Abstract:
Cycle timing of a charge pump is adapted according to monitoring of operating characteristics of a charge pump and/or peripheral elements coupled to the charge pump. In some examples, this adaptation provides maximum or near maximum cycle times while avoiding violation of predefine constraints (e.g., operating limits) in the charge pump and/or peripheral elements.

Description:
FIELD OF INVENTION 
     This invention relates to control of timing of a charge pump. 
     BACKGROUND 
     Various configurations of charge pumps, including Series-Parallel and Dickson configurations, rely of alternating configurations of switch elements to propagate charge and transfer energy between the terminals of the charge pump. Energy losses are associated with propagation determine the efficiency of the converter. 
     Referring to  FIG. 1 , a single phase Dickson charge pump  100  is illustrated in a step-down mode coupled to a low voltage load  110  and high voltage source  190 . In the illustrated configuration, generally the load is driven (on average) by a voltage that is ⅕ times the voltage provided by the source and a current that is 5 times the current provided by the source. The pump is driven in alternating cycles, referred to as cycle 1 and cycle 2, such that the switches illustrated in  FIG. 1  are closed in the indicated cycles. In general, the duration of each cycle is denoted T and the corresponding switching frequency F=½T. 
       FIGS. 2A-B  illustrate the equivalent circuit in each of cycles 2 and 1, respectively, illustrating each closed switch as an equivalent resistance R. Each of the capacitors C 1  through C 4  has equal capacitance C. In a first conventional operation of the charge pump, the high voltage source is a voltage source, for example, a v in =25 volt source, such that the load is driven by v out =5 volts. In operation the voltage across capacitors C 1  through C 4  are approximately 5 volts, 10 volts, 15 volts, and 20 volts, respectively. 
     One source of energy loss in the charge pump relates the resistive losses through the switches (i.e., through the resistors R in  FIGS. 2A-B ). Referring to  FIG. 2A , during cycle 2, charge transfers from capacitor C 2  to capacitor C 1  and from C 4  to C 1 . The voltages on these pairs of capacitors equilibrate assuming that the cycle time T is sufficiently greater than the time constant of the circuit (e.g., that the resistances R are sufficiently small. Generally, the resistive energy losses in this equilibration are proportional to the time average of the square of the current passing between the capacitors and therefore passing to the load  110 . Similarly, during cycle 1, capacitors C 3  and C 2  equilibrate, capacitor C 4  charges, and capacitor C 1  discharges, also generally resulting in a resistive energy loss that is proportional to the time average of the square of the current passing to the load  110 . 
     For a particular average current passing to the load  110 , assuming that the load presents an approximately constant voltage, it can be shown than the resistive energy loss decreases as the cycle time T is reduced (i.e., switching frequency is increased). This can generally be understood by considering the impact of dividing the cycle time by one half, which generally reduces the peak currents in the equilibration by one half, and thereby approximately reduces the resistive energy loss to one quarter. So the resistive energy loss is approximately inversely proportional to the square of the switching frequency. 
     However, another source of energy loss relates to capacitive losses in the switches, such that energy loss grows with the switching frequency. Generally, a fixed amount of charge is lost with each cycle transition, which can be considered to form a current that is proportional to the switching frequency. So this capacitive energy loss is approximately proportional to the square of the switching frequency. 
     Therefore, with a voltage source and load there an optimal switching frequency that minimizes the sum of the resistive and capacitive energy losses, respectively reduced with increased frequency and increased with increased frequency. 
     SUMMARY 
     In one aspect, in general, cycle timing of a charge pump is adapted according to monitoring of operating characteristics of a charge pump and/or peripheral elements coupled to the charge pump. In some examples, this adaptation provides maximum or near maximum cycle times while avoiding violation of predefine constraints (e.g., operating limits) in the charge pump and/or peripheral elements. 
     In another aspect, in general, an apparatus has a charge pump having a plurality of switch elements arranged to operate in a plurality cycles. These cycles switch according to a timing pattern. Each cycle is associated with a different configuration of the switch elements, with the switch elements being configured to provide charging and discharging paths for a plurality of capacitive elements. A controller is coupled to the charge pump with an output for controlling the timing pattern of the switching of the cycles of the charge pump and one or more sensor inputs for accepting sensor signals charactering operation of the charge pump and/or operation of peripheral circuits coupled to the charge pump. The controller is configured adjust the timing pattern of the cycles of the charge pump according variation of the one or more sensor inputs within cycles of operation of the charge pump. 
     Aspects may include one or more of the following features. 
     The controller is configured to adjust the timing pattern of the switching of the cycles of the charge pump by adjusting a cycles switching frequency of the charge pump. 
     The controller is configured to adjust the timing pattern of the switching of the cycles of the charge pump by determining a switching time to end each successive cycle according to variation of the or more sensor inputs during said cycle. 
     The one or more sensor inputs comprise an output voltage sensor input representing an output voltage of the charge pump, and wherein the controller is configured to adjust the timing pattern according to variation of the output voltage sensor input. 
     The controller is configured to adjust the timing pattern to maintain the variation of the output voltage with a desired range, for instance, the desired range comprises a fixed range. 
     The desired range comprises a range dependent on a second sensor input of the controller. 
     The second sensor input represents an output voltage of a regulator coupled to the output of the charge pump, and the controller is configured to adjust the timing pattern to maintain a desired voltage margin between the output of the charge pump and the output of the regulator. 
     The one or more sensor inputs comprise a regulator sensor input representing operating characteristic of a regulator coupled to the output of the charge pump. 
     The regulator sensor input represents an output voltage of the regulator. 
     The regulator sensor input represents a duty cycle of switching operation of the regulator. 
     The one or more sensor inputs comprise an internal sensor input representing an internal signal of the charge pump. 
     The internal signal comprises a voltage across a device in the charge pump, and wherein the controller is configured to adjust the timing to maintain the voltage across the device within a predetermined range. 
     The charge pump comprises a Dickson charge pump. 
     Advantages of one or more aspects can include providing efficient power conversion while maintaining voltages and/or currents within desired operating ranges. For example, switching frequency may be reduced while still maintaining internal voltages or currents across circuit elements (e.g., voltages across transistors or capacitors) within desired ranges for those elements. 
     Other features and advantages of the invention are apparent from the following description, and from the claims. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a single-phase 1:5 Dickson charge pump; 
         FIGS. 2A-B  are equivalent circuits of the charge pump of  FIG. 1  in two states of operation; 
         FIGS. 3 and 4  are circuits having a switchable compensating circuit coupled to the charge pump; 
         FIG. 5  is a circuit for measuring a charge pump current; 
         FIG. 6  is a schematic illustrating charge transfer during one cycle of the charge pump illustrated in  FIG. 4 ; 
         FIGS. 7A-C  are graphs of output voltage of the charge pump illustrated in  FIG. 4  at different output current and switching frequency conditions; and 
         FIG. 8  is a single-phase series-parallel charge pump. 
     
    
    
     DESCRIPTION 
     As introduced above, as one example, a charge pump  100  illustrated in  FIG. 1  may be operated in an “adiabatic” mode in which one or both of a low-voltage peripheral  110  and a high-voltage peripheral  190  may comprise a current source. For example, Patent Publication WO 2012/151466, published on Nov. 8, 2012, and incorporated herein by reference, describes configurations in which the source and/or load comprise regulating circuits. In particular, in  FIGS. 1 and 2A -B, the low-voltage load  110  can effectively comprise a current source rather than a voltage source in an example of what is referred to as “adiabatic” operation of a charge pump. If the current source maintains a constant current from the charge pump, then currents illustrated in  FIG. 2A  maintain substantially constant values during the illustrated state. Therefore, the resistive losses in the switches through which the current passes are lower than the resistive loss in the voltage load case, and also substantially independent of the switching frequency and the cycle time T. As in the voltage driven case, there capacitive losses in the switches grow with increasing switching frequency, which suggests that lowering the switching frequency is desirable. However, other factors, which may depend on internal aspects of the charge pump, voltage or current characteristics at the terminals of the charge pump, and/or internal aspects of the peripheral elements, such as the source and/or load, may limit the cycle time (e.g., impose a lower limit on the switching frequency). 
     Referring to  FIG. 3 , in a first mode of operation, a load  320  can be considered to comprise a constant current source  312  with an output current IO. In some implementations, the load  320  also includes an output capacitor, which for the analysis below can be considered to be small enough such that current passing to the load  320  can be considered to be substantially constant. As introduced above with reference to  FIGS. 2A-B , the charge transfer between capacitors in the charge pump  100  during the alternating states of operation of the charge pump  100  are therefore substantially constant in the adiabatic mode of operation. 
     Continuing to refer to  FIG. 3 , a compensation circuit  340  is introduced between the charge pump  100  and the load  320 . A switch  344  is controllable to selectively introduce a compensation capacitor  342  to the output of the charge pump  100 . 
     Various factors can affect the efficiency of the power conversion illustrated in  FIG. 3 , including the voltage of an input voltage source  392 , the switching frequency of the charge pump  100 , and the output current IO (or somewhat equivalently the input or output current of the charge pump  100 ). The efficiency is also dependent on whether or not the compensation capacitor  342  is coupled to the output path via the switch  344 . As a general approach, a controller  350  accepts inputs that characterize one or more factors that affect efficiency and outputs a control signal that sets the state of the switch  344  according to whether efficiency is expected to be improved introducing the compensation capacitor versus not. A further discussion of logic implemented by the controller  350  is provided later in this Description. 
     Referring to  FIG. 4 , in another example, a configuration of a charge pump  100  has a regulator  320  coupled via a compensation circuit  340  to the low-voltage terminal of a charge pump  100 , and a voltage source  392  coupled to the high-voltage terminal of the charge pump  100 . The regulator  320  (also referred to below generally interchangeably as a “converter”) illustrated in  FIG. 4  is a Buck converter, which consists of switches  322 ,  324 , an inductor  326 , and an output capacitor  328 . The switches open and close (i.e., present high and low impedance, respectively) in alternating states, such that the switch  322  is open when then the switch  324  is closed, and the switch  322  is closed when the switch  324  is open. These switches operate at a frequency than can be lower, higher, or equal to the switches in the charge pump  100 , with a duty cycle defined as the fraction of time that the switch  322  in the regulator  320  is closed. A preferred embodiment is when the switching frequency of the charge pump  100  is lower than the regulator  320 . However, in the case the charge pump  100  is at a higher frequency than the regulator  320 , the charge-pump  100  is disabled when the regulator  320  is off (low duty cycle) and the charge-pump  100  is enabled when the regulator  320  is on. 
     In general, the regulator  320  operates at its highest power efficiency when it operates at its highest duty cycle. In some examples, a controller of the regulator (not shown) adjusts the duty cycle in a conventional manner to achieve a desired output voltage VO. During the cycles of the regulator  320  in which the switch  322  is closed, the current passing from the charge pump  100  to the regulator  320  is effectively constant, equal to the current through the inductor  326 . Assuming that the switching frequency of the regulator  320  is substantially higher than the switching frequency of the charge pump  100 , the charge pump  100  can be considered to be driven by a pulsed current source with an average current equal to the duty cycle times the inductor current. 
     Note that as introduced above, in situations in which the regulator  320  sinks a pulsed current, then for a particular average current, the resistive energy loss generally increases as the duty cycle of the current decreases, approximately inversely with the duty cycle. There is a range of low duty cycles, and thereby high peak current relative to the average current, in which the resistive losses with a pulsed current exceed the losses for the same average current that would result from the charge pump  100  driving a relatively constant output voltage, for example, across a large output capacitor. Therefore, for a selected range of low duty cycles, the controller  350  closes the switch  344  and introduces a relatively large compensation capacitor  342  at the output of the charge pump  100 . The result is that the charge pump  100  is presented with a substantially constant voltage, and therefore operates in a substantially “non-adiabatic” mode. Therefore, the controller  350  is effectively responsive to the output voltage because the duty cycle is approximately proportional to the output voltage. Thereby operating the charge pump  100  in an adiabatic mode at high output voltage and in a non-adiabatic mode at low output voltage; and switches between the adiabatic and non-adiabatic modes at a threshold duty cycle to maintain an optimum efficiency of the overall power conversion. 
     Examples of control logic implemented in the controller  350  in configurations such as those illustrated in  FIGS. 4 and 5  can be under in view of the following discussion. 
     In general, a charge pump can operate in one of two unique operating conditions, or in the region in between them. In a slow switching limit (SSL) regime the capacitor currents in the charge pump have the time to settle to their final values and capacitor voltages experience significant change in magnitude from beginning to end of a cycle of the charge pump operation. In the fast switching limit (FSL) regime, the capacitors do not reach equilibrium during a cycle of the charge pump operation, for instance, due to a combination of one or more of high capacitances, high switching frequency, and high switch resistances. 
     Another factor relates to the capacitance at the output of the charge pump  100 , which in the circuits of  FIG. 4  can be increased by closing the switch  344  to add the compensation capacitor  342  to the output. For small output capacitance, the output current of the charge pump  100  is effectively set by the pulsed current characteristic of the regulator  320 . As discussed above, for a given average current, the resistive power losses in the pulsed current case are approximately inversely proportional the duty cycle. 
     For large output capacitance, the RMS of the output current of the charge pump  100  is effectively determined by the equilibration of the internal capacitors of the charge pump  100  with the compensation capacitor  342  and the regulator  320 . For a given average current, this resistive power loss is approximately inversely proportional to the square of the peak-to-peak voltage across the internal capacitors in the charge pump  100 . 
     Four combinations of FSL/SSL and constant/pulsed IO modes of operation are possible. In some examples, each of these four modes is affected in different ways based on the addition of a compensation capacitor  342  as shown in  FIGS. 3 and 4 . 
     Case one: In FSL mode, with constant output current IO as in  FIG. 3 , introduction of the compensation capacitor  342  does not substantially affect conversion efficient. 
     Case two: In FSL mode with pulsed output current as in  FIG. 4 , efficiency increases when the compensation capacitor  342  is introduced, thereby reducing the RMS current seen by the charge pump  100 . 
     Case three: In SSL mode, with constant output current IO as in  FIG. 3 , efficiency generally increases without introduction of the compensation capacitor  342 , thereby yielding adiabatic operation. 
     Case four: In SSL mode, with pulsed load current as in  FIG. 4 , efficiency depends on the relation between the average output current, the duty cycle, and how far the charge pump  100  is operating from the SSL/FSL boundary. For example, at low duty cycle, efficiency generally increases with introduction of the compensation capacitor  342 , thereby yielding non-adiabatic operation. In contrast, at high duty cycle, efficiency generally increases without introduction of the compensation capacitor  342 , thereby yielding adiabatic operation. Furthermore, when the charge pump  100  is in SSL mode, the farther from the SSL/FSL boundary, the lower the duty cycle at which the efficiency trend reverses. 
     Depending on the relative values of charge pump capacitors, switch resistances and frequency, it is possible that the charge pump operate in a regime between FSL and SSL. In this case, there is effectively a transition point between case four and case two at which the compensation capacitor is introduced according to the overall efficiency of the conversion. As described above, knowledge of the average charging current and its duty cycle is necessary in case four for determining if introduction of the compensation capacitor will improve efficiency. 
     In some implementations, the controller  350  does not have access to signals or data that directly provide the mode in which the power conversion is operating. One approach is for the controller to receive a sensor signal that represents the input current of the charge pump, and infer the operating mode from that sensor signal. 
     As an example, a sensor signal determined as a voltage across the switch at the high voltage terminal of the converter (e.g., the switch between source  109  and the capacitor C 4  in  FIG. 1 ) can be used to represent the current because when the switch is closed, the voltage is the current times the switch resistance. 
     An alternative circuit shown in  FIG. 5  provides a scaled version of the input current IIN. The input switch  510 , with closed resistance R is put in parallel with a second switch with closed resistance kR, for example, fabricated as a CMOS switch where the factor k depends on the geometry of the switch. When the switches are closed the differential amplifier  530  controls the gate voltage of a transistor  540  such that the voltage drop across the two switches are equal, thereby yielding the scaled input current IIN/k, which can be used to form a sensor input signal for the controller. 
     The sensed input current can be used to determine whether the compensation capacitor should be switched in, for example, according to a transition between case four and case two described above. 
     One possible method for determining the operation mode of the charge pump  100  consists of taking two or more measurements of the input current IIN and establishing that the difference between the values of consecutive samples is substantially zero for SSL mode, or is above a pre-determined threshold for FSL mode. 
     Another method is to measure the difference in the voltage of a capacitor in the charge pump  100 . Once the input current IIN is known, the controller  350  can infer the operating mode based upon the voltage ripple on the capacitor over a full cycle. Note that the controller  350  does not necessarily know the particular sizes of capacitors that are used in the charge pump  100 , for example, because the capacitors are discrete capacitors that are not predetermined. However, the capacitor values can be inferred from knowledge of the current, voltage ripple, and frequency, thereby allowing the controller  350  to determine whether the charge pump  100  is operating in the FSL or SSL mode. The controller  350  can then select adiabatic or non-adiabatic charging by controlling the switch  344  to selectively introduce the compensation capacitor  342 . 
     Other controller logic is used in other implementations. For example, an alternative is for the controller to measure efficiency given by:
 
η= VO /( N*VIN )
 
     where η is the efficiency, VO is the measured converter output voltage, VIN is the measured converter input voltage, and N is the charge pump conversion ratio. 
     The controller directly measures the effect of selecting adiabatic vs. non-adiabatic charging on converter efficiency by comparing the average value of the output voltage VO over a complete charge pump cycle. 
     Other controller logic uses combinations of the approaches described above. For instance, the controller can confirm that the assessment of charge pump operating mode and estimation of efficiency increase by changing the charge pump charging mode. 
     A traditional method for operating the charge pump  100  at a fixed frequency in which the switching occurs independently of the load requirement (i.e., the switches in  FIG. 1  operate on a fixed time period). Referring to  FIG. 6 , during one cycle of the switching of the charge pump  100 , a current I 1  discharges from the capacitor C 1  and a current IP discharges other of the capacitors in the charge pump  100 . For a particular intermediate current IX, the longer the cycle time T, the larger the drop in voltage provided by the capacitor C 1 . A consequence of this is that the switching frequency generally limits the maximum intermediate current IX because the switching frequency for a particular load determines the extent of voltage excursions, and in some cases current excursions (i.e., deviations, variation), at various points and between various points within the charge pump  100  and at its terminals. For a particular design of charge pump  100 , or characteristics of load and/or source of the charge pump  100 , there are operational limits on the excursions. 
     Referring to  FIGS. 7A-C , the intermediate voltage VX of the charge pump  100  is shown in various current and timing examples. Referring to  FIG. 7A , at a particular intermediate current IX, the intermediate voltage VX generally follows a saw-tooth pattern such that it increases rapidly at the start of each state, and then generally falls at a constant rate. Consequently, the rate of voltage drop depends on the output current IO. At a particular output current IO and switching time, a total ripple voltage  6  results, and a margin over the output voltage VO is maintained, as illustrated in  FIG. 7A . (Note that the graphs shown in  FIGS. 7A-B  do not necessarily show certain features, including certain transients at the state transition times, and related to the high frequency switching of the regulator  320 ; however these approximations are sufficient for the discussion below). 
     Referring to  FIG. 7B , in the output current IO in the circuit in  FIG. 4  increases, for instance by approximately a factor of two, the ripple of the intermediate voltage VX increases, and the minimum intermediate voltage VMIN decreases and therefore for a constant output voltage VO the margin (i.e. across inductor  316 ) in the regulator  320  decreases. However, if the voltage margin decreases below a threshold (greater than zero), the operation of the regulator  320  is impeded. 
     Referring to  FIG. 7C , to provide the regulator  320  with a sufficient voltage margin voltage the switching frequency can be increases (and cycle time decreased), for example, to restore the margin shown in  FIG. 7A . Generally, in this example, doubling the switching frequency compensates for the doubling of the output current IO. However more generally, such direct relationships between output current IO or other sensed signals and switching frequency are not necessary. 
     In general, a number of embodiments adapt the switching frequency of the charge pump  100  or determine the specific switching time instants based on measurements within the charge pump  100  and optionally in the low-voltage and/or high-voltage peripherals coupled to the terminals of the charge pump  100 . 
     In a feedback arrangement shown in  FIG. 4 , the controller  350  adapts (e.g., in a closed loop or open loop arrangement) the switching frequency. For any current up to a maximum rated current with a fixed switching frequency, the charge pump  100  generally operates at a switching frequency lower than (i.e., switching times greater than) a particular minimum frequency determined by that maximum rated current. Therefore, when the current is below the maximum, capacitive losses may be reduced as compared to operating the charge pump  100  at the minimum switching frequency determined by the maximum rated current. 
     One approach to implementing this feedback operation is to monitor the intermediate voltage VX and adapt operation of the charge pump to maintain VMIN above a fixed minimum threshold. One way to adapt the operation of the charge pump  100  is to adapt a frequency for the switching of the charge pump  100  in a feedback configuration such that as the minimum intermediate voltage VMIN approaches the threshold, the switching frequency is increased, and as it rises above the threshold the switching frequency is reduced. One way to set the fixed minimum threshold voltage is as the maximum (e.g., rated) output voltage VO of the regulator  320 , plus a minimum desired margin above that voltage. As introduced above, the minimum margin (greater than zero) is required to allow a sufficient voltage differential (VX−VO) to charge (i.e., increase its current and thereby store energy in) the inductor  326  at a reasonable rate. The minimum margin is also related to a guarantee on a maximum duty cycle of the regulator  320 . 
     A second approach adapts to the desired output voltage VO of the regulator  320 . For example, the regulator  320  may have a maximum output voltage VO rating equal to 3.3 volts. With a desired minimum margin of 0.7 volts, the switching of the charge pump  100  would be controlled to keep the intermediate voltage VX above 4.0 volts. However, if the converter is actually being operated with an output voltage VO of 1.2 volts, then the switching frequency of the charge pump  100  can be reduced to the point that the intermediate voltage VX falls as low as 1.9 volts and still maintain the desired margin of 0.7 volts. 
     In a variant of the second approach, rather than monitoring the actual output voltage VO, an average of the voltage between the switches  312 ,  314  may be used as an estimate of the output voltage VO. 
     In yet another variant, the switching frequency of the charge pump  100  is adapted to maintain the intermediate voltage VX below a threshold value. For example, the threshold can be set such that the intermediate voltage VX lowers or rises a specific percentage below or above the average of the intermediate voltage VX (e.g. 10%). This threshold would track the intermediate voltage VX. Similarly, a ripple relative to an absolute ripple voltage (e.g. 100 mV) can be used to determine the switching frequency. 
     Note also that the voltage ripple on the output voltage VO depends (not necessarily linearly) on the voltage ripple on the intermediate voltage VX, and in some examples the switching frequency of the charge pump  100  is increased to reduced the ripple on the output voltage VO to a desired value. 
     Other examples measure variation in internal voltages in the charge pump  100 , for example, measuring the ripple (e.g., absolute or relative to the maximum or average) across any of the capacitors C 1  through C 4 . Such ripple values can be used instead of using the ripple on the intermediate voltage VX in controlling the switching frequency of the charge pump  100 . Other internal voltages and/or currents can be used, for example, voltages across switches or other circuit elements (e.g., transistor switches), and the switching frequency can be adjusted to avoid exceeding rated voltages across the circuit elements. 
     In addition to the desired and/or actual output voltages or currents of the regulator  320  being provided as a control input to the controller  350 , which adapts the switching frequency of the charge pump  100 , other control inputs can also be used. One such alternative is to measure the duty cycle of the regulator  320 . Note that variation in the intermediate voltage VX affects variation in current in the Buck converters inductor  326 . For example, the average of the intermediate voltage VX is generally reduced downward with reducing of the switching frequency of the charge pump  100 . With the reduction of the average output voltage VO, the duty cycle of the regulator  320  generally increases to maintain the desired output voltage VO. Increasing the duty cycle generally increases the efficiency of a Buck converter. So reducing the switching frequency of the charge pump  100  can increase the efficiency of the regulator  320 . 
     It should be understood that although the various signals used to control the switching frequency may be described above separately, the switch frequency can be controlled according to a combination of multiple of the signals (e.g., a linear combination, nonlinear combination using maximum and minimum functions, etc.). In some examples, an approximation of an efficiency of the charge pump is optimized. 
     The discussion above focuses on using the controller  350  to adjust the switching frequency of the charge pump  100  in relatively slow scale feedback arrangement. The various signals described above as inputs to the controller  350  can be used on an asynchronous operating mode in which the times at which the charge pump  100  switches between cycles is determined according to the measurements. As one example, during state one as illustrated in  FIG. 6 , the intermediate voltage VX falls, and when VX−VO reaches a threshold value (e.g., 0.7 volts), the switches in the charge pump  100  are switched together from state one to state two. Upon the transition to state two, the intermediate voltage VX rises and then again begins to fall, and when VX−VO again reaches the threshold value, the switches in the charge pump  100  are switched together from state two back to state one. 
     In some examples, a combination of asynchronous switching as well as limits or control on average switching frequency for the charge pump are used. 
     Unfortunately, as the intermediate current IX decreases the switching frequency of the charge pump  100  decreases as well. This can be problematic at low currents because the frequency could drop below 20 kHz, which is the audible limit for human hearing. Therefore, once the frequency has dropped below a certain limit, a switch  344  closes and introduces a compensation capacitor  342 . This force the converter into non-adiabatic operation allowing the frequency to be fixed to a lower bound (e.g. 20 kHz). Consequently, the compensation capacitor  342  is introduces when either the duty cycle is low or when the output current IO is low. 
     Note that the examples above concentrate on a compensation circuit that permits selectively switching a compensation capacitor of a certain fixed capacitance onto the output of the charge pump. More generally, a wide variety of compensation circuits can be controlled. One example is a variable capacitor, which can be implemented as a switched capacitor bank, for example, with power of two capacitances. The optimal choice of capacitance generally depends on the combination of operating conditions (e.g., average current, pulsed current duty cycle, etc.) and/or circuit configurations (e.g., type of regulators, sources, load, pump capacitors), with the determining of the desired capacitance being based on prior simulation or measurement or based on a mechanism that adjusts the capacitance, for instance, in a feedback arrangement. In addition, other forms of compensation circuits, for example, introducing inductance on the output path, networks of elements (e.g., capacitors, inductors). 
     Note that the description focuses on a specific example of a charge pump. Many other configurations of charge pumps, including Dickson pumps with additional stages or parallel phases, and other configurations of charge pumps (e.g., series-parallel), can be controlled according to the same approach. In addition, the peripherals at the high and/or low voltage terminals are not necessarily regulators, or necessarily maintain substantially constant current. Furthermore, the approaches described are applicable to configurations in which a high voltage supply provides energy to a low voltage load, or in which a low voltage supply provides energy to a high voltage load, or bidirectional configurations in which energy may flow in either direction between the high and the low voltage terminal of the charge pump. It should also be understood that the switching elements can be implemented in a variety of ways, including using Field Effect Transistors (FETs) or diodes, and the capacitors may be integrated into a monolithic device with the switch elements and/or may be external using discrete components. Similarly, at least some of the regulator circuit may in some examples be integrated with some or all of the charge pump in an integrated device. 
     Implementations of the approaches described above may be integrated into an integrated circuit that includes the switching transistors of the charge pump, either with discrete/off-chip capacitors or integrated capacitors. In other implementations, the controller that determines the switching frequency of the charge pump and/or the compensation circuit may be implemented in a different device than the charge pump. The controller can use application specific circuitry, a programmable processor/controller, or both. In the programmable case, the implementation may include software, stored in a tangible machined readable medium (e.g., ROM, etc.) that includes instructions for implementing the control procedures described above. 
     It is to be understood that the foregoing description is intended to illustrate and not to limit the scope of the invention, which is defined by the scope of the appended claims. Other embodiments are within the scope of the following claims.