Plural stages switching capacitor converter

Abstract

A power converter comprising one or more switch blocks. Each switch block has: a plurality of switch-pairs each having two switches connected in series to each other; a plurality of primary nodes each interconnecting the switches in a respective switch-pair; and a plurality of secondary nodes, each switch-pair being connected in series to an adjacent switch-pair through a said secondary node to form a serial chain of switch-pairs, the secondary nodes including a secondary node at one end of said serial chain and a secondary node at another end of said serial chain. Each adjacent pair of said primary nodes is connectable to a flying capacitor. Each pair of said secondary nodes is connectable to one or more of the following: one or more bypass capacitors, and one or more other said switch blocks. The power converter further comprises a first terminal formed by any two of the secondary nodes in any one of the switch blocks, and a second terminal formed by any two of the secondary nodes in any one of the switch blocks.

Claims

1. A power converter comprising: one or more switch blocks each having: a plurality of switch-pairs each having two switches connected in series to each other; a plurality of primary nodes each interconnecting the switches in a respective switch-pair; and a plurality of secondary nodes, each switch-pair being connected in series to an adjacent switch-pair through a respective secondary node to form a serial chain of switch-pairs; each adjacent pair of the primary nodes connectable to a flying capacitor; and each pair of the secondary nodes connectable to one or more of the following: at least one of a plurality of bypass capacitors, and one or more of the switch blocks; the power converter further comprising: a low voltage side and a high voltage side, the low voltage side having a first terminal directly connected to both a first secondary node of the secondary nodes and a first terminal of a first bypass capacitor of the plurality of bypass capacitors, and a second terminal directly connected to both a second secondary node of the secondary nodes and a second terminal of the high voltage side; and the high voltage side having a first terminal directly connected to both a first terminal of a second bypass capacitor of the plurality of bypass capacitors and a third secondary node of the secondary nodes, and the second terminal directly connected to the second terminal of the low voltage side and the second secondary node of the secondary nodes; wherein the power converter is a bidirectional switched-capacitor (SC) converter, wherein one of the low voltage side and the high voltage side is configured to be connected to a power source, and the other of the low voltage side and the high voltage side is configured to be connected to a load, wherein the power source and the load are interchangeable to each other, wherein the power source and the load are directly connected to the last secondary node, wherein the flying capacitor is not connected to an inductor, wherein the power converter is absent both an input capacitor filter connected to the power source in parallel and an output capacitor filter connected to the load in parallel, and wherein each switch-pair has a first switch and a second switch connected in series to each other, wherein the power converter is operated in two operating states and in the two operating states, the flying capacitor is alternately in parallel with the low voltage side and the first bypass capacitor wherein timing durations of an ON state of each of the first switches are equal to one another and equal to timing durations of an ON state of each corresponding second switch of the switch-pairs.

2. The power converter according to claim 1 comprising a plurality of the switch blocks, one defining a first-stage switch block and the others defining ith-stage switch blocks (i=2, 3, . . . , n, wherein n is the last switch block) with two secondary nodes of each ith-stage switch block connected to two secondary nodes of one or more earlier stage switch blocks.

3. The power converter according to claim 2 wherein the low voltage side is connected to the first secondary node of the first-stage switch block and a second secondary node of any switch block other than the first-stage switch block.

4. The power converter according to claim 3 wherein the high voltage side is connected to a secondary node of the first-stage switch block and to a secondary node of the nth-stage switch block.

5. The power converter according to claim 3 comprising two of the switch blocks, one defining a first-stage switch block and the other defining a second-stage switch block with two secondary nodes of the second-stage switch block connected to two secondary nodes of the first-stage switch block.

6. The power converter according to claim 3 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired conversion ratio.

7. The power converter according to claim 2 wherein the low voltage side is connected to any one of the secondary nodes of any of the switch block and any one of the remaining secondary nodes of any of the switch block.

8. The power converter according to claim 7 wherein the high voltage side is connected to a secondary node of the first-stage switch block and to a secondary node of the nth-stage switch block.

9. The power converter according to claim 7 comprising two of the switch blocks, one defining a first-stage switch block and the other defining a second-stage switch block with two secondary nodes of the second-stage switch block connected to two secondary nodes of the first-stage switch block.

10. The power converter according to claim 7 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired conversion ratio.

11. The power converter according to claim 2 wherein the high voltage side is connected to a secondary node of the first-stage switch block and to a secondary node of the ith-stage switch block.

12. The power converter according to claim 11 comprising two of the switch blocks, one defining a first-stage switch block and the other defining a second-stage switch block with two secondary nodes of the second-stage switch block connected to two secondary nodes of the first-stage switch block.

13. The power converter according to claim 11 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired conversion ratio.

14. The power converter according to claim 2 comprising two of the switch blocks, one defining the first-stage switch block and the other defining a second-stage switch block with two secondary nodes of the second-stage switch block connected to two secondary nodes of the first-stage switch block.

15. The power converter according to claim 14 comprising a third switch block defining a third-stage switch block with two secondary nodes of the third-stage switch block connected to two secondary nodes of the second-stage switch block.

16. The power converter according to claim 15 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired conversion ratio.

17. The power converter according to claim 14 comprising a third switch block defining a third-stage switch block with one secondary node of the third-stage switch block connected to one secondary node of the second-stage switch block and another secondary node of the third-stage switch block connected to one secondary node of the first-stage switch block.

18. The power converter according to claim 17 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired conversion ratio.

19. The power converter according to claim 14 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired conversion ratio.

20. The power converter according to claim 2 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired conversion ratio.

21. The power converter according to claim 2, wherein the high voltage side is connected to any one of the secondary nodes of any of the switch block and any one of the remaining secondary nodes of any of the switch block.

22. The power converter according to claim 1 configured to convert a first voltage at the low voltage side to a second voltage at the high voltage side at a desired integral conversion ratio.

23. The power converter according to claim 22 wherein the conversion ratio is fractional.

24. The power converter according to claim 23 comprising one or more reconfiguration switches connected to one or more switch blocks such that the conversion ratio is variable in real-time, the power converter thereby being reconfigurable.

25. The power converter according to claim 22 comprising one or more reconfiguration switches connected to one or more switch blocks such that the conversion ratio is variable in real-time, the power converter thereby being reconfigurable.

26. The power converter according to claim 1, wherein the bypass capacitor is connected between one secondary node that forms the serial chain and the first secondary node, and is not connected between the one secondary node that forms the serial chain and the last secondary node.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) Preferred embodiments in accordance with the best mode of the present invention will now be described, by way of example only, with reference to the accompanying figures, in which:

(2) FIG. 1 is a schematic diagram of a prior grid-connected single-phase distributed energy resource (DER) system;

(3) FIG. 2 is a schematic diagram of a prior series-parallel switched-capacitor (SC) converter;

(4) FIG. 3 is a schematic diagram of a prior ladder-type switched-capacitor (SC) converter, as per [18] and [19];

(5) FIG. 4 is a schematic diagram of a prior Fibonacci switched-capacitor (SC) converter, as per [20] and [21];

(6) FIG. 5 is a schematic diagram of a prior N x step-up switched-capacitor (SC) converter, as per [16];

(7) FIG. 6(a) is a schematic diagram of a prior reconfigurable switched-capacitor (SC) converter, as per [25] and [26];

(8) FIG. 6(b) is a basic block diagram of the prior reconfigurable switched-capacitor (SC) converter of FIG. 6(a), as per [25] and [26];

(9) FIG. 7(a) is a graph comparing switch numbers of a series-parallel SC converter, a Fibonacci SC converter, a N×SC converter, and a proposed SC converter in accordance with an embodiment of the present invention;

(10) FIG. 7(b) is a graph comparing switch voltage stress of a series-parallel SC converter, a Fibonacci SC converter, a N×SC converter, and a proposed SC converter in accordance with an embodiment of the present invention;

(11) FIG. 8(a) is a graph comparing capacitor numbers of a series-parallel SC converter, a Fibonacci SC converter, a N×SC converter, and a proposed SC converter in accordance with an embodiment of the present invention;

(12) FIG. 8(b) is a graph comparing capacitor voltage stress of a series-parallel SC converter, a Fibonacci SC converter, a N×SC converter, and a proposed SC converter in accordance with an embodiment of the present invention;

(13) FIG. 9(a) is a schematic diagram of a two-time bidirectional SC converter in accordance with an embodiment of the present invention;

(14) FIG. 9(b) is a schematic diagram of a three-time bidirectional SC converter in accordance with an embodiment of the present invention;

(15) FIG. 9(c) are timing diagrams of the SC converters shown in FIGS. 9(a) and 9(b);

(16) FIGS. 10(a) and (b) are schematic diagrams of a two-time bidirectional SC converter in accordance with an embodiment of the present invention, showing current flow paths in two respective phases of a step-up mode of operation;

(17) FIGS. 11(a) and (b) are schematic diagrams of a two-time bidirectional SC converter in accordance with an embodiment of the present invention, showing current flow paths in two respective phases of a step-down mode of operation;

(18) FIGS. 12(a) and (b) are schematic diagrams of a three-time bidirectional SC converter in accordance with an embodiment of the present invention, showing current flow paths in two respective phases of a step-up mode of operation;

(19) FIGS. 13(a) and (b) are schematic diagrams of a three-time bidirectional SC converter in accordance with an embodiment of the present invention, showing current flow paths in two respective phases of a step-down mode of operation;

(20) FIG. 14 is a schematic diagram of a general switch block of an N×SC converter in accordance with an embodiment of the present invention;

(21) FIG. 15(a) is a schematic block diagram of a switch block of a two-time SC converter in accordance with an embodiment of the present invention;

(22) FIG. 15(b) is a schematic block diagram of a switch block of a three-time SC converter in accordance with an embodiment of the present invention;

(23) FIG. 15(c) is a schematic block diagram of a switch block of an N-time SC converter in accordance with an embodiment of the present invention;

(24) FIGS. 16(a) and (b) are schematic block diagrams of two-stage SC converters in accordance with embodiments of the present invention, with each stage of each converter based on a two-time switch block, and with the converters of FIGS. 16(a) and 16(b) providing conversion ratios of 3 and 4 respectively;

(25) FIGS. 17(a) to (f) are schematic block diagrams of three-stage SC converters in accordance with embodiments of the present invention, with each stage of each converter based on a two-time switch block, and with the converters of FIGS. 17(a) to 17(f) providing conversion ratios of 4, 5, 6, 6, 7, and 8 respectively;

(26) FIG. 18 is a flow diagram of a general method for designing SC converters in accordance with an embodiment of the present invention;

(27) FIG. 19(a) is a schematic diagram of a five-time bidirectional SC converter in accordance with an embodiment of the present invention;

(28) FIG. 19(b) are timing diagrams of the SC converter shown in FIG. 19(a);

(29) FIG. 20(a) is a schematic diagram of a six-time bidirectional SC converter in accordance with an embodiment of the present invention;

(30) FIG. 20(b) is a schematic diagram of a seven-time bidirectional SC converter in accordance with an embodiment of the present invention;

(31) FIG. 20(c) is a schematic diagram of an eight-time bidirectional SC converter in accordance with an embodiment of the present invention;

(32) FIG. 20(d) is a schematic diagram of a nine-time bidirectional SC converter in accordance with an embodiment of the present invention;

(33) FIG. 21(a) to (d) are schematic diagrams of a five-time bidirectional SC converter in accordance with an embodiment of the present invention, showing four main operating states of a step-up mode of operation;

(34) FIGS. 22(a) to (c) are schematic block diagrams of SC converters in accordance with embodiments of the present invention, with the converter of FIG. 22(a) providing a conversion ratio of 3/2 or 2/3, the converter of FIG. 22(b) providing a conversion ratio of 5/2 or 2/5, and the converter of FIG. 22(c) providing a conversion ratio of 7/2 or 2/7; and

(35) FIGS. 23(a) to (b) are schematic block diagrams of reconfigurable SC converters in accordance with embodiments of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

(36) Referring to the accompanying figures, there is provided a power converter comprising one or more switch blocks. Each switch block has a plurality of switch-pairs each having two switches connected in series to each other. In the figures, each switch is labeled S.sub.xya. Subscript a is a letter, and the letter is the same for each of the two switches that form a switch-pair. Subscript y is a number differentiating one switch from the other in a switch-pair. Subscript x is a number denoting the switch block.

(37) Each switch block further comprises a plurality of primary nodes each interconnecting the switches in a respective switch-pair. In the figures, each primary node is labeled as X.sub.p with the subscript p being a number differentiating each primary node from the other primary nodes.

(38) Each switch block also comprises a plurality of secondary nodes. Each switch-pair is connected in series to an adjacent switch-pair through a said secondary node to form a serial chain of switch-pairs, with the secondary nodes including a secondary node at one end of said serial chain and a secondary node at another end of said serial chain. In the figures, each secondary node is labeled as Y.sub.p with the subscript p being a number differentiating each secondary node from the other secondary nodes.

(39) In the figures, the primary and secondary nodes are also labeled NA.sub.q where A is a letter denoting the switch block and the subscript q is a number with even numbers designating the primary nodes and odd numbers designating the secondary nodes.

(40) Each adjacent pair of said primary nodes is connectable to a flying capacitor. A flying capacitor is labeled as C.sub.fxa in the figures, where subscript x is a number denoting the switch block to which the flying capacitor is connected, and subscript a is a letter differentiating one flying capacitor from another connected to the switch block.

(41) Each pair of said secondary nodes is connectable to one or more of the following: one or more bypass capacitors, and one or more other said switch blocks. A bypass capacitor is labeled as C.sub.xya in the figures, where subscript x is a number denoting the switch block to which the bypass capacitor is connected. Subscript y is a number and subscript a is a letter with both differentiating one bypass capacitor from another connected to the switch block.

(42) The power converter further comprises a first terminal formed by any two of the secondary nodes in any one of the switch blocks, and a second terminal formed by any two of the secondary nodes in any one of the switch blocks. In some of the embodiments shown in the figures, the first terminal is a low voltage terminal V.sub.L, and the second terminal is a high voltage terminal V.sub.H. The power converter converts a low voltage at the low voltage terminal V.sub.L to a high voltage at the high voltage terminal V.sub.H, or vice versa. In other embodiments shown in the figures, the first terminal is an input terminal V.sub.in, and the second terminal is an output terminal V.sub.o. It will be appreciated that the input terminal V.sub.in can be a low voltage terminal V.sub.L, and the output terminal V, can be a high voltage terminal V.sub.H, or vice versa.

(43) The power converter comprises a plurality of said switch blocks described above, one defining a first-stage switch block and the others defining nth-stage switch blocks with two secondary nodes of each nth-stage switch block connected to two secondary nodes of one or more earlier stage switch blocks.

(44) For example, in the embodiments shown in FIG. 16, the power converter comprises two of said switch blocks, one defining a first-stage switch block and the other defining a second-stage switch block with two secondary nodes of the second-stage switch block connected to two secondary nodes of the first-stage switch block.

(45) FIGS. 17(a), (b), and (d) show embodiments where the power converter comprises a third switch block defining a third-stage switch block with two secondary nodes of the third-stage switch block connected to two secondary nodes of the second-stage switch block. FIGS. 17(c), (e), and (f) show embodiments where the power converter comprises a third switch block defining a third-stage switch block with one secondary node of the third-stage switch block connected to one secondary node of the second-stage switch block and another secondary node of the third-stage switch block connected to one secondary node of the first-stage switch block.

(46) The first terminal can be a low voltage terminal V.sub.L connected to any two secondary nodes of the first-stage switch block. In some embodiments, the first terminal is a low voltage terminal connected to two adjacent secondary nodes of the first-stage switch block. For example, FIGS. 16, 17, and 19 show the first terminal as a low voltage terminal V.sub.L connected to the first two adjacent secondary nodes of the first-stage switch block. FIG. 22(a) on the other hand shows the first terminal as a low voltage terminal V.sub.L connected to the first and third secondary nodes.

(47) The second terminal can be a high voltage terminal V.sub.H connected to a secondary node of the first-stage switch block and to a secondary node of the last nth-stage switch block.

(48) The power converter is configured to convert a first voltage at the first terminal to a second voltage at the second terminal at a desired conversion ratio. The conversion ratio can be represented as M where the second voltage is the first voltage multiplied by a factor of M. M can be an integer (e.g. 2, 3, 4, . . . ). However, M can also be fractional. Accordingly, in general,

(49) $M=\frac{m}{n}\mathrm{or}M=\frac{n}{m},$
where m and n are integers and m<n.

(50) The power converter can also comprise one or more reconfiguration switches connected to one or more switch blocks such that the conversion ratio is variable in real-time, the power converter thereby being reconfigurable. In FIG. 23(a), five reconfiguration switches S.sub.5xa, S.sub.5xb, S.sub.6x, S.sub.7xa, and S.sub.7xb are shown. FIG. 23(b) is the power converter shown in FIG. 23(a) but with the addition of further reconfiguration switches S.sub.1, S.sub.2a, S.sub.2b, S.sub.3a, S.sub.3b, and S.sub.4.

(51) The power converter is also termed an “SC converter” or an “SC structure” throughout this specification, with the “SC” referring to the switched capacitor structure of the converter. An “M-time SC converter” or an “M-time SC structure” is a power converter that provides a conversion ratio of M. Similarly, an “N×SC converter” or an “N-time SC converter” is a power converter that provides a conversion ratio of N. For example, a “two-time SC structure” is a power converter that provides an output voltage that is the input voltage multiplied by a factor of 2. An

(52) $“\frac{m}{n}\text{-}\mathrm{time}\mathrm{SC}\mathrm{structure}”$
is a power converter that provides an output voltage that is the input voltage multiplied by a factor of

(53) $\frac{m}{n}.$

(54) Switch blocks as described above are also termed as “basic blocks”, “basic structures”, or “basic SC structures” throughout this specification. A switch block can also be qualified by the number of switch-pairs the switch block contains, and therefore the conversion ratio the switch block itself can provide. For example, a “basic two-time SC structure” is a switch block with two switch-pairs to provide a conversion ratio of 2, and a “basic three-time structure” is a switch block with three switch-pairs to provide a conversion ratio of 3.

(55) Both the power converter and the switch blocks can be termed “bidirectional” since input and output terminals can be reversed to provide step-up and step-down between the input and output terminals.

(56) This invention describes a configuration method and apparatus of a series of bidirectional SC converters that possess many advantageous properties:

(57) (1) Using fewer switches as compared to other topologies, and that of the voltage stress of the switches is low (refer to FIG. 7);

(58) (2) The capacitor number is relatively low, and the voltage stress of the capacitors is also relatively low (refer to FIG. 8);

(59) (3) Very high efficiency.

(60) (4) Small size and light weight;

(61) (5) Capable of operating in the high temperature environment;

(62) (6) Simple control, with the duty ratio of all switches of the converter being typically (but not necessarily) set at 0.5;

(63) (7) Achieving flexible conversion gain of M=2, 3, . . . , n, or

(64) $M=\frac{1}{2},\frac{1}{3},\mathrm{.Math.},\frac{1}{n},M=\frac{m}{n}$
where m and n are positive integers and m<n.

(65) (8) Achieving very high-conversion gain at high efficiency.

(66) This invention is on a series of power converter architectures that can achieve high efficiency and flexible conversion gain ratio even high-voltage-gain conversion and that allows bi-directional power flow. The SC converters are composed of two or more basic structures, where the basic structures are N-time bidirectional SC structures (N=2, 3, 4, 5, . . . ). By combining two or more of the basic structures, bidirectional SC converters that can achieve an M-time conversion ratio can be obtained.

(67) By strategically placing additional switches in these bidirectional SC converters, and along with well-designed control, SC converters with reconfiguration gain ratio can be obtained. Furthermore, by replacing each switch in the proposed topologies with a set of back-to-back switch and reconfiguring the control scheme, bidirectional AC-AC converters can be obtained.

(68) According to this invention, the derivable SC converters are composed of a combination of two or more basic structures made up of various possible SC structures. For ease of communication, we limit our discussion to the (a) two-time bidirectional SC structure and the (b) three-time bidirectional SC structure shown in FIG. 9. The operation of these basic structures will first be introduced before the proposed SC converters are illustrated.

(69) A. Operation of the Basic Structures

(70) Both the two-time and the three-time bidirectional SC structures work in two modes: the step-up mode and the step-down mode. Assume that the flying capacitors and the bypass capacitors are large and that the voltages of these capacitors are constant.

(71) 1) Step-Up Mode of the Two-Time Bidirectional SC Structure:

(72) In step-up mode, the low voltage side V.sub.L is connected to a power source and the high voltage side V.sub.H is connected to the load. According to its operation timing diagram shown in FIG. 9(c), there are two operating states, which are shown in FIG. 10. In these two states, the flying capacitor C.sub.f1 is alternatively paralleled with the low voltage side V.sub.L and the bypass capacitor C.sub.11. In one phase, the flying capacitor C.sub.f1 is paralleled with the low voltage side V.sub.L (see FIG. 10(a)). In this state, the flying capacitor C.sub.f1 is charged by the low side voltage source, and at the end of this state, the voltage of the flying capacitor V.sub.cf1 would be equal to the low side voltage V.sub.L, i.e.,
V.sub.cf1=V.sub.L.  (1)

(73) In the other phase, as shown in FIG. 10(b), the flying capacitor C.sub.f1 is paralleled with the bypass capacitor C.sub.11. In this state, C.sub.f1 would discharge to C.sub.11, which leads to the bypass capacitor voltage being equal to the flying capacitor's voltage, i.e.,
V.sub.c11=V.sub.cf1.  (2)

(74) Throughout this specification, an equation is initially cited with a number in round brackets and further references to the same equation are made by citing said number in round brackets.

(75) Hence, in steady state, according to (1) and (2), the voltage of the bypass capacitor will be equal to the low side voltage, i.e.,
V.sub.c11=V.sub.L.  (3)

(76) According to the circuit, the high voltage side V.sub.H is the sum of the bypass capacitor voltage V.sub.c11 and the low side voltage V.sub.L, i.e.,
V.sub.H=V.sub.c11+V.sub.L.  (4)

(77) Therefore, the high side voltage V.sub.H is double of the low side voltage V.sub.L, that is
V.sub.H=2.Math.V.sub.L  (5)

(78) Hence, in the step-up mode, the voltage-conversion ratio of two-time bidirectional SC structure is N=2.

(79) 2) Step-Down Mode of the Two-Time Bidirectional SC Structure:

(80) In this mode, the high voltage side V.sub.H is connected to a power source and the low voltage side V.sub.L is connected to a load. Here, there are two operating states. In State 1, as shown in FIG. 11(a), the flying capacitor C.sub.f1 is paralleled with the bypass capacitor C.sub.11, and it is charged by the power source to its voltage level, i.e.,
V.sub.cf1=V.sub.c11.  (6)

(81) In state 2, as shown in FIG. 11(b), the flying capacitor would parallel with and discharge to the load. This makes the low side voltage equals with the voltage of the flying capacitor, i.e.,

(82) $\begin{array}{cc}{V}_L=V_{\mathrm{cf}1}.& \left(7\right)\\ \mathrm{Since}& \\ V_L=V_{c11}.& \left(8\right)\\ \mathrm{and}& \\ V_L=V_{11}+V_L.& \left(9\right)\\ \mathrm{therefore}& \\ V_L=\frac{V_H}{2}.& \left(10\right)\end{array}$

(83) Hence, in the step-down mode, the conversion ratio of the two-time bidirectional SC structure is =1/2.

(84) 3) Step-Up Mode of the Three-Time Bidirectional SC Structure:

(85) The three-time bidirectional SC structure is shown in FIG. 9(b) and its timing diagram is shown in FIG. 9(c). For the step-up mode, the power source is connected to the low voltage side V.sub.L, and the high voltage side V.sub.H is connected to the load. The three-time bidirectional SC structure operating in the step-up mode has two states, which are shown in FIG. 12. In State 1, as shown in FIG. 12(a), the two flying capacitors, C.sub.fx, and C.sub.fxb, are respectively paralleled to the bypass capacitor C.sub.11 and the low voltage side V.sub.L. The voltages of the flying capacitors are equal to the voltage of their paralleled components, respectively, i.e.,

(86) $\begin{array}{cc}\{\begin{array}{c}{V}_{\mathrm{cfx}}=V_L\\ V_{\mathrm{cfxb}}=V_{c11b}\end{array}.& \left(11\right)\end{array}$

(87) In State 2 (FIG. 12(b)), C.sub.fx and C.sub.fxb are respectively paralleled to the two bypass capacitors C.sub.11 and C.sub.11b, which makes the two bypass capacitors' voltages equal to the voltages of their paralleled flying capacitors, i.e.,

(88) $\begin{array}{cc}\{\begin{array}{c}{V}_{c11b}=V_{\mathrm{cfxb}}\\ V_{c11}=V_{\mathrm{cfx}}\end{array}.& \left(12\right)\end{array}$

(89) Hence, the voltages of both the bypass capacitors are equal to the low side voltage, i.e.,
V.sub.c11b=V.sub.c11=V.sub.L.  (13)

(90) The high side voltage is the sum of the two bypass capacitors' voltages V.sub.c11, and V.sub.c11b and the low side voltage V.sub.L, i.e.,
V.sub.H=V.sub.c11+V.sub.L.  (14)

(91) Therefore, the high side voltage V.sub.H is triple of the low side voltage V.sub.L, that is
V.sub.H==3.Math.V.sub.L.  (15)

(92) Hence, the conversion ratio of the three-time bidirectional SC structure in the step-up mode is N=3.

(93) 4) Step-Down Mode of the Three-Time Bidirectional SC Structure:

(94) In this mode, the power source is connected to the high voltage side V.sub.H and the load is connected to the low voltage side V.sub.L. There are two operating states in this mode, as shown in FIG. 13. In State 1, the two flying capacitors C.sub.fx and C.sub.fxb are paralleled to C.sub.11 and C.sub.11b, respectively. The voltages of the flying capacitors at the end of each charging state is equal to that of the two bypass capacitors, i.e.,

(95) $\begin{array}{cc}\{\begin{array}{c}{V}_{\mathrm{cfx}}=V_{c11}\\ V_{\mathrm{cfxb}}=V_{c11b}\end{array}.& \left(16\right)\end{array}$

(96) In State 2, the two flying capacitors C.sub.fx and C.sub.fxb are respectively paralleled to the low voltage side V.sub.L and the bypass capacitor C.sub.11. Both the two flying capacitors C.sub.f1 and C.sub.f1b are discharged to the voltage level of

(97) $\begin{array}{cc}\{\begin{array}{c}{V}_L=V_{\mathrm{fx}}\\ V_{c11}=V_{\mathrm{fxb}}\end{array}.& \left(17\right)\end{array}$

(98) At steady state,

(99) 0$\begin{array}{cc}{V}_L=V_{c11}=V_{c11b}& \left(18\right)\\ \mathrm{and}& \\ V_H=V_{c11}+V_{c11b}+V_L.& \left(19\right)\\ \mathrm{Hence},& \\ V_L=\frac{V_H}{3}.& \left(20\right)\end{array}$

(100) The conversion ratio of the three-time bidirectional SC structure in the step-down mode is N=1/3.

(101) 5) N-Time Bidirectional SC Structure:

(102) For an N-time SC structure, which is shown in FIG. 14, there will be N number of X nodes and N+1 number of Y nodes. Similarly, using the same approach given above, the operation of the N-time SC structure, where N≥2, can be analyzed.

(103) B. Configuration Method

(104) FIG. 15 respectively shows the simplified basic blocks of a two-time and three-time SC structure as that given in FIGS. 9(a) and 9(b), and an N-time SC structure as given in FIG. 15(c). For the block diagram of the two-time SC structure, the flying capacitor is connected to nodes X.sub.1 and X.sub.2 and the bypass capacitor and/or input voltage source are connected to Y.sub.1, Y.sub.2, and Y.sub.3. For the three-time SC structure, the two flying capacitors are connected to the nodes X.sub.1, X.sub.2, and X.sub.3, and the bypass capacitors and/or voltage source are connected to nodes Y.sub.1, Y.sub.2, Y.sub.3, and Y.sub.4.

(105) The configuration approach is to connect any two or more of these SC structures to form the SC converters. FIG. 16 is an example of forming two-stage SC converters based on two units of the two-time SC structures with different conversion ratios M. FIG. 16(a) is a three-time SC converter formed by two units of the two-time SC structure. Here, nodes Y.sub.1 and Y.sub.2 of the second-stage SC structure are connected to nodes Y.sub.2 and Y.sub.3 of the first-stage SC structure. FIG. 16(b) is another possible combination of the two-stage SC converter based on two units of the two-time SC structure, which has a conversion ratio of M=4. The combination is for nodes Y.sub.1 and Y.sub.2 of the second-stage SC structure to connect nodes Y.sub.1 and Y.sub.3 of the first-stage SC structure. Similarly, numerous combinations of the two-stage SC converters with two basic structures can be formed.

(106) FIG. 17 is an example of forming three-stage SC converters based on three units of the two-time SC structures with different conversion ratios. FIGS. 17(a)-17(c) are the combinations of a two-time SC structure with the two-stage SC converter given in FIG. 16(a), and FIGS. 17(d)-17(f) are the combinations of a two-time SC structure with the two-stage SC converter given in FIG. 16(b). A three-stage SC converter with a conversion ratio of M=4 as shown in FIG. 17(a) is formed by connecting nodes Y.sub.1, and Y.sub.2 of the third-stage SC structure to nodes Y.sub.2 and Y.sub.3 of the second-stage SC structure shown in FIG. 16(a), where node Y.sub.2 of the second-stage SC structure is also node Y.sub.3 of the first-stage SC structure. A three-stage SC converter with a conversion ratio of M=5 as shown in FIG. 17(b) is formed by connecting nodes Y.sub.1, and Y.sub.2 of the third-stage SC structure to nodes Y.sub.1 and Y.sub.3 of the second-stage SC structure given in FIG. 16(a), where node Y.sub.1 of the second-stage SC structure is also node Y of the first-stage SC structure. A three-stage SC converter with conversion ratio of M=6 as shown in FIG. 17(c) is formed by connecting nodes Y.sub.1 and Y.sub.2 of the third-stage SC structure to nodes Y.sub.1 of the first-stage SC structure and Y.sub.3 of the second-stage SC structure as shown in the FIG. 16(a). Using the same approach, FIGS. 17(d)-17(f) can be formed. Similarly, numerous combinations of three-stage SC converters with three basic structures can be formed.

(107) Hence, higher-stage SC converters can be formed using same approach as that given for deriving the three-stage SC converters. The input nodes of the highest-stage SC structure can be connected to any two nodes of a previous stage. It is important to emphasize that the positions of the input voltage source and the flying capacitors or series-connected bypass capacitors can be interchanged. An overview of the logic flow of the configuration method for deriving the M-time SC converters is shown in FIG. 18.

(108) C. m-Time or

(109) $\frac{1}{m}\text{-}\mathrm{time}$
(m is Integer) Bidirectional SC Converters

(110) By adopting a combination of two or more of the basic structures, a series of m-time and

(111) $\frac{1}{m}\text{-}\mathrm{time}$
bidirectional SC DC-DC converters can be derived. The converter is a cascade of one or more multiple stages of the basic structures. Here, the step-up mode operation is used to introduce the proposed bidirectional SC topologies, which are using V.sub.L as the input and V.sub.H as the output. The number 2 is used to represent the two-time bidirectional SC structure and 3 to represent the three-time bidirectional SC structure.

(112) For this series of SC converters, the input and output are of common ground. The input is connected to V.sub.L of the first stage.

(113) TABLE-US-00001 TABLE I Two-stage converters first-stage V.sub.L second-stage V.sub.H connected V.sub.L connected connected conversion Combination nodes nodes nodes ratio (M) 1 22 NA.sub.3, NA.sub.1 NA.sub.5, NA.sub.3 NB.sub.5, NA.sub.1 3/⅓ 2 22 NA.sub.3, NA.sub.1 NA.sub.5, NA.sub.1 NB.sub.5, NA.sub.1 4/¼ 3 23 NA.sub.3, NA.sub.1 NA.sub.5, NA.sub.3 NB.sub.7, NA.sub.1 4/¼ 4 23 NA.sub.3, NA.sub.1 NA.sub.5, NA.sub.1 NB.sub.5, NA.sub.1 6/⅙ 5 32 NA.sub.3, NA.sub.1 NA.sub.7, NA.sub.5 NB.sub.5, NA.sub.1 4/¼ 6 32 NA.sub.3, NA.sub.1 NA.sub.7, NA.sub.5 NB.sub.5, NA.sub.1 5/⅕ 7 32 NA.sub.3, NA.sub.1 NA.sub.7, NA.sub.3 NB.sub.5, NA.sub.1 6/⅙ 8 33 NA.sub.3, NA.sub.1 NA.sub.7, NA.sub.5 NB.sub.7, NA.sub.1 5/⅕ 9 33 NA.sub.3, NA.sub.1 NA.sub.7, NA.sub.3 NB.sub.7, NA.sub.1 7/ 1/7 10 33 NA.sub.3, NA.sub.1 NA.sub.7, NA.sub.1 NB.sub.7, NA.sub.1 9/ 1/9

(114) 1) One-Stage SC Converters:

(115) They are composed of only one of the basic structures. The conversion gain M of this converter is directly corresponding to the gain of the adopted SC structure N.

(116) 2) Two-Stage SC Converters:

(117) They are composed of two basic structures. Hence, there are four possible combinations for any two particular types of SC structures. For example, a two-time SC structure plus a three-time SC structure gives the following combinations: 22, 23, 32, and 33, where the first number represents the basic structure the first-stage used, and the second number represents the basic structure of the second-stage used. There are different ways of connecting the second-stage structure to the first-stage structure even with the same basic structures, which results in a different conversion ratio. Table I shows the various possible combinations of the two-stage SC converters for a two-time plus three-time SC structure combination. Please note that NX.sub.y (refer to FIG. 9(a)) represents the y node of the X stage, where A represents the first stage, B represents the second stage, and so on. For example, in the case of Type 6 combination with a 32 combination as given in Table I, the first-stage is a three-time SC structure and the second stage is a two-time SC structure, where nodes NA.sub.3 and NA.sub.1 of the first-stage three-time structure are respectively connected to the positive and ground of the input voltage source. The nodes NA.sub.7 and NA.sub.3 of this structure are respectively connected to NB.sub.3 and NB.sub.1, which are the input nodes of the second-stage two-time SC structure. The output of the converter is obtained from NB.sub.5 (positive potential) and NA.sub.1 (ground), where gives equivalently the output V.sub.H. FIG. 19(a) shows the overall circuit connection of this converter, which is a five-time bidirectional SC converter. Here, the three-time bidirectional SC structure, which is the first-stage structure of the converters, will firstly step up the input voltage to three times the value. The input of the second-stage two-time bidirectional SC structure is connected to nodes NA.sub.7 and NA.sub.3, such that the input of the second-stage is ⅔ the output of the first-stage structure, i.e., 2V.sub.L. Since the second-stage SC structure doubles its input voltage, its output voltage will be 4V.sub.L. This output, which is in series connection with the input power source, forms a five-time output voltage 5V.sub.L. In the case of reversing the operation to step down mode, the output will be

(118) $\frac{1}{5}{V}_H.$

(119) Similarly, the operations of all other SC converters with different conversion ratios can be deduced using same approach. FIG. 20 shows various six-time to nine-time bidirectional SC converters configured using the two-time and three-time SC structures.

(120) 3) Three-Stage SC Converters:

(121) They are composed of a cascade of three basic structures. The detail to this is omitted in this document as the approach is similar to that given in the case of two-stage SC converters, as depicted in Table I.

(122) D. Operation of m-Time and

(123) $\frac{1}{m}\text{-}\mathrm{time}$
Bidirectional SC Converters

(124) This section discusses the switching operations of the m-time bidirectional SC converter using the five-time bidirectional SC converter in the step-up mode operation as an illustration.

(125) According to the timing diagram shown in FIG. 19(b), there are four main states of operation (ignoring the dead-time period), which are shown in FIG. 21. In State 1, switches S.sub.10u, S.sub.10d, and S.sub.10b are ON, switches S.sub.11u, S.sub.11d, and S.sub.11b are OFF, and the flying capacitors C.sub.f1, and C.sub.f1b are paralleled to the power source and the bypass capacitor C.sub.11, respectively. Simultaneously, switches S.sub.20u, and S.sub.20d are ON, switches S.sub.20u, and S.sub.20d are OFF, and the flying capacitor C.sub.f2 is paralleled to the two series connected bypass capacitors C.sub.11, and C.sub.11b. In State 2, switches S.sub.20u, S.sub.20d, and S.sub.10b are OFF, switches S.sub.11u, S.sub.11d, and S.sub.11b are ON, and the flying capacitors C.sub.f1, and C.sub.f1b are paralleled to the two bypass capacitors C.sub.11, and C.sub.11b, respectively. Concurrently, switches S.sub.20u, and S.sub.20d are ON, switches S.sub.20u, and S.sub.20d are OFF, and the flying capacitor C.sub.f2 is paralleled to the two series-connected bypass capacitors C.sub.11, and C.sub.11b. In State 3, switches S.sub.10u, S.sub.10d, and S.sub.10b are ON, switches S.sub.11u, S.sub.11d, and S.sub.11b are OFF, the flying capacitors C.sub.f1, and C.sub.f1b are paralleled to the power source and the bypass capacitor C.sub.11, respectively. Also, switches and S.sub.20u, and S.sub.20d are OFF, switches S.sub.20u, and S.sub.20d are ON, the flying capacitor C.sub.f2 is paralleled to the bypass capacitor C.sub.12. In State 4, switches S.sub.10u, S.sub.10d, and S.sub.10b are OFF, switches S.sub.11u, S.sub.11d, and S.sub.11b are ON, the flying capacitors C.sub.f1, and C.sub.f1b are paralleled to the two bypass capacitors C.sub.11, and C.sub.11b, respectively. Concurrently, switches S.sub.20u, and S.sub.20d are OFF, switches S.sub.20u, and S.sub.20d are ON, and the flying capacitor C.sub.f2 is paralleled to the bypass capacitor C.sub.12. The switching operation is the same in the case of the step-down mode. However, because the role of the input source and the load are interchanged, the flow of the current will be reversed.

(126) $E.\frac{m}{2}\text{-}\mathrm{time}\mathrm{and}\frac{2}{m}\text{-}\mathrm{time}$
SC Converters

(127) In the previous section, the low voltage side V.sub.L of the first-stage three-time SC structure is connected to nodes NA.sub.1, and NA.sub.3 and its conversion ratio is 3 for the step-up mode and 1/3 for the step-down mode. Instead, if a capacitor is paralleled to the series-connected switches S.sub.10d, and S.sub.11d, and the low voltage side V.sub.L is connected at nodes NA.sub.1, and NA.sub.5 (as shown in FIG. 22), then the conversion of three-time SC structure becomes 3/2 for the step-up mode and 2/3 for the step-down mode.

(128) With this simple modification, a series of bidirectional SC converters with conversion ratios of

(129) $M=\frac{m}{2}$
for the step-up mode and

(130) $M=\frac{2}{m}$
for the step-down mode can be obtained. An example of various SC converters with conversion ratio of (3/2, 2/3),

(131) $\left(\frac{3}{2},\frac{2}{3}\right),\left(\frac{5}{2},\frac{2}{5}\right),\mathrm{and}\left(\frac{7}{2},\frac{2}{7}\right)$
and (7/2, 2/7) are shown in FIG. 22.

(132) $F.\frac{n}{m}\text{-}\mathrm{time}\mathrm{and}\frac{m}{n}\text{-}\mathrm{time}$
(m<n, and m, and n are Positive Integers) SC Converters

(133) (a) Type I: Input and Output are of Common Ground.

(134) In sections III-C and III-E, SC converters with m-time and

(135) 0$\frac{m}{2}\text{-}\mathrm{time}$
time are introduced. In these two series of SC converters, the low side voltage are all connected to nodes A and B of the converters (refer to FIGS. 20 and 22). If a capacitor is connected to nodes A and B instead of the low voltage side V.sub.L, while V.sub.L is connected to the common ground A and any of the other nodes B, C, . . . , etc., a conversion ratio of

(136) $M=\frac{m}{n}\mathrm{or}M=\frac{n}{m}$
can be achieved. Table II gives an example of such bidirectional SC converters with M=5 and M=7.

(137) TABLE-US-00002 TABLE II $\frac{m}{n}\mathrm{type}\mathrm{SC}\mathrm{converters}$ Con- Conversion version FIG. V.sub.L V.sub.H ratio FIG. V.sub.L V.sub.H ratio (M) FIG. 18(a) A, B A, E ⅕ FIG. 21(b) A, B A, E ⅖ N = 5 A, C A, E ⅖ N = 5 A, C A, E ⅗ A, D A, E ⅗ A, D A, E ⅘ FIG. 19(b) A, B A, F 1/7 FIG. 21(c) A, B A, F 2/7 N = 7 A, C A, F 2/7 N = 7 A, C A, F 4/7 A, D A, F 3/7 A, D A, F 5/7 A, E A, F 5/7 A, E A, F 6/7

(138) (b) Type II: Input and Output are not of Common Ground.

(139) If the input of the bidirectional SC converter described above is connected to any of the two nodes of B, C, . . . , etc., and the output is the stack of the bypass capacitors, an SC converter without common ground and with conversion ratio

(140) $M=\frac{m}{n}\mathrm{or}M=\frac{n}{m},$
can be obtained.
G. Reconfigurable SC Converters

(141) Previous sections have illustrated many series of SC converters with conversion ratio of

(142) $M=\frac{m}{n}\mathrm{or}M=\frac{n}{m},$
depending on the direction of the power flow. From the illustrations, these converters are composed of two or more units of the two-time and/or three-time SC structures. It is possible to convert these converters into reconfigurable converters with variable conversion gain M that can be changed in real time through control by introducing some additional switches to these converters. For example, FIG. 23 shows two reconfigurable SC converters based on the SC topology shown in FIG. 20(d). For the converters shown in FIG. 23(a), five extra switches have been added as compared with the converter shown in FIG. 20(d) to achieve a variable ratio. Table. III shows the operating states of the switches for different conversion ratios, where (Φ.sub.10, Φ.sub.11) and (Φ.sub.20, Φ.sub.21) are two pairs of complementary signals with dead-time.

(143) TABLE-US-00003 TABLE III Conversion ratio of reconfigurable SC converters of topology shown in FIG. 23(a) Conversion ratio (M) Switch 1 2 3 4 5 6 7 9 S.sub.5xa OFF OFF OFF OFF Φ.sub.20 OFF OFF OFF S.sub.5xb OFF OFF OFF OFF ON or Φ.sub.20 OFF OFF OFF S.sub.6x OFF OFF ON OFF ON OFF ON ON S.sub.7xa OFF OFF OFF Φ.sub.20 OFF OFF Φ.sub.20 OFF S.sub.7xb OFF OFF OFF ON or Φ.sub.20 OFF OFF ON or Φ.sub.20 OFF S.sub.9x OFF OFF OFF OFF OFF Φ.sub.20 OFF Φ.sub.20 S.sub.10d OFF Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 S.sub.10a ON Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 Φ.sub.10 S.sub.10b ON ON Φ.sub.10 ON Φ.sub.10 ON Φ.sub.10 Φ.sub.10 S.sub.11d OFF Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 S.sub.11a ON Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 Φ.sub.11 S.sub.11b ON ON Φ.sub.11 ON Φ.sub.11 ON Φ.sub.11 Φ.sub.11 S.sub.20a ON ON ON Φ.sub.20 Φ.sub.20 Φ.sub.20 Φ.sub.20 Φ.sub.20 S.sub.20b ON ON ON Φ.sub.20 Φ.sub.20 Φ.sub.20 Φ.sub.20 Φ.sub.20 S.sub.21d OFF OFF OFF Φ.sub.21 Φ.sub.21 Φ.sub.21 Φ.sub.21 Φ.sub.21 S.sub.21a ON ON ON Φ.sub.21 Φ.sub.21 Φ.sub.21 Φ.sub.21 Φ.sub.21 S.sub.21b ON ON ON Φ.sub.21 Φ.sub.21 Φ.sub.21 Φ.sub.21 Φ.sub.21

(144) It is further possible to have four additional groups of switches, namely, (S.sub.1), (S.sub.2a, S.sub.2b), (S.sub.3a, S.sub.3b), and (S.sub.4), and a capacitor C.sub.10 introduced to the SC converter in FIG. 23(a) for enhanced reconfiguration of the input voltage V.sub.L such that it can be flexibly connected to different Y nodes of the SC structures through control. A diagram of the resulted converter is shown in FIG. 23(b). Only one out of the four groups of switches is kept ‘ON’ for selecting a particular input node. Different possible conversion ratios exist for the turning on of each group of switches, and the conversion ratio is shown in Table IV. In particular, note that this converter can achieve a new type of reconfigurable fractional conversion operation where real-time conversion of varying voltage gain can be achieved. An SC converter of this nature was never reported in any literature. The possibility of achieving such fractional conversion allows output voltage near a desired voltage to be obtained for any input voltage source using the SC converter. By adopting a linear regulator in cascade with this SC converter, a well-regulated DC output voltage with high efficiency and very fast response, and without any magnetics, is achievable for any input voltage source.

(145) TABLE-US-00004 TABLE IV Conversion ratio of reconfigurable SC converters Configuration S.sub.2a, NO. type S.sub.1 ‘ON’ S.sub.2b ‘ON’ S.sub.3a, S.sub.3b ‘ON’ S.sub.4 ‘ON’ 1 1x 1 1 1 1 2 2x 2, ½ 1 1 1 3 3x 3, ⅓ 3/2, ⅔ 1 1 4 4x 4, ¼ 2, ½ 2, ½ 4/3, ¾ 5 5x 5, ⅕ 5/2, ⅖ 5/3, ⅗ 5/4, ⅘ 6 6x 6, ⅙ 3, ⅓ 3, ⅓ 3/2, ⅔ 7 7x 7, 1/7 7/2, 2/7 7/3, 3/7 7/5, 5/7 8 9x 9, 1/9 9/2, 2/9 3, ⅓ 3/2, ⅔
H. AC-AC SC Converters

(146) If the MOSFET switches of the converters discussed in the previous sections are replaced by bidirectional switches, a series of SC converters that achieve AC-AC conversion can be derived.

(147) Possible Applications

(148) There are two critical application areas for such bidirectional SC converters, which are the high-voltage-gain step-up conversion for distributed energy resources and in low power IC electronic applications. In distributed energy resources applications, it is required that the converter is of high-voltage-conversion ratio, high efficiency, and functional in high temperature environment, which are the key features of the proposed SC converters. On the other hand, the proposed SC converters have other attractive merits such as using fewer switches and capacitors, having lower voltage stress, and a simple control as compared to other types of SC converters. Also, as the converter is only composed of switches and capacitors, it is easy to fabricate it into an IC in the case of low power applications.

(149) Advantages Over Prior Power Converters

(150) Although patent [24] proposed a high-voltage-gain SC converter by using the basic structure of the two-time SC structure, their method of achieving high-voltage-gain conversion is restricted to simply cascading multiples of the two-time SC structure. The conversion ratio of their patented converter and approach must be

(151) $M=2^N\mathrm{or}M=\frac{1}{2^N}$
(where N is integer). In our invention, the method of configuring the SC converter is based on an N-time SC structure and is not limited to the two-time SC structure. The idea is to combine one or multiple of SC structures to get an SC converter with a flexible conversion ratio, like

(152) $M=\frac{m}{n},$
etc., and it is not fixed at 2.sup.M or

(153) $\frac{1}{2^N}.$

(154) Patent [27] proposed an SC converter which uses the three-time SC structure. However, this patent is focused on the two-stage multi-output converter, in which the second stage is an inductor based step-down DC-DC converter.

(155) Patents [26], [28]-[30] proposed various types of reconfiguration SC converters. However, they are all of different topologies as compared to that proposed in this invention.

(156) Variants

(157) It can be appreciated that the aforesaid embodiments are only exemplary embodiments adopted to describe the principles of the present invention, and the present invention is not merely limited thereto. Various variants and modifications may be made by those of ordinary skill in the art without departing from the spirit and essence of the present invention, and these variants and modifications are also covered within the scope of the present invention. Accordingly, although the invention has been described with reference to specific examples, it can be appreciated by those skilled in the art that the invention can be embodied in many other forms. It can also be appreciated by those skilled in the art that the features of the various examples described can be combined in other combinations.

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