Patent Publication Number: US-2023134427-A1

Title: Switched Capacitor Converter and Control Method

Description:
PRIORITY CLAIM 
     This application claims the benefit of U.S. Provisional Application No. 63/274,150, filed on Nov. 1, 2021, entitled “Switched Capacitor Converter and Control Method,” which application is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a switched capacitor converter, and, in particular embodiments, to a high efficiency switched capacitor converter. 
     BACKGROUND 
     With the popularization of fast charging of mobile phones, charge pump voltage conversion circuits are gradually being used more and more widely due to their high power conversion efficiency. The fast charging power of a single battery has also been increased from the initial low power (e.g., 25 W) to today&#39;s high power (e.g., 65 W). The output voltage of the corresponding USB adapter has also been increased from the initial lower voltage (e.g., 10 V) to today&#39;s high voltage (e.g., 20V). The most basic 2:1 charge pump can no longer meet the needs of a single battery with a 20V USB adapter input voltage. The 2:1 charge pump has been gradually replaced by the 4:1 charge pump. The functions of the 4:1 charge pump are compatible with the functions of the 2:1 charge pump. The 4:1 charge pump is used in applications having a high voltage conversion ratios (e.g., from 20V to 5V). There are several 4:1 charge pump circuits. The commonly used 4:1 charge pump is the Dickson charge pump as shown in  FIG.  1   . The Dickson charge pump has the highest efficiency among 4:1 charge pumps. 
       FIG.  1    illustrates a schematic diagram of a 4:1 Dickson dual-phase switched capacitor converter. The 4:1 Dickson dual-phase switched capacitor converter  100  comprises a first phase  110  and a second phase  130 . The first phase  110  comprises eight switches  111 ,  112 ,  113 ,  114 ,  115 ,  116 ,  117 ,  118 . Switches  111 - 116  are connected in series between an input power source VIN and the ground GND. Switches  117  and  118  are connected in series, and further in parallel with the series connected switches  115 ,  116 . A flying capacitor  121  is connected between a common node of switches  111 ,  112 , and a common node of switches  115 ,  116 . A flying capacitor  120  is connected between a common node of switches  112 ,  113 , and a common node of switches  117 ,  118 . A flying capacitor  119  is connected between a common node of switches  113 ,  114 , and a common node of switches  115 ,  116 . 
     The second phase  130  comprises eight switches  131 ,  132 ,  133 ,  134 ,  135 ,  136 ,  137 ,  138 . Switches  131 - 136  are connected in series between the input power source VIN and the ground GND. Switches  137  and  138  are connected in series, and further in parallel with the series connected switches  135 ,  136 . A flying capacitor  141  is connected between a common node of switches  131 ,  132 , and a common node of switches  135 ,  136 . A flying capacitor  140  is connected between a common node of switches  132 ,  133 , and a common node of switches  137 ,  138 . A flying capacitor  139  is connected between a common node of switches  133 ,  134 , and a common node of switches  135 ,  136 . 
     An input capacitor  101  is connected between VIN and ground to filter the input voltage. An output capacitor  102  is connected between VOUT and ground to filter the output voltage. 
     In operation, all switches alternately switch at a specific operating frequency with a 50% duty cycle. In a first half cycle, the switches  111 ,  113 ,  115  and  117  are turned on, and the switches  112 ,  114 ,  116 , and  118  are turned off. The flying capacitor  121  and the output capacitor  102  are connected in series. VIN charges the series connected capacitor  121  and  102 . In addition, VIN supplies power to the output terminal VOUT. The flying capacitor  120  charges the flying capacitor  119  and the output capacitor  102  through the turned on switches  113 ,  115  and  117 . In addition, the flying capacitor  120  supplies power to the output terminal VOUT. 
     In a second half cycle, the switches  112 ,  114 ,  116 , and  118  are turned on and the switches  111 ,  113 ,  115 , and  117  are turned off. The flying capacitor  120  and the output capacitor  102  are connected in series. The flying capacitor  121  charges the flying capacitor  120  and the output capacitor  102  through the switches  112 ,  116  and  118 . In addition, the flying capacitor  121  supplies power to the output terminal VOUT. At the same time, the flying capacitor  119  charges the output capacitor  102  through switches  114  and  116 . In addition, the flying capacitor  119  supplies power to the output terminal VOUT. 
     Also, in the first half cycle, the switches  132 ,  134 ,  136 , and  138  are turned on and the switches  131 ,  133 ,  135 , and  137  are turned off. The flying capacitor  140  and the output capacitor  102  are connected in series. The flying capacitor  141  charges the flying capacitor  140  and the output capacitor  102  through the switches  132 ,  136  and  138 . In addition, the flying capacitor  141  supplies power to the output terminal VOUT. At the same time, the flying capacitor  139  charges the output capacitor  102  through switches  134  and  136 . In addition, the flying capacitor  139  supplies power to the output terminal VOUT. 
     Also, in the second half cycle, the switches  131 ,  133 ,  135  and  137  are turned on, and the switches  132 ,  134 ,  136 , and  138  are turned off. The flying capacitor  141  and the output capacitor  102  are connected in series. VIN charges the series connected capacitor  141  and  102  through switches  131  and  135 . In addition, VIN supplies power to the output terminal VOUT. The flying capacitor  140  charges the flying capacitor  139  and the output capacitor  102  through the turned on switches  133 ,  135  and  137 . In addition, the flying capacitor  139  supplies power to the output terminal VOUT. 
     In operation, when the switching frequency is fast enough, the voltage on the flying capacitors  119 ,  120 ,  121 ,  139 ,  140 ,  141  and VOUT on the output capacitor  102  fluctuate around a constant value (DC bias voltage) with each switching state. The DC bias voltage of the voltages on the flying capacitors  119 ,  139 , and the output capacitor  102  is equal to one quarter of the input voltage VIN (VIN/4). The DC bias voltage of the voltages on the flying capacitors  120  and  140  is equal to one half of the input voltage VIN (VIN/2). The DC bias voltage of the voltages on the flying capacitors  121  and  141  is equal to three-quarters of the input voltage VIN (3×VIN/4). The power conversion ratio of the Dickson dual-phase switched capacitor converter shown in  FIG.  1    is equal to 4:1. 
     According to the foregoing description, the Dickson dual-phase switched capacitor converter is highly efficient. When the flying capacitors  121  and  141  are charged, only two switches are connected in series. When the flying capacitors  121  and  141  are discharged, only three switches are connected in series. When the flying capacitors  120  and  140  are charged and discharged, only three switches are connected in series. When the flying capacitors  119  and  139  are charged, three switches are connected in series. When the flying capacitors  119  and  139  are discharged, only two switches are connected in series. Moreover, the effective current flowing through all flying capacitors in the Dickson dual-phase switched capacitor converter are the same. At the same time, in order to improve the efficiency of the Dickson dual-phase switched capacitor converter, the on-resistance of the switches  115 ,  116 ,  135  and  136  is half of the other switches. This is because the current of these switches is twice the current flowing through the flying capacitors. 
     The Dickson dual-phase switched capacitor converter shown in  FIG.  1    may be of a 2:1 power conversion ratio. In operation, the switches  112 ,  113 ,  132 , and  133  may be configured to operate in an always-on state during normal operation. The remaining switches alternately switch at a specific operating frequency with a 50% duty cycle. In a first half cycle, the switches  111 ,  115 , and  118  of the first phase  110  are turned on, and the switches  114 ,  116 , and  117  of the first phase  110  are turned off. The flying capacitors  121 ,  120 ,  119  are connected in parallel, and further connected in series with the output capacitor  102 . VIN charges the flying capacitors  121 ,  120 ,  119  and the output capacitor  102  through the switches  111 ,  112 ,  113 ,  115  and  118 . In addition, VIN supplies power to the output terminal VOUT. 
     In a second half cycle, the switches  114 ,  116 , and  117  are turned on, and the switches  111 ,  115 , and  118  are turned off. The flying capacitors  121 ,  120 , and  119  charge the output capacitor  102  and supply power to VOUT through the switches  112 ,  113 ,  114 ,  116  and  117 . 
     Also, in the first half cycle, the switches  134 ,  136 , and  137  of the second phase  130  are turned on, and the switches  131 ,  135 , and  138  of the second phase  130  are turned off. The flying capacitors  141 ,  140  and  139  charge the output capacitor  102  through switches  132 ,  133 ,  134 ,  136  and  137 . In addition, and the flying capacitors  141 ,  140 ,  139  supply power to the output VOUT. 
     Also, in the second half cycle, the switches  131 ,  135 , and  138  are turned on, and the switches  134 ,  136 , and  137  are turned off. The flying capacitors  141 ,  140  and  139  are connected in parallel, and further connected in series with the output capacitor  102 . VIN charges the flying capacitors  141 ,  140 , and  139  and the output capacitor  102  through switches  131 ,  132 ,  133 ,  135  and  138 . In addition, VIN supplies power to the output terminal VOUT. 
     In operation, when the switching frequency is fast enough, the voltages on the flying capacitors  119 ,  120 ,  121 ,  139 ,  140 ,  141 , and VOUT on the output capacitor  102  fluctuate around a constant value with each switching state. Among them, the voltages on the flying capacitors  119 ,  120 ,  121 ,  139 ,  140 ,  141 , and output capacitor  102  are equal to one half of the input voltage VIN (VIN/2). The power conversion ratio of the Dickson dual-phase switched capacitor converter shown in  FIG.  1    is equal to 2:1. 
     The Dickson dual-phase switched capacitor converter shown in  FIG.  1    can achieve high efficiency. However, the circuit is complicated. There are sixteen switches and six flying capacitors. The largest DC voltage on the flying capacitor is three-quarters of VIN. Due to the DC piezoelectric effect of ceramic capacitors (the capacitance value decreases exponentially with the increase of DC piezoelectricity)  FIG.  2    shows the capacitance value variation in response to different DC bias voltages. In order to achieve the required capacitance value, a larger capacitor is needed. Such a larger capacitor increases the cost and area of the Printed Circuit Board (PCB) on which the Dickson dual-phase switched capacitor converter is mounted. 
     As power consumption has become more important, there may be a need for further improving the performance of the Dickson dual-phase switched capacitor converter shown in  FIG.  1   . It is desirable to have a simplified structure so as to achieve a cost-effective power solution. 
     SUMMARY 
     These and other problems are generally solved or circumvented, and technical advantages are generally achieved, by preferred embodiments of the present disclosure which provide a high efficiency switched capacitor converter. 
     In accordance with an embodiment, a switched capacitor converter comprises a first leg comprising a plurality of first leg switches connected in series between ground and a first voltage node, a second leg comprising a plurality of second leg switches connected in series between ground and a second voltage node, a first flying capacitor connected between a first switch common node and a third switch common node of the first leg, wherein the first switch common node is a common node of a first switch and a second switch of the first leg, and the third switch common node is a common node of a third switch and a fourth switch of the first leg, a second flying capacitor connected between a first switch common node and a third switch common node of the second leg, wherein the first switch common node is a common node of a first switch and a second switch of the second leg, and the third switch common node is a common node of a third switch and a fourth switch of the second leg, a third flying capacitor connected between the first voltage node and the second voltage node, a first upper switch connected between the first voltage node and ground, a second upper switch coupled between the second voltage node and an input terminal, and an output terminal coupled to a second switch common node of the first leg and a second switch common node of the second leg, and wherein the second switch common node of the first leg is a common node of the second switch and the third switch of the first leg, and the second switch common node of the second leg is a common node of the second switch and the third switch of the second leg. 
     The switched capacitor converter further comprises a fourth flying capacitor connected between a third voltage node and a fourth voltage node, a third upper switch connected between the third voltage node and ground, a fourth upper switch connected between the fourth voltage node and the input terminal, a fifth upper switch connected between an uppermost switch common node of the first leg and the fourth voltage node, and a sixth upper switch connected between an uppermost switch common node of the second leg and the third voltage node. 
     In accordance with yet another embodiment, a method comprises providing a switched capacitor converter comprising a first leg comprising a plurality of first leg switches and a second leg comprising a plurality of second leg switches, a first flying capacitor connected to the first leg, a second flying capacitor connected to the second leg, and a third flying capacitor connected between the first leg and the second leg, and a first upper switch and a second upper switch connected to two terminals of the third flying capacitor respectively, in a first half cycle, configuring the plurality of first leg switches, the plurality of second leg switches, the first upper switch and the second upper switch such that the third flying capacitor, the first flying capacitor and an output capacitor are connected in series, and the second flying capacitor and the output capacitor are connected in parallel, and in a second half cycle, configuring the plurality of first leg switches, the plurality of second leg switches, the first upper switch and the second upper switch such that the first flying capacitor and the output capacitor are connected in parallel, and the third flying capacitor, the second flying capacitor and the output capacitor are connected in series. 
     The foregoing has outlined rather broadly the features and technical advantages of the present disclosure in order that the detailed description of the disclosure that follows may be better understood. Additional features and advantages of the disclosure will be described hereinafter which form the subject of the claims of the disclosure. It should be appreciated by those skilled in the art that the conception and specific embodiment disclosed may be readily utilized as a basis for modifying or designing other structures or processes for carrying out the same purposes of the present disclosure. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the disclosure as set forth in the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG.  1    illustrates a schematic diagram of a 4:1 Dickson dual-phase switched capacitor converter; 
         FIG.  2    shows the capacitance value variation in response to different DC bias voltages; 
         FIG.  3    illustrates a schematic diagram of a 4:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  4    illustrates the 4:1 dual-phase switched capacitor converter configured to operate in a first half cycle in accordance with various embodiments of the present disclosure; 
         FIG.  5    illustrates the 4:1 dual-phase switched capacitor converter configured to operate in a second half cycle in accordance with various embodiments of the present disclosure; 
         FIG.  6    illustrates the gate drive signals of the 4:1 dual-phase switched capacitor converter shown in  FIG.  3    in accordance with various embodiments of the present disclosure; 
         FIG.  7    illustrates two equivalent circuit diagrams for operating in two different half cycles in accordance with various embodiments of the present disclosure; 
         FIG.  8    illustrates three equivalent circuit diagrams for operating in two different half cycles in accordance with various embodiments of the present disclosure; 
         FIG.  9    illustrates four equivalent circuit diagrams for operating in two different operating modes in accordance with various embodiments of the present disclosure; 
         FIG.  10    illustrates the gate drive signals of the 4:1 dual-phase switched capacitor converter shown in  FIG.  3    in accordance with various embodiments of the present disclosure; 
         FIG.  11    illustrates a power conversion system including the 4:1 dual-phase switched capacitor converter and a DC/DC regulator stage connected in cascade in accordance with various embodiments of the present disclosure; 
         FIG.  12    illustrates a power conversion system including the 4:1 dual-phase switched capacitor converter and an output filter in accordance with various embodiments of the present disclosure; 
         FIG.  13    illustrates a schematic diagram of a 4:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  14    illustrates a schematic diagram of a 2:1 or a 4:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  15    illustrates a schematic diagram of an 8:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  16    illustrates a schematic diagram of an 8:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  17    illustrates a schematic diagram of a 6:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  18    illustrates a schematic diagram of a 6:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  19    illustrates a schematic diagram of a 2×N:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  20    illustrates a schematic diagram of a 2×N:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  21    illustrates an alternative schematic diagram of an 8:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  22    illustrates a schematic diagram of an 8:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure; 
         FIG.  23    illustrates a power conversion system including the 8:1 single-phase switched capacitor converter as a front stage and a DC/DC regulator stage or an LC liter as a second stage in accordance with various embodiments of the present disclosure; 
         FIG.  24    illustrates a schematic diagram of a 4:1 single-phase switched capacitor converter with one inductive element in accordance with various embodiments of the present disclosure; 
         FIG.  25    illustrates a schematic diagram of a 4:1 dual-phase switched capacitor converter with two inductive elements in accordance with various embodiments of the present disclosure; 
         FIG.  26    illustrates the gate drive signals of the 4:1 single-phase switched capacitor converter shown in  FIG.  13    in accordance with various embodiments of the present disclosure; 
         FIG.  27    illustrates two equivalent circuit diagrams for operating in two different half cycles in accordance with various embodiments of the present disclosure; 
         FIG.  28    illustrates four equivalent circuit diagrams for operating in two different operating modes in accordance with various embodiments of the present disclosure; 
         FIG.  29    illustrates the gate drive signals of the 4:1 single-phase switched capacitor converter shown in  FIG.  13    in accordance with various embodiments of the present disclosure; 
         FIG.  30    illustrates a flow chart of a method for controlling the switched capacitor converter shown in  FIGS.  3  and  13    in accordance with various embodiments of the present disclosure; and 
         FIGS.  31 - 35    illustrate a process of generating a 4:1 dual-phase switched capacitor converter based on two 4:1 single-phase switched capacitor converters in accordance with various embodiments of the present disclosure. 
     
    
    
     Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated. The figures are drawn to clearly illustrate the relevant aspects of the various embodiments and are not necessarily drawn to scale. 
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     The making and using of the presently preferred embodiments are discussed in detail below. It should be appreciated, however, that the present disclosure provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the disclosure, and do not limit the scope of the disclosure. 
     The present disclosure will be described with respect to preferred embodiments in a specific context, namely to a high efficiency switched capacitor converter. The invention may also be applied, however, to a variety of power systems. Hereinafter, various embodiments will be explained in detail with reference to the accompanying drawings. 
       FIG.  3    illustrates a schematic diagram of a 4:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The 4:1 dual-phase switched capacitor converter  200  comprises fourteen switches, four flying capacitors, one input capacitor and one output capacitor. A first phase  210  of the 4:1 dual-phase switched capacitor converter includes seven switches  211 ,  213 ,  214 ,  215 ,  216 ,  217 , and  218  coupled between a power source VIN and the ground GND. A flying capacitor  212  is connected in series with switches  211  and  213  between VIN and ground. A flying capacitor  219  is connected between a common node of switches  214 ,  216  and a common node of switches  217 ,  218 . 
     A second phase  220  of the 4:1 dual-phase switched capacitor converter includes seven switches  221 ,  223 ,  224 ,  225 ,  226 ,  227 , and  228  coupled between the power source VIN and the ground GND. A flying capacitor  222  is connected in series with switches  221  and  223  between VIN and ground. A flying capacitor  229  is connected between a common node of switches  224 ,  226  and a common node of switches  227 ,  228 . An input capacitor  201  is connected between VIN and ground to filter the input voltage. An output capacitor  202  is connected between VOUT and ground to filter the output voltage. Throughout the description, a first leg of the 4:1 dual-phase switched capacitor converter is a switch leg comprising switches  224 ,  226 ,  227  and  228 . A second leg of the 4:1 dual-phase switched capacitor converter is a switch leg comprising switches  215 ,  216 ,  217  and  218 . Switch  223  may be referred to as a first upper switch. Switch  221  may be referred to as a second upper switch. Switch  213  may be referred to as a third upper switch. Switch  211  may be referred to as a fourth upper switch. Switch  225  may be referred to as a fifth upper switch. Switch  214  may be referred to as a sixth upper switch. 
     In operation, the 4:1 dual-phase switched capacitor converter  200  functions as a 4:1 step-down charge pump. All switches switch alternately with a 50% duty cycle at a specific operating frequency. 
       FIG.  4    illustrates the 4:1 dual-phase switched capacitor converter configured to operate in a first half cycle in accordance with various embodiments of the present disclosure. The switches  213 ,  216 , and  218  are turned on, and the switches  211 ,  214 ,  215 , and  217  are turned off. The flying capacitor  219  charges the output capacitor  202  through switches  216  and  218 . In addition, the flying capacitor  219  supplies power to the output terminal VOUT (the current path is indicated by the dotted line in  FIG.  4   ). Since the flying capacitor  219  and the output capacitor  202  are connected in parallel, the average voltage on the flying capacitor  219  is equal to the output voltage VOUT. 
     In the first half cycle, the switches  221 ,  224 ,  225 , and  227  are also turned on, and the switches  223 ,  226 , and  228  are turned off. The flying capacitors  222 ,  229  and the output capacitor  202  are connected in series. VIN charges the flying capacitors  222 ,  229  and the output capacitor  202  through switches  221 ,  224  and  227 . In addition, VIN supplies power to the output terminal VOUT (the current path is indicated by the dashed line in  FIG.  4   ). The flying capacitors  222  and  229  and the output capacitor  202  are connected in series. The sum of the average voltages on the three capacitors is equal to the input voltage VIN. At the same time, the flying capacitor  229  and the output capacitor  202  are connected in series. The flying capacitor  212  charges the flying capacitor  229  and the output capacitor  202  through switches  213 ,  225  and  227  (the current path is indicated by the dashed line in  FIG.  4   ). In addition, the flying capacitor  212  supplies power to the output terminal VOUT. The flying capacitor  229  and the output capacitor  202  are connected in series. The flying capacitor  212  is connected in parallel with the series-connected capacitors  229  and  202 . Therefore, the average voltage on the flying capacitor  212  is equal to the sum of the average voltages on the flying capacitor  229  and the output capacitor  202 . 
       FIG.  5    illustrates the 4:1 dual-phase switched capacitor converter configured to operate in a second half cycle in accordance with various embodiments of the present disclosure. The switches  211 ,  214 ,  215 , and  217  are turned on, and the switches  213 ,  216 , and  218  are turned off. The flying capacitors  212 ,  219  and the output capacitor  202  are connected in series. VIN charges the flying capacitors  212 ,  219  and the output capacitor  202  through switches  211 ,  214 , and  217  (the current path is indicated by the dashed line in  FIG.  5   ). In addition, VIN supplies power to the output terminal VOUT. The flying capacitors  212 ,  219  and the output capacitor  202  are connected in series. The sum of the average voltages on the three capacitors is equal to the input voltage VIN. As described in the first half cycle, the average voltage across the flying capacitor  219  is equal to the output voltage VOUT. Therefore, the average voltage on the flying capacitor  212  is equal to twice the output voltage VOUT. The sum of the voltages on the flying capacitors  212 ,  219  and the output capacitor  202  is equal to the input voltage VIN. Therefore, the voltage on the flying capacitor  212  is equal to one half of the input voltage VIN. 
     Also, in the second half cycle, the switches  223 ,  226 , and  228  are turned on, and the switches  221 ,  224 ,  225 , and  227  are turned off. The flying capacitor  229  charges the output capacitor  202  through the switches  226  and  228  (the current path is indicated by the dotted line in  FIG.  5   ). In addition, the flying capacitor  229  supplies power to the output terminal VOUT. At this time, the flying capacitor  229  and the output capacitor  202  are connected in parallel. Therefore, the average voltage on the flying capacitor  229  is equal to the output voltage VOUT. At the same time, the flying capacitor  219  and the output capacitor  202  are connected in series. The flying capacitor  222  charges the flying capacitor  219  and the output capacitor  202  through switches  223 ,  215 , and  217  (the current path is indicated by the dashed line in  FIG.  5   ). In addition, the flying capacitor  222  supplies power to the output terminal VOUT. 
     The flying capacitor  219  and the output capacitor  202  are connected in series and further connected in parallel with the flying capacitor  222 . Therefore, the average voltage on the flying capacitor  222  is equal to the sum of the average voltage on the flying capacitor  219  and the output capacitor  202 . As mentioned above, the average voltage on the flying capacitor  219  is equal to the output voltage VOUT. As such, the average voltage on the flying capacitor  212  is equal to twice the output voltage VOUT. In other words, the average voltage on the flying capacitor  212  is equal to one half of the input voltage VIN. 
     In operation, when the switching frequency is fast enough, the voltages on the flying capacitors  212  and  222  fluctuate around one half (VIN/2) of the input voltage VIN with the change of each switching state. The voltage on the flying capacitors  219  and  229  and the output capacitor  202  fluctuates around a quarter (VIN/4) of the input voltage VIN with each change of the switching state. The constant value of the output capacitor  202  is one-fourth (VIN/4) of the input voltage VIN. The power conversion ratio of the dual-phase switched capacitor converter shown in  FIGS.  4 - 5    is equal to 4:1. 
     Referring back to  FIG.  3   , if the switches  211 ,  213 ,  221 , and  223  are configured to operate in an always-on mode during normal operation, and the switches  214 ,  224  are configured to operate in an always-off mode, the remaining switches configured to operate at a specific operating frequency with a 50% duty cycle is switched alternately. In this configuration, flying capacitors  212  and  222  are connected between VIN and GND. The voltages across the flying capacitors  212  and  222  are equal to the input voltage VIN. 
     In a first half cycle, the switches  216  and  218  are turned on, and the switches  215  and  217  are turned off. The switches  225  and  227  are turned on, and the switches  226  and  228  are turned off. The flying capacitor  229  and the output capacitor  202  connected in series. VIN charges the flying capacitor  229  and the output capacitor  202  through switches  211 ,  225  and  227 . In addition, VIN supplies power to the output terminal VOUT. At this time, the flying capacitor  229  and the output capacitor  202  are connected in series. The sum of the average voltages on the flying capacitor  229  and the output capacitor  202  is equal to the input voltage VIN. 
     Also, in the first half cycle, the flying capacitor  219  charges the output capacitor  202  through switches  216  and  218 . In addition, the flying capacitor  219  supplies power to the output terminal VOUT. Because the flying capacitor  219  is connected in parallel with the output capacitor  202 , the average voltage on the flying capacitor  219  is equal to the output voltage VOUT. 
     In a second half cycle, the switches  215  and  217  are turned on and the switches  216  and  218  are turned off. The switches  226  and  228  are turned on, and the switches  225  and  227  are turned off. The flying capacitor  219  and the output capacitor  202  connected in series. VIN charges the flying capacitor  219  and the output capacitor  202  through switches  221 ,  215  and  217 . In addition, VIN supplies power to the output terminal VOUT. At this time, the flying capacitor  219  and the output capacitor  202  are connected in series. The sum of the average voltages on the flying capacitor  219  and the output capacitor  202  is equal to the input voltage VIN. As mentioned above, the average voltage of the flying capacitor  219  is equal to the output voltage VOUT. Therefore, the average voltages on the flying capacitor  219  and the output capacitor  202  are equal to one half of the input voltage (VIN/2). 
     Also, in the second half cycle, the flying capacitor  229  charges the output capacitor  202  through switches  226  and  228 . In addition, the flying capacitor  229  supplies power to the output terminal VOUT. Because the flying capacitor  229  is connected in parallel with the output capacitor  202 , the average voltage on the flying capacitor  229  is equal to the output voltage VOUT. The output voltage is equal to one half of the input voltage (VIN/2). 
     In operation, when the switching frequency is fast enough, the voltages on the flying capacitors  219 ,  229 , and the output capacitor  202  fluctuate around a constant value (VIN/2) with each switching state. The power conversion ratio of the dual-phase switched capacitor converter is equal to 2:1. 
     From the previous analysis, the following conclusions can be drawn: the power converter in the present disclosure only needs fourteen switches, four flying capacitors, one input capacitor and one output capacitor. At the same time, the maximum voltage on the flying capacitors is one half of the input voltage (VIN/2) instead of three-quarters of the input voltage (3×VIN/4). 
     Through the foregoing description, various embodiments of the present disclosure shows that during the charging and discharging processes of the flying capacitors  212  and  222 , three switches are connected in series to establish the charging and discharging paths. It is the same as the flying capacitors  120  and  140  in the Dickson dual-phase switched capacitor converter. The effective value of the current flowing through the flying capacitors in the present disclosure is the same as that in the Dickson dual-phase switched capacitor converter. As such, the power consumption of the present disclosure is the same as that in the Dickson dual-phase switched capacitor converter. 
     Through the foregoing description, various embodiments of the present disclosure shows that during the charging process of the flying capacitors  219  and  229 , three switches are connected in series to establish the charging paths. During the discharging process of the flying capacitors  219  and  229 , two switches are connected in series to establish the discharging paths. It is the same as the flying capacitors  119  and  139  of the Dickson dual-phase switched capacitor converter. The effective value of the current flowing through the flying capacitors in the present disclosure is twice that in the Dickson dual-phase switched capacitor converter. This requires the on-resistance of the switches  216 ,  217 ,  218 ,  226 ,  227 , and  228  to be the same as the switches  115 ,  116 ,  135 , and  136  of the Dickson dual-phase switched capacitor converter. Since the present disclosure uses two less switches than the Dickson dual-phase switched capacitor converter, the four switches  117 ,  118 ,  137 , and  138  in the Dickson dual-phase switched capacitor converter can be made into two switches under the same chip area. These two switches have the same on-resistance as switches  115 ,  116 ,  135 ,  136  so as to meet the on-resistance requirements of the six switches  216 ,  217 ,  218 ,  226 ,  227 , and  228  in the present disclosure. Under this on-resistance arrangement, the dual-phase switched capacitor converter shown in  FIG.  3    has the same efficiency as the Dickson dual-phase switched capacitor converter shown in  FIG.  1   . Because the present disclosure uses less two flying capacitors, and these two flying capacitors are the capacitors with the highest DC voltage bias in the Dickson dual-phase switched capacitor converter shown in  FIG.  1   , the dual-phase switched capacitor converter shown in  FIG.  3    greatly reduces the requirements on the electrical characteristics and quantity of the flying capacitors, thereby reducing the circuit cost and PCB area. 
       FIG.  6    illustrates the gate drive signals of the 4:1 dual-phase switched capacitor converter shown in  FIG.  3    in accordance with various embodiments of the present disclosure. As shown in  FIG.  6   , in a first half cycle, the switches  213 ,  216 ,  218 ,  221 ,  224 ,  225  and  227  are turned on, and the switches  211 ,  214 ,  215 ,  217 ,  223 ,  226  and  228  are turned off. In a second half cycle, the switches  213 ,  216 ,  218 ,  221 ,  224 ,  225  and  227  are turned off, and the switches  211 ,  214 ,  215 ,  217 ,  223 ,  226  and  228  are turned on. 
       FIG.  7    illustrates two equivalent circuit diagrams for operating in two different half cycles in accordance with various embodiments of the present disclosure. Circuit  702  is the equivalent circuit of the dual-phase switched capacitor converter shown in  FIG.  3    configured to operate in the first half cycle. Circuit  704  is the equivalent circuit of the dual-phase switched capacitor converter shown in  FIG.  3    configured to operate in the second half cycle. 
     In the first half cycle, as indicated by circuit  702 , VIN (4×Vo) charges C 202  through a conductive path formed by C 222  and C 229 . Through this conductive path, VIN also provides power to a load coupled to Vo. The flying capacitor C 212  charges C 202  through C 229 . C 212  also provides power to the load coupled to Vo. The flying capacitor C 219  and C 202  are connected in parallel. The flying capacitor C 219  charges C 202  and provides power to the load coupled to Vo. 
     In the second half cycle, as indicated by circuit  704 , VIN (4×Vo) charges C 202  through a conductive path formed by C 212  and C 219 . Through this conductive path, VIN also provides power to a load coupled to Vo. The flying capacitor C 222  charges C 202  through C 219 . C 222  also provides power to the load coupled to Vo. The flying capacitor C 229  and C 202  are connected in parallel. The flying capacitor C 229  charges C 202  and provides power to the load coupled to Vo. 
     As indicated by the two equivalent circuits, the charging and discharging paths of the flying capacitor in the two half cycles are not symmetrical. This leads to the fact that when the input power supply Vin charges C 202  through the flying capacitors C 222  and C 229 , C 202  is in parallel with the flying capacitor C 219 . At the same time, VIN and C 219  provide power for the load. Due to the voltage difference between these two current supplying paths, charge transferring may occur between the flying capacitors on the two current supplying paths, thereby causing unnecessary charge sharing losses. 
     As shown in the voltage waveforms in the dashed rectangle  706 , in the most part of the first half cycle, the voltage across C 219  (VC 219 ) and the voltage on Vo (Vin-VC 222 -VC 229 ) are equal. In the second half cycle, due to the asymmetrical charging and discharging paths, the total voltage change rates of the two paths are not the same. As shown in the dashed rectangle  706 , at the moment of entering the first half cycle, the voltage of the path connecting the power supply Vin (that is, Vin charges Vo through C 222  and C 229 ) is significantly higher than that of the path connecting C 219  and Vo. This voltage difference causes Vin to supply power to the output capacitor and load through C 222 , C 229 . However, part of the current is used to charge C 219  so as to reach the same voltage as the output capacitor C 202 . This charge transfer between flying capacitors (increasing the voltage of C 219  to a higher level) is unnecessary, and causes significant power losses. The power losses can be avoided through using control mechanisms described below with respect to  FIGS.  8 - 10   . 
       FIG.  8    illustrates three equivalent circuit diagrams for operating in two different half cycles in accordance with various embodiments of the present disclosure. The operating principle shown in  FIG.  8    is similar to that shown in  FIG.  7    except that a third equivalent circuit  808  is added to avoid the power loss caused by charge transferring between flying capacitors. As shown in  FIG.  8   , a transition period can be added between the first half cycle and the second half cycle. In the transition period, C 219  is disconnected from C 202 . The voltage across C 219  is maintained until the voltage of the path (Vin-VC 222 -VC 229 ) is equal to the voltage on C 219 . Once the voltage (Vin-VC 222 -VC 229 ) is equal to that on C 219 , C 219  is connected in parallel with C 202  to supply power to the output capacitor C 202  and the load. The delayed connection of C 219  can effectively reduce or eliminate the charge transferring, thereby reducing the power loss between the flying capacitors. 
       FIG.  9    illustrates four equivalent circuit diagrams for operating in two different operating modes in accordance with various embodiments of the present disclosure. The operating principle shown in  FIG.  9    is similar to that shown in  FIG.  8    except that a fourth equivalent circuit  906  is added to avoid the power loss caused by charge transferring. A first transition period shown in the dashed rectangle  908  is added during the transition from the second half cycle to the first half cycle. A second transition period shown in the dashed rectangle  906  is added during the transition from the first half cycle to the second half cycle. 
       FIG.  10    illustrates the gate drive signals of the 4:1 dual-phase switched capacitor converter shown in  FIG.  3    in accordance with various embodiments of the present disclosure. As shown in  FIG.  10   , in a first half cycle, the switches  213 ,  221 ,  224 ,  225  and  227  are turned on, and the switches  211 ,  214 ,  215 ,  217 ,  223 ,  226  and  228  are turned off. The switches  216  and  218  are turned on after a first delay. The first delay is added according to the operating principle shown in the dashed rectangle  908  in  FIG.  9   . In a second half cycle, the switches  213 ,  216 ,  218 ,  221 ,  224 ,  225  and  227  are turned off, and the switches  211 ,  214 ,  215 ,  217  and  223  are turned on. The switches  226  and  228  are turned on after a second delay. The second delay is added according to the operating principle shown in the dashed rectangle  906  in  FIG.  9   . 
     It should be noted that the control mechanisms shown in  FIGS.  8 - 10    is also applicable to the implementation of the higher step-down ratio power converters. For example, the control mechanisms are applicable to a 2×N:1 dual-phase switched capacitor converter described below with respect to  FIG.  19   . 
     According to the operating principle shown in  FIG.  7   , a large charge transfer current occurs between the capacitors at the moment of the transition between two different half cycles. After adding the first delay time and the second delay time shown in  FIG.  10   , the peak current can be effectively eliminated and the charge transfer loss can be reduced. 
     It should be noted the control mechanism described above with respect to  FIG.  10    is applied to the 4:1 dual-phase switched capacitor converter, but it is understood that the control mechanism may be implemented using other types of switched capacitor converters described in the present disclosure. 
       FIG.  11    illustrates a power conversion system including the 4:1 dual-phase switched capacitor converter and a DC/DC regulator stage connected in cascade in accordance with various embodiments of the present disclosure. Depending on different applications and design needs, the 4:1 dual-phase switched capacitor converter (e.g., converter  200 ) can be used as a front stage in a multi-level DC/DC conversion system to achieve a high-efficiency fixed-ratio voltage conversion. The 4:1 dual-phase switched capacitor converter and a DC/DC regulator stage  250  are connected in cascade between VIN and VLOAD. The DC/DC regulator stage  250  is employed to achieve dynamic voltage regulation. In this system, the output capacitor for the 4:1 dual-phase switched capacitor converter  200  can be very small, or the output capacitor can be removed. The small output capacitor is used only to filter out very high frequency components of VOUT, while allowing VOUT to vary in a frequency approximately equal to twice the switching frequency. The variations of VOUT allow soft charging and discharging of flying capacitors, which reduces the charge sharing loss caused by current spikes when charge transferring occurs between capacitors. 
       FIG.  12    illustrates a power conversion system including the 4:1 dual-phase switched capacitor converter and an output filter in accordance with various embodiments of the present disclosure. The 4:1 dual-phase switched capacitor converter shown in  FIG.  12    similar to that shown in  FIG.  3    except that an LC filter is connected to VOUT. The LC filter comprises an inductor  206  and a capacitor  202 . The capacitor  202  is connected in parallel with a load resistor  204 . Similar to the circuit configuration illustrated in  FIG.  11   , the inductor at the output of the 4:1 dual-phase switched capacitor converter allows the voltage at VOUT to vary and limits the current spike when the output capacitor  202  is charged, which in turn allows soft charging and discharging of flying capacitors, which reduces the charge sharing loss caused by current spikes when charge transferring occurs between capacitors. 
     In some applications, the output current may be small. In order to further reduce the cost of chips and circuits and PCB area, the circuit in  FIG.  3    can be simplified from a dual-phase converter to a single-phase converter shown in  FIG.  13   . 
       FIG.  13    illustrates a schematic diagram of a 4:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The 4:1 single-phase switched capacitor converter  300  comprises switches  303 ,  305 , a flying capacitor  304 , a first phase  310 , a second phase  320 , an input capacitor  304 , and an output capacitor  306 . 
     The flying capacitor  304  is connected between the switches  303  and  305 . The switch  303  is connected between the input terminal VIN and the flying capacitor  304 . The switch  305  is connected between the flying capacitor  304  and the ground GND. The first phase  310  comprises four switches  311 ,  312 ,  313 ,  314  connected in series between a common node of the switch  303  and the flying capacitor  304 , and the ground GND. A flying capacitor  315  is connected between a common node of switches  311  and  312 , and a common node of switches  313  and  314 . 
     The second phase  320  comprises four switches  321 ,  322 ,  323 ,  324  connected in series between a common node of the switch  305  and the flying capacitor  304 , and the ground GND. A flying capacitor  325  is connected between a common node of switches  321  and  322 , and a common node of switches  323  and  324 . Throughout the description, a first leg of the 4:1 single-phase switched capacitor converter is a switch leg comprising switches  321 ,  322 ,  323  and  324 . A second leg of the 4:1 single-phase switched capacitor converter is a switch leg comprising switches  311 ,  312 ,  313  and  314 . Switch  305  may be referred to as a first upper switch. Switch  303  may be referred to as a second upper switch. 
     In operation, when the 4:1 single-phase switched capacitor converter  300  is configured as a 4:1 step-down converter, all the switches are switched on and off alternately at a specific operating frequency with a 50% duty cycle. 
     In operation, in a first half cycle, the switch  303  is turned on, and the switch  305  is turned off. The switches  312  and  314  of the first phase  310  are turned on, and the switches  311  and  313  are turned off. The switches  321  and  323  of the second phase  320  are turned on, and the switches  322  and  324  are turned off. The flying capacitors  304 ,  325  and the output capacitor  306  are connected in series. VIN charges the flying capacitors  304 ,  325  and the output capacitor  306  through switches  303 ,  321 , and  323 . In addition, VIN supplies power to the output terminal VOUT. At this time, the flying capacitors  304  and  325  are connected in series with the output capacitor  306 . The sum of the average voltages on the flying capacitors  304 ,  325  and the output capacitor  306  is equal to the input voltage VIN. 
     Also, in the first half cycle, the flying capacitor  315  charges the output capacitor  306  through switches  312  and  314 . In addition, the flying capacitor  315  supplies power to the output VOUT. Because the flying capacitor  315  is connected in parallel with the output capacitor  306 , the average voltage on the flying capacitor  315  is equal to the output voltage VOUT. 
     In a second half period, the switch  305  is turned on. The switch  303  is turned off. The switches  311  and  313  of the first phase  310  are turned on, and the switches  312  and  314  are turned off. The switches  322  and  324  of the second phase  320  are turned on, and the switches  321  and  323  are turned off. The flying capacitor  315  and the output capacitor  306  are connected in series. The flying capacitor  304  charges the flying capacitor  315  and the output capacitor  306  through the switches  305 ,  311 , and  313 . In addition, the flying capacitor  304  supplies power to the output terminal VOUT. At this time, the flying capacitor  315  and the output capacitor  306  are connected in series, and further connected in parallel with the flying capacitor  304 . Therefore, the average voltage on the flying capacitor  304  is equal to the sum of the average voltages on the flying capacitor  315  and the output capacitor  306 . In other words, the average voltage on the flying capacitor  304  is twice the output voltage VOUT. 
     Also, in the second half period, the flying capacitor  325  charges the output capacitor  306  through the switches  322  and  324 . In addition, the flying capacitor  325  supplies power to the output VOUT. Because the flying capacitor  325  is connected in parallel with the output capacitor  306 , the average voltage on the flying capacitor  325  is equal to the output voltage VOUT. 
     As mentioned above, the sum of the average voltages on the flying capacitors  304 ,  325  and the output capacitor  306  is equal to the input voltage VIN, and the average voltage on the flying capacitor  304  is equal to one half of the input voltage (VIN/2). In this way, when the switching frequency is fast enough, the voltages of the flying capacitors  304 ,  315 ,  325  and the output capacitor  306  fluctuate around an average value with each switching state. The average voltage on the flying capacitor  304  is equal to one half of the input voltage (VIN/2). The average voltages on the flying capacitors  315 ,  325  and the output capacitor  306  are equal to the output voltage VOUT. The power conversion ratio of the single-phase switched capacitor converter shown in  FIG.  13    is equal to 4:1. 
       FIG.  14    illustrates a schematic diagram of a 2:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The structure of the single-phase switched capacitor converter shown in  FIG.  14    is similar to that shown in  FIG.  13    except that a switch  302  added to achieve a 2:1 conversion ratio. 
     In operation, the switches  302  and  303  are always in the on state, and the switch  305  is always in the off state. In addition, switch  321  comprises two back-to-back connected MOSFET switches as shown in  FIG.  14   . The remaining switches alternately switch at a specific operating frequency with a 50% duty cycle. In this configuration, the flying capacitor  304  is short-circuited by the switches  302  and  303 . The voltage across the flying capacitor  304  is equal to zero. 
     In a first half cycle, the switches  311  and  313  of the first phase  310  are turned on, and the switches  312  and  315  are turned off. The switches  322  and  324  of the second phase  320  are turned on, and the switches  321  and  323  are turned off. The flying capacitor  315  and the output capacitor  306  are connected in series. VIN charges the flying capacitor  315  and the output capacitor  306  through switches  311  and  313 . In addition, VIN supplies power to the output terminal VOUT. The sum of the average voltage on the flying capacitor  315  and the output capacitor  306  is equal to the input voltage VIN. 
     Also, in the first half cycle, the flying capacitor  325  charges the output capacitor  306  through the switches  322  and  324 . In addition, the flying capacitor  325  supplies power to the output VOUT. Because the flying capacitor  325  is connected in parallel with the output capacitor  306 , the average voltage on the flying capacitor  325  is equal to the output voltage VOUT. 
     In a second half cycle, the switches  312  and  314  of the first phase  310  are turned on, and the switches  311  and  313  are turned off. The switches  321  and  323  of the second phase  320  are turned on, and the switches  322  and  324  are turned off. The flying capacitor  325  and the output capacitor  306  are connected in series. VIN charges the flying capacitor  325  and the output capacitor  306  through switches  302 ,  321  and  323 . In addition, VIN supplies power to the output terminal VOUT. 
     Also, in the second half cycle, the flying capacitor  325  and the output capacitor  306  are connected in series. The sum of the average voltage on the flying capacitor  325  and the output capacitor  306  is equal to the input voltage VIN. As mentioned earlier, the average voltage of the flying capacitor  325  is equal to the output voltage VOUT. Therefore, the average voltage on the flying capacitor  325  and the output capacitor  306  is equal to one half of the input voltage (VIN/2). At the same time, the flying capacitor  315  charges the output capacitor  306  through the switches  312  and  314  and supplies power to the output VOUT. Because the flying capacitor  315  is connected in parallel with the output capacitor  306 , the average voltage on the flying capacitor  315  is equal to the output voltage VOUT. VOUT is equal to one half of the input voltage (VIN/2). 
     In this configuration, when the switching frequency is fast enough, the voltages on the flying capacitors  315 ,  325 , and the output capacitor  306  fluctuate around a constant value (VIN/2) with each switching state. The power conversion ratio of the single-phase switched capacitor converter shown in  FIG.  14    is equal to 2:1. 
     In some embodiments, the dual-phase switched capacitor converter shown in  FIG.  3    and the single-phase switched capacitor converter shown in  FIG.  13    can also be extended to a 2N:1 step-down ratio, where N is an integer. When N is equal to three, the switched capacitor converter is a 6:1 dual-phase switched capacitor converter or a 6:1 single-phase switched capacitor converter, which are discussed below with respect to  FIGS.  17  and  18   , respectively. When N is equal to four, the switched capacitor converter is an 8:1 dual-phase switched capacitor converter or an 8:1 single-phase switched capacitor converter, which are discussed below with respect to  FIGS.  15  and  16   , respectively. Moreover, a 2×N:1 dual-phase switched capacitor converter or a 2×N:1 single-phase switched capacitor converter, which are discussed below with respect to  FIGS.  19  and  20   . 
       FIG.  15    illustrates a schematic diagram of an 8:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The 8:1 dual-phase switched capacitor converter  400  comprises eighteen switches, eight flying capacitors, one input capacitor and one output capacitor. A first phase  410  includes switches  411 ,  413 ,  414 ,  415 ,  416 ,  417 ,  418 ,  419 , and  420 , and flying capacitors  412 ,  421 ,  422 , and  423 . A second phase  430  includes switches  431 ,  433 ,  434 ,  435 ,  436 ,  437 ,  438 ,  439 , and  440 , and flying capacitors  432 ,  441 ,  442 , and  443 . The two phases share the input capacitor  401 , which is connected between the input terminal VIN and the ground GND. The two phases share the output capacitor  402 , which is connected between the input and output terminals VOUT and the ground GND. Throughout the description, a first leg of the 8:1 dual-phase switched capacitor converter is a switch leg comprising switches  434 ,  436 ,  437 ,  438 ,  439 , and  440 . A second leg of the 8:1 dual-phase switched capacitor converter is a switch leg comprising switches  415 ,  416 ,  417 ,  418 ,  419 , and  420 . Switch  433  may be referred to as a first upper switch. Switch  431  may be referred to as a second upper switch. Switch  413  may be referred to as a third upper switch. Switch  411  may be referred to as a fourth upper switch. Switch  435  may be referred to as a fifth upper switch. Switch  414  may be referred to as a sixth upper switch. 
     In operation, all the switches switch alternately with a 50% duty cycle at a specific operating frequency. Among them, the working principle of the circuit formed by the switches  411 ,  413 ,  414 ,  415 ,  431 ,  433 ,  434 ,  435 , flying capacitors  412 ,  432  and the input capacitor  401  is the same as that of the corresponding parts in  FIG.  3   . Therefore, the average voltages across the flying capacitors  412  and  432  are equal to one half of the input voltage (VIN/2). The operating principle of the circuit formed by the switches  418 ,  419 ,  420 ,  438 ,  439 ,  440 , flying capacitors  423 ,  443 , and output capacitor  402  is the same as the corresponding parts in  FIG.  3   . Therefore, the average voltages across the flying capacitors  423  and  443  are equal to the output voltage VOUT. 
     In a first half cycle, the switches  411 ,  414 ,  415 ,  417 , and  419  of the first phase  410  are turned on, and the switches  413 ,  416 ,  418 , and  420  are turned off. The switches  433 ,  436 ,  438 , and  440  of the second phase  430  are turned on, and the switches  431 ,  434 ,  435 ,  437 , and  439  are turned off. The flying capacitors  412 ,  421  and the output capacitor  402  are connected in series. VIN charges the flying capacitors  412 ,  421  and the output capacitor  402  through the switches  411 ,  414 , and  419 . In addition, VIN supplies power to the output terminal VOUT. At this time, the flying capacitors  412  and  421  are connected in series with the output capacitor  402 . The sum of the average voltages on the flying capacitors  412 ,  421  and the output capacitor  402  is equal to the input voltage VIN. Because the voltage on the flying capacitor  412  is equal to one half of the input voltage, the sum of the voltage on the flying capacitor  421  and the output capacitor  402  is equal to one half of the input voltage VIN. 
     Also, in the first half cycle, the flying capacitor  423  and the output capacitor  402  are connected in series. The flying capacitor  422  charges the flying capacitor  423  and the output capacitor  402  through the switches  417 ,  419 , and  440 . In addition, the flying capacitor  422  supplies power to the output terminal VOUT. Because the voltage on the flying capacitor  423  is equal to the output voltage VOUT, the average voltage on the flying capacitor  422  is equal to twice the output voltage (2×VOUT). 
     Also, in the first half cycle, the flying capacitor  421  and the output capacitor  402  are connected in series. The flying capacitor  432  charges the flying capacitor  421  and the output capacitor  402  through the switches  433 ,  415 , and  419 . In addition, the flying capacitor  432  supplies power to the output terminal VOUT. The flying capacitor  442  and the output capacitor  402  are connected in series. The flying capacitor  441  charges the flying capacitor  442  and the output capacitor  402  through the switches  436 ,  419 , and  440 . In addition, the flying capacitor  441  supplies power to the output terminal VOUT. The voltage on the flying capacitor  441  is equal to the sum of the average voltages on the flying capacitor  442  and the output capacitor  402 . The flying capacitor  443  charges the output capacitor  402  through the switches  438  and  440 , and supplies power to the output terminal VOUT. 
     In a second half cycle, the switches  413 ,  416 ,  418 , and  420  of the first phase  410  are turned on, and the switches  411 ,  414 ,  415 ,  417 , and  419  are turned off. The switches  431 ,  434 ,  435 ,  437 , and  439  of the second phase  430  are turned on, and the switches  433 ,  436 ,  438 , and  440  are turned off. The flying capacitors  432 ,  441  and the output capacitor  402  are connected in series. VIN charges the flying capacitors  432 ,  441  and the output capacitor  402  through the switches  431 ,  434 , and  440 , and supplies power to the output terminal VOUT. Because the voltage on the flying capacitor  432  is equal to one half of the input voltage VIN, the sum of the average voltages on the flying capacitor  441  and the output capacitor  402  is equal to one half of the input voltage (VIN/2). 
     Also, in the second half cycle, the flying capacitor  443  and the output capacitor  402  are connected in series. The flying capacitor  442  charges the flying capacitor  443  and the output capacitor  402  through the switches  437 ,  439 , and  420 . In addition, the flying capacitor  442  supplies power to the output terminal VOUT. Because the voltage on the flying capacitor  443  is equal to the output voltage VOUT, the average voltage on the flying capacitor  442  is equal to twice the output voltage (2×VOUT). 
     Also, in the second half cycle, the flying capacitor  441  and the output capacitor  402  are connected in series. The flying capacitor  412  charges the flying capacitor  441  and the output capacitor  402  through the switches  413 ,  435 , and  439  and supplies power to the output terminal VOUT. Also, in the second half cycle, the flying capacitor  443  and the output capacitor  402  are connected in series. The flying capacitor  442  charges the flying capacitor  443  and the output capacitor  402  through the switches  437 ,  439 , and  420 , and supplies power to the output terminal VOUT. The average voltage on the flying capacitor  442  is equal to the sum of the average voltages on the flying capacitor  443  and the output capacitor  402 . Therefore, the average voltage on the flying capacitor  442  is equal to twice the output voltage (2×VOUT). 
     As mentioned above, the voltage on the flying capacitor  441  is equal to the sum of the average voltages on the flying capacitor  442  and the output capacitor  402 . Therefore, the voltage on the flying capacitor  441  is equal to three times the output voltage (3×VOUT). Similarly, it can be concluded that the voltage on the flying capacitor  421  is three times the output voltage (3×VOUT). Because the sum of the average voltages on the flying capacitors  421 ,  441  and the output capacitor  402  is equal to the voltages on the flying capacitors  412  and  432 , and the voltages on the flying capacitors  412  and  432  are equal to one half of the input voltage, the output voltage VOUT is equal to one-eighth of the voltage (VIN/8). 
     In this configuration, when the switching frequency is fast enough, the voltages on the flying capacitors  412 ,  432 ,  421 ,  441 ,  422 ,  442 ,  423 ,  443  and the output capacitor  402  fluctuate around a constant value with each switching state. The power conversion ratio of the dual-phase switched capacitor converter shown in  FIG.  15    is equal to 8:1. 
     In some embodiments, the voltages on the flying capacitors  412  and  432  are equal to one half of the input voltage or four times the output voltage (VIN/2 or 4×VOUT). The voltages on the flying capacitors  421  and  441  are equal to three times the output voltage (3×VOUT). The voltages on the flying capacitors  422  and  442  are equal to twice the output voltage (2×VOUT). The voltages on the flying capacitors  423  and  443  are equal to the output voltage (VOUT). Switches  416 ,  417 ,  418 ,  419 ,  420 ,  436 ,  437 ,  438 ,  439 , and  440 , as well as capacitors  421 ,  422 ,  423 ,  441 ,  442 ,  443 , and output capacitor  402  forms a cross-coupled two-phase switched capacitor converter. 
       FIG.  16    illustrates a schematic diagram of an 8:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The operating principle of the single-phase switched capacitor converter has been described above with respect to  FIG.  13   , and hence is not discussed again herein. 
     As shown in  FIG.  16   , a first switch  440 , a second switch  439 , a third switch  438 , a fourth switch  437 , a fifth switch  436  and a sixth switch  434  of the first leg are connected in series between ground and a first voltage node (a common node of  433  and  432 ). A first switch  420 , a second switch  419 , a third switch  418 , a fourth switch  417 , a fifth switch  416  and a sixth switch  415  of the second leg are connected in series between ground and a second voltage node (a common node of  432  and  431 ). 
     The first flying capacitor  443  is connected between the common node of the first switch  440  and the second switch  439  of the first leg, and the common node of the third switch  438  and the fourth switch  437  of the first leg. The second flying capacitor  423  is connected between the common node of the first switch  420  and the second switch  419  of the second leg, and the common node of the third switch  418  and the fourth switch  417  of the second leg. 
     The third flying capacitor  432  is connected between the first voltage node and the second voltage node. The fourth flying capacitor  442  is connected between a common node of the fourth switch  437  and the fifth switch  436  of the first leg, and the common node of the first switch  440  and the second switch  439  of the second leg. The fifth flying capacitor  422  is connected between a common node of the fourth switch  417  and the fifth switch  416  of the second leg, and the common node of the first switch  420  and the second switch  419  of the first leg. 
     The sixth flying capacitor  441  is connected between a common node of the fifth switch  436  and the sixth switch  434  of the first leg, and the common node of the first switch  440  and the second switch  439  of the first leg. The seventh flying capacitor  421  is connected between a common node of the fifth switch  416  and the sixth switch  415  of the second leg, and the common node of the first switch  420  and the second switch  419  of the second leg. The first upper switch  433  is connected between the first voltage node and ground. The second upper switch  431  connected between the second voltage node and the input terminal. 
     Referring back to  FIG.  15   , the 8:1 dual-phase switched capacitor converter further comprises an eighth flying capacitor  412  connected between a third voltage node (a common node of  413  and  412 ) and a fourth voltage node (a common node of  412  and  411 ), a third upper switch  413  connected between the third voltage node and ground, a fourth upper switch  411  connected between the fourth voltage node and the input terminal, a fifth upper switch  435  connected between the common node of the fifth switch  436  and the sixth switch  434  of the first leg, and the fourth voltage node, and a sixth upper switch  414  connected between the common node of the fifth switch  416  and the sixth switch  415  of the second leg, and the third voltage node. 
       FIG.  17    illustrates a schematic diagram of a 6:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The 6:1 dual-phase switched capacitor converter  500  comprises sixteen switches, six flying capacitors, one input capacitor and one output capacitor. A first phase  510  includes switches  511 ,  513 ,  514 ,  515 ,  517 ,  518 ,  519 , and  520 , and flying capacitors  512 ,  522 , and  523 . A second phase  530  includes switches  531 ,  533 ,  534 ,  535 ,  537 ,  538 ,  539 , and  540 , and flying capacitors  532 ,  542 , and  543 . The two phases share the input capacitor  501 , which is connected between the input terminal VIN and the ground GND. The two phases share the output capacitor  502 , which is connected between the input and output terminals VOUT and the ground GND. Throughout the description, a first leg of the 6:1 dual-phase switched capacitor converter is a switch leg comprising switches  534 ,  537 ,  538 ,  539 , and  540 . A second leg of the 6:1 dual-phase switched capacitor converter is a switch leg comprising switches  515 ,  517 ,  518 ,  519 , and  520 . Switch  533  may be referred to as a first upper switch. Switch  531  may be referred to as a second upper switch. Switch  513  may be referred to as a third upper switch. Switch  511  may be referred to as a fourth upper switch. Switch  535  may be referred to as a fifth upper switch. Switch  514  may be referred to as a sixth upper switch. 
     The operating principle of the 6:1 dual-phase switched capacitor converter is similar to that of the 8:1 dual-phase switched capacitor converter  FIG.  15   , and hence is not discussed again herein. 
       FIG.  18    illustrates a schematic diagram of a 6:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The operating principle of the single-phase switched capacitor converter has been described above with respect to  FIG.  13   , and hence is not discussed again herein. 
     As shown in  FIG.  18   , a first switch  540 , a second switch  539 , a third switch  538 , a fourth switch  537  and a fifth switch  534  of the first leg are connected in series between ground and a first voltage node (a common node of  533  and  532 ). A first switch  520 , a second switch  519 , a third switch  518 , a fourth switch  517  and a fifth switch  515  of the second leg are connected in series between ground and a second voltage node (a common node of  531  and  532 ). 
     The first flying capacitor  543  is connected between the common node of the first switch  540  and the second switch  539  of the first leg, and the common node of the third switch  538  and the fourth switch  537  of the first leg. The second flying capacitor  523  is connected between the common node of the first switch  520  and the second switch  519  of the second leg, and the common node of the third switch  518  and the fourth switch  517  of the second leg. 
     The third flying capacitor  532  is connected between the first voltage node and the second voltage node. The fourth flying capacitor  542  is connected between a common node of the fourth switch  537  and the fifth switch  534  of the first leg, and the common node of the first switch  520  and the second switch  519  of the second leg. The fifth flying capacitor  522  is connected between a common node of the fourth switch  517  and the fifth switch  515  of the second leg, and the common node of the first switch  540  and the second switch  539  of the first leg. The first upper switch  533  is connected between the first voltage node and ground. The second upper switch  531  connected between the second voltage node and the input terminal. 
     Referring back to  FIG.  17   , the 6:1 dual-phase switched capacitor converter  500  further comprises a sixth flying capacitor  512  connected between a third voltage node (a common node of  512  and  513 ) and a fourth voltage node (a common node of  512  and  511 ), a third upper switch  513  connected between the third voltage node and ground, a fourth upper switch  511  connected between the fourth voltage node and the input terminal, a fifth upper switch  535  connected between the common node of the fourth switch  537  and the fifth switch  534  of the first leg, and the fourth voltage node, and a sixth upper switch  514  connected between the common node of the fourth switch  517  and the fifth switch  515  of the second leg, and the third voltage node. 
       FIG.  19    illustrates a schematic diagram of a 2×N:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure. After a given integer N, the number of switches and flying capacitors required by the circuit of the present invention is determined. In the 2×N:1 dual-phase switched capacitor converter  600 , the number of switches is equal to 2×N+10. The number of flying capacitors is equal to 2×N. 
     Throughout the description, a first leg of the 2×N:1 dual-phase switched capacitor converter is a switch leg comprising switches  634 ,  636 ,  637 ,  638 ,  639 ,  640  and  641 . A second leg of the 2×N:1 dual-phase switched capacitor converter is a switch leg comprising switches  615 ,  616 ,  617 ,  618 ,  619 ,  620  and  621 . Switch  633  may be referred to as a first upper switch. Switch  631  may be referred to as a second upper switch. Switch  613  may be referred to as a third upper switch. Switch  611  may be referred to as a fourth upper switch. Switch  635  may be referred to as a fifth upper switch. Switch  614  may be referred to as a sixth upper switch. 
       FIG.  20    illustrates a schematic diagram of a 2×N:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The operating principle of the single-phase switched capacitor converter has been described above with respect to  FIG.  13   , and hence is not discussed again herein. 
     As shown in  FIG.  20   , (N+2) switches of the first leg are connected in series between ground and a first voltage node (a common node of  632  and  633 ). (N+2) switches of the second leg are connected in series between ground and a second voltage node (a common node of  632  and  631 ). 
     A first flying capacitor  645  of the (2×N−1) flying capacitors is connected between the common node of the first switch  641  and the second switch  640  of the first leg, and the common node of the third switch  639  and the fourth switch  638  of the first leg. A second flying capacitor  625  of the (2×N−1) flying capacitors is connected between the common node of the first switch  621  and the second switch  620  of the second leg, and the common node of the third switch  619  and the fourth switch  618  of the second leg. 
     A third flying capacitor  632  is connected between the first voltage node and the second voltage node. Let M represent an integer between 2 and N−1. One terminal of a (2×M)th flying capacitor is connected to a common node of an (M+2)th switch and an (M+3)th switch of the first leg, and the other terminal of the (2×M)th flying capacitor is connected to the common node of the first switch and the second switch of either the second leg when M is an even number, or the first leg when M is an odd number. 
     One terminal of a (2×M+1)th flying capacitor is connected between a common node of an (M+2)th switch and an (M+3)th switch of the second leg, and the other terminal of the (2×M)th flying capacitor is connected to the common node of the first switch and the second switch of either the first leg when M is an even number, or the second leg when M is an odd number. 
     As a result of this arrangement, when M is 2, a fourth flying capacitor is connected between a common node of the fourth switch and the fifth switch of the first leg, and the common node of the first switch and the second switch of the second leg. A fifth flying capacitor is connected between a common node of the fourth switch and the fifth switch of the second leg, and the common node of the first switch and the second switch of the first leg. 
     Similarly, when M is equal to N−2, and N is an even number, a (2×N−4)th flying capacitor  643  is connected between a common node of an Nth switch  637  and an (N+1)th switch  636  of the first leg, and the common node of the first switch  621  and the second switch  620  of the second leg. A (2×N−3)th flying capacitor  623  is connected between a common node of an Nth switch  617  and an (N+1)th switch  616  of the second leg, and the common node of the first switch  641  and the second switch  640  of the first leg. 
     When M is equal to N−1, and N is an even number, N−1 is an odd number. A (2×N−2)th flying capacitor  642  is connected between a common node of the (N+1)th switch  636  and an (N+2)th switch  634  of the first leg, and the common node of the first switch  641  and the second switch  640  of the first leg. A (2×N−1)th flying capacitor  622  is connected between a common node of the (N+1)th switch  616  and an (N+2)th switch  615  of the second leg, and the common node of the first switch  621  and the second switch  620  of the second leg. The first upper switch  633  is connected between the first voltage node and ground. The second upper switch  631  is connected between the second voltage node and the input terminal. 
     Referring back to  FIG.  19   , the 2×N:1 dual-phase switched capacitor converter  600  further comprises a (2×N)th flying capacitor  612  connected between a third voltage node (a common node of  612  and  613 ) and a fourth voltage node (a common node of  612  and  611 ), a third upper switch  613  connected between the third voltage node and ground, a fourth upper switch  611  connected between the fourth voltage node and the input terminal, a fifth upper switch  635  connected between the common node of the (N+1)th switch  636  and the (N+2)th switch  634  of the first leg, and the fourth voltage node, and a sixth upper switch  614  connected between the common node of the (N+1)th switch  616  and the (N+2)th switch  615  of the second leg, and the third voltage node. 
     The switched capacitor converter shown in  FIG.  19    is able to achieve a voltage conversion ratio of equal to 2×N:1 as described above with respect to  FIG.  19   . In some embodiments, 2×N is equal to the number of flying capacitors of the switched capacitor converter. In some embodiments, the switched capacitor converter shown in  FIG.  19    is able to achieve a N:1 conversion ratio through configuring the first upper switch (e.g., switch  633 ), the second upper switch (e.g., switch  631 ), the third upper switch (e.g., switch  613 ), the fourth upper switch (e.g., switch  611 ) as always-on switches and configuring the fifth upper switch (e.g., switch  635 ) and the sixth upper switch (e.g., switch  614 ) as always-off switches. 
     In some embodiments, the dual-phase switched capacitor converter shown in  FIG.  3    and the single-phase switched capacitor converter shown in  FIG.  13    can also be extended to a 2 N :1 step-down ratio, where N is an integer. When N is equal to three, the switched capacitor converter is an 8:1 dual-phase switched capacitor converter or an 8:1 single-phase switched capacitor converter, which are discussed below with respect to  FIGS.  21  and  22   , respectively. 
       FIG.  21    illustrates an alternative schematic diagram of an 8:1 dual-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The 8:1 dual-phase switched capacitor converter  700  comprises twenty switches, six flying capacitors, one input capacitor and one output capacitor. A first phase  210  includes switches  231 ,  233 ,  234 ,  235 ,  213 ,  214 ,  215 ,  216 ,  217  and  218 , and flying capacitors  232 ,  212  and  219 . A second phase  220  includes switches  241 ,  243 ,  244 ,  245 ,  223 ,  224 ,  225 ,  226 ,  227  and  228 , and flying capacitors  242 ,  222 , and  229 . The two phases share the input capacitor  201 , which is connected between the input terminal VIN and the ground GND. The two phases share the output capacitor  202 , which is connected between the output terminals VOUT and the ground GND. 
     Throughout the description, a first leg of the 8:1 dual-phase switched capacitor converter is a switch leg comprising switches  228 ,  227 , 226  and  224 . A second leg of the 8:1 dual-phase switched capacitor converter is a switch leg comprising switches  218 ,  217 ,  216 , and  214 . Switch  223  may be referred to as a first upper switch. Switch  244  may be referred to as a second upper switch. Switch  213  may be referred to as a third upper switch. Switch  234  may be referred to as a fourth upper switch. Switch  225  may be referred to as a fifth upper switch. Switch  214  may be referred to as a sixth upper switch. Switch  243  may be referred to as a seventh upper switch. Switch  241  may be referred to as an eighth upper switch. Switch  235  may be referred to as a ninth upper switch. Switch  233  may be referred to as a tenth upper switch. Switch  231  may be referred to as an eleventh upper switch. Switch  245  may be referred to as a twelfth upper switch. 
     As shown in  FIG.  21   , a first switch  228 , a second switch  227 , a third switch  226 , and a fourth switch  224  of the first leg are connected in series between ground and a first voltage node (a common node of  223  and  224 ). A first switch  218 , a second switch  217 , a third switch  216  and a fourth switch  215  of the second leg are connected in series between ground and a second voltage node (a common node of  214  and  213 ). 
     The first flying capacitor  229  is connected between the common node of the first switch  228  and the second switch  227  of the first leg, and the common node of the third switch  226  and the fourth switch  224  of the first leg. The second flying capacitor  219  is connected between the common node of the first switch  218  and the second switch  217  of the second leg, and the common node of the third switch  216  and the fourth switch  215  of the second leg. 
     The third flying capacitor  222  is connected between the first voltage node and the second voltage node. The fourth flying capacitor  212  is connected between a third voltage node (a common node of  213  and  214 ) and a fourth voltage node (a common node of  212  and  234 ). The first upper switch  223  is connected between the first voltage node and ground. The second upper switch  244  is connected between the second voltage node and a fifth voltage node. The third upper switch  213  is connected between the third voltage node and ground. The fourth upper switch  234  is connected between the fourth voltage node and a sixth voltage node. The fifth upper switch  225  is connected between the common node of the third switch  226  and the fourth switch  224  of the first leg, and the fourth voltage node. The sixth upper switch  214  is connected between the common node of the third switch  216  and the fourth switch  215  of the second leg, and the third voltage node. 
     The seventh upper switch  243  is connected between the fifth voltage node and ground. A fifth flying capacitor  242  is connected between the fifth voltage node and a seventh voltage node. The eighth upper switch  241  is connected between the seventh voltage node and the input terminal (VIN). The ninth upper switch  235  is connected between the seventh voltage node and the fourth voltage node. A sixth flying capacitor  232  is connected between the sixth voltage node and an eighth voltage node. The tenth upper switch  233  is connected between the sixth voltage node and ground. The eleventh upper switch  231  is connected between the eighth voltage node and the input terminal VIN. The twelfth upper switch  245  is connected between the second voltage node and the eighth voltage node. 
     In operation, all the switches switch alternately with a 50% duty cycle at a specific operating frequency. Among them, the working principle of the circuit formed by the switches  231 ,  233 ,  234 ,  235 ,  241 ,  243 ,  244 ,  245 , the flying capacitors  232 ,  242  and the input capacitor  201  is the same as that of the corresponding parts in  FIG.  3   . Therefore, the average voltages across the flying capacitors  232  and  242  are equal to one half of the input voltage (VIN/2). The operating principle of the circuit formed by the switches  216 ,  217 ,  218 ,  226 ,  227 ,  228 , the flying capacitors  229 ,  219 , and output capacitor  202  is the same as the corresponding parts in  FIG.  3   . Therefore, the average voltages across the flying capacitors  219  and  229  are equal to the output voltage VOUT. 
     In a first half cycle, the switches  231 ,  234 ,  235 ,  214 ,  215  and  217  of the first phase  210  are turned on, and the switches  233 ,  213 ,  216 , and  218  are turned off. The switches  243 ,  223 ,  226  and  228  of the second phase  220  are turned on, and the switches  241 ,  244 ,  245 ,  224 ,  225  and  227  are turned off. The flying capacitors  232 ,  212 ,  219  and the output capacitor  202  are connected in series. VIN charges the flying capacitors  232 ,  212 ,  219  and the output capacitor  202  through the switches  231 ,  234 ,  214  and  217 . In addition, VIN supplies power to the output terminal VOUT. At this time, the flying capacitors  232 ,  212  and  219  are connected in series with the output capacitor  202 . The sum of the average voltages on the flying capacitors  232 ,  212 ,  219  and the output capacitor  202  is equal to the input voltage VIN. Because the voltage on the flying capacitor  232  is equal to one half of the input voltage, the sum of the voltages on the flying capacitors  212 ,  219  and the output capacitor  202  is equal to one half of the input voltage VIN. 
     Also, in the first half cycle, the flying capacitor  219  and the output capacitor  202  are connected in series. The flying capacitor  222  charges the flying capacitor  219  and the output capacitor  202  through the switches  223 ,  215 , and  217 . In addition, the flying capacitor  222  supplies power to the output terminal VOUT. Because the voltage on the flying capacitor  219  is equal to the output voltage VOUT, the average voltage on the flying capacitor  222  is equal to twice the output voltage (2×VOUT). 
     Also, in the first half cycle, the flying capacitor  242 ,  212 ,  219  and the output capacitor  202  are connected in series. The flying capacitor  242  charges the flying capacitor  212 ,  219  and the output capacitor  202  through the switches  243 ,  235 ,  214  and  217 . In addition, the flying capacitor  242  supplies power to the output terminal VOUT. The voltage on the flying capacitor  242  is equal to the sum of the average voltages on the flying capacitor  212 ,  219  and the output capacitor  202 . Since the voltage on the flying capacitor  219  is equal to the output voltage VOUT, the average voltage on the flying capacitor  242  is equal to four times the output voltage (4×VOUT). Also, since the average voltage on flying capacitor  242  is also equal to VIN/2, the ratio of VIN to VOUT is 8:1. The flying capacitor  229  also charges the output capacitor  202  through the switches  226  and  228 , and supplies power to the output terminal VOUT. 
     In a second half cycle, the switches  233 ,  213 ,  216 , and  218  of the first phase  210  are turned on, and the switches  231 ,  234 ,  235 ,  214 ,  215  and  217  are turned off. The switches  241 ,  244 ,  245 ,  224 ,  225  and  227  of the second phase  220  are turned on, and the switches  223 ,  243 ,  226 , and  228  are turned off. The flying capacitors  242 ,  222 ,  229  and the output capacitor  202  are connected in series. VIN charges the flying capacitors  242 ,  222 ,  229  and the output capacitor  202  through the switches  241 ,  244 ,  224  and  227 , and supplies power to the output terminal VOUT. Because the voltage on the flying capacitor  242  is equal to one half of the input voltage VIN, the sum of the average voltages on the flying capacitor  222 ,  229  and the output capacitor  202  is equal to one half of the input voltage (VIN/2). 
     Also, in the second half cycle, the flying capacitor  229  and the output capacitor  202  are connected in series. The flying capacitor  212  charges the flying capacitor  229  and the output capacitor  202  through the switches  213 ,  225 , and  227 . In addition, the flying capacitor  212  supplies power to the output terminal VOUT. Because the voltage on the flying capacitor  229  is equal to the output voltage VOUT, the average voltage on the flying capacitor  212  is equal to twice the output voltage (2×VOUT). 
     Also, in the second half cycle, the flying capacitor  232 ,  222 ,  229  and the output capacitor  202  are connected in series. The flying capacitor  232  charges the flying capacitor  222 ,  229  and the output capacitor  202  through the switches  233 ,  245 ,  224  and  227 . In addition, the flying capacitor  232  supplies power to the output terminal VOUT. The voltage on the flying capacitor  232  is equal to the sum of the average voltages on the flying capacitor  222 ,  229  and the output capacitor  202 . Since the voltage on the flying capacitor  229  is equal to the output voltage VOUT, the average voltage on the flying capacitor  232  is equal to four times the output voltage (4×VOUT). Also, since the average voltage on flying capacitor  232  is also equal to VIN/2, the ratio of VIN to VOUT is 8:1. The flying capacitor  219  also charges the output capacitor  202  through the switches  216  and  218 , and supplies power to the output terminal VOUT. 
     In this configuration, when the switching frequency is fast enough, the voltages on the flying capacitors  232 ,  242 ,  212 ,  222 ,  219 ,  229  and the output capacitor  402  fluctuate around a constant value with each switching state. The power conversion ratio of the dual-phase switched capacitor converter shown in  FIG.  21    is equal to 8:1. 
     In some embodiments, the voltages on the flying capacitors  242  and  232  are equal to one half of the input voltage or four times the output voltage (VIN/2 or 4×VOUT). The voltages on the flying capacitors  212  and  222  are equal to twice the output voltage (2×VOUT). The voltages on the flying capacitors  219  and  229  are equal to the output voltage (VOUT). 
       FIG.  22    illustrates a schematic diagram of an 8:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The operating principle of the single-phase switched capacitor converter has been described above with respect to  FIG.  13   , and hence is not discussed again herein. 
     As shown in  FIG.  22   , a first switch  228 , a second switch  227 , a third switch  226 , and a fourth switch  224  of the first leg are connected in series between ground and a first voltage node (a common node of  223  and  224 ). A first switch  218 , a second switch  217 , a third switch  216  and a fourth switch  215  of the second leg are connected in series between ground and a second voltage node (a common node of  214  and  213 ). 
     The first flying capacitor  229  is connected between the common node of the first switch  228  and the second switch  227  of the first leg, and the common node of the third switch  226  and the fourth switch  224  of the first leg. The second flying capacitor  219  is connected between the common node of the first switch  218  and the second switch  217  of the second leg, and the common node of the third switch  216  and the fourth switch  215  of the second leg. 
     The third flying capacitor  222  is connected between the first voltage node and the second voltage node. The fourth flying capacitor  212  is connected between a third voltage node (a common node of  213  and  214 ) and a fourth voltage node (a common node of  212  and  234 ). The first upper switch  223  is connected between the first voltage node and ground. The second upper switch  244  is connected between the second voltage node and a fifth voltage node. The third upper switch  213  is connected between the third voltage node and ground. The fourth upper switch  235  is connected between the fourth voltage node and a sixth voltage node. The fifth upper switch  225  is connected between the common node of the third switch  226  and the fourth switch  224  of the first leg, and the fourth voltage node. The sixth upper switch  214  is connected between the common node of the third switch  216  and the fourth switch  215  of the second leg, and the third voltage node. The seventh upper switch  243  is connected between the fifth voltage node and ground. A fifth flying capacitor  242  is connected between the fifth voltage node and the sixth voltage node. The eighth upper switch  241  is connected between the sixth voltage node and the input terminal (VIN). 
     The major advantage of the 8:1 switched capacitor converters illustrated in  FIGS.  21  and  22    is that the 8:1 switched capacitor converters only require six and five flying capacitors to reach an 8:1 conversion ratio. In comparison with the switched capacitor converters shown in  FIGS.  15  and  16   , the switched capacitor converters illustrated in  FIGS.  21  and  22    save two flying capacitors. It is more advantageous for some applications where it is critical to use less passive components. 
     Similar to the cascading converter configuration shown in  FIG.  11   , the 8:1 voltage converters shown in  FIGS.  21  and  22    also can be used as a front stage in a multi-stage DC/DC conversion system to achieve a high-efficiency fixed-ratio voltage conversion. 
       FIG.  23    illustrates a power conversion system including the 8:1 single-phase switched capacitor converter as a front stage and a DC/DC regulator stage or an LC liter as a second stage in accordance with various embodiments of the present disclosure. Using the 8:1 single-phase switched capacitor converter shown in  FIG.  22    as an example, as shown in  FIG.  23   , the power conversion system  750  comprises the 8:1 single-phase switched capacitor converter shown in  FIG.  22    and a DC/DC regulator stage  250 . The 8:1 single-phase switched capacitor converter and the DC/DC regulator stage  250  are connected in cascade between VIN and VLOAD. 
     The DC/DC regulator stage  250  is employed to achieve dynamic voltage regulation. In this system, the output capacitor for the 8:1 single-phase switched capacitor converter can be very small, or the output capacitor can be removed. The small output capacitor is used only to filter out very high frequency components of VOUT, while allowing VOUT to vary in a frequency approximately equal to twice the switching frequency. The variations of VOUT allow soft charging and discharging of flying capacitors, which reduces the charge sharing loss caused by current spikes when charge transferring occurs between capacitors. 
     Similar to  FIG.  12   , an LC filter can be connected to VOUT. As shown in  FIG.  23   , the LC filter comprises an inductor  206  and a capacitor  202 . The capacitor  202  is connected in parallel with a load resistor  204 . Similar to the configuration of connecting switched capacitor converter and the DC/DC regulator  250  in cascade, the inductor at the output of the 8:1 single-phase switched capacitor converter allows the voltage at VOUT to vary and limits the current spike when the output capacitor  202  is charged, which in turn allows soft charging and discharging of flying capacitors, which reduces the charge sharing loss caused by current spikes when charge transferring occurs between capacitors. 
     Along the same line of inserting inductive elements to reduce current spikes during charge sharing between flying capacitors, inductors can also be added in series with the third flying capacitor of the single phase 4:1 switched capacitor converter shown in  FIG.  13   . 
       FIG.  24    illustrates a schematic diagram of a 4:1 single-phase switched capacitor converter with one inductive element in accordance with various embodiments of the present disclosure. As shown in  FIG.  24   , an inductor  330  is added in series with the third flying capacitor  304  between the first voltage node and the second voltage node of the 4:1 single-phase switched capacitor converter shown in  FIG.  13   . 
     In operation, the inductor  330  is able to limit the current spike along the charging and discharging path of the third flying capacitor  304 , which reduces the charge sharing loss between the flying capacitors. In some embodiments the value of the inductor  330  can be selected to resonate with the series capacitance of the charging and discharging path of the third flying capacitor  304  at the switching frequency of the switches. Such an arrangement helps to achieve zero-voltage-switching and zero-current switching of some of the switches in the circuit, thereby further reducing the switching losses of the switched capacitor converter. 
       FIG.  25    illustrates a schematic diagram of a 4:1 dual-phase switched capacitor converter with two inductive elements in accordance with various embodiments of the present disclosure. Similarly, inductors can also be added in series with both the third flying capacitor and the fourth flying capacitor of the 4:1 dual-phase switched capacitor converter shown in  FIG.  3   . 
     As shown in  FIG.  25   , inductors  2312  and  2311  are added in series with the third flying capacitor  222  and the fourth flying capacitor  212  respectively. In operation, both inductors  2311  and  2312  are able to limit the current spikes along the charging and discharging path of the flying capacitors  212  and  222 , thereby reducing the charge sharing loss between the flying capacitors. 
     In some embodiments, the value of the inductor  2312  and  2311  can be selected to resonate with the series capacitance of the charging and discharging path of the third flying capacitor  222  and fourth flying capacitor  212  respectively at the switching frequency of the switches. Such an arrangement helps to achieve zero-voltage-switching and zero-current switching of some of the switches in the circuit, thereby further reducing the switching losses of the switched capacitor converter. 
       FIG.  26    illustrates the gate drive signals of the 4:1 single-phase switched capacitor converter shown in  FIG.  13    in accordance with various embodiments of the present disclosure. As shown in  FIG.  26   , in a first half cycle, the switches  323 ,  312 ,  314 ,  303  and  321  are turned on, and the switches  322 ,  324 ,  313 ,  305  and  311  are turned off. In a second half cycle, the switches  323 ,  312 ,  314 ,  303  and  321  are turned off, and the switches  322 ,  324 ,  313 ,  305  and  311  are turned on. 
       FIG.  27    illustrates two equivalent circuit diagrams for operating in two different half cycles in accordance with various embodiments of the present disclosure. Circuit  2702  is the equivalent circuit of the single-phase switched capacitor converter shown in  FIG.  13    configured to operate in the first half cycle. Circuit  2704  is the equivalent circuit of the single-phase switched capacitor converter shown in  FIG.  13    configured to operate in the second half cycle. 
     In the first half cycle, as indicated by the equivalent circuit  2702 , VIN charges C 306  through a conductive path formed by C 304  and C 325 . Through this conductive path, VIN also provides power to a load coupled to VOUT. The flying capacitor C 315  and C 306  are connected in parallel. The flying capacitor C 315  charges C 306  and provides power to the load coupled to VOUT. 
     In the second half cycle, as indicated by the equivalent circuit  2704 , the flying capacitor C 304  charges C 306  through C 315 . C 304  also provides power to the load coupled to VOUT. The flying capacitor C 325  and C 306  are connected in parallel. The flying capacitor C 325  charges C 306  and provides power to the load coupled to VOUT. 
     As indicated by the two equivalent circuits  2702  and  2704 , the charging and discharging paths of the flying capacitors in the two half cycles are not symmetrical. Due to the voltage difference between these two current supplying paths, charge transferring may occur between the capacitors on the two current supplying paths, thereby causing corresponding losses. The power losses can be avoided through using similar control mechanisms described below with respect to  FIGS.  9 - 10   . 
       FIG.  28    illustrates four equivalent circuit diagrams for operating in two different operating modes in accordance with various embodiments of the present disclosure. In order to avoid the power loss caused by charge transferring, two transition periods have been added. A first transition period shown in the dashed rectangle  2808  is added during the transition from the second half cycle to the first half cycle. A second transition period shown in the dashed rectangle  2806  is added during the transition from the first half cycle to the second half cycle. 
     In the first transition period ( 2808 ), C 315  is disconnected from C 306 . The voltage across C 315  is maintained until the voltage of the charging path (VIN-VC 304 -VC 325 ) is equal to the voltage on C 315 . Once the voltage (VIN-VC 304 -VC 325 ) is equal to the voltage on C 315 , C 315  is connected in parallel with C 306  to supply power to the output capacitor C 306  and the load. The delayed connection of C 315  can effectively reduce or eliminate the charge transferring, thereby reducing the power loss caused by the charge transferring between the flying capacitors. 
     In the second transition period ( 2806 ), C 325  is disconnected from C 306 . The voltage across C 325  is maintained until the voltage of the charging path (VC 304 -VC 315 ) is equal to the voltage on C 325 . Once the voltage (VC 304 -VC 315 ) is equal to the voltage on C 325 , C 325  is connected in parallel with C 306  to supply power to the output capacitor C 306  and the load. The delayed connection of C 325  can effectively reduce or eliminate the charge transferring, thereby reducing the power loss caused by the charge transferring between the flying capacitors. 
       FIG.  29    illustrates the gate drive signals of the 4:1 single-phase switched capacitor converter shown in  FIG.  13    in accordance with various embodiments of the present disclosure. As shown in  FIG.  29   , in a first half cycle, the switches  323 ,  303  and  321  are turned on, and the switches  313 ,  305 ,  311 ,  322  and  324  are turned off. The switches  312  and  314  are turned on after a first delay. The first delay is added according to the operating principle shown in the dashed rectangle  2808  in  FIG.  28   . In a second half cycle, the switches  323 ,  303 ,  321 ,  312  and  314  are turned off, and the switches  313 ,  305  and  311  are turned on. The switches  322  and  324  are turned on after a second delay. The second delay is added according to the operating principle shown in the dashed rectangle  2806  in  FIG.  28   . 
     It should be noted the control mechanism described above with respect to  FIG.  29    is applied to the 4:1 single-phase switched capacitor converter, but it is understood that the control mechanism may be implemented using other types of switched capacitor converters described in the present disclosure. 
       FIG.  30    illustrates a flow chart of a method for controlling the switched capacitor converter shown in  FIGS.  3  and  13    in accordance with various embodiments of the present disclosure. This flowchart shown in  FIG.  30    is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. For example, various steps illustrated in  FIG.  30    may be added, removed, replaced, rearranged, and repeated. 
     At step  3002 , a switched capacitor converter is provided. The switched capacitor converter comprises a first leg comprising a plurality of first leg switches and a second leg comprising a plurality of second leg switches, a first flying capacitor connected to the first leg, a second flying capacitor connected to the second leg, and a third flying capacitor connected between the first leg and the second leg, and a first upper switch and a second upper switch connected to two terminals of the third flying capacitor respectively. 
     At step  3004 , in a first half cycle, the plurality of first leg switches, the plurality of second leg switches, the first upper switch and the second upper switch are configured such that the third flying capacitor, the first flying capacitor and an output capacitor are connected in series, and the second flying capacitor and the output capacitor are connected in parallel. 
     At step  3006 , in a second half cycle, the plurality of first leg switches, the plurality of second leg switches, the first upper switch and the second upper switch are configured such that the first flying capacitor and the output capacitor are connected in parallel, and the third flying capacitor, the second flying capacitor and the output capacitor are connected in series. 
     Referring back to  FIG.  13   , the switched capacitor converter is a single-phase switched capacitor converter. The switched capacitor converter comprises a first switch, a second switch, a third switch and a fourth switch of the first leg connected in series between ground and a first voltage node, a first switch, a second switch, a third switch and a fourth switch of the second leg connected in series between ground and a second voltage node, the first flying capacitor connected between a common node of the first switch and the second switch of the first leg, and a common node of the third switch and the fourth switch of the first leg, the second flying capacitor connected between a common node of the first switch and the second switch of the second leg, and a common node of the third switch and the fourth switch of the second leg, the third flying capacitor connected between the first voltage node and the second voltage node, the first upper switch connected between the first voltage node and ground, and the second upper switch connected between the second voltage node and the input terminal. 
     The method further comprises in the first half cycle, configuring the second switch and the fourth switch of the first leg, and the second upper switch to be turned on, and configuring the first switch and the third switch of the second leg to be turned on after a first delay, and in the second half cycle, configuring the second switch and the fourth switch of the second leg, and the first upper switch to be turned on, and configuring the first switch and the third switch of the first leg to be turned on after a second delay. 
     The first delay is determined based upon a comparison between a voltage across the second flying capacitor and a first charging voltage equal to an input voltage minus a sum of a voltage across the first flying capacitor and a voltage across the third flying capacitor, and wherein the first switch and the third switch of the second leg are both turned on once the voltage across the second flying capacitor is equal to the first charging voltage. 
     The second delay is determined based upon a comparison between a voltage across the first flying capacitor and a second charging voltage equal to the voltage across the third flying capacitor minus the voltage across the second flying capacitor, and wherein the first switch and the third switch of the first leg are both turned on once the voltage across the first flying capacitor is equal to the second charging voltage. 
     Referring back to  FIG.  24   , the switched capacitor converter is a single-phase switched capacitor converter similar to that shown in  FIG.  13   , but with an inductor  330  connected in series with the third flying capacitor  304 , where the method further comprises in the first half cycle, configuring the second switch and the fourth switch of the first leg, the first switch and the third switch of the second leg, and the second upper switch to be turned on with a 50% duty cycle, and in the second half cycle, configuring the second switch and the fourth switch of the second leg, the first switch and the third switch of the first leg, and the first upper switch to be turned on with a 50% duty cycle. 
     Referring back to  FIG.  3   , the switched capacitor converter is a dual-phase switched capacitor converter. The switched capacitor converter comprises a first switch, a second switch, a third switch and a fourth switch of the first leg connected in series between ground and a first voltage node, a first switch, a second switch, a third switch and a fourth switch of the second leg connected in series between ground and a second voltage node, the first flying capacitor connected between a common node of the first switch and the second switch of the first leg, and a common node of the third switch and the fourth switch of the first leg, the second flying capacitor connected between a common node of the first switch and the second switch of the second leg, and a common node of the third switch and the fourth switch of the second leg, the third flying capacitor connected between the first voltage node and the second voltage node, the first upper switch connected between the first voltage node and ground, the second upper switch connected between the second voltage node and the input terminal, a fourth flying capacitor connected between a third voltage node and a fourth voltage node, a third upper switch connected between the third voltage node and ground, a fourth upper switch connected between the fourth voltage node and the input terminal, a fifth upper switch connected between the common node of the third switch and the fourth switch of the first leg and the fourth voltage node, and a sixth upper switch connected between the common node of the third switch and the fourth switch of the second leg and the third voltage node. 
     The method further comprises in the first half cycle, configuring the fifth upper switch, the third upper switch, the second switch and the fourth switch of the first leg, the first switch and the third switch of the second leg, and the second upper switch to be turned on with a 50% duty cycle, and in the second half cycle, configuring the sixth upper switch, the fourth upper switch, the second switch and the fourth switch of the second leg, the first switch and the third switch of the first leg, and the first upper switch to be turned on with a 50% duty cycle. 
     The method further comprises in the first half cycle, configuring the fifth upper switch, the third upper switch, the second switch and the fourth switch of the first leg, and the second upper switch to be turned on, and configuring the first switch and the third switch of the second leg to be turned on after a first delay, and in the second half cycle, configuring the sixth upper switch, the fourth upper switch, the second switch and the fourth switch of the second leg, and the first upper switch to be turned on, and configuring the first switch and the third switch of the first leg to be turned on after a second delay. 
     The first delay is determined based upon a comparison between a voltage across the second flying capacitor and a first charging voltage equal to an input voltage minus a sum of a voltage across the first flying capacitor and a voltage across the third flying capacitor, and wherein the first switch and the third switch of the second leg are both turned on once the voltage across the second flying capacitor is equal to the first charging voltage. 
     The second delay is determined based upon a comparison between a voltage across the first flying capacitor and a second charging voltage equal to an input voltage minus a sum of a voltage across the fourth flying capacitor and the voltage across the second flying capacitor, and wherein the first switch and the third switch of the first leg are both turned on once the voltage across the first flying capacitor is equal to the second charging voltage. 
     Referring back to  FIG.  25   , the switched capacitor converter is a dual-phase switched capacitor converter similar to that shown in  FIG.  3   , but with an inductor  2312  connected in series with the third flying capacitor  222  and an inductor  2311  connected in series with the fourth flying capacitor, where the method further comprises in the first half cycle, configuring the fifth upper switch, the third upper switch, the second switch and the fourth switch of the first leg, the first switch and the third switch of the second leg, and the second upper switch to be turned on with a 50% duty cycle, and in the second half cycle, configuring the sixth upper switch, the fourth upper switch, the second switch and the fourth switch of the second leg, the first switch and the third switch of the first leg, and the first upper switch to be turned on with a 50% duty cycle. 
     Referring back to  FIGS.  22  and  23   , the switched capacitor converter is a single-phase switched capacitor converter comprising a first switch, a second switch, a third switch and a fourth switch of the first leg connected in series between ground and the first voltage node, a first switch, a second switch, a third switch and a fourth switch of the second leg connected in series between ground and the second voltage node, the first flying capacitor connected between the common node of the first switch and the second switch of the first leg, and the common node of the third switch and the fourth switch of the first leg, the second flying capacitor connected between the common node of the first switch and the second switch of the second leg, and the common node of the third switch and the fourth switch of the second leg, the third flying capacitor connected between the first voltage node and the second voltage node, the first upper switch connected between the first voltage node and ground, the second upper switch connected between the second voltage node and a fifth voltage node, a fourth flying capacitor connected between a third voltage node and a fourth voltage node, a third upper switch connected between the third voltage node and ground, a fourth upper switch connected between the fourth voltage node and a sixth voltage node, a fifth upper switch connected between the fourth voltage node, and the common node of the third switch and the fourth switch of the first leg, a sixth upper switch connected between the third voltage node, and the common node of the third switch and the fourth switch of the second leg, a fifth flying capacitor connected between the fifth voltage node and the sixth voltage node and an eighth upper switch connected between the sixth voltage node and the input terminal. 
     The method further comprises in the first half cycle, configuring the second switch and the fourth switch of the first leg, and the second upper switch, the third upper switch, the fifth upper switch and the eighth upper switch to be turned on, and configuring the first switch and the third switch of the second leg to be turned on after a first delay, and in the second half cycle, configuring the second switch and the fourth switch of the second leg, and the first upper switch, the fourth upper switch, the sixth upper switch and the seventh upper switch to be turned on, and configuring the first switch and the third switch of the first leg to be turned on after a second delay. 
     In some embodiments, the first delay is determined based upon a comparison between a voltage across the second flying capacitor and a first charging voltage equal to an input voltage minus a sum of a voltage across the first flying capacitor, a voltage across the third flying capacitor and a voltage across the fifth flying capacitor, and wherein the first switch and the third switch of the second leg are both turned on once the voltage across the second flying capacitor is equal to the first charging voltage. The second delay is determined based upon a comparison between a voltage across the first flying capacitor and a second charging voltage equal to the voltage across the fifth flying capacitor minus a sum of a voltage across the fourth flying capacitor and the voltage across the second flying capacitor, and wherein the first switch and the third switch of the first leg are both turned on once the voltage across the first flying capacitor is equal to the second charging voltage. 
       FIGS.  31 - 35    illustrate a process of generating a 4:1 dual-phase switched capacitor converter based on two 4:1 single-phase switched capacitor converters in accordance with various embodiments of the present disclosure.  FIG.  31    illustrates a schematic diagram of a 4:1 single-phase switched capacitor converter in accordance with various embodiments of the present disclosure. The switched capacitor converter shown in  FIG.  31    is the same as that shown in  FIG.  13   , and hence is not discussed again to avoid repetition. 
       FIG.  32    illustrates a schematic diagram of a switched capacitor converter after two 4:1 single-phase switched capacitor converters are combined. These two 4:1 single-phase switched capacitor converters are arranged in a symmetrical manner as shown in  FIG.  32   . The control signals of the left side and the control signals of the right side are of a phase shift of 180 degrees. The bottom four switches including switches  314  and  324  on the left side, and switches  314  and  324  on the right side can be combined into two switches because the connections of these four switches are the same.  FIG.  33    illustrates a schematic diagram of a switched capacitor converter after the four bottom switches of  FIG.  32    have been combined into two switches. 
     As shown in  FIG.  33   , the middle four switches including switches  312  and  322  on the left side, and switches  312  and  322  on the right side can be combined into two switches because the connections of these four switches are the same. After the four middle switches have been combined into two switches, the corresponding flying capacitors can be simplified.  FIG.  34    illustrates a schematic diagram of a switched capacitor converter after the four middle switches shown in  FIG.  33    have been combined into two switches.  FIG.  35    illustrated a 4:1 dual-phase switched capacitor converter after the components of  FIG.  34    have been rearranged. The switched capacitor converter shown in  FIG.  35    is the same as that shown in  FIG.  3   . 
     Although embodiments of the present disclosure and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the disclosure as defined by the appended claims. 
     Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present disclosure, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present disclosure. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.