Low power mode for multistage converter
By adopting a switching sequence of three switch configurations within the switching cycle of a multi-level power converter, the problems of insufficient regulation and shallow magnetization slope of the flying capacitor under light load are solved, and the efficiency and stability of the converter are improved.
Patent Information
- Application Number
- CN202480008578.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2024-01-18
- Filing Date
- 2024-01-19
- Publication Date
- 2025-09-05
AI Technical Summary
Multi-stage power converters face the problems of insufficient regulation of flying capacitors and delayed demagnetization of power inductors due to shallow magnetization slopes under light loads, which affects efficiency.
A control circuit and switching sequence are used to optimize inductor current regulation during a switching cycle of a multi-level power converter by switching between at least three switching configurations and controlling the switches to present different voltage amplitudes at the switching node, including switching between different voltage configurations during magnetization and demagnetization.
The efficiency of the multi-level converter at light load is improved, and higher power inductor demagnetization efficiency and flying capacitor balance are achieved through the improved switching sequence, thereby improving the overall performance of the system.
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Figure CN120604442A_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates generally to circuits for electronic devices, including but not limited to personal audio devices such as wireless telephones and media players, and more particularly to closed-loop control of power converters, including multi-level power converters. Background Art
[0002] Personal audio devices, including wireless phones (such as mobile / cellular phones, cordless phones, MP3 players, and other consumer audio devices), are widely used. Such personal audio devices may include circuitry for driving a pair of headphones, one or more speakers, haptic actuators, camera stabilization motors, and / or other loads. Such circuitry typically includes a driver comprising a power amplifier for driving an output signal to such loads. Typically, a power converter is used to provide a supply voltage to the power amplifier in order to amplify the signal being driven to the speaker, headphones, other transducers, or other loads. A switching power converter is an electronic circuit that converts power from one direct current (DC) voltage level to another. Examples of such switching DC-DC converters include, but are not limited to, boost converters, buck converters, buck-boost converters, inverting buck-boost converters, and other types of switching DC-DC converters. Thus, using a power converter, a DC voltage, such as that provided by a battery, can be converted to another DC voltage for powering a power amplifier. A power converter can be used to provide a supply voltage rail to one or more components within the device. In addition to driving audio transducers, power converters can also be used for other applications, such as driving haptic actuators or other electrical or electronic loads. Additionally, a power converter may also be used to charge the battery from an electrical energy source (eg, an AC to DC adapter).
[0003] To achieve power efficiency at light loads, the power converter may need to limit the magnitude of the reverse current, as reverse current can cause power loss and reverse power to the power source (e.g., a battery). Limiting the reverse current can be achieved using demagnetization or synchronous demagnetization with a zero-crossing detector, with synchronous demagnetization typically achieving higher power efficiency. To achieve power efficiency even at light loads, the power converter can also reduce the switching frequency at low loads to reduce non-conduction loss terms.
[0004] A type of power converter known as a multi-level power converter (e.g., an n-level power converter, where n ≥ 3) may face unique challenges at lighter loads. For example, a multi-level converter may include one or more flying capacitors that need to be regulated within a limited voltage range for reasons of operation including within a safe operating region. However, at light loads, there may not be enough current available to actively balance the one or more flying capacitors. Furthermore, using a typical continuous conduction mode sequence for a multi-level converter, such as a duty cycle of 0.5 for a 3-level converter (e.g., where the duty cycle is equal to the output voltage V for buck mode operation of a 3-level converter), the output voltage V OUT With input voltage V IN The magnetization and magnetization slope may become shallow at multiple duty cycles. This shallow slope may not allow the power inductor of the power converter to demagnetize in time for the next switching pulse.
[0005] Figure 1 1 shows selected components of an example circuit 100 for driving a load 120 as known in the art. Figure 1 As shown, the modulator 110 may receive a control parameter REF (eg, which may be an indication of a desired output voltage V to be driven to the load 120). OUT or the desired current I to be driven through the modulator's power inductor L and generates a switching control signal for controlling switching of the analog power stage 101 (such as, for example, a power converter) based on the control parameter.
[0006] A common type of power converter used in electronic circuits is a 3-level power converter. Figure 1 The simulated power stage 101 is depicted as a 3-level power converter as is known in the art. Figure 1 As shown, the analog power stage 101 can receive an input voltage V IN , and is configured to generate an output voltage V based on a switching signal received from the modulator 110 OUT In addition, the analog power stage 101 may include an output having a voltage L XThe analog power stage 101 may include a power inductor 102 coupled between the switching node and the output. In addition, the analog power stage 101 may include a flying capacitor 104 having a first capacitor terminal and a second capacitor terminal. In addition, the analog power stage 101 may include a plurality of switches 106a, 106b, 106c, and 106d, wherein the switch 106a is coupled between the input and the first capacitor terminal, the switch 106b is coupled between the first capacitor terminal and the switching node, the switch 106c is coupled between the second capacitor terminal and the switching node, and the switch 106d is coupled between the second capacitor terminal and the ground voltage. In operation, the switches 106a, 106b, 106c, and 106d may be controlled by the modulator 110 to adjust the output voltage V OUT regulated to the desired target voltage.
[0007] In operation, the switch 106 can be controlled to set the output voltage V OUT Adjust to the desired target voltage. Figure 2A and 2B As shown, the buck operation of the analog power stage 101 may include cyclic, periodic switching of the switch 106 between a first state (φ1), a second state (φ2), a third state (φ3), and a fourth state (φ4). Figure 2A As shown, for a duty cycle D less than 0.5, during a first state in the VCS configuration, switches 106a and 106c may be activated (and switches 106b and 106d may be deactivated), during a second state in the GS configuration, switches 106c and 106d may be activated (and switches 106a and 106b may be deactivated), during a third state in the GCS configuration, switches 106b and 106d may be activated (and switches 106a and 106c may be deactivated), and during a fourth state in the GS configuration, switches 106c and 106d may be activated (and switches 106a and 106b may be deactivated).
[0008] In addition, if Figure 2B As shown, for a duty cycle D greater than 0.5, during a first state in the VS configuration, switches 106a and 106b may be activated (and switches 106c and 106d may be deactivated), during a second state in the VCS configuration, switches 106a and 106c may be activated (and switches 106b and 106d may be deactivated), during a third state in the VS configuration, switches 106a and 106b may be activated (and switches 106c and 106d may be deactivated), and during a fourth state in the GCS configuration, switches 106b and 106d may be activated (and switches 106a and 106c may be deactivated).
[0009] The acronyms VS, VCS, GS, and GCS represent the current paths in each corresponding configuration, where “V” represents the supply voltage, “C” represents the flying capacitor 104 , “S” represents the switching node, and “G” represents the ground voltage.
[0010] like Figure 1 、 2A The multi-level converter depicted in FIG2B may have a dedicated balancing loop (not shown) for the flying capacitor 104 that uses the current flowing to the load 120 to regulate the flying capacitor 104. Under light load conditions, the loop may be closed and unable to regulate the flying capacitor 104. However, to ensure that the inductor current I L Such adjustments may be required to produce a predictable waveform and ensure a safe operating area.
[0011] One solution to such a problem could be to operate the multi-level converter in a two-stage operation where the power supply (e.g., input voltage V IN ) and ground, the switching node voltage L X For example, this two-stage switching can be achieved by periodically switching Figure 2A and 2B This is achieved by switching between the VS configuration and the GS configuration shown in FIG. Such two-stage switching at light loads can eliminate the complexity when the duty cycle D is close to 0.5 and simplify the balancing of the flying capacitor 104 because no current flows through the flying capacitor 104 in such two-stage operation. However, such two-stage operation may not be as power-efficient as three-stage switching. Summary of the Invention
[0012] According to the teachings of the present disclosure, one or more disadvantages and problems associated with operation of multi-level converters under low load conditions may be reduced or eliminated.
[0013] According to an embodiment of the present disclosure, a system may include a multi-level power converter, the multi-level power converter including a plurality of switches and a power inductor electrically coupled to the plurality of switches, wherein the power inductor is coupled to a switching node of the multi-level power converter, wherein the multi-level power converter is capable of applying three or more switching voltages to the switching node. The system may also include a control circuit for generating a control signal that defines a switching sequence for the plurality of switches of the multi-level power converter, the control circuit being configured to control the plurality of switches to switch between at least three switching configurations during a switching cycle of the multi-level power converter in which the power inductor is magnetized and demagnetized, during magnetization and demagnetization of the power inductor, such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least three switching configurations.
[0014] According to these and other embodiments of the present disclosure, a method for a multi-level power converter can be provided, the multi-level power converter including a plurality of switches and a power inductor electrically coupled to the plurality of switches, wherein the power inductor is coupled to a switching node of the multi-level power converter, wherein the multi-level power converter is capable of applying three or more switching voltages to the switching node. The method can include generating control signals that define a switching sequence for the plurality of switches of the multi-level power converter, and during a switching cycle of the multi-level power converter in which the power inductor is magnetized and demagnetized, during magnetization and demagnetization of the power inductor, controlling the plurality of switches to switch between at least three switching configurations such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least three switching configurations.
[0015] According to these and other embodiments of the present disclosure, a computer program product including a computer-usable medium having computer-readable code embodied therein may be provided. The computer program product may include computer-readable program code for, in a multi-level power converter including a plurality of switches and a power inductor electrically coupled to the plurality of switches, wherein the power inductor is coupled to a switching node of the multi-level power converter, wherein the multi-level power converter is capable of applying three or more switching voltages to the switching node, the computer-readable program code for: generating control signals that define a switching sequence for the plurality of switches of the multi-level power converter; and, during a switching cycle of the multi-level power converter in which the power inductor is magnetized and demagnetized, controlling the plurality of switches to switch between at least three switching configurations during the magnetization and demagnetization periods of the power inductor, such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least three switching configurations.
[0016] Those skilled in the art can easily see the technical advantages of the present disclosure from the drawings, descriptions and claims included herein. The objects and advantages of the embodiments will be realized and achieved at least by the elements, features and combinations particularly pointed out in the claims.
[0017] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the present disclosure, as claimed. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The present embodiment and its advantages may be more fully understood by referring to the following description taken in conjunction with the accompanying drawings, in which like reference numerals represent like features, and in which:
[0019] Figure 1a circuit diagram showing selected components of an example circuit for driving a load using a 3-level power converter as is known in the art;
[0020] Figure 2A and 2B As known in the art Figure 1 The operation of the two-phase 3-level buck converter shown in;
[0021] Figure 3 A block diagram illustrating selected components of an example system for driving a load using a switched analog power stage according to an embodiment of the present disclosure; and
[0022] Figure 4 The embodiment according to the present disclosure is shown Figure 3 Example waveforms of the inductor current of the switching simulated power stage depicted in FIG. DETAILED DESCRIPTION
[0023] Figure 3 1 is a block diagram illustrating selected components of an example system 300 for driving a load 320 using a switching analog power stage 301 according to an embodiment of the present disclosure. Figure 3 As shown, system 300 may include an analog power stage 301 , a modulator 310 , a compensator 312 , an inductor current measurement block 314 , a continuous conduction mode (CCM) compensation block 316 , a discontinuous conduction mode (DCM) current duty cycle calculation block 318 , and a load 320 .
[0024] The analog power stage 301 may include any suitable system, device, or apparatus configured to, based on a switching control signal provided from the modulator 310, generate a current from the supply voltage V IN Driving power inductor current I L and voltage V OUT In some embodiments, the analog power stage 301 may include an inductive and / or capacitive based power converter. In certain embodiments, the analog power stage 301 may include a multi-stage power converter that is the same as or similar to the multi-stage power converter discussed in the background section of this application.
[0025] The modulator 310 may include any suitable system, device, or apparatus configured to receive a duty cycle signal D representing a target duty cycle for switching switches of the analog power stage 301 and generate switching signals (e.g., SW1 . . . N) for controlling the switching of the switches integrated into the analog power stage 301. In some embodiments, the modulator 310 may include a pulse width modulator.
[0026] The compensator 312 may include any suitable system, device, or apparatus configured to receive a signal equal to the control parameter REF (eg, a signal indicating a desired output voltage V to be driven to the load 320).OUT digital or analog signal) and the measured output voltage V OUT (or such as power inductor current I L or another regulated physical quantity such as other voltages) and converts this error signal into a command current I CMD , the command current I CMD It can be used to adjust the output voltage V according to the error signal OUT Required power inductor current I L The target amplitude (e.g., average current, peak current, etc.)
[0027] The inductor current measurement block 314 may include a circuit configured to measure the current I L The inductor current measurement block 314 may include any suitable combination of analog components (eg, analog-to-digital converters, comparators, etc.) and / or digital components (eg, estimators, interpolators, etc.).
[0028] In CCM operation of the system 300 , the CCM compensator 316 may be configured to operate based on the command current I CMD and the measured power inductor current I L The error signal between φ and φ is used to generate the duty cycle signal D. However, in DCM and pulse frequency modulation (PFM) operation, the inductor current measurement block 314 and the CCM compensator 316 may be bypassed.
[0029] In DCM and PFM operation, which may occur at low load conditions (e.g., the current delivered by the analog power stage 301 to the load 320 is below a threshold current level), the control loop of the CCM compensator 316 may be disabled and replaced by a feed-forward DCM current duty cycle calculation block 318 that calculates the current duty cycle based on the input voltage V IN and the output voltage V OUT The duration between pulses will command the current I CMD is converted into a duty cycle signal D, as described in more detail below. Any error in the calculation of the duty cycle signal D can be corrected by the outer control loop of the compensator 312. In addition, the integrator of the CCM compensator 316 can be kept reset during DCM and PFM operation and can be released when the operation of the system 300 transitions to CCM operation.
[0030] To further illustrate the operation of the DCM current duty cycle calculation block 318, it should be noted that in the 3-level power converter disclosed in the Background section, as the duty cycle approaches 0.5, the inductor current I L The slope (e.g., dI LThis shallow slope can result in low peak current, reducing the charge delivered in the DCM pulse and thus potentially not allowing the power inductor to fully demagnetize before the subsequent pulse.
[0031] To overcome such disadvantages, during DCM and PFM operations, the DCM current duty cycle calculation block 318 may employ a modified switching sequence in multi-level operation that is different from the background art portion (e.g., Figure 2A and 2B ) described in the “normal” switching sequence that can be used during CCM operation. Figure 4 As shown, under this modified switching sequence, during the magnetizing phase, the DCM current duty cycle calculation block 318 can switch the analog power stage 301 to the VS configuration to increase the power inductor current I L In the shallow demagnetization stage, the DCM current duty cycle calculation block 318 may switch the analog power stage 301 to the VCS configuration or the GCS configuration to slowly reduce the power inductor current I L In the non-shallow demagnetization stage, the DCM current duty cycle calculation block 318 can switch the analog power stage 301 to the GS configuration to quickly reduce the power inductor current I at a faster rate than in the shallow demagnetization stage. L , in order to quickly reduce the power inductor current I L Drive to zero.
[0032] Compared to the two-stage operation described in the background section, switching in a modified switching sequence (i.e., switching in which three or more switching voltages may be applied to the switching nodes of the power converter during a switching cycle) may be a more power-efficient operation. L Any height of the current ripple can be adjusted by appropriately weighting the relative times of the VS, VCS, GCS, and GS configurations. Furthermore, the presence of the VCS and GCS states in the switching sequence can allow the flying capacitor 104 to be balanced using the load current, which may not be possible in two-stage operation. Furthermore, in some embodiments, the modified switching sequence can use asynchronous demagnetization (e.g., via the body diode of either or both switches 106c and 106d) during the GS configuration. Using such asynchronous demagnetization can provide better efficiency than comparable two-stage operation because the VCS and GCS configurations can account for a majority of the time that the power inductor 102 carries non-zero current.
[0033] The foregoing description may apply to operation of the system 300 in buck mode. Operation of the system 300 in boost mode may be similar to that described above with respect to buck mode, but wherein magnetization of the power inductor is performed via a GS configuration and demagnetization of the power inductor is performed via a VS configuration.
[0034] In some embodiments, system 300 may be embodied in a program of computer-readable instructions and executed by a processing device, including but not limited to a processor, an application specific integrated circuit, a digital signal processor, or any other suitable processing device.
[0035] In accordance with the foregoing discussion, a system may include a multi-level power converter comprising a plurality of switches and a power inductor electrically coupled to the plurality of switches, wherein three or more switching voltages may be applied to the power inductor of the power converter, and wherein the power inductor is coupled to a switching node of the multi-level power converter. The system may also include a control circuit for generating a control signal that defines a switching sequence for the plurality of switches of the multi-level power converter, the control circuit being configured to control the plurality of switches to switch between at least three switching configurations during a switching cycle of the multi-level power converter in which the power inductor is magnetized and demagnetized, during magnetization and demagnetization of the power inductor, such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least three switching configurations. As described herein, the control circuit may be configured to control the plurality of switches to switch between the at least three switching configurations when operating in a discontinuous conduction mode or a pulse frequency modulation mode of operation.
[0036] Furthermore, the control circuit may be configured to convert a target current magnitude of the current through the power inductor into a duty cycle of switching of the multi-level power converter when operating in a discontinuous conduction mode or a pulse frequency modulation mode of operation.
[0037] As used herein, when two or more elements are referred to as being “coupled” to each other, the term means that the two or more elements are in electrical or mechanical communication, as applicable, whether indirectly or directly, with or without intervening elements.
[0038] This disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that would be understood by a person of ordinary skill in the art. Similarly, the appended claims encompass all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that would be understood by a person of ordinary skill in the art, where appropriate. In addition, in the appended claims, references to a device or system or component of a device or system that is adapted to, arranged to, capable of, configured to, enabled to, operable to, or operable to perform a particular function encompass such device, system, or component, regardless of whether it or such particular function is activated, turned on, or unlocked, as long as such device, system, or component is so adapted, arranged, capable of, configured to, enabled to, operable to, or operable to. Therefore, without departing from the scope of this disclosure, the systems, devices, and methods described herein may be modified, added to, or omitted. For example, the components of the systems and devices may be integrated or separate. In addition, the operations of the systems and devices disclosed herein may be performed by more, fewer, or other components, and the described methods may include more, fewer, or other steps. In addition, the steps may be performed in any appropriate order. As used herein, "each" refers to every member of a set or every member of a subset of a set.
[0039] Although exemplary embodiments are shown in the drawings and described below, the principles of the present disclosure can be implemented using any number of technologies, whether currently known or not. The present disclosure should not be limited in any way to the exemplary embodiments and technologies shown in the drawings and described above.
[0040] Unless specifically noted otherwise, items depicted in the drawings are not necessarily drawn to scale.
[0041] All examples and conditional language described herein are intended for teaching purposes to help readers understand the present disclosure and the concepts contributed by the inventors to further the art, and are not to be construed as being limited to such specifically enumerated examples and conditions. Although the embodiments of the present disclosure have been described in detail, it should be understood that various changes, substitutions, and modifications may be made thereto without departing from the spirit and scope of the present disclosure.
[0042] Although specific advantages are listed above, various embodiments may include some, none, or all of the advantages listed. In addition, other technical advantages will become apparent to those of ordinary skill in the art after reading the preceding drawings and descriptions.
[0043] To assist the Patent Office and any reader of any patent issuing in this application in interpreting the appended claims, applicants wish to note that they do not intend for any appended claim or claim element to invoke 35 U.S.C. §112(f) unless the words "means for" or "step for" are expressly used in a particular claim.
Claims
1. A system comprising: a multi-level power converter comprising a plurality of switches and a power inductor electrically coupled to the plurality of switches, wherein the power inductor is coupled to a switching node of the multi-level power converter, wherein the multi-level power converter is capable of applying three or more switching voltages to the switching node; and a control circuit configured to generate control signals defining a switching sequence for the plurality of switches of the multi-level power converter, the control circuit being configured to control the plurality of switches to switch between at least three switching configurations during magnetization and demagnetization of the power inductor during a switching cycle of the multi-level power converter in which the power inductor is magnetized and demagnetized, such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least three switching configurations.
2. The system according to claim 1, wherein: The control circuit is configured to control the plurality of switches to switch between the at least three switching configurations when operating in a discontinuous conduction mode of operation or a pulse frequency modulation mode of operation.
3. The system according to claim 1 or 2, wherein: The control circuit is configured to control the plurality of switches to switch between the at least three switch configurations when operating in a continuous conduction mode of operation.
4. The system according to claim 1 or 2, wherein: The control circuit is configured to convert a target current magnitude through the power inductor into a duty cycle for switching of the multi-level power converter when operating in a discontinuous conduction mode of operation or a pulse frequency modulation mode of operation.
5. The system according to any one of claims 1 to 4, wherein: The control circuit is configured to: during demagnetization of the power inductor, control the multiple switches to switch between at least two switching configurations, so that the voltage on the switching node presents a different corresponding voltage amplitude in each of the at least two switching configurations, and the current through the power inductor changes differently with respect to time in each of the at least two switching configurations.
6. A method for use in a multi-level power converter, the multi-level power converter comprising a plurality of switches and a power inductor electrically coupled to the plurality of switches, wherein: The power inductor is coupled to a switching node of the multi-level power converter, wherein the multi-level power converter is capable of applying three or more switching voltages to the switching node, the method comprising: generating a control signal that defines a switching sequence of the plurality of switches of the multi-level power converter; and During a switching cycle of the multi-level power converter in which the power inductor is magnetized and demagnetized, the plurality of switches are controlled to switch between at least three switching configurations during magnetization and demagnetization of the power inductor such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least three switching configurations.
7. The method according to claim 6, further comprising: The plurality of switches are controlled to switch between the at least three switching configurations when operating in a discontinuous conduction mode of operation or a pulse frequency modulation mode of operation.
8. The method according to claim 6 or 7, further comprising: The plurality of switches are controlled to switch between the at least three switching configurations when operating in a continuous conduction mode of operation.
9. The method according to claim 6 or 7, further comprising: A target current magnitude through the power inductor is converted into a duty cycle for switching of the multi-level power converter when operating in a discontinuous conduction mode of operation or a pulse frequency modulation mode of operation.
10. The method according to any one of claims 6 to 9, further comprising: During demagnetization of the power inductor, the plurality of switches are controlled to switch between at least two switch configurations so that the voltage on the switching node exhibits a different corresponding voltage amplitude in each of the at least two switch configurations, and the current through the power inductor changes differently with respect to time in each of the at least two switch configurations.
11. A computer program product comprising a computer usable medium having computer readable code physically embodied therein, the computer program product further comprising computer readable program code for use in a multi-level power converter comprising a plurality of switches and a power inductor electrically coupled to the plurality of switches, wherein: The power inductor is coupled to a switching node of the multi-level power converter, wherein the multi-level power converter is capable of applying three or more switching voltages to the switching node, the computer readable program code being configured to: generating a control signal that defines a switching sequence of the plurality of switches of the multi-level power converter; and During a switching cycle of a multi-level power converter in which the power inductor is magnetized and demagnetized, the plurality of switches are controlled to switch between at least three switching configurations during magnetization and demagnetization of the power inductor such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least three switching configurations.
12. The computer program product of claim 11, further comprising: Computer readable program code for controlling the plurality of switches to switch between the at least three switching configurations when operating in a discontinuous conduction mode of operation or a pulse frequency modulation mode of operation.
13. The computer program product according to claim 11 or 12, further comprising: Computer readable program code for controlling the plurality of switches to switch between the at least three switching configurations when operating in a continuous conduction mode of operation.
14. The computer program product according to claim 11 or 12, further comprising: Computer readable program code for converting a target current magnitude through the power inductor into a duty cycle for switching of the multi-level power converter when operating in a discontinuous conduction mode of operation or a pulse frequency modulation mode of operation.
15. The computer program product according to any one of claims 11 to 15, further comprising: Computer-readable program code for controlling the plurality of switches to switch between at least two switching configurations during demagnetization of the power inductor such that a voltage on the switching node exhibits a different respective voltage magnitude in each of the at least two switching configurations and a change in a current through the power inductor with respect to time is different in each of the at least two switching configurations.