Patent Publication Number: US-11664727-B2

Title: Switched-capacitor power converters

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of the priority date of U.S. Provisional Application No. 62/189,909, filed on Jul. 8, 2015, the contents of which are hereby incorporated by reference in their entirety. 
    
    
     FIELD OF INVENTION 
     This invention relates to power converters, and in particular, to dc-dc power converters. 
     BACKGROUND 
     It is known in the art that electrical devices require electric power to operate. However, some electrical devices are more omnivorous than others. For example, a tungsten filament light bulb will operate over a wide range of voltages. Although it may be dim at low voltages, and although it may burn out prematurely at high voltages, it does not simply stop operating. 
     Digital circuits, however, are more finicky in their requirements. A digital circuit demands power with particular characteristics. A processor that receives power falling short of these characteristics will not just compute more slowly. It will simply shut down. 
     Unfortunately, power is not always delivered in a form that a microprocessor-based system will find acceptable. For example, in a handheld device, the battery voltage ranges from fully charged to almost zero. Thus, most such systems require something that accepts power in raw form and delivers it to the system in a form that the system finds more palatable. 
     This critical but unglamorous task falls upon the power converter. 
     A variety of power converters are known. These include power converters described in U.S. Pat. Nos. 8,860,396, 8,743,553, 8,723,491, 8,503,203, 8,693,224, 8,724,353, 8,339,184, 8,619,445, 8,817,501, U.S. Patent Publ. 2015/0077175, and U.S. Pat. No. 9,041,459. 
     The contents of all the foregoing patents are herein incorporated by reference. 
     SUMMARY 
     In one aspect, the invention features an apparatus for providing electric power to a load. Such an apparatus includes a power converter that accepts electric power in a first form and provides electric power in a second form. The power converter includes a control system, and first and second stages in series. The first stage accepts electric power in the first form. The control system controls operation of the first and second stages. The first stage is either a switching network or a regulating network. The second stage is a regulating network when the first stage is a switching network. On the other hand, the second stage is a switching network when the first stage is a regulating network. 
     Among the embodiments are those in which the control system controls at least in part based on a voltage measured between the first and second stages. 
     Also among the embodiments are those in which the first stage is a regulating network, those in which the first stage is a switching network, and those in which it is the second stage that is a switching network, such as a cascade multiplier. In either case, the switching network can be a cascade multiplier. 
     In some embodiments, at least one of the stages includes a switching network having first and second terminals. Among these are embodiments in which these terminals are isolated, embodiments in which they have a common ground, and embodiments in which they have separate grounds. 
     In other embodiments, at least one of the stages includes a switching network having a first and second switching circuits, each of which has first and second terminals. In these embodiments, the first terminal of the second switching circuit connects to the second terminal of the first switching circuit. Among these are embodiments in which the two switching circuits have different voltage-transformation ratios, and embodiments in which they have the same voltage-transformation ratios. 
     In some embodiments, the switching network includes first and second switching circuits in series, whereas in others, it includes first and second switching circuits in series-parallel. 
     Some embodiments of the power converter further include a third stage in series with the first stage and the second stage so that the second stage is between the first stage and the third stage. These embodiments include those in which the first and third stages are switching networks, those in which the first and third stages are regulating networks, and those in which the third stage is operated with a duty cycle that causes the third stage to become a magnetic filter. 
     In some embodiments, the switching network includes a cascade multiplier. Among these are those embodiments in which the cascade multiplier is a single-phase cascade multiplier, those in which it is asymmetric, those in which it is a step-down, multiplier, and any those in which it is any combination thereof. Also among these embodiments are those in which the cascade multiplier is a dual-phase cascade multiplier. In this case, the cascade multiplier could be a symmetric cascade multiplier, or one that includes parallel pumped capacitors, or one that lacks DC capacitors. 
     In some of the foregoing embodiments, the cascade multiplier creates an auxiliary voltage to drive an additional circuit. Among these are embodiments that include a level shifter connected to be driven by the auxiliary voltage, and those in which a gate driver is connected to be driven by the auxiliary voltage. 
     In some embodiments, the switching network includes first and second dual-phase cascade multipliers, and a phase node shared by both cascade multipliers. In these embodiments, the first cascade multiplier, which is stacked on the second, is asynchronous and the second cascade multiplier is synchronous. Among these embodiments are those in which the first and second cascade multipliers operate at the same frequency, and those in which the first and second cascade multipliers operate at different frequencies. 
     In some embodiments, the regulating network includes a buck converter. Among these are embodiments in which the buck converter includes first and second terminals with the same reference voltage. Examples include those in which the buck converter&#39;s first and second terminals are at different reference voltages, those in which the buck converter has three terminals, and those in which the buck converter has a floating node at a floating voltage. In embodiments that have a floating node, the floating node can be between two loads or between two sources. 
     A variety of other regulating networks are contemplated. These include a buck-boost converter, a boost converter, and even a four-terminal non-inverting buck-boost converter. 
     In some embodiments that use a boost converter as a regulating network, the switching network includes a step-down single-phase asymmetric cascade multiplier. In some of these embodiments, selection switches connected to the regulating network cause the switching network to output a fraction of its normal output voltage. In others, switches are oriented so that cathodes of parasitic diodes corresponding to the switches connect to each other. Among these embodiments are those in which the first stage is a regulating network. 
     Embodiments include those in which those in which the regulating network regulates plural wires, those in which it regulates at most one wire, and those in which it regulates a particular one of plural wires based on an input voltage to the regulating network. 
     Also among the embodiments are those in which the regulating network has plural output ports and those in which it is a multi-tap boost converter. Among these are embodiments in which the switching network includes a single-phase step-down switched-capacitor circuit. 
     In yet other embodiments, the power converter floats above ground. 
     In some embodiments, the switching network is reconfigurable. In other embodiments, it is the regulating network that is reconfigurable. In yet others, both are reconfigurable. In either case, there are embodiments in which a magnetic filter connects to whichever of the two are reconfigurable. Thus, a magnetic filter could be connected to either the reconfigurable switching network or the reconfigurable regulating network. 
     In some embodiments, the switching network includes a dual-phase switched capacitor circuit. Among these are embodiments in which the switched capacitor circuit includes pump capacitors in series and DC capacitors in series. 
     In some embodiments, the switching network includes a dual-phase switching circuit including DC capacitors that store charge from the regulating network only during a dead-time transition during which the switching network is between states. 
     In yet other embodiments, the regulating network includes an inductor that promotes adiabatic charge transfer within the switching network. 
     Some embodiments also include a magnetic filter connected to the switching network to promote adiabatic charge transfer within the switching network. Among these are embodiments in which the magnetic filter is connected between the switching network and a load, those in which the magnetic filter is connected between the switching network and a source, and those in which the regulating network and the magnetic filter cooperate to promote adiabatic charge transfer within the switching network. 
     Embodiments further include those that have a circuit connected to the switching network to constrain current flow out of the switching network, and those that have a circuit connected to the switching network to promote adiabatic charge transfer within the switching network. 
     In some embodiments, the switching network includes a two-phase step-down switching network and the regulating network is a step-down network. Among these are embodiments in which the switching network includes a cascade multiplier. In those embodiments that include a cascade multiplier, the regulating network can include a buck converter. Also among these embodiments are those in which regulating network promotes adiabatic charge transfer. 
     In still other embodiments, the switching network includes a step-down single-phase asymmetric cascade multiplier and the regulating network includes a converter that causes voltage to step down. In some of these embodiments, it is the first stage that is a switching network. 
     In some embodiments, the regulating network includes a multiple-tap buck converter configured to have two operating modes. Among these are embodiments in which the switching network provides first and second voltage rails that, in operation, are maintained at different voltages. 
     Yet other embodiments are those in which the regulating network includes a buck converter having multiple taps and configured have three operating modes. Among these are embodiments in which the switching network provides first, second, and third voltage rails that, in operation, are maintained at different voltages. 
     Other embodiments of the apparatus are those in which the switching network includes a two-phase switched-capacitor circuit and the regulating network is a buck converter. 
     Also among the embodiments are those in which the regulating network includes parallel first and second regulating circuits. 
     In some embodiments, the power converter includes first and second outputs. In operation, the first output and second outputs being maintained at corresponding first and second voltage differences. The first voltage different is a difference between a first voltage and a second voltage, and the second voltage difference is a difference between a third voltage and the second voltage. 
     In some embodiments, the regulating network includes first, second, and third regulating circuits in parallel. 
     In other embodiments, the power converter includes first second, and third outputs. In operation, the first, second, and third outputs are maintained at corresponding first second, and third voltage differences. The first voltage different is a difference between a first voltage and a second voltage. The second voltage difference is a difference between a third voltage and the second voltage. And the third voltage difference is a difference between a fourth voltage and the second voltage. 
     In some embodiments, the power converter has a first terminal and a second terminal such that, in operation, a first voltage different is maintained across the first terminal and a second voltage difference is maintained across the second terminal. The first voltage difference is a difference between a first voltage and a second voltage, and the second voltage difference is a difference between a third voltage and the second voltage, with the second voltage being variable. Some of these embodiments also have a third stage that provides the second voltage. Also among these are embodiments in which the third stage includes a switched-mode power converter, a switched capacitor converter, a buck converter, or a cascade multiplier. 
     In some embodiments, the power converter is configured to provide AC output with a non-zero DC offset. 
     In other embodiments, the switching network includes a reconfigurable asynchronous cascade multiplier, and the regulating network is connected to the switching network to enable the switching network to cause either a step up in voltage or a step down in voltage. In some cases, the the regulating network includes a four-switch buck-boost converter. 
     In still other embodiments, the first stage is a switching network that includes a reconfigurable cascade multiplier that operates synchronously in a single-phase, and the regulating network includes a four switch buck boost converter. Among these are embodiments in which the regulating network connects to the switching network at a point that enables the switching network to step voltage up or step voltage down. 
     Embodiments also include those in which the switching network includes a cascade multiplier with a charge pump embedded therein. The charge pump can have a variety of characteristics. For example, the charge pump can be reconfigurable, or it can be a fractional charge pump. Alternatively, the embedded charge pump operates in multiple modes, each of which corresponds to a voltage transformation ratio. Or the cascade multiplier might include a reconfigurable two-phase asynchronous step-down cascade multiplier. In any of these embodiments, the regulating network could include a two-phase boost converter. 
     In still other embodiments, the power converter further includes a third stage in series with the first stage and the second stage, wherein the second stage is between the first stage and the third stage, both of which are switching networks. The regulating circuit includes a buck converter, and both switching networks include a single-phase asynchronous step-up cascade multiplier. These embodiments include those in that further include a stabilizing capacitor at an output of the regulating network. 
     In still other embodiments, the power converter further includes a third stage in series with the first stage and the second stage, with the second stage being between the first stage and the third stage. In these embodiments, the first stage and the third stage are switching networks, the regulating circuit includes a buck-boost converter, the first switching network includes a single-phase asynchronous step-up cascade multiplier, and the second switching network includes a single-phase synchronous step-up cascade multiplier. Among these embodiments are those that also have a stabilizing capacitor at an output of the regulating network. 
     In some embodiments, the power converter further includes a third stage in series with the first and second stage, with the second stage being between the first stage and the third stage. The first and third stage are both regulating networks. However, the first stage includes a boost converter, and the third stage includes a buck converter. The switching network includes first and second cascade multipliers having equal numbers of stages. Some of these embodiments also have a phase pump shared by the first and second cascade multipliers. In others, the first and second cascade multipliers operate 180 degrees out of phase. And in yet others, the cascade multipliers comprise corresponding first and second switch stacks, and an output of the switching network is a voltage difference between a top of the first switch stack and a top of the second switch stack. 
     In some embodiments, the power converter further includes a third stage in series with the first and second stages, with the second stage being between the first stage and the third stage. In these embodiments, the first stage and the third stage are regulating networks, the first stage includes a three-level boost converter, the third stage includes a buck converter, and the switching network includes first and second cascade multipliers having unequal numbers of stages. 
     In other embodiments, the switching network receives current that has a first portion and a second portion, wherein the first portion comes from the regulating network, and the second portion, which is greater than the first, bypasses the regulating network. 
     In some embodiments, the power converter further includes a third stage in series with the first stage and the second stage, the second stage being between the first stage and the third stage. The first stage is a first regulating network, the third stage is a second regulating network, and the first stage includes a boost converter. The third stage includes a buck converter. The switching network includes cascade multipliers having unequal numbers of stages. Among these embodiments are those in which the second stage includes an additional inductor connected to the first stage. 
     Yet other embodiments include a third stage. In these embodiments, the first stage includes a regulating network, the third stage includes a regulating network, the power converter provides a load with a first voltage difference, the first stage provides a second voltage difference to the second stage, the second stage provides a third voltage difference to the third stage, the first voltage difference is a voltage difference between a first voltage and a second voltage, the second voltage difference is a voltage difference between a third voltage and a fourth voltage, the third voltage difference is a voltage difference between a fifth voltage and a sixth voltage, the fourth voltage differs from the second voltage, and the sixth voltage differs from the second voltage. Among these embodiments are those in which the second stage includes a reconfigurable switching network. 
     In some embodiments, the first stage includes a switching network having a reconfigurable dual phase cascade multiplier with an embedded inductor configured to promote adiabatic charge transfer between capacitors in the cascade multiplier. In some embodiments, the inductor is embedded at a location through which a constant current passes. Also among these embodiments are those in which the second stage includes a zeta converter, and those in which the cascade multiplier includes a phase pump with the inductor being embedded therein. In others of these embodiments, the cascade multiplier includes pump capacitors, and the inductor is embedded at a location that maximizes the number of paths that pass between the inductor and a pump capacitor. 
     In some embodiments, the switching network includes a dual-phase cascade multiplier with pump capacitors in series. Among these are embodiments in which the switching network has a variable transfer function and embodiments in which the switching network includes a phase pump that includes an embedded charge pump. In this latter case, the embedded charge pump includes switch sets, pump capacitors, and a controller that operates the switch sets to cause transitions between a first operating mode and a second operating mode, each of which corresponds to a transfer function for the cascade multiplier. Among these cases are those in which the controller operates the switch sets so that the embedded controller causes the cascade multiplier to have a transfer function in which the cascade multiplier provides either a voltage gain or a voltage attenuation. 
     In another aspect, the invention features an apparatus for providing electric power to a load includes a power converter that accepts electric power in a first form and provides electric power in a second form. The power converter includes a control system, a first stage, and a second stage in series. The first stage accepts electric power in the first form. The control system controls operation of the first and second stage. The first stage is either a switching network or a regulating network. The second stage is a regulating circuit when the first stage is a switching network, and a switching network otherwise. 
     These and other features will be apparent from the following detailed description and the accompanying figures, in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    shows a power converter having a regulating circuit and a switching network in series; 
         FIG.  2    shows a power converter that is the converse of that shown in  FIG.  1   ; 
         FIG.  3    shows a power converter having a switching network with two switching circuits in series; 
         FIG.  4    shows a power converter having a switching network with two switching circuits in series-parallel; 
         FIG.  5    shows a switching network between two regulating networks; 
         FIG.  6    shows a regulating network between two switching networks; 
         FIG.  7    shows an equivalent circuit for a switching network in which the input and output are isolated; 
         FIG.  8    shows an equivalent circuit for a switching network in which the input and output have a common ground; 
         FIG.  9    shown an equivalent circuit for a switching network in which the input and output have a non-common ground; 
         FIG.  10    shows a first implementation of the switching network in  FIG.  1   ; 
         FIG.  11    shows a second implementation of the switching network in  FIG.  1    in which the switching network is a dual-phase symmetric cascade multiplier having parallel pumped capacitors; 
         FIG.  12    shows a third implementation of the switching network in  FIG.  1    in which the switching network has a dual-phase asymmetric cascade multiplier stacked on top of dual-phase symmetric cascade multiplier with shared phase nodes; 
         FIG.  13 A  shows a variant of the power converter in  FIG.  10   ; 
         FIG.  13 B  shows a power converter similar to that shown in  FIG.  13 A , but with the order of the regulating network and the switching network having been reversed; 
         FIG.  14 A  shows a second implementation of the switching network in  FIG.  1   ; 
         FIGS.  14 B and  14 C  show implementations of the phase pump shown in  FIG.  14 A ; 
         FIG.  15 A  shows a buck converter used to implement a regulating network; 
         FIGS.  15 B- 15 C  show non-isolating variants of the buck converter of  FIG.  15 A ; 
         FIGS.  16 A- 16 B  show non-isolating buck-boost converters used to implement a regulating network in any of the foregoing power converters; 
         FIGS.  17 A- 17 B  show non-isolating boost converters used to implement a regulating network in any of the foregoing power converters; 
         FIGS.  18 A- 18 B  show four-terminal non-inverting buck-boost converters; 
         FIG.  19    shows the power converter of  FIG.  1    with a reconfiguring switching network; 
         FIG.  20    shows the power converter of  FIG.  1    with a reconfiguring regulating network; 
         FIG.  21    shows a power converter in which the regulating circuit has more than two output ports; 
         FIG.  22    shows a power converter similar to that shown in  FIG.  21   , but with a dual-phase switched-capacitor circuit instead of as a single-phase switched-capacitor circuit; 
         FIG.  23    shows a power converter with a magnetic filter between a switching network and a load; 
         FIG.  24    shows a power converter with a magnetic filter between a switching network and a power source; 
         FIG.  25    shows the power converter of  FIG.  22    modified to include a magnetic filter between the switching network and the load; 
         FIG.  26    shows a power converter that uses a two-phase step-down switching network connected in series with a step-down regulating network; 
         FIG.  27    shows a power converter similar to that shown in  FIG.  19    but with the order of the switching network and the regulating network reversed; 
         FIG.  28    shows a power converter in which the regulating network is a buck converter with multiple taps; 
         FIG.  29    shows a power converter similar to that shown in  FIG.  28   , but with the buck converter having four instead of three taps; 
         FIG.  30    shows the power converter of  FIG.  26    with a two-phase switched-capacitor circuit implementing the switching network and a buck converter implementing the regulating network; 
         FIG.  31    shows a power converter with two voltage outputs; 
         FIG.  32    shows a power converter with three voltage outputs; 
         FIG.  33    shows a power converter floating above ground; 
         FIG.  34    is an embodiment in which a 4-switch buck-boost converter implements the regulating network and a reconfigurable single-phase asymmetric cascade multiplier implements the switching network; 
         FIG.  35    is a particular embodiment of the power converter in  FIG.  2    in which a dual-inductor buck converter implements the regulating network and a reconfigurable dual-phase asymmetric step-up cascade multiplier implements the switching network; 
         FIG.  36    shows an implementation of a power converter in which the switching network has a separate charge pump embedded within a cascade multiplier; 
         FIG.  37    shows the embedded charge pump of  FIG.  36   ; 
         FIG.  38    shows the power converter of  FIG.  6    in which a buck converter implements the regulating circuit, a single-phase asymmetric step-up cascade multiplier implements the first switching network, and a single-phase symmetric step-up cascade multiplier implements the second switching network; 
         FIG.  39    shows the power converter of  FIG.  38    in which the buck converter is replaced with a buck-boost converter; 
         FIG.  40    shows a power converter in which two cascade multipliers with equal numbers of stages implements the switching network; 
         FIG.  41    shows a power converter in which two cascade multipliers with unequal numbers of stages implements the switching network; 
         FIG.  42    shows a power converter in which the bulk of the current into the switching network bypasses the boost converter; 
         FIG.  43    shows a power converter having floating regulating networks and a grounded switching network; and 
         FIG.  44    shows an implementation of  FIG.  2    in which inductors embedded in the switching network promote adiabatic charge transfer within the switching network. 
     
    
    
     DETAILED DESCRIPTION 
       FIG.  1    shows a power converter having two stages in series. Depending on details of the circuitry within the two stages, and on the operation of the controller, the power converter will be a dc-dc converter, an ac-dc converter, a dc-ac converter, or an ac-ac converter. 
     Each stage is either a regulating network  16 A or a switching network  12 A. The illustrated power converter separates the function of voltage/current transformation from that of regulation. As shown in  FIG.  1   , it does so by providing a regulating network  16 A in series with a switching network  12 A. The two stages can operate at the same frequency, at different frequencies, in phase, and out of phase. 
     A power source  14  and a load  18 A are shown only for clarity. These components are not actually part of the power converter. They merely represent the source of the power to be converted, and the ultimate consumer of that power. Dashed lines between these components and the power converter indicate that they are optional. Other components shown connected with dashed lines in this and other figures are likewise optional. For example, a dashed wire between the regulating network  16 A and the switching network  12 A is also optional. 
     In  FIG.  1   , the power source  14  is a voltage source. However, since power is the product of voltage and current, the power source  14  could just as easily be a current source. Examples of a suitable power source  14  include, but are not limited to, a battery, a solar panel, a fuel-cell, and a power supply. 
     The power source  14  need not deliver a constant stream of power. In fact, if it did, the power converter would not be nearly as necessary. After all, among the tasks of a power converter is to deliver a constant stream of power with specific characteristics to the load  18 A notwithstanding variations in the power stream provided by the power source  14 . The power source  14  is merely a source of power, or equivalently, since power is the time-derivative of energy, a source of energy. 
     The load  18 A can be any type of electrical load. What is essential, is that it be a net energy consumer. Examples of a load  18 A include a microprocessor, LED, RF PA, or a DSP. In fact, the load  18 A might even be another power converter. 
     The arrows shown in the figure represent power flow, and not magnitude of power flow. Hence, each stage can be bidirectional. In such cases, if the load  18 A supplies power, then the load  18 A acts as a power source  14  and the power source  14  acts as a load  18 A. However, in some embodiments, one or more stages are unidirectional. In addition, embodiments exist in which a stage can be a step-up stage, a step-down stage or a step-up/down stage. 
     The illustrated regulating network  16 A can itself comprise two or more constituent regulating circuits operating as a combination in order to regulate some electrical parameter. These regulating circuits can have different voltage ratings and connect to each other in different ways. In some embodiments, the regulating circuits connect in series. In others, they connect in parallel, in series-parallel, or in parallel-series. 
     The regulating circuits that comprise a regulating network  16 A can be of different types. For example, a regulating network  16 A may comprise a buck converter in combination with a linear regulator. Examples of suitable regulating circuits include a buck converter, a boost converter, a buck-boost converter, a fly-back converter, a push-pull converter, a forward converter, a full bridge converter, a half-bridge converter, a multi-level converter (buck or boost), a resonant converter, a Cuk converter, a SEPIC converter, a Zeta converter, and a linear regulator. 
     Like the regulating network  16 A, the switching network  12 A can also be made of a combination of cooperating switching circuits. These individual switching circuits can have different transformation ratios, the same transformation ratios, and different voltage ratings. They can also be different kinds of switching circuits, such as series parallel or cascade multiplier circuits. 
     A cascade multipliers includes a switch stack, a phase pump, pump capacitors, and, optionally, dc capacitors. The phase pump comprises a pair of switches that cooperate to create a pump signal V clk . In general, the two states of the clock are separated by a brief dead-time to allow transients and the like to decay. In cascade multipliers that require a complement to the clock signal, the phase pump includes another pair of switches to generate the complement. The switch stack is a series of switches connected between the input and the output of the cascade multiplier. 
     In those cases in which the switching circuit is a cascade multiplier, it can be asymmetric, symmetric, series-pumped, or parallel-pumped. Additional types of switching circuits include series-parallel switching circuits, parallel-series switching circuits, voltage-doubling circuits, and Fibonacci circuits. These constituent switching circuits can connect to each other in series, in parallel, in series-parallel, or in parallel-series. Some configurations of the illustrated power converter permit adiabatic charge transfer into or out of a capacitor in the switching network  12 A. 
     Other configurations feature a reconfigurable switching network  12 A that transitions between two or more states in the course of transferring charge. This charge transfer depends on the voltage across the capacitor&#39;s terminals. Reconfiguring the switching network  12 A involves causing switches in the network to change state to cause this voltage to change. Reconfiguration can occur, for example, when the voltage or current transformation between the ports of the switching network  12 A is to be changed. 
       FIG.  1    also shows a controller that controls the operation of one or more stages in the power converter. The controller operates in response to an I/O signal and a clock signal. In some embodiments, the I/O signal is a digital communication signal. The clock signal can be a signal from a clock or it can be a signal from some analog reference. This might be a signal set by the user. Alternatively, another subsystem sets this signal and sends it to the power converter. 
     In some embodiments, the controller receives multiple sensor inputs from the power converter and provides control signals along first and second paths P 1 , P 2 . Examples of sensor signals provided to the sensor inputs are V O , V X , V IN , I IN , I X  and I 0 . Among the foregoing sensor inputs, the negative terminals of V IN , V X , and V O  can be at ground, above ground, or below ground depending upon their corresponding regulating circuits and switching networks. In fact, since voltage reflects a difference in potential energy between two points, there is nothing particularly special about ground. 
     The controller&#39;s function is to control both the regulating network  16 A and the switching network  12 A in an effort to control V IN , I IN , V O , and I O . In carrying this out, the controller can use either feed-forward control or feedback control. Feed-forward control involves choosing an output control signal based on an input, whereas feedback control involves choosing an output control signal based on an output. 
     Additional control methods that are applicable include voltage-mode control, current-mode control, hysteretic control, PFM control, pulse-skipping control, and ripple-based control. In embodiments that rely upon voltage-mode control, control can be linear or non-linear. In embodiments that rely upon current-mode control, current can be based on both an average value of current or a peak value of current. 
     It is possible to interconnect the regulating network and the switching network in a variety of ways.  FIGS.  1 ,  2     5 , and  6  show four fundamental building blocks. 
     In particular,  FIG.  1    shows a switching network  12 A in series with a regulating network  16 A, with the load  18 A connected to the switching network  12 A and the power source connected to the regulator network  16 A. 
       FIG.  2    is similar to  FIG.  1    but with the power source  14  and load  18 A having been swapped. Thus, in  FIG.  2   , the power source  14  connects to the switching network  12 A and the load  18 A connects to the regulating network  16 A. When power is supplied from the load  18 A in the power converter shown in  FIG.  1   , the result is a power converter that is equivalent to that shown in  FIG.  2   . 
     As mentioned above, it is possible for a switching network  12 A to comprise two or more switching circuits. FIG. shows a particular example in which a switching network  12 A has two switching circuits in series. Each switching circuit is a stage. Assuming the same switched-capacitor topology for each stage, the resulting switching network  12 A achieves a larger transformation ratio with the same number of switches and capacitors. Alternatively, the switching network  12 A can achieve the same transformation ratio, but with fewer switches and capacitors. On the other hand, a disadvantage of the power converter shown in  FIG.  3    is that the voltage stresses on the components in at least one of the two stages increases when compared to the single stage case. 
       FIG.  4    shows an embodiment in which the switching network  12 A has first and second switching circuits connected in series-parallel. The first switching circuit achieves a 4:1 transformation ratio and the second switching circuit achieves a 3:1 transformation ratio. As a result, an intermediate voltage V X  between the regulating network  16 A and the switching network  12 A can be any fraction of the output voltage V O . In the illustrated power converter, the intermediate voltage V X  equals the output voltage V O . However, had the first switching circuit provided a 4:1 transformation ratio and had the second switching circuit provided a 2:1 transformation ratio, then the intermediate voltage VA would have been larger than the output voltage V O . Similarly, had the first switching circuit provided a 4:1 transformation ratio and had the second switching circuit provided a 7:2 transformation ratio, then the intermediate voltage V X  would have been smaller than the output voltage V O . 
       FIG.  5    and  FIG.  6    show representative three-stage embodiments. 
     The embodiment of  FIG.  5    is similar to that of  FIG.  1   , but with the inclusion of an additional regulating network  16 B connected to the switching network  12 A. As a result, the switching network  12 A is between two regulating networks  16 A,  16 B. 
     Conversely, the embodiment of  FIG.  6    is similar to that of  FIG.  2   , but with the inclusion of an additional switching network  12 B connected to the regulating network  16 A. As a result, the regulating network  16 A is between two switching networks  12 A,  12 B. 
     The four building blocks described above combine in various ways. For example, combining the building block in  FIG.  5    with that in  FIG.  1    would result in a power converter in which a first regulating network connects to an input of a first switching network, the output of which connects to an input of a second regulating network. The output of this second regulating network leads to an input of a second switching network. In the resulting power converter, the power source  14  connects to an input of the first regulating network and the load  18 A connects to an output of the second switching network.  FIGS.  7 - 9    are circuits that are suitable for modeling the behavior of a switching network  12 A. In particular, a switching network  12 A provides a voltage transformation from a first voltage V 1  to a second voltage V 2 , with the second voltage V 2  and the first voltage V 1  being related by a ratio of integers. Commonly used ratios are 1:3, 1:2, 1:1, 2:1, and 3:1. The output resistor R, accounts for voltage drops resulting from finite resistance of various components. For example, in a switching network  12 A that is intended to provide a 1:2 transformation ratio, it would not be uncommon to have an actual transformation ratio of around 1:1.9 instead of the ideal 1:2 ratio. The model shown in  FIG.  7    differs from that shown in  FIGS.  8 - 9    because the second voltage V 2  can be isolated from the first voltage V 1 . In addition, it is possible to arbitrarily separate the negative terminal of the first voltage V 1  and the negative terminal of the second voltage V 2 . This can be achieved by combining a traditional switched-capacitor circuit with a capacitive isolation stage. However, this comes at the price of increased component cost, size, and a reduction of efficiency. 
     The model shown in  FIG.  8    differs from that shown in  FIG.  7    and  FIG.  9    because of its common ground. A common ground is desirable in certain applications. For example, many devices that rely on a battery, such as cell-phones, tablets, and notebooks, use the same ground throughout the device. 
     The model shown in  FIG.  9    has a non-common ground. In particular, an offset voltage V off  separates the negative terminal of the transformer winding on the first voltage V 1  side and the negative terminal of the transformer winding on the second voltage V 2  side. The switched-capacitor topology sets the extent of the offset voltage V 1 . This ability to set the offset voltage is advantageous in certain applications. 
       FIG.  10    shows a particular implementation of the switching network  12 A in  FIG.  1   . In the illustrated embodiment, the switching network  12 A is a step-down single-phase asymmetric cascade multiplier having first and second sets of one or more switches. These sets of switches will be herein referred to as first and second “switches”  1 ,  2  for convenience, with the understanding that each can be implemented by multiple switches operating in unison. The switching network  12 A further includes pump capacitors C 5 -C 7 , and dc capacitors C 1 -C 4 . The pump capacitors C 5 -C 7  are in parallel because their negative terminals all connect to a pump signal V c1k . The dc capacitors C 1 -C 4  are in parallel because their negative terminals connect to ground. In operation, these dc capacitors C 1 -C 4  store charge from the pump capacitors C 5 -C 7 . 
     During normal operation, the switching network  12 A alternates between a first and second state at a specific frequency and duty cycle, such as 50%. 
     During the first state, the first switch  1  is closed and the second switch  2  is open. During the second state, the first switch  1  is open and the second switch  2  is closed. The frequency at which the first and second switches  1 ,  2  both transition between states can be the same as or different from that at which the regulating network  16 A switches between states. In cases where these frequencies are the same, they can, but need not be in phase. 
     The pump capacitors C 5 -C 7  swing up and down as the pump signal V clk  alternates between zero volts and the output voltage V O . At each clock cycle, charge moves between a pump capacitor C 5 -C 7  and a dc capacitor C 1 -C 4 . In the particular embodiment shown, charge from a dc capacitor C 1  makes its way to the last dc capacitor C 4  after three clock cycles. Overall, the switching network  12 A can be modeled using the circuit model shown in  FIG.  9    with a transformation ratio of 1:1 and an offset voltage V off  of 3V O . 
     In an alternative embodiment, shown in  FIG.  11   , the switching network  12 A is a dual-phase symmetric cascade multiplier having parallel pumped capacitors. All switches operate in the same manner already described in connection with  FIG.  10   . Cascade multipliers are described in connection with the description of FIG. 15 in U.S. Pat. No. 8,860,396, the contents of which are herein incorporated by reference. 
     A particular feature of the embodiment shown in  FIG.  11    is the absence of dc capacitors inside the cascade multiplier (i.e., capacitors C 1 , C 2  are at the input and output terminals). As a result, it is necessary to add a first switch LA, a second switch  2 A, and a first dc capacitor C 2 . The sole function of the first dc capacitor C 2  is to keep the node voltage relatively constant. As a result, the capacitance of the first dc capacitor C 2  depends on the amount of charge that is expected to flow in and out of the first dc capacitor C 2  as well as the voltage ripple requirement of the node voltage. 
     In operation, the first switch LA and the second switch  2 A are never in a closed state at the same time. To as great an extent as is possible, the first switch  1 A is synchronized with a first switch set  1  so that when the first switch  1 A is open, so are all the switches in the first switch set  1 , and when the first switch  1 A is closed, so are all the switches in the first switch set  1 . Similarly, to as great an extent as is possible, the second switch  2 A is synchronized with the second switch set  2  so that when the second switch  2 A is open, so are all the switches in a second switch set  2 , and when the second switch  2 A is closed, so are all the switches in the second switch set  2 . As a result, when the pump signal V clk  is high, a pump capacitor C 8  connects to the first dc capacitor C 2 . When the pump signal V clk  is low, a pump capacitor C 5  is connected to the first dc capacitor C 2 . 
     An advantage of the embodiment shown in  FIG.  11    is that it becomes possible to create additional dc voltages. For example, it is possible to create an auxiliary voltage across a second dc capacitor C 3 . This auxiliary voltage thus becomes available to drive other circuits, included such circuits as gate drivers and level shifters, or any other circuit that would require, during its operation, a voltage that falls between the input voltage V IN  and the output voltage V O  of the power converter. 
     Yet another advantage is the possibility for using charge that is stored in the second dc capacitor C 3  to supply a linear regulator, thus creating a regulated voltage. 
     In yet another embodiment, shown in  FIG.  12   , the switching network  12 A features a dual-phase asymmetric cascade multiplier stacked on top of dual-phase symmetric cascade multiplier with shared phase pump nodes, i.e. the pump signal V clk  and its complement. All switches operate in the same manner already described in connection with  FIG.  10   . 
     Because the nodes are shared in the illustrated embodiment, both cascade multipliers are operated at the same frequency. However, sharing the phase pump is not required. 
     Additionally, in the particular embodiment shown, the transformation ratio of each stage is relatively low. However, there is no special constraint on transformation ratio. For example, it would be quite possible for the dual-phase asymmetric cascade multiplier to have a transformation ratio of 2:1, while the dual-phase symmetric cascade multiplier has a transformation ratio of 10:1. 
     An advantage of the structure shown in  FIG.  12    is that the symmetric cascade multiplier lacks dc capacitors and has fewer switches than a corresponding asymmetric cascade multiplier. Thus, the combination of the two as shown in the figure has fewer switches and fewer dc capacitors. On the other hand, the first and second switches S 1 , S 2  block twice the voltage as other switches. 
       FIG.  13 A  shows a power converter that is a variant of that shown in  FIG.  10   . In the power converter shown in  FIG.  13 A , the intermediate voltage V X  is applied across the dc capacitors C 1 , C 3  instead of across the dc capacitors C 1 , C 2  as shown in  FIG.  10   . The corresponding circuit model would be that shown in  FIG.  9   , but with a transformation ratio of 2:1 and with an offset voltage V off  of 2V O . In some cases, depending on the nature of the regulating network  16 A, the configuration shown in  FIG.  13 A  permits a wider input voltage V IN  range, than the configuration in  FIG.  10   . 
       FIG.  13 B  shows a power converter similar to that shown in  FIG.  13 A , but with the order of the regulating network  16 A and the switching network  12 A having been reversed. Unlike the configuration shown in  FIG.  13 A , in which the switching network  12 A causes the voltage to step down, in the configuration shown in  FIG.  13 B , the switching network  12 A causes the voltage to step up. 
       FIG.  14 A  shows a power converter similar to that shown in  FIG.  10    with the exception that the cascade multiplier is a two-phase cascade multiplier instead of a single-phase cascade multiplier. In addition, the pump capacitors C 1 -C 3  are in series instead of in parallel. As a result, the pump capacitors C 1 -C 3  avoid having an excessively high voltage across them. On the other hand, the capacitance required is higher than that required in the switching network  12 A shown in  FIG.  10   . Yet another disadvantage of connecting pump capacitors C 1 -C 3  in series is that, when adiabatic charge transfer occurs between such capacitors during charge redistribution, the loss associated with such redistribution is greater than it would be with the switching network  12 A shown in  FIG.  10   . 
     The cascade multiplier includes a phase pump  32 .  FIGS.  14 B- 14 C  show examples of suitable phase pumps. Unlike conventional phase pumps, those shown in  FIGS.  14 B- 14 C  include embedded charge pumps. The resulting phase pumps can thus generate pump signals with variable gain. In particular, the phase pump  32  shown in  FIG.  14 B  provides voltage attenuation; the phase pump  32  shown in  FIG.  14 C  provides voltage gain. 
     The phase pump  32  shown in  FIG.  14 B  includes a first pair of switches  1 , a second pair of switches  2 , a third pair of switches  3 , a fourth pair of switches  4 , a first pump capacitor C 1 , and a second pump capacitor C 2 . In response to receiving an output voltage V O , the illustrated phase pump  32  produces a pump signal V clk  and its complement. 
     In operation, the phase pump  32  operates in either a first operating mode or a second operating mode. In the first operating mode, the pump signal V clk  alternates between 0 volts and V O /2 volts. In the second operating mode, the pump signal V clk  alternates between 0 volts and V O  volts. 
     Operation in the first mode requires that the phase pump  32  transition between four states according to the following switching pattern in Table 1A: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1A 
               
               
                   
                   
               
               
                   
                 State 
                 V clk   
                 1 
                 2 
                 3 
                 4 
               
               
                   
                   
               
             
            
               
                   
                 first 
                 0 V 
                 OFF 
                 ON 
                 ON 
                 OFF 
               
               
                   
                 second 
                 V O /2 
                 OFF 
                 ON 
                 OFF 
                 ON 
               
               
                   
                 third 
                 0 V 
                 OFF 
                 ON 
                 ON 
                 OFF 
               
               
                   
                 fourth 
                 V O /2 
                 ON 
                 OFF 
                 ON 
                 OFF 
               
               
                   
                   
               
            
           
         
       
     
     Operation in the second mode requires that the phase pump  32  transition between two states according to the following switching pattern in Table 1B: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1B 
               
               
                   
                   
               
               
                   
                 State 
                 V clk   
                 1 
                 2 
                 3 
                 4 
               
               
                   
                   
               
             
            
               
                   
                 first 
                 0 V 
                 OFF 
                 ON 
                 ON 
                 OFF 
               
               
                   
                 second 
                 V O   
                 ON 
                 OFF 
                 OFF 
                 ON 
               
               
                   
                   
               
            
           
         
       
     
     Switching between the first and second mode enables the phase pump  32  to change the transfer function of the cascade multiplier. For example, if the phase pump  32  in  FIG.  14 A  were implemented as shown  FIG.  14 B , then in the first mode, the transformation ratio would be 1:2 with an offset voltage V off  of 2V O  volts, but in the second mode the transformation ratio would be 1:1 with an offset voltage V off  of 3V O  volts. 
     The phase pump  32  shown in  FIG.  14 C  includes a first set of switches  1 , a second set of switches  2 , a first pump capacitor C 1 , and a second pump capacitor C 2 . In response to receiving an output voltage V O , the illustrated phase pump  32  produces a pump signal V clk  and its complement. 
     In normal operation, the phase pump  32  transitions between a first and a second state. During the first state, the switches in the first set of switches  1  are closed while those in the second set of switches  2  are opened. During the second state, the switches in the first set of switches  1  are opened while those in the second set of switches  2  are closed. 
     Unlike the phase pump  32  shown in  FIG.  14 B , which provided an alternating signal with a peak below the output voltage V O , this phase pump  32  provides an alternating signal with a peak above the output voltage V O . Since the peak voltage of the pump signal V clk  is twice that of the output voltage V O , the phase pump  32  shown in  FIG.  14 C  produces a higher transformation ratio and offset voltage V off  than a standard phase pump that uses two pairs of switches. 
     For example, if the phase pump  32  shown in  FIG.  14 A  were implemented as shown in  FIG.  14 C , the transformation ratio would be 2:1 with an offset voltage V off  of 5V O  volts compared to 1:1 with an offset voltage V off  of 3V O  volts for a standard phase pump. 
       FIG.  15 A  shows a buck converter that can be used in connection with implementing a regulating network  16 A. The buck converter is similar to that shown as configuration “A1” in the table in the appendix. 
     In  FIG.  15 A , the buck converter has an input terminal, an output terminal, and a common negative terminal. The common negative terminal is maintained at a common voltage V com . The input terminal is maintained at a first voltage V 1  that differs from the common voltage V com  by V 1  volts. The output terminal is maintained at a second voltage V 2  that differs from the common voltage by V 2  volts. 
     The buck converter includes a first switch S 1 , a second switch S 2 , an inductor L 1 , and a driver circuit  20 A. The driver circuit  20 A receives a control signal VR and outputs suitable voltages for controlling the first and second switches S 1 , S 2 . 
     It is not actually necessary for the input terminal and the output terminal to share a common negative terminal. In fact, there are six possible configurations of non-isolated regulating circuits that have two switches S 1 , S 2 , an inductor L 1 , and four terminals. Two of them are buck converters. These are shown in  FIGS.  15 B- 15 C . Two are buck-boost converters, which are shown in  FIGS.  16 A- 16 B . And the remaining two are boost converters, which are shown in  FIGS.  17 A- 17 B . If one is willing to have four switches S 1 , S 2 , S 3 , S 4 , additional possibilities emerge, two of which are shown in  FIGS.  18 A- 18 B . 
     Examples of configurations other than those described above for regulating circuits are shown in the appendix. All of the exemplary regulating circuits shown in the appendix can be used within the regulating network  16 A. 
     The buck converters shown in  FIGS.  15 B- 15 C  each have a positive input terminal and output terminal with their own respective negative terminal. For ease of discussion, voltages at each terminal of the buck converters in  FIGS.  15 B- 15 C  have been assigned names and practical values. Each buck converter has first and second switches S 1 , S 2 , an inductor L 1 , and a drive circuit  20 A. The drive circuit  20 A receives a control signal VR and, in response, outputs voltages that control the first and second switches S 1 , S 2 . The drive circuit  20 A is referenced to a ground potential (i.e., 0 V), which is the negative input terminal in  FIG.  15 B , and the negative output terminal in  FIG.  15 C . A level shifter or a boot strap circuit might be required within the driver circuit  20 A to provide appropriate voltage signals to control the first and second switches S 1 , S 2 . 
     In operation, the buck converters in  FIGS.  15 B- 15 C  transition between a first state and a second state. In the first state, the first switch S 1  is closed and the second switch S 2  is open. In the second state, the first switch S 1  is open and the second switch S 2  is closed. In a power converter that uses this regulating network  16 A, the voltage +V 2  at the positive output terminal is lower than the voltage +V 1  at the positive input terminal. 
     In the buck converter shown in  FIG.  15 B , the negative output terminal, which carries a floating voltage, −V 2 , is between two loads  18 A,  18 B. Meanwhile, the voltage +V 2  is constrained to float between +V 1  and −V 2 . In the buck converter shown in  FIG.  15 C , the negative input terminal, which carries a floating voltage, −V 1 , is coupled between two sources  14 A,  14 B. Meanwhile, the voltage +V 2  is constrained to float between +V 1  and −V 1 . 
       FIGS.  16 A- 16 B  show four-terminal buck-boost converters that are used to implement the regulating network  16 A. In  FIG.  16 A , the voltage −V 2  floats between +V 1  and +V 2 . In  FIG.  16 B , the voltage −V 1  floats between +V 1  and +V 2 . 
     Each buck-boost converter has first and second switches S 1 , S 2 , an inductor L 1 , and a driver circuit  20 A that receives a control signal VR and, in response, outputs voltage signals that control the switches S 1 , S 2 . The buck-boost converters transition between first and second states. In the first state, the first switch S 1  is closed and the second switch S 2  is open. Conversely, in the second state, the first switch S 1  is open and the second switch S 2  is closed. In a power converter that uses this regulating network  16 A, the voltage +V 2  at the positive output terminal can be higher or lower than the voltage +V 1  at the positive input terminal. 
       FIGS.  17 A- 17 B  show boost converters that are used to implement the regulating network  16 A. In the boost converter shown in  FIG.  17 A , the voltage +V 1  is between +V 2  and −V 2 . In the boost converter shown in  FIG.  17 B , the voltage +V 1  is between +V 2  and −V 1 . 
     Each boost converter features first and second switches S 1 , S 2 , an inductor L 1 , and a drive circuit  20 A that receives a control signal VR and, in response, outputs voltages suitable for driving the first and second switches S 1 , S 2 . 
     In operation, each boost converter transitions between first and second states. In the first state, the first switch S 1  is closed and the second switch S 2  is open. In contrast, in the second state, the first switch S 1  is open and the second switch S 2  is closed. In the regulating network  16 A implemented using the boost converter of  FIG.  17 A or  17 B , the voltage +V 2  at the positive output terminal is higher than the voltage +V 1  at the positive input terminal. 
     The regulating network  16 A can also be implemented using non-isolating regulating circuits that have a first switch S 1 , a second switch S 2 , a third switch S 3 , a fourth switch S 4 , an inductor L 1 , and four ports. A variety of configurations are shown in the table in the appendix. 
       FIGS.  18 A- 18 B  show two embodiments of such four-terminal non-inverting buck-boost converters, each of which can operate in buck mode or boost mode depending on the switch configuration. In buck mode, the regulator causes voltage to step down, whereas in boost mode, it causes voltage to step up. 
     When operating in buck mode, the first switch S 1  is closed and the second switch S 2  is opened. The remaining switches are then operated to transition between first and second states. In the first state, the third switch S 3  is closed and the fourth switch S 4  is open. In the second state, the third switch S 3  is open and the fourth switch S 4  is closed. In buck mode, +V 2 &lt;+V 1  while −V 2 &lt;+V 1 . 
     When operating in boost mode, the third switch S 3  is closed while the fourth switch S 4  is open. The remaining switches are then operated to transition between first and second states. In the first state, the first switch S 1  is closed and the second switch S 2  is opened. In the second state, the first switch S 1  is open and the second switch S 2  is closed. When operated in boost mode, +V 2 &gt;+V 1  while −V 2 &lt;+V 1 . 
     A converter along the lines shown in  FIGS.  18 A- 18 B  is desirable because it widens acceptable voltage limits at its terminals. However, it does so at the cost of increased component cost and size, as well as a reduction in efficiency. 
     A disadvantage of the power converters shown in  FIGS.  10 - 13    is that the offset voltage V off  is fixed to specific fraction of the output voltage V O . For example, in the power converter shown in  FIG.  10   , the offset voltage V off  is 4V O . In the power converter shown in  FIG.  13    the offset voltage V off  is 2V O . This is acceptable if the input voltage V IN  or the output voltage V O  is constrained over a narrow range. However, if the input voltage V IN  or output voltage V O  varies over a range that is wider than this narrow range, this can place the regulating network  16 A outside acceptable voltage limits associated with its specific implementation. This leads to gaps in the operating range or over voltage of the switches. 
     The power converter shown in  FIG.  19    overcomes the foregoing disadvantages. The illustrated power converter is a species of that shown in  FIG.  1    with the switching network  12 A implemented using a step-down single-phase asymmetric cascade multiplier having selection switches S 3 -S 10  and with the regulating network  16 A implemented using the regulating circuit shown in  FIG.  17 A . 
     The illustrated switching network  12 A is an example of a reconfigurable switched-capacitor network. There are many ways to implement such a reconfigurable switched-capacitor network. In fact, in principle, if one can add any number of switches, there are an infinite number of ways to implement such a reconfigurable switched-capacitor network. The regulating network  16 A includes first and second active switches  3 ,  4  and an inductor L 1 . The first and second active switches  3 ,  4  cycle between first and second states at a particular duty cycle and frequency. 
     Depending on the upon the required offset voltage V off , which is set by input voltage V IN  and output voltage V O , the offset voltage V off  can be set to a fraction of the output voltage V O  by selectively enabling and disabling the selection switches S 3 -S 10 . In particular, the state of each selection switch for the various offset voltages V off  is shown in Table 2: 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 V LX   
                 V off   
                 S3 
                 S4 
                 S5 
                 S6 
                 S7 
                 S8 
                 S9 
                 S10 
               
               
                   
               
             
            
               
                 V 1 /V 2   
                 3 V 4   
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
               
               
                 V 2 /V 3   
                 2 V 4   
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
               
               
                 V 3 /V 4   
                 1 V 4   
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
               
               
                 V 4 /gnd 
                 0 V 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
               
               
                   
               
            
           
         
       
     
     Some of the disabled switches (i.e., OFF) will see a higher voltage than the active switches in the regulating network  16 A. 
     For example, suppose V 4  equals one volt. Then V 3  equals two volts, V 2  equals three volts, and V 4  equals four volts. When operating in the mode described on the first line of Table 2, switches S 3  and S 7  are ON: switch S 6  has three volts across it and switch S 5  has two volts across it, while the active switches  3 ,  4  only have one volt across them. In general, the selection switches S 3 -S 10  will either have to have a higher voltage rating than the active switches  3 ,  4  or they will need to be implemented as cascaded low-voltage switches. 
     Another issue with this circuit is that the voltage across the selection switches S 3 -S 10  can change polarity. This poses a difficulty because a MOSFET has a parasitic diode in parallel with it, the polarity of which depends on where the body contact of the MOSFET is tied. For example, in one embodiment, the first active switch  3  of the regulating network  16 A is a MOSFET having a parasitic diode D 1  with its positive terminal connected to the inductor L 1 . As a result, the first active switch  3  can only block a voltage that is higher at the terminal on the output side of the active switch  3  than the voltage at the inductor side of the active switch  3 . Hence, the selection switches S 3 -S 10  must be able to block in both directions. One way to do this is to connect two switches back-to-back with their bodies tied such that the cathodes (negative terminals) of their corresponding parasitic diodes connect to each other. Another way to do this is to provide circuitry for changing polarity of the parasitic diode on the fly, for example by providing a body-snatcher circuit. 
     The illustrated power converter further includes a disconnect switch S 11  to protect the low voltage switches in the power converter in the event of a fault (described in U.S. Pat. No. 8,619,445). The disconnect switch S 11  must be a high-voltage switch to achieve this function. Since this switch is not routinely operated, it can be made large to reduce its resistance. However, doing so increases die cost. 
     In some practices, because a boost converter is practical only when its duty cycle is between about 5% and 95%, there will be gaps in the space of available output voltages. 
     There are at least two ways to fill these gaps. A first way is to press the disconnect switch S 11  into service as a linear regulator at the input of the regulating network  16 A. Another way is to place a linear regulator at the output of the regulating network  16 A. These both come at the cost of efficiency. Of the two, placing the linear regulator at the input is preferable because doing so impairs efficiency less than placing the linear regulator at the output. 
     In principle, it is possible to reconfigure either the regulating network  16 A or the switching network  12 A.  FIG.  20    shows a circuit in which the regulating network  16 A is configured to accept or produce, depending upon direction of power transfer, voltages V 1 -V 4 . In operation, the regulating network  16 A regulates at least one wire. However, in some embodiments, the regulating network  16 A regulates more than one wire. In those embodiments in which the regulating network  16 A regulates more than one wire, it does so depending upon the value of the input voltage V IN . For example, if the input voltage V IN  is low, the regulating network  16 A will regulate V 3 . If the input voltage V IN  is high the regulating network  16 A will regulate V 1 . This regulating network  16 A reconfigures instead of the switching network  12 A. 
     Instead of using a series of selection switches to present different voltages to a regulating network  16 A with two output ports, as shown  FIG.  19   , it is also quite possible to use a regulating network  16 A with more than two output ports.  FIG.  21    shows a power converter having such a configuration. 
     The power converter shown in  FIG.  21    includes both a reconfigurable switching network  12 A and a reconfigurable switching regulating network  16 A. Reconfiguration is carried in both cases by reconfiguration switches. These reconfiguration switches are not involved in actual operation of the network. Their function is to select different tap points on the network. 
     In the power converter shown in  FIG.  21   , the reconfigurable switching network  12 A is a single-phase step-down switched-capacitor circuit. The reconfigurable regulating network  16 A is a multi-tap boost converter having active switches S 1 -S 5 , a cascode switch S 6 , an inductor L 1 , and a disconnect switch S 11 . 
     During normal operation, only two of the active switches S 1 -S 5  are opening and closing at some specific frequency. The remaining active switches are disabled. The boost converter connected to multiple taps on the switching network  12 A. This allows the boost converter to regulate the voltage difference between two dc capacitors by controlling the time ratio of the enabled active switches. Such control results in a regulated output voltage V O . Since the voltage difference between two dc capacitors is the output voltage V O , the active switches S 1 -S 5  only need to support the output voltage V O , which is low voltage. In the illustrated examples, each active switch S 1 -S 5  only has to support one volt. However, the disabled switches would normally have to see a higher voltage. Selection switches S 6 -S 10  within the switching network  12 A block this voltage, thereby sparing the disabled active switches from having to endure it. 
     Table 3 below shows the proper configuration of the switches to achieve a particular LX signal V LX . 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 V LX   
                 S1 
                 S2 
                 S3 
                 S4 
                 S5 
                 S6 
                 S7 
                 S8 
                 S9 
                 S10 
               
               
                   
               
             
            
               
                 V 1 /V 2   
                 3 
                 4 
                 OFF 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 ON 
                 OFF 
                 OFF 
               
               
                 V 2 /V 3   
                 OFF 
                 3 
                 4 
                 OFF 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 ON 
                 OFF 
               
               
                 V 3 /V 0   
                 OFF 
                 OFF 
                 3 
                 4 
                 OFF 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 ON 
               
               
                 V 0 /gnd 
                 OFF 
                 OFF 
                 OFF 
                 3 
                 4 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
               
               
                   
               
            
           
         
       
     
     The disconnect switch S 11  is rated to handle the highest voltage. Its function is to disconnect the input from the output. However, it can also be used during startup, during a power to ground short, and to function as a linear regulator in the manner already discussed in connection with  FIG.  19   . 
     The power converter of  FIG.  21    has the same number of switches as that shown in  FIG.  19   . However, it has fewer high-voltage switches. In particular, the power converter shown in  FIG.  19    has eight high-voltage switches, whereas the power converter in  FIG.  21    has only five. On the other hand, the power converter shown in  FIG.  19    has only two active switches instead of five for the power converter of  FIG.  21   . This means that the power converter shown in  FIG.  19    requires smaller gate drivers and fewer level shifters. 
     In both cases, selection switches must be able to block in both directions. Thus, both the power converter of  FIG.  19    and that of  FIG.  21    include bidirectional switches or body-snatchers. 
     One disadvantage of the power converter of  FIG.  21    is that the active switches see both positive and negative polarity. This makes reconfiguring the power converter of  FIG.  21    much more difficult and costly than reconfiguring the power converter shown in  FIG.  19   . 
       FIG.  22    shows a power converter similar to that shown in  FIG.  21   , but with the exception that the switching network  12 A is implemented as a dual-phase switched-capacitor circuit instead of as a single-phase switched-capacitor circuit. In addition, both the pump capacitors C 4 -C 9  and dc capacitors C 0 -C 3  are in series. This means that their negative terminals are not pegged to a common voltage. Despite these differences, the power converters shown in  FIGS.  21 - 22    operate in a similar manner. 
     The switching network  12 A shown in  FIG.  22    has more components than that shown in  FIG.  21   . However, each dc capacitor in the dual-phase switching network  12 A shown in  FIG.  22    can have a smaller capacitance than a corresponding dc capacitor in the single-phase switching network  12 A shown in  FIG.  21   . This is because, in the single-phase switching network  12 A shown in  FIG.  21   , the dc capacitors store charge from the pump capacitors. In contrast, in the dual-phase switching network  12 A of  FIG.  22   , the dc capacitors only store charge from the boost converter during the dead-time during which the switching network  12 A is transitioning between first and second states. 
     In the power converters described thus far, adiabatic charging and discharging of capacitors in the switching network  12 A is made possible by an inductor in the regulating network  16 A. However, it is possible to separate the function of enabling adiabatic charge transfer and regulation by providing a separate magnetic filter. In  FIG.  23   , the power converter of  FIG.  1    is modified to include a magnetic filter between the load  18 A and the switching network  12 A. In  FIG.  24   , the power converter of  FIG.  1    is modified to include a magnetic filter between the power source  14  and the switching network  12 A. 
     It is also possible to incorporate a magnetic filter into the power converters shown in  FIGS.  5 - 6   . In fact, as the duty cycle of the second regulating network  16 B shown in  FIG.  5    approaches 100%, the second regulating network  16 B effectively becomes a magnetic filter. For a regulating network  12 A implemented as shown in  FIG.  15 C , the second regulating network  16 B can be transformed into a magnetic filter by permanently closing the first switch S 1  and opening the second switch S 2 . 
     In some embodiments, the regulating network  16 B participates in enabling adiabatic charge transfer even when a magnetic filter is present. For example, the magnetic filter may cause a first capacitor to charge adiabatically while the regulating network  16 A causes the same first capacitor to discharge adiabatically, or vice versa. 
       FIG.  25    shows the power converter of  FIG.  22    modified to include a magnetic filter between the switching network  12 A and the load  18 A. The illustrated magnetic filter comprises an inductor L 2  and a capacitor C 0 . As described in  FIGS.  23 - 24   , the presence of a magnetic filter provides for adiabatic charging or discharging of capacitors in the switching network  12 A. The magnetic filter constrains the flow of current at the output of the switching network  12 A thereby reducing the redistribution current among the capacitors in the switching network  12 A, and hence loss arising from such redistribution. 
     The use of a magnetic filter provides another way to span the gap that arises when, in order to meet a voltage requirement, a regulating network  16 A would have to operate at a duty cycle outside its permissible range of duty cycles. In embodiments without a magnetic filter, these gaps were filled by using a switch as a linear regulator. However, linear regulators are inefficient. 
     When a magnetic filter is made available, one can avoid using an inefficient linear regulator to span the gap by chopping the output of the switching network  12 A and passing it through the magnetic filter to produce a dc output. In some embodiments, switches in the switching network  12 A carry out the chopping. In other embodiments, an additional switch S 12  can be added to aid in chopping. Note that elements shown connected with dotted lines are optional. In those embodiments in which a buck-boost converter implements the regulating network  16 A, neither a linear regulator nor voltage chopping at the switching network  12 A is required. 
     Table 4 below summarizes operation of two embodiments, one with and one without an additional switch S 12 . Option 1 of the table shows how the switches in the switching network  12 A transition between first and second states to carry out chopping. Option 2 shows how the use of the additional switch S 12  effectively adds a third state between the first and second states. A benefit of Option 2 is that it avoids having two series-connected switches conduct, thus reducing losses. In addition, Option 2 provides for a body diode that can conduct when the switching network  12 A is transiting between states. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 State 3 
                 1A 
                 2A 
                 1B 
                 2B 
                 1 
                 2 
                 S12 
               
               
                   
               
             
            
               
                 OPTION 1 
                 ON 
                 ON 
                 ON 
                 ON 
                 OFF 
                 OFF 
                 — 
               
               
                 OPTION 2 
                 OFF 
                 OFF 
                 OFF 
                 OFF 
                 OFF 
                 OFF 
                 ON 
               
               
                   
               
            
           
         
       
     
       FIG.  26    shows a power converter that uses a two-phase step-down switching network  12 A connected in series with a step-down regulating network  16 A to limit an output voltage V O  to be between two volts and four volts. The switching network  12 A can be of any type. However, a good choice is a cascade multiplier in part because the regulating network  16 A will then permit adiabatic charge transfer between capacitors in the switching network  12 A. A buck converter having first and second switches  3 ,  4 , an inductor L 1 , and a capacitor C 1  implement the regulating network  16 A. 
     During normal operation the regulating network  16 A alternates between a first and second state at a specific frequency and duty cycle, with the duty cycle determining the transformation ratio. During the first state, the first switch  3  closes and the second switch  4  opens. During the first switch  3  opens and the second switch  4  closes. 
       FIG.  27    shows a power converter similar to that shown in  FIG.  19   , but with a wide output voltage V O  range instead of a wide input voltage V IN  range. Unlike the power converter in  FIG.  19   , the power converter of  FIG.  27    has a regulating network  16 A that causes voltage to step down instead of to step up. In addition, the order of the switching network  12 A and the regulating network  16 A are opposite to that shown in  FIG.  19   . The resulting configuration enables adiabatic charge transfer between at least some capacitors in the switching network  12 A. 
     Operation of the power converter in  FIG.  27    proceeds along the lines set forth in connection with  FIG.  19   . In particular, a controller controls the switches according to the timing pattern in Table 2. 
     Another way to obtain a wide voltage range is to use a step-down switching network  12 A and to implement the regulating network  16 A with a buck converter with multiple taps, as shown in  FIG.  28   . The switching network  12 A takes an input voltage V IN  and provides two voltage rails: a first rail at two volts and a second rail at four volts. The buck converter features two modes of operation: a first mode in which the LX signal V LX  alternates between zero volts and two volts during a switching cycle, and a second mode in which the LX signal V LE  alternates between two volts and four volts in a switching cycle. The timing pattern for the switches is set forth in Table 5, with switches labeled “ON” being closed during the complete switching cycle and the switches labeled “OFF” being open during the complete switching cycle. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 V LX   
                 1A 
                 2A 
                 1B 
                 2B 
                 1C 
                 2C 
               
               
                   
                   
               
             
            
               
                   
                 0 V/2 V 
                 3 
                 4 
                 ON 
                 OFF 
                 ON 
                 OFF 
               
               
                   
                 2 V/4 V 
                 ON 
                 OFF 
                 3 
                 4 
                 OFF 
                 ON 
               
               
                   
                   
               
            
           
         
       
     
     An advantage of the power converter shown in  FIG.  28    is that each switch only has to support two volts. In addition, the switches are configured to avoid the need for body-snatcher circuitry. Switches  1 B and  2 A in particular have body diodes that point to each other and therefore block voltages with any polarity. 
     To obtain an even wider output range than that given by the power converter shown in  FIG.  28   , though at the cost of more switches, one can implement the regulating network  16 A with a buck converter having three, rather than two, modes of operation. Otherwise, operation is similar to that described in connection with  FIG.  28   . 
     In  FIG.  29   , the switching network  12 A maintains three voltage rails at two volts, four volts, and six volts, respectively. In the first operating modes, the LX signal V LX  alternates between zero volts and two volts during a switching cycle. In the second operating mode, the LX signal V LX  alternates between two volts and four volts during a switching cycle. In the third operating mode, the LX signal V LX  alternates between four volts and six volts during a switching cycle. 
     The timing diagram for the three operating modes is shown in Table 6: 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 V LX   
                 1A 
                 2A 
                 1B 
                 2B 
                 1C 
                 2C 
                 1D 
                 2D 
               
               
                   
               
             
            
               
                 0 V/2 V 
                 3 
                 4 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
               
               
                 2 V/4 V 
                 ON 
                 OFF 
                 3 
                 4 
                 ON 
                 OFF 
                 OFF 
                 OFF 
               
               
                 4 V/6 V 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 3 
                 4 
                 OFF 
                 ON 
               
               
                   
               
            
           
         
       
     
     Switches labeled “ON” in Table 6 are closed during the complete switching cycle. Switches labeled “OFF” are open during the complete switching cycle. As is apparent, each switch only has to support at most two volts. In addition, the switches are properly configured such that body snatcher circuits are not required. In particular, switch pair  1 B,  2 A and switch pair  1 C,  2 B show two body diodes pointing at each other. These switch pairs can therefore block voltages of any polarity. 
       FIG.  30    shows the power converter of  FIG.  26    with a two-phase switched-capacitor circuit implementing the switching network  12 A and a buck converter implementing the regulating network  16 A. 
     The buck converter, which has two modes of operation, alternates between the switch configurations shown in Table 5. In the first mode, the LX signal V LX  alternates between zero volts and two volts during a switching cycle. In the second mode, the LX signal V LX  alternates between two volts and four volts during a switching cycle. The switches labeled “ON” are closed during the complete switching cycle and the switches labeled “OFF” are open during the complete switching cycle. Each switch only needs to be able support two volts. During normal operation the switching network  12 A alternates between the first and second states at a specific frequency and duty cycle. In some embodiments, the duty cycle is 50%. 
       FIG.  31    shows a power converter with first and second regulators in parallel. This provides first and second outputs. In the particular example shown, the first output V O1  is between four volts and two volts while the second output V O2  is between two volts and zero volts. 
     The first regulator includes first and second switches  3 ,  4  and a first inductor L 1 . The second regulator includes third and fourth switches  5 ,  6  and a second inductor L 2 . 
     During normal operation the first regulator alternates between a first and second state at a specific frequency and duty cycle. This duty cycle determines the transformation ratio. During the first state, the first switch  3  is closed and the second switch  4  is opened. During the second state, the states are reversed. The second regulator works in the same way with the third switch  5  replacing the first switch  3  and the fourth switch  6  replacing the second switch  4 . The switching network  12 A, the first regulator, and the second regulator can operate at the same or difference frequency and with any phase difference between them. 
       FIG.  32    shows another embodiment with multiple output voltages. In this case, there are three regulating networks  16 A,  16 B,  16 C corresponding to three output voltages, V O1 , V O2 , and V O3 . Unlike the power converter shown in  FIG.  31   , these voltages are less limited on the bottom end. 
       FIG.  33    shows a power converter in which a switching network  12 A in series with a regulating network  16 A are floated above ground. The voltage upon which the switching network  12 A and regulating network  16 A float comes from a third stage. This third stage can be implemented using a switch-mode power converter such as a buck converter or switched-capacitor converter such as a cascade multiplier, or any other type of power converter. The resulting series connected stages to provide a higher output voltage than they normally would be able to. Example voltages are provided in the figure. In particular, in  FIG.  33   , the third stage produces a two-volt rail. This effectively boosts the output voltage V O  by two volts. 
     An advantage of the configuration shown in  FIG.  33    is that only low voltages have to be applied across the terminals of the regulating network  16 A. Thus, only low-voltage transistors are needed. These switch very fast. As a result, one can reduce the size of the inductor. 
       FIGS.  34 - 44    show additional embodiments with particular features to be described below. With the exception of a brief dead-time between transitions, during which all switches are open to avoid difficulties that arise from the finite switching time of a real switch, all switches in switch set  1  and switch set  2  are always in opposite states, all switches in switch set  3  and switch set  4  are always in opposite states, and all switches in switch set  5  and switch set  6  are always in opposite states. 
       FIG.  34    shows an embodiment in which a 4-switch buck-boost converter implements the regulating network  16 A and a reconfigurable single-phase asymmetric cascade multiplier implements the switching network  12 A. In this power converter, the regulating network  16 A connects to the middle of the cascade multiplier within the switching network  12 A thereby enabling the switching network  12 A to cause voltage to either step-up or step-down. 
     The regulating network  16 A includes an inductor L 1 , a first switch  3 , a second switch  4 , a third switch  5 , and a fourth switch  6 . 
     When the regulating network  16 A operates in its boost mode, the intermediate voltage V X  is higher than the input voltage V IN . In this mode, the third switch  5  and the fourth switch  6  are active, the first switch  3  is closed, and the second switch  4  is open. 
     Conversely, when the regulating network  16 A operates in its buck mode, the intermediate voltage V X  is lower than the input voltage V IN . In this mode, the first switch  3  and the second switch  4  are active, the third switch  5  is closed, and the fourth switch  6  is open. 
     Meanwhile, the switching network  12 A includes first and second switch sets  1 ,  2 , four selection switches S 1 -S 4 , four dc capacitors C 1 -C 4 , and three pump capacitors C 5 -C 7 . The voltages on the four dc capacitors C 1 -C 4  are 4/2V X , 3/2V X , 2/2V X , and 1/2V X , respectively. 
     In operation, the four selection switches S 1 -S 4  select different dc capacitors C 1 -C 4  within the switching network  12 A for presentation to the load  18 A. By properly choreographing the enabling and disabling of the selection switches S 1 -S 4  according to a distinct pattern, one can produce an ac output with a dc offset. This is particularly useful for envelope tracking when providing power to an RF power amplifier. 
       FIG.  35    illustrates a variation on the embodiment of  FIG.  2    in which a dual-inductor buck converter implements the regulating network  16 A and a reconfigurable dual-phase asymmetric step-up cascade multiplier implements the switching network  12 A. 
     The regulating network  16 A is a dual-inductor buck converter (shown as configuration “C 1 ” in the table in the appendix) having a first inductor L 1 , a second inductor L 2 , a first capacitor C 0 , a first switch  3 , and a second switch  4 . In some embodiments, the first and second inductors L 1 , L 2  are uncoupled. In others, the first and second inductors L 1 , L 2  are coupled. These include embodiments that use both positive and negative coupling. 
     Unlike in a single-inductor buck converter, the input current into the dual-inductor converter is relatively constant. This results in lower rms current through the switching network  12 A. Both terminals connected to the switching network  12 A draw a relatively constant current. Because of this behavior, and because a pump capacitor would always be available to feed each inductor, the dual-inductor buck converter is best used with a full-wave cascade multiplier. It is also possible to use a half-wave cascade multiplier. However, in that case, the pump capacitors would only be feeding the inductors half the time. This requires providing high capacitance dc capacitors. 
     The switching network  12 A includes first and second switch sets  1 ,  2 , eight selection switches S 1 -S 8 , four dc capacitors C 1 -C 4 , and six pump capacitors C 5 -C 10 . 
     A third inductor L 3  that feeds the switching network  12 A promotes adiabatic charge transfer within the switching network  12 A. Because it is only filtering a voltage ripple on the capacitors seen at the input of the switching network  12 A, and because it does not have a particularly large voltage across it, this third inductor L 3  has a much smaller inductance than those required within the regulating network  16 A. 
     Enabling and disabling different selection switches S 1 -S 8  reconfigures the switching network  12 A, thus enabling one to change the offset voltage V off  of the switching network  12 A. Table 7 shows switching patterns used to achieve four different offset voltages. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 7 
               
               
                   
               
               
                 V off   
                 S1 
                 S2 
                 S3 
                 S4 
                 S5 
                 S6 
                 S7 
                 S8 
               
               
                   
               
             
            
               
                 3 V 4   
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
               
               
                 2 V 4   
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
               
               
                 1 V 4   
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
               
               
                 0 V 
                 OFF 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 OFF 
                 ON 
               
               
                   
               
            
           
         
       
     
     In the particular example shown, the load connected to the output of the power converter comprises a plurality of light-emitting diodes connected in series with each other and with the current path through a transistor biased by a voltage V B . This permits control over the LED current, thus enabling the brightness of the LED, which is proportional to the LED current I LED , to be controlled. The combination of a power converter and a circuit to control the LED current I LED , which amounts to a current sink, is commonly called an LED driver. In most embodiments, the current sink is somewhat more complicated than a single transistor. However, the principles illustrated in  FIG.  35    are applicable to such cases as well. 
     Instead of using a linear regulator to fill the gaps as discussed in reference to  FIG.  19   , a current sink along the lines shown in  FIG.  35    can be used. However, this is also a somewhat inefficient method. 
     In another embodiment of the power converter of  FIG.  1   , which is shown in  FIG.  36   , a two-phase boost converter implements the regulating network  16 A while a reconfigurable dual-phase asymmetric step-down cascade multiplier implements the switching network  12 A. The particular cascade multiplier shown features an embedded reconfigurable fractional charge pump  22 . 
     The two-phase boost converter includes a first inductor L 1 , a second inductor L 2 , a first switch  5 , a second switch  6 , a third switch  7  and a fourth switch  8 . A circuit  20 A within the regulating network  16 A receives control signals from a controller via a first path P 1 . During normal operation, the circuit  20 A provides first drive signals provided to the first and second switches  5 ,  6  and second drive signals to the third and fourth switches  7 ,  8 . The first and second drive signals are in phase quadrature. Controlling the duty cycle of at which the switches  4 - 8  switch regulates the output voltage V O . 
     The switching network  12 A includes six selection switches S 1 -S 6 , six pump capacitors C 5 -C 10 , four dc capacitors C 1 -C 4 , first and second switch sets  1 ,  2 , and a circuit  20 B that provides drive signals to the first and second switch sets  1 ,  2  and to the six selection switches S 1 -S 6  based on control signals received along a path P 2  from the controller. 
     The reconfigurable fractional charge pump  22  has multiple modes. In the particular example described herein, the modes are a 1:1 mode and a 3:2 mode. 
     The reconfigurable fractional charge pump  22  enables the parent cascade multiplier in which it is embedded to output half ratios. Table 8 shows the available transformation ratios (V 4 :V O ) for the parent cascade multiplier, and both the switch states and the transformation ratio of the embedded reconfigurable fractional charge pump  22  that would be required to achieve those transformation ratios. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 V 4 :V 0   
                 S1 
                 S2 
                 S3 
                 S4 
                 S5 
                 S6 
                 22 
               
               
                   
               
             
            
               
                 4.5:1.0 
                 ON 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 3:2 
               
               
                 4.0:1.0 
                 ON 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 1:1 
               
               
                 3.5:1.0 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 3:2 
               
               
                 3.0:1.0 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 1:1 
               
               
                 2.5:1.0 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 ON 
                 3:2 
               
               
                 2.0:1.0 
                 OFF 
                 OFF 
                 ON 
                 OFF 
                 OFF 
                 ON 
                 1:1 
               
               
                   
               
            
           
         
       
     
     A particular benefit of providing half ratios is that the resulting power converter operates without the gaps described in connection with  FIG.  36   . 
     For example, suppose that the output voltage V O  is one volt and that the input voltage V IN  is 3.5 volts. The transformation ratio is 4:1. This requires a duty cycle of 50%, which is well within the permissible range for the regulating circuit (i.e., the dual-phase boost converter). 
     Suppose now that the input voltage V IN , drops to 3.05 volts. At this point, the required duty cycle at the regulating circuit would drop to 5%, which is below the acceptable limit. Ordinarily, this would result in a gap. But not for the circuit shown in  FIG.  36   . This is because one only has to switch to a 3.5:1 transformation ratio. This raises the required duty cycle back up to 65%, which puts it back within the permissible range of the regulating circuit. 
     In addition, to eliminating gaps, the ability to provide half ratios enables the regulating circuit to run with a duty cycle between 25% and 75%. This has many benefits, including reducing the rms current and thus boosting the efficiency. 
       FIG.  37    shows details of the reconfigurable fractional charge pump  22  shown in  FIG.  36   . The reconfigurable charge pump  22  includes a first switch set  3 , a second switch set  4 , a selection switch S 0 , a dc capacitor C 1 , and first and second pump capacitors C 2 , C 3 . The reconfigurable fractional charge pump  22  is connected to have an input voltage V 1 , an output voltage V 2 , and a ground V 3 . 
     The reconfigurable fractional charge pump  22  operates in either a first mode or a second mode. When operating in the first mode, the reconfigurable fractional charge pump  22  provides a transformation ratio V 1 :V 2  of 3:2. When operating in the second mode, the transformation ratio is 1:1. 
     To operate in the first mode, the selection switch S 0  opens, and the first and second switch sets  3 ,  4  switch open and close at some specific frequency. In some embodiments, the switches open and close with a 50% duty cycle. The first switch set  3  and the second switch set  4  are always in opposite states. 
     To operate in the second mode, the selection switch S 0  closes, and the first and second switch sets  3 ,  4  open. 
       FIGS.  38 - 39    show alternative embodiments of the power converter shown in  FIG.  6    in which a regulating network  16 A is between first and second switching networks  12 A,  12 B. This configuration enables at least one switching network  12 A,  12 B to be adiabatically charged. In addition, the overall transformation ratio becomes the product of the transformation ratios of the first and second switching networks  12 A,  12 B. 
     In the embodiment shown in  FIG.  38   , a buck converter implements the regulating network  16 A, a single-phase asymmetric step-up cascade multiplier implements the first switching network  16 A, and a single-phase symmetric step-up cascade multiplier implements the second switching network  16 B. 
     The first switching network  12 A includes four dc capacitors C 1 -C 4 , three pump capacitors C 5 -C 7 , and first and second switches  1 ,  2 . In the configuration shown, the first switching network  12 A is not adiabatically charged. Hence, it operates with a duty cycle of near 50%. However this is not required because stability is not an issue. In operation, the first switching network  12 A provides a first voltage V 1  that is four times the input voltage V IN . However, the intermediate voltage V X  that the regulating network  16 A receives from the first switching network  12 A is twice the input voltage V IN . 
     The regulating network  16 A includes a first switch  5 , a second switch  6 , and an inductor L 1 . The regulating network  16 A controls the duty cycle of the first and second switches  5 ,  6  to regulate its output voltage V O . 
     The second switching network  12 B includes first and second switch sets  3 ,  4 , two dc capacitors C 11 -C 12 , and three pump capacitors C 8 -C 10 . Unlike the first switching network  12 A, there is an inductor L 1  that feeds the second switching network  12 B. As a result, the second switching network  12 B is adiabatically charged. 
     A dc capacitor C 12  connected at the output of the regulating network  16 A impedes adiabatic operation and is thus optional. This dc capacitor C 12  is typically added only to maintain stability. As a result, its capacitance is much smaller than that of other capacitors in the network. 
     Since the second switching network  12 B is adiabatically charged and its transformation ratio is 1:4, operating it at a duty cycle of 50% promotes stability. The overall output voltage V O  of the power converter is given by V O =8V IN (D+1), where the duty cycle D is equal to the duty cycle D of the second switch  6  of the regulating network  16 A. 
       FIG.  39    shows a power converter similar to that shown in  FIG.  38   , except that a buck-boost converter implements the regulating network  16 A and that the first and second switching networks  12 A,  12 B connect to the regulating network  16 A differently. The result is a different input-to-output transfer function. 
     The regulating network  16 A includes an inductor L 1 , a first switch  5 , and a second switch  6 . 
     The first and second switching networks  12 A,  12 B are the same as those shown in  FIG.  38   . As was the case in  FIG.  38   , the second switching network  12 B is adiabatically charged, albeit from a different node. The second switching network  12 B includes first and second dc capacitors C 12 , C 13  that connect to an output of the regulating network  16 A. These capacitors impede adiabatic operation, and are thus optional. However, they are often useful for maintaining stability. Preferably, the values of their capacitances are much smaller than those used in other capacitors within the first and second switching networks  12 A,  12 B. 
     The differences between the power converter in  FIG.  39    and that in  FIG.  38    enable the power converter shown in  FIG.  39    to have an output voltage V O  that is either positive or negative. Specifically, for a given duty cycle D, of the regulating network&#39;s second switch  6 , the output voltage V O  is given by where V O =V IN (20D)/(2D−1). Thus, the output voltage V O  is positive when the duty cycle D exceeds 0.5 and negative when the duty cycle D falls short of 0.5. 
       FIGS.  40 - 43    show embodiments of the power converter shown in  FIG.  5   . Each embodiment features a first regulating network  16 A and a second regulating network  16 B. In each embodiment, controlling the duty cycle D of the switches in both the first and second regulating networks  16 A,  16 B permits control over the output voltage V O  of the power converter. Additionally, in each embodiment, an inductor present in the regulating network  16 A permits adiabatic charge transfer between capacitors in the switching network  12 A. The extent of this adiabatic charge transfer is one of the differences among the different configurations shown in  FIGS.  40 - 43   . 
     In the embodiments shown, the first regulating network  16 A is implemented as a step-up converter while the second regulating network  16 B is implemented as a step-down converter. However, this does not have to be the case. For example, the order could be reversed, with the first regulating network  16 A causing a step-down in voltage, and the second regulating network  16 B causing a step-up in voltage. Or, both the first and second regulating networks  16 A,  16 B could cause a step-up or a step-down in voltage. An advantage of the particular configuration shown in the figures is that if the switching network  12 A were a reconfigurable switching network, such as that shown in  FIG.  19   , the illustrated configuration would permit filling-in the gaps in coverage. 
     The illustrated embodiments feature a controller to control operation of switches in the first and second regulating networks  16 A,  16 B. Such a controller can be used to implement a variety of control techniques that can be used in connection with controlling the operation of the first and second regulating networks  16 A,  16 B. In some embodiments, the controller implements feed-forward control over the first regulating network  16 A and feedback control over the second regulating network  16 B. In other embodiments, the controller implements feedback over the first regulating network  16 A and feed-forward control over the second regulating network  16 B. 
     In the embodiment shown in  FIG.  40   , the first regulating network  16 A is a boost converter and the second regulating network  16 B is a buck converter. The boost converter has a boost-converter inductor L 1  and first and second boost-converter switches  3 ,  4 . The buck converter has a buck-converter inductor L 2  and first and second buck-converter switches  5 ,  6 . 
     The switching network  12 A includes first and second switch sets  1 ,  2 , three dc capacitors C 1 -C 3 , and six pump capacitors C 4 -C 9  spread across two symmetric step-up cascade-multipliers. The two cascade multipliers share a common phase pump and operate 180 degrees out of phase. The operation of this switching network  12 A is similar to that of a dual-phase version, or full-wave, cascade multiplier. The main distinction arises from separation of the bottom and top of the switch stacks. 
     Because the stack switches are separate, it is possible to create an intermediate voltage V X3  that is a difference between the voltages present at the tops of the switch stacks. In the embodiment shown, the voltage at the top of a first switch stack is 4V X , whereas the voltage at the top of a second switch stack is 3V X +V IN . Thus, the intermediate voltage V X3  is the difference between these, which is V X −V IN . 
     In the embodiment shown in  FIG.  41   , the first regulating network  16 A is a three-level boost converter and the second regulating network  16 B is a buck converter. The boost converter has a boost-converter inductor L 1 , four switches  3 ,  4 ,  5 ,  6 , and a capacitor C 13 . The buck converter has a buck-converter inductor L 2  and first and second buck-converter switches  7 ,  8 . 
       FIG.  41    shows a power converter similar to that shown in  FIG.  40   , but with the first regulating network  16 A being a three-level boost converter. The three-level boost converter requires less inductance for the same amount of filtering compared to the boost converter shown in  FIG.  40   . In addition, it operates with a reduced voltage stress across its switches. However, it also has many more switches and an additional capacitor. The second regulating network  16 B is again a buck converter like that shown in  FIG.  40   . 
     The switching network  12 A includes first and second switch sets  1 ,  2 , three dc capacitors C 1 -C 3 , and nine pump capacitors C 4 -C 12  spread across two symmetric step-up cascade-multipliers. The two cascade multipliers share a common phase pump and operate 180 degrees out of phase. Unlike the switching network  12 A shown in  FIG.  40   , the two cascade multipliers in  FIG.  41    have different numbers of stages. Thus, asymmetry in the number of stages results in a third intermediate voltage V X3  presented to the second regulating network  16 B. In particular, the third intermediate voltage, which is 2V X , is a difference between a first voltage V 1 , which is equal to 6V X , and a second voltage V 2 , which is equal to 4V X . 
     In operation, the three-level boost converter operates in two modes. In each mode, the boost converter cycles through first, second, third, and fourth states at a particular frequency. Each state corresponds to a particular configuration of switches. Table 9A shows the four states in the first mode, and Table 9B shows the four states in the second mode. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 9A 
               
               
                   
                   
               
               
                   
                 State 
                 V LX   
                 3 
                 4 
                 5 
                 6 
               
               
                   
                   
               
             
            
               
                   
                 first 
                 V X   
                 ON 
                 OFF 
                 ON 
                 OFF 
               
               
                   
                 second 
                 V X /2 
                 OFF 
                 ON 
                 ON 
                 OFF 
               
               
                   
                 third 
                 V X   
                 ON 
                 OFF 
                 ON 
                 OFF 
               
               
                   
                 fourth 
                 V X /2 
                 ON 
                 OFF 
                 OFF 
                 ON 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 9B 
               
               
                   
                   
               
               
                   
                 State 
                 V LX   
                 3 
                 4 
                 5 
                 6 
               
               
                   
                   
               
             
            
               
                   
                 first 
                 0 V 
                 OFF 
                 ON 
                 OFF 
                 ON 
               
               
                   
                 second 
                 V X /2 
                 OFF 
                 ON 
                 ON 
                 OFF 
               
               
                   
                 third 
                 0 V 
                 OFF 
                 ON 
                 OFF 
                 ON 
               
               
                   
                 fourth 
                 V X /2 
                 ON 
                 OFF 
                 OFF 
                 ON 
               
               
                   
                   
               
            
           
         
       
     
     Within each mode, the three-level boost converter regulates its output by controlling its generalized duty cycle. The generalized duty cycle is equal to a first time interval divided by a second time interval. The first time interval is equal to the amount of time the three-level boost converter spends in either the first state or the third state. The second time interval is the amount of time the three-level boost converter spends in either the second state or the fourth state. 
     When the three-level buck converter operates in the first mode, the intermediate voltage V X  is greater than two times the input voltage V IN . In contrast, when the three-level buck converter operates in the second mode, the intermediate voltage V X  is less than two times the input voltage V IN . 
     An advantage over the power converter shown in  FIG.  41    over that shown in  FIG.  40    is that it is less complex. In addition, losses resulting from charge redistribution within the switching network  12 A will be reduced because the capacitors within the switching network  12 A will enjoy the benefits of adiabatic charge transfer. 
     The power converter of  FIG.  42    combines features of those shown in  FIGS.  40 - 41   . As was the case in the power converter shown in  FIG.  40   , the switching network  12 A receives both the input voltage V IN  and the first intermediate voltage V X  to produce a third intermediate voltage V X3 . However, like  FIG.  41   , the number of stages is unequal, with the asymmetry producing the third intermediate voltage V X3 . 
     In the switching network  12 A shown in  FIG.  42   , the first regulating network  16 A no longer drives the phase pump, as was the case in  FIGS.  40 - 41   . Thus, the phase pump no longer enjoys the benefit of adiabatic charge transfer resulting from the intervention of the inductor L 1  in the first regulating network  16 A. To make up for this, the switching network  12 A has an additional inductor L 3  that promotes adiabatic charge transfer. 
     In operation, a first voltage V 1  is equal to V X +5V IN , a second voltage V 2  is equal to V X +3V IN , and a third intermediate voltage V X3  is equal to 2V IN . 
     An advantage of the power converter shown in  FIG.  42    over that shown in  FIG.  41    is that only a fraction of the input current actually passes through the three-level boost converter. The bulk of the current instead bypasses the three-level boost converter and proceeds directly into the phase pump. 
     Additionally, since the additional inductor L 3  only has to promote adiabatic charge transfer, it can have a smaller inductance that the inductor L 1  in the boost converter. This, in turn, reduces resistive inductor losses. 
     However, a disadvantage of the power converter shown in  FIG.  42    is that an additional inductor L 3  is required. In addition, the cascade multiplier requires more stages to achieve the same voltage gain. For example, the first voltage V 1  is equal to 6V X  in  FIG.  41    while it is equal to V X +5V IN  in the circuit shown in  FIG.  42   . 
       FIG.  43    shows a power converter in which a boost converter implements the first regulating network  16 A, a buck converter implements the second regulating network  16 B, and a dual-phase asymmetric step-up cascade multiple implements the switching network  12 A. 
     The first regulating network  16 A includes a first switch  3 , a second switch  4 , and an inductor L 1 . The second regulating network  16 B includes a first switch  5 , a second switch  6 , and an inductor L 2 . The switching network  12 A includes a first switch set  1 , a second switch set  2 , four dc capacitors C 1 -C 4 , and six pump capacitors C 5 -C 10 . 
     In the power converter shown in  FIG.  43   , only the switching network  12 A is connected to ground. The first and second regulating networks  16 A,  16 B both float. This reduces the voltage stress across the switches in the first and second regulating networks  16 A,  16 B. Unfortunately, this also narrows the acceptable input voltage V IN  range and output voltage V O  range. This disadvantage can be overcome by using a reconfigurable switching network  12 A, but at the added cost of more switches. 
       FIG.  44    shows a particular implementation of the power converter in  FIG.  2    in which a reconfigurable dual-phase symmetric step-up cascade multiplier implements the switching network  12 A and a Zeta converter implements the regulating network  16 A. 
     The regulating network  16 A includes a first inductor L 3 , a second inductor L 4 , a capacitor C 10 , a first switch  3 , and a second switch  4 . Depending upon the duty cycle, a Zeta converter can step-up or step-down the voltage. However, a disadvantage of the Zeta converter is the requirement for more passive components. In addition, a Zeta converter is more difficult to stabilize because of the additional poles and zero introduced. 
     The switching network  12 A includes first and second switch sets  1 ,  2 ; two selection switches S 1 -S 2 , three dc capacitors C 1 -C 3 , six pump capacitors C 4 -C 9 , a first inductor L 1 , and a second inductor L 2 . 
     In operation, the switching network  12 A transitions between a first mode and a second mode. During the first mode, the first selections switch S 1  is closed and the second selection switch S 2  is open. The intermediate voltage V X  is then V IN /2. During the second mode, the first selection switch S 1  is open and the second selection switch S 2  is closed. In the second mode, the intermediate voltage V X  becomes the input voltage V 1h . 
     One way to achieve adiabatic inter-capacitor charge transfer within the switching network  12 A is to place a small inductor in series with the second switch S 2 . However, although this would promote adiabatic charge transfer during the first mode, it would not do so during the second mode. 
     Another way to achieve adiabatic inter-capacitor charge transfer within the switching network  12 A is to embed the first inductor L 1  within the charge pump and the second inductor L 2  in series with the ground terminal of the charge pump. 
     Preferably the first inductor L 1  is embedded at a location that carries a constant current and that connects to charging and discharging paths of as many pump capacitors C 4 -C 9  as possible. A suitable location is therefore at the phase pump. 
     A charge pump typically has two nodes that carry constant current. As shown in  FIG.  44   , the first inductor L 1  is at one of these nodes and the second inductor L 2  is at the other. However, only one of these inductors is actually required to promote adiabatic charge transfer.