resonant converter can provide bidirectional power flow. The phase shift modulation for stacked half bridge resonant converter can also be used in this topology. 
     Stacked Serial-Half-Bridge Rectifier 
       FIG.  15 A  illustrates a three-stacked serial-half-bridge rectifier applied in a three-phase resonant converter, in accordance with an embodiment of the present disclosure. The resonant rectifier in  FIG.  15 A  employs three serial-half-bridges, including diodes D 1  through D 12 , in stack on the secondary side. First serial-half-bridge including diodes D 1  through D 4  is connected in parallel with two output capacitors C O1  and C O2 . Second serial-half-bridge including diodes D 5  through D 8  is connected in parallel with two output capacitors C O3  and C O4 . Third serial-half-bridge including diodes D 9  through D 12  is connected in parallel with two output capacitors C O5  and C O6 . A total of six output capacitors C O1 , C O2 , C O3 , C O4 , C O5 , and C O6  are connected in series to provide output voltage V O  to a load R. 
     One end of the secondary side winding of first transformer TR 1  is connected to the middle point between diodes D 1  and D 2 , while the other end of the secondary side winding of first transformer TR 1  is connected to the middle point between diodes D 3  and D 4 . One end of the secondary side winding of second transformer TR 2  is connected to the middle point between diodes D 5  and D 6 , while the other end of the secondary side winding of second transformer TR 2  is connected to the middle point between diodes D 7  and D 8 . One end of the secondary side winding of third transformer TR 3  is connected to the middle point between diodes D 9  and D 10 , while the other end of the secondary side winding of third transformer TR 3  is connected to the middle point between diodes D 11  and D 12 . 
     Variable switching frequency control can be applied to regulate the output voltage and output power of the stacked half bridge resonant converter with the three-stacked serial-half-bridge rectifier of one embodiment of the present disclosure. The blocking capacitor C s1  to C s3  are applied to establish required DC bias voltage for the proper operation of the rectifier in  FIG.  15 A . The six output capacitor voltages V CO1  to V CO6  are self-balanced. 
       FIG.  15 B  illustrates an n-stacked serial-half-bridge rectifier applied in an n-phase resonant converter, in accordance with an embodiment of the present disclosure. In  FIG.  15 B , a total of n number of serial-half-bridges are stacked as the rectification stage of the n-stacked half bridge resonant converter. The output voltage is n times of each output capacitor voltage. 
     The total n number of the separated transformer can be integrated to less than n number of transformers.  FIG.  15 C  illustrates an n-stacked serial-half-bridge rectifier applied in an n-phase resonant converter with an integrated transformer, in accordance with an embodiment of the present disclosure. 
     As shown in  FIG.  15 C , an n-stacked serial-half-bridge rectifier employs only one integrated transformer, which has a total of n windings on the primary side and n windings on the secondary side. 
       FIG.  15 D  illustrates an n-stacked serial-half-bridge rectifier applied in an n-phase resonant converter for synchronous rectification and bidirectional operation, in accordance with an embodiment of the present disclosure. In  FIG.  15 D , all diodes of the n-stacked serial-half-bridges rectifier are replaced with a total of 4n active switches for synchronous rectification. The resonant converter can provide bidirectional power flow. 
     Generalization of Stacked Resonant Converter 
     Various resonant converters and rectifiers based on stacked half bridge, stacked full bridge and stacked serial-half-bridge are described separately in previous sections.  FIG.  16    illustrates a generalized stacked resonant converter, in accordance with an embodiment of the present disclosure. A total of n separated transformers is used with a total n primary side windings and n secondary side windings. On the primary side, four different topologies can be used as the inverting stage. The first is the n-stacked half bridge structure with transformer star connection. The second is the n-stacked half bridge structure, which is the primary side of the topology in  FIG.  7 A . The third topology is the n-stacked serial-half-bridge structure, which is the primary side of the topology in  FIG.  9 A . The fourth topology is the n-stacked full bridge structure, which is the primary side of the topology in  FIG.  11 C . 
     On the secondary side, a total five different topologies can be used as rectifiers. The first is the n-stacked half bridge structure with transformer star connection, which is the rectifier of the topology in  FIG.  12 C . In this situation, secondary side blocking capacitors are required for proper operation of the rectifier. The second is the n-stacked half bridge structure, which is the rectifier of the topology in  FIG.  13 C . The third topology is the n-stacked full bridge structure, which is the rectifier of the topology in  FIG.  14 B . The fourth topology is the n-stacked serial-half-bridge structure, which is the rectifier of the topology in  FIG.  15 B . In this situation, secondary side blocking capacitors are required for proper operation of the rectifier. The fifth rectifier is the conventional n-phase diode bridges structure, which can have a half-wave or a full-wave structure. 
     N separated transformers are applied to provide required turns ratio and galvanic isolation. The n transformers can be further integrated into less than n transformers. The rectifier stage diodes can be replaced by active switches for synchronous rectification and bidirectional operation. Variable switching frequency control, PWM duty cycle modulation and phase shift modulation can be applied to regulate the output voltage and output power in this system. 
       FIG.  17    illustrates a generalized stacked resonant converter including multiple circuits in parallel on both the primary and secondary sides, in accordance with an embodiment of the present disclosure. On the primary side, a total of m stacked structures is connected in parallel with the input voltage. Each stacked structure includes n stacked basic elements, which is the primary structure in  FIG.  16   . Thus, there is a total of m×n basic elements on the primary side with dedicated series and parallel connections. A total of m×n separated transformers, TR (1,1)  to TR (n,m) , are utilized with a total of m×n primary side windings and m×n secondary side windings. If the basic stacking element is half bridge with transformer star connection, one end of every primary side winding is connected as a single point as star connection and the other end of every primary side winding is coupled to the middle point of every half bridge through the corresponding resonant tank. Otherwise, all the m×n primary side windings are directly coupled to the basic stacking elements through the resonant tanks. 
     On the secondary side, a total p stacked structures are in connected parallel. Each stacked structure includes q stacked basic circuit elements, which is similar to the rectifier stage in  FIG.  16   . In order to perform proper rectification, the product of p and q (i.e., p×q) is equal to the product of m and n (i.e., m×n). Similarly, if the basic stacking element is half bridge with transformer star connection, one end of every secondary side winding is connected at a single point as star connection and the other end of every secondary side winding is coupled to the middle point of every half bridge through a blocking capacitor. Otherwise, all the m×n secondary side windings are connected to the basic stacking elements through the blocking capacitors. Variable switching frequency control, PWM duty cycle modulation and phase shift modulation can be applied to regulate the output voltage and output power in this system. The m×n transformers can be integrated to less than m×n transformers for system simplicity. The rectifier stage diodes can be replaced by active switches for synchronous rectification and bidirectional operation. 
     For the purposes of describing and defining the present disclosure, it is noted that terms of degree (e.g., “substantially,” “slightly,” “about,” “comparable,” etc.) may be utilized herein to represent the inherent degree of uncertainty that may be attributed to any quantitative comparison, value, measurement, or other representation. Such terms of degree may also be utilized herein to represent the degree by which a quantitative representation may vary from a stated reference (e.g., about 10% or less) without resulting in a change in the basic function of the subject matter at issue. Unless otherwise stated herein, any numerical value appearing in the present disclosure are deemed to be both the stated value, and alternatively modified by a term of degree (e.g., “about”). 
     Although various embodiments of the present disclosure have been described in detail herein, one of ordinary skill in the art would readily appreciate modifications and other embodiments without departing from the spirit and scope of the present disclosure as stated in the appended claims.