Charge-Pump Circuits

1. Definition and Purpose

1.1 Definition and Purpose

Charge-pump circuits are a specialized class of DC-DC converters that utilize capacitors as energy storage elements to generate a higher output voltage from a lower input voltage. Unlike traditional inductive step-up (boost) regulators that utilize inductors, charge pumps exploit the switching action of capacitors, which leads to several advantageous characteristics such as compact size, high efficiency, and minimal electromagnetic interference. Their mechanism typically involves a configuration of switches or diodes that control the charging and discharging of capacitors in a cyclical process. The fundamental mode of operation of a charge-pump can be understood by considering the two primary functions it performs: charge transfer and voltage conversion. In essence, the circuit captures energy from the input source and sequentially transfers it through capacitors, thereby elevating the voltage to the desired level. For instance, in a basic two-stage charge pump configuration, two capacitors are used with a switching sequence that allows for doubling the output voltage relative to the input. To elaborate further, during the charging phase of a cycle, one capacitor is charged to the input voltage while the other capacitor is effectively isolated from the output. Upon the transition to the discharge phase, the previously charged capacitor is connected in series with the input, thus summing the voltages. Mathematically, if the input voltage $ V_{in} $ is applied to a charger capacitor $ C_{1} $, the output voltage $ V_{out} $ can be represented as:

$$ V_{out} = n \cdot V_{in} $$

where $ n $ is the multiplication factor, determined by the number of stages in the charge pump. For instance, a two-stage charge pump would allow $ n $ to equal 2, thereby theoretically producing an output voltage that is twice that of the input. A significant advantage of charge-pump circuits is their applicability in diverse real-world applications, particularly in scenarios where space is at a premium and simplicity is valued. Typical use cases include:

Battery-powered devices: Charge pumps are commonly used in handheld devices for generating voltages required for power-hungry components such as LCDs and microcontrollers.
Electroluminescent (EL) displays: EL backlighting circuits often employ charge pumps to achieve the high-voltage requirements for powering the display panels.
RFID tags: Many passive RFID tags utilize charge pumps to harvest energy from incoming radio waves, which is then utilized to power the onboard circuitry.

In summary, charge-pump circuits stand at the intersection of simplicity and functionality, offering viable solutions to common voltage conversion challenges in compact electronic systems. Their efficient performance in specific applications underscores the importance of understanding and utilizing this technology in modern electronics design.

Diagram Description: A diagram would illustrate the operation of charge-pump circuits, showing the charging and discharging phases of the capacitors along with a representation of voltage levels during each phase. This visual representation would clarify how the capacitors interact to increase voltage, which is complex to convey through text alone.

1.2 Basic Operating Principles

Charge-pump circuits are a versatile and efficient means of converting electrical energy, particularly useful in applications requiring voltage conversion. Understanding the basic operating principles of these circuits is foundational for any advanced study or development in power electronics.

The Fundamentals of Charge-Pumps

At their core, charge-pump circuits exploit the principle of capacitive energy storage to move charge between capacitors to achieve voltage conversion without relying on inductors. The fundamental action of a charge pump can be understood through its basic component—a capacitor—which alternately stores and releases energy to produce a higher or lower voltage output.

Basic Components

A typical charge-pump circuit consists of:

Capacitors: These are the storing elements used to accumulate charge.
Diodes: They control the direction of current flow, ensuring that charge moves in the correct direction.
Switching Elements: Often MOSFETs or similar devices are used to intermittently connect capacitors and diodes to the supply voltage and ground.

Operating Mechanism

The operation phases of a charge pump can be broadly categorized into two main stages: charge phase and pump phase.

Charge Phase

In this phase, the switch connects the input voltage source to one side of the capacitor, allowing it to charge up. If we define the input voltage as $ V_{in} $, the voltage across the capacitor, $ V_{C} $, can be expressed as:

$$ V_{C} = V_{in} $$

As the capacitor charges, it accumulates energy in the form of electric potential. Once charged, the configuration of the circuit then transitions to the next phase.

Pump Phase

In the pump phase, the switch reconfigures the circuit, disconnecting the capacitor from the input and connecting it to the output. The action of the diodes allows the capacitor to discharge its stored energy into the load or the next capacitor in the bank. The output voltage can be expressed based on the number of stages in the pump and the desired voltage multiplication effect:

$$ V_{out} = (N \cdot V_{in}) - V_{D} $$

where $ N $ is the number of charge-pump stages and $ V_{D} $ is the forward voltage drop of the diodes.

Applications and Practical Relevance

Charge-pump circuits are particularly relevant in battery-operated devices and low-power systems where space and component count must be minimized. Applications include:

Voltage Doublers: Used in LCD displays and battery-powered devices to increase voltage levels without bulky inductors.
On-Chip Power Supplies: Integrated circuits often deploy charge pumps for dual power supply rails, reducing board space.
Tone Generators and Signal Processing: Often utilized in precision timing circuits that require specific voltage levels.

In conclusion, charge-pump circuits represent a fascinating and efficient method of voltage manipulation, offering numerous advantages in modern electronics.

1.3 Types of Charge Pumps

Charge pumps are increasingly pivotal in modern electronics, providing excellent solutions for boosting or inverting voltage with minimal components. Their operation hinges on the clever manipulation of capacitors and switching elements to achieve power transfer efficiency that is often remarkable when compared to traditional linear regulation methods. Within this domain, several types of charge pumps exist, each designed for specific applications based on the voltage requirements and load conditions.

Switched Capacitor Charge Pumps

The simplest and most widely recognized type of charge pump is the switched capacitor charge pump. This circuit uses capacitors as energy storage elements and employs switches (often implemented with transistors) to alternate the configuration and connectivity of these capacitors. A key feature of switched capacitor charge pumps is their ability to multiply input voltage.

Consider a basic 2x charge pump. This circuit typically consists of two capacitors, C1 and C2, and two switches. During the first phase, S1 is closed, and the input voltage V_in charges C1. In the subsequent phase, S2 closes, connecting the charged capacitor C1 in series with the input, effectively doubling the voltage seen at the output.

$$ V_{out} = 2 \times V_{in} $$

This simple arrangement allows for efficient voltage boosting in portable devices, enabling them to run off lower voltage batteries while providing higher operating voltages for components such as microcontrollers or RF transceivers.

Voltage Doublers and Inverters

Building upon the basic switched capacitor design, voltage doublers can provide a more complex operation where the output voltage is effectively tripled or quadrupled. An example would be the standard voltage doubler configured with two diodes and two capacitors, where the output is drawn across both capacitors in a cascading manner. Voltage inverters operate on a similar principle, using additional switches to flip the voltages, effectively giving a negative output.

Real-world applications of such configurations are prevalent in battery-powered systems, where converting a low voltage from a single-cell battery to higher levels can significantly enhance the performance of various electronic components.

Series and Parallel Charge Pumps

Charge pumps can also be categorized based on their connection scheme—series or parallel. In series configurations, the output voltage is additive, similar to how you would connect batteries in series. Conversely, parallel configurations allow for current sharing among multiple charge pumps, thus increasing the output current capability without raising voltage levels.

This flexibility makes charge pumps versatile enough to address specific needs in circuit design, such as achieving a high output current for power-hungry devices without the need for large transformers often required in conventional power supply designs.

Optimal Usage Considerations

While charge pumps offer many advantages, engineers must carefully consider the load conditions and efficiency requirements of their application. Switched capacitor charge pumps, for instance, can exhibit increased losses at high frequencies due to parasitic capacitance and resistance. Thus, a judicious choice between charge pump types is often necessary, considering trade-offs such as size, efficiency, and output stability.

The understanding gained from exploring various charge pump types enables engineers to select the most suitable configuration, optimizing performance and reliability within their specific applications. With ongoing advancements in semiconductor technology, charge pumps are anticipated to continue evolving, further enhancing their effectiveness and application range.

Diagram Description: The diagram would visually illustrate the configuration of a basic 2x switched capacitor charge pump, showing how the capacitors and switches interact during the charging and output phases. This representation would clarify the flow of voltage and the roles played by each component.

2. Capacitor Selection and Sizing

2.1 Capacitor Selection and Sizing

Charge-pump circuits utilize capacitors to generate higher or lower voltage levels through a sequence of charging and discharging processes. The selection and sizing of these capacitors are crucial for efficient operation, performance stability, and reliability of the entire circuit. Understanding the dynamic behavior of capacitors under varying load conditions and the implications for energy storage and transfer efficiency is essential for engineers designing robust charge-pump systems.

Understanding Capacitor Functions in Charge Pumps

Capacitors in charge-pump circuits primarily serve as energy storage elements. They store energy when the circuit is in a charging phase and release it during the discharging phase. The voltage output of a charge pump is largely determined by the values and characteristics of these capacitors. It is critical to consider both the capacitance value and the voltage rating to ensure that the circuit operates within safe limits.

Key Factors in Capacitor Selection

Capacitance Value: The capacitance value impacts the amount of charge a capacitor can store. A larger capacitance results in a greater charge storage capability, which translates into higher output current capabilities.
Equivalent Series Resistance (ESR): This parameter plays a vital role in determining the performance of a charge-pump circuit. Lower ESR values reduce power losses during charge and discharge cycles, thus improving efficiency and response time.
Voltage Rating: The selected capacitors must have a voltage rating significantly higher than the maximum voltage the circuit will impose to avoid dielectric breakdown under operational conditions.
Temperature Coefficient: Capacitors exhibit variations in capacitance with temperature changes. Choosing capacitors with appropriate temperature coefficients is crucial to maintaining consistent performance across different environmental conditions.

Sizing Capacitors in Charge Pumps

The sizing of capacitors is not merely a function of the required capacitance value but must also account for transient response and load conditions. To minimize voltage ripple, one can evaluate the required capacitance based on the desired output voltage stability during load transients. The formula that relates capacitance (C), output voltage (V), load current (I), and frequency (f) is derived from the relationship of charge and time:

$$ C = \frac{I}{{f \cdot \Delta V}} $$

Here, ΔV is the maximum acceptable ripple voltage. Rearranging the formula provides an approach to sizing capacitors according to load characteristics:

$$ C = \frac{I \cdot T}{{\Delta V}} $$

where T is the period in which the load current draws power. This equation illustrates how to determine the ideal capacitance needed to ensure that output voltage remains stable even during transient conditions.

Real-World Applications

Charge-pump circuits with optimally selected and sized capacitors find widespread applications in battery-operated devices, such as mobile phones, portable medical devices, and camera flashes. For example, integrating a charge pump in a battery management system enables the efficient regulation of battery voltages across various levels, ensuring the robustness of the system during peak demands and sluggish operational phases.

Ultimately, careful capacitor selection and sizing can have profound implications for the efficiency, performance, and reliability of charge-pump circuits, making it a crucial concern for engineers and designers.

Diagram Description: The diagram would illustrate the charging and discharging phases of capacitors in a charge-pump circuit, showing the relationship between voltage, current, and capacitance over time. It would provide a clear visual representation of how capacitance values influence output voltage stability, especially during load transients.

2.2 Diode Characteristics and Selection

Charge-pump circuits are vital in managing voltage levels in various electronics applications, acting as essential components for voltage generation and regulation. While the design of these circuits primarily revolves around capacitors and switches, diodes play a crucial role in ensuring efficient operation, determining the overall performance, reliability, and efficiency of the charge pump. Understanding diode characteristics is thus paramount when it comes to selecting the appropriate diode for any charge pump application.

Diode Characteristics

Diodes are semiconductor devices that allow current to flow in one direction while blocking it in the opposite direction. Their behavior can be characterized by several key parameters:

Forward Voltage Drop (Vf): This is the voltage required for the diode to conduct. Typical Vf ranges from approximately 0.2 V for Schottky diodes to 0.7 V for silicon diodes.
Reverse Breakdown Voltage (Vr): The maximum reverse voltage the diode can withstand before it breaks down and allows a substantial current to flow in the reverse direction.
Current Rating (If): The maximum current the diode can handle in the forward direction without degradation.
Capacitance: At reverse bias, diodes exhibit junction capacitance that can affect the performance of high-frequency circuits.
Recovery Time: The time it takes for a diode to transition from conducting in the forward direction to blocking in the reverse direction. Fast recovery characteristics are crucial in high-frequency applications.

These characteristics influence how diodes perform under varying conditions, especially under the different states experienced in a charge pump cycle.

Selecting the Right Diode for Charge Pumps

When designing a charge pump, selecting the right diode involves balancing performance with the requirements of the specific application. Here are several factors to consider during the selection process:

Application Requirements: Evaluate the expected operating voltage and current in the charge pump. Ensure that the selected diode can handle the peak values without approaching its limits.
Forward Voltage Drop: A lower forward voltage drop helps in maximizing efficiency. For instance, in applications requiring high conversion efficiency, Schottky diodes are often preferred due to their lower Vf compared to standard diodes.
Speed: In applications where switching frequency is high, fast recovery diodes are essential to prevent significant losses from reverse recovery effects, which can negatively impact circuit efficiency.
Thermal Management: Do consider the diode's power dissipation capabilities. Calculate the thermal performance and ensure that the diode can operate within safe limits in terms of temperature rise.

Each charge pump application may have unique conditions that necessitate different diode characteristics. For example, in a boost converter operating at high frequency, a Schottky diode would effectively minimize conduction losses, whereas a standard silicon diode may suffice in a low-frequency application where power losses due to forward drop are less critical.

Case Study: Voltage Doublers

Voltage doubler charge pumps provide a classic context for diode selection. In a voltage doubler, diodes are strategically used to direct current flow during both charging and discharging phases of the capacitors. A practical scenario involves a boost converter that seeks to double a 5V input, commanding diodes that can comfortably handle the voltage swing and reverse recovery efficiently. For high efficiency in such designs, engineers opt for Schottky diodes, often reported to yield conversion efficiencies greater than 85%. However, if the application requires operating voltages that exceed the breakdown limits of common Schottky types, silicon diodes may be deployed, albeit at the cost of increased conduction losses. In conclusion, a comprehensive understanding of diode characteristics and judicious selection based on application requirements are vital steps in designing effective charge pump circuits. This understanding not only optimizes the performance of the charge pump but also enhances the reliability and lifespan of the overall system. By keeping these principles in mind, engineers can ensure robust designs capable of meeting demanding electronic specifications.

Diagram Description: A diagram would visually illustrate the current flow and operation of diodes in a voltage doubler charge pump, highlighting the roles of different diodes during the charging and discharging phases. This representation would clarify how diodes manage voltage transformations and current directions, which is complex to convey through text alone.

2.3 Switching Frequency Impact

The switching frequency of charge-pump circuits plays a crucial role in determining their performance and efficiency. As engineers and researchers design these circuits, understanding how various switching frequencies affect their output characteristics becomes essential. From voltage ripple to the overall efficiency and heat generation, the implications of switching frequency are numerous and significant.

Understanding Switching Frequency

The switching frequency, defined as the rate at which the circuit alternates between charging and discharging states, directly influences several key parameters of the charge pump. This frequency, often in the range of kilohertz (kHz) to megahertz (MHz), governs the converter's speed and response time, but it also has cascading effects on efficiency, output voltage ripple, and component stresses.

Impact on Efficiency

Typically, an increase in switching frequency can lead to improved conversion efficiency due to faster charging and discharging cycles. However, as the frequency rises, energy losses associated with switching losses—due to the inherent characteristics of semiconductor devices—also tend to increase. At very high frequencies, these losses may outweigh the benefits of speedy operation, leading to decreased overall efficiency.

To illustrate this, consider the power loss in a MOSFET switch, which can be expressed as:

$$ P_{loss} = (I_{d} \cdot V_{ds})_{avg} + \frac{1}{2} \cdot V_{ds} \cdot I_{d} \cdot f_{sw} $$

In this equation, $P_{loss}$ represents the total power loss, where $I_{d}$ is the drain current through the switch, $V_{ds}$ is the drain-source voltage, and $f_{sw}$ is the switching frequency. The term $(I_{d} \cdot V_{ds})_{avg}$ captures the conduction losses, while the second term accounts for switching losses that grow with frequency. These dependencies emphasize that optimizing the switching frequency is not merely about increasing it, but finding a balance that maximizes efficiency.

Output Voltage Ripple

Another critical aspect of switching frequency is its impact on the output voltage ripple, which is the deviation of the output voltage from its average value. A higher switching frequency typically results in reduced ripple voltage, as the charge pump can more rapidly stabilize the output. This effect can be expressed through the ripple voltage equation:

$$ V_{ripple} = \frac{I_{out}}{f_{sw} \cdot C_{out}} $$

Here, $I_{out}$ is the output current and $C_{out}$ is the output capacitance. As the switching frequency $f_{sw}$ increases, the voltage ripple $V_{ripple}$ decreases, leading to a more stable output. However, it is pertinent to note that the chosen output capacitance and load conditions will also play pivotal roles in determining the practical ripple experienced in real applications.

Component Stress and Thermal Considerations

With that said, operating at higher frequencies also puts additional stress on circuit components, particularly capacitors and inductors. These components may experience increased thermal loads due to their higher operational switching speeds, leading to potential reliability issues. Thermal management in high-frequency applications thus becomes a critical factor in the design of charge pumps.

In practical applications, such as telecommunications and power management systems, the implications of switching frequency manifest in the smart choice of components and circuit architectures that can handle the associated thermal and operational stresses. Engineers must balance switching losses, output stability, and component reliability when selecting operating frequencies for their specific applications.

Concluding Remarks

Ultimately, switching frequency serves as a pivotal design parameter in charge-pump circuits. By comprehensively understanding its impacts on efficiency, output stability, and component reliability, engineers can optimize their designs for a wide array of applications ranging from portable electronics to automotive systems.

Diagram Description: A diagram would effectively illustrate the relationship between switching frequency, efficiency, output voltage ripple, and the thermal considerations of circuit components. By visually representing these interdependencies, such as showing how increasing frequency impacts both efficiency and voltage ripple, the complexity of these interactions could be better understood.

3. Output Voltage and Ripple

3.1 Output Voltage and Ripple

The output voltage and ripple in charge-pump circuits are critical parameters influencing their performance and suitability for various applications. Charge pumps utilize capacitors as energy storage elements, which operate by transferring charge between capacitors to generate regulated voltage levels from a lower input voltage. Understanding how these parameters are calculated and managed is essential for advanced electronics design.

Output Voltage Calculation

To derive the output voltage of a standard charge pump, consider the basic configuration which includes capacitors (C), switches (often represented as diodes), and an input voltage (V_in). The fundamental operation involves charging the capacitor to the input voltage, and then transferring this charge to produce an output voltage (V_out). Let’s start with a simple charge pump circuit: 1. Charging Phase: When the switch is closed, the capacitor charges up to the input voltage: $$ V_C = V_{in} $$ 2. Discharging Phase: When the switch changes position, the capacitor discharges and transfers its stored charge to an output capacitor. The output voltage can be conceptualized following the fundamental charge conservation principle. When the charge Q on the capacitor is transferred to the output capacitor, the following holds: $$ Q = C \cdot V_{in} $$ Based on conservation, when the charge is shared among the output capacitor (C_out) and the original capacitor: $$ C \cdot V_{in} = C_{out} \cdot V_{out} $$ From this, we can rearrange the equation to derive the output voltage after a few cycles: $$ V_{out} = \frac{C}{C_{out}} \cdot V_{in} $$ This expression suggests that the output voltage is proportional to the ratio of the capacitors involved, highlighting how selecting the appropriate component values can optimize voltage conversion.

Ripple Voltage in Charge Pumps

A significant characteristic of output voltage in charge pumps is the ripple voltage, which manifests as a variation in voltage due to the charging and discharging cycles of the capacitor. Ripple can affect the stability and overall performance of the circuit. The ripple voltage (V_ripple) can be quantified during the discharge phase of the output capacitor. For a given output current (I_out) and the capacitance value (C_out), the ripple voltage can be calculated using the following formula: $$ V_{ripple} = \frac{I_{out}}{f \cdot C_{out}} $$ Where: - $ I_{out} $ is the output current, - $ f $ is the switching frequency of the charge pump. This equation illustrates the relationship between load current, capacitance, and ripple voltage. A higher capacitance or lower output current will result in reduced ripple voltage. Consequently, selecting a capacitor with a higher capacitance can greatly minimize ripple, improving the quality of the output voltage signal in practical applications.

Practical Importance and Applications

Understanding the output voltage and ripple in charge pumps is not mere academic exercise; it has profound implications in practical applications. Charge pumps are commonly used in power management systems, including battery-powered devices, where efficiency and size are compact. For instance, in mobile devices, a low ripple voltage is crucial for maintaining stable operation of sensitive analog components. Additionally, the principles behind optimizing output voltage and minimizing ripple hold relevance in led driving circuits and RF amplifiers where precision voltage levels are pivotal. In summary, mastering the intricacies of output voltage and ripple in charge pump circuits equips engineers and designers to innovate and implement reliable and efficient electronic systems capable of meeting modern technological demands.

Diagram Description: The diagram would illustrate the charge-pump circuit configuration, showing the charging and discharging phases of the capacitors and the relationship between input and output voltages. It would visually represent the dynamics of charge transfer and help clarify the conservation of charge principle.

3.2 Efficiency Calculations

Understanding the efficiency of charge-pump circuits is fundamental for optimizing performance in various applications, including power management systems and voltage regulation. Efficiency, in this context, refers to the ratio of output power to input power, encapsulating how effectively a circuit converts electrical energy.

Defining Efficiency

To quantify the efficiency of a charge pump, we utilize the equation:

$$ \text{Efficiency} (\eta) = \frac{P_{out}}{P_{in}} \times 100\% $$

Where:

P_out is the output power, calculated as P_out = V_out × I_out, with V_out representing the output voltage and I_out the output current.
P_in is the input power, calculated as P_in = V_in × I_in.

In practical charge pump applications, measuring both I_in and I_out can be challenging due to varying load conditions. Thus, simulated and theoretical calculations are often used for efficiency estimations.

Voltage Gain and Efficiency Trade-offs

One crucial factor to consider is the voltage gain (or conversion ratio), denoted as:

$$ V_{gain} = \frac{V_{out}}{V_{in}} $$

A higher voltage gain often leads to decreased efficiency, primarily due to the increased losses in the switching components. To illustrate:

When a charge pump operates in the voltage-doubling mode, it can ideally convert an input voltage into double the output voltage (2×). However, added complexities arise—such as capacitor discharge rates and switching losses—leading to diminished efficiency.
A typical charge pump might boast an efficiency of 70-90%, depending on the configuration and load conditions.

Loss Mechanisms in Charge Pumps

Several loss mechanisms directly influence the efficiency of charge pumps:

Switching Losses: These occur during the ON/OFF transitions of MOSFETs or other switching devices. Rapid switching can cause transient currents and voltages that lead to heat generation.
Capacitor ESR (Equivalent Series Resistance): Non-ideal capacitor behavior adds a resistive component to the circuit, resulting in power losses during charging and discharging cycles.
Diode Forward Voltage Drop: In scenarios where a diode is used to direct current flow, the inherent voltage drop reduces the effective output voltage, impacting the calculated efficiency.

Optimizing Efficiency

To maximize efficiency, engineers can adopt several strategies:

Minimize Ripple Voltage: By ensuring appropriate capacitor selection and minimizing ripple, engineers can enhance the overall performance.
Choose Low-ESR Capacitors: These components can significantly reduce losses associated with charge and discharge cycles.
Optimize Switching Frequency: Finding an optimal balance between frequency and efficiency can help mitigate unwanted losses.

In conclusion, while charge-pump circuits offer valuable solutions for voltage conversion, maximizing their efficiency requires a thorough understanding of the involved processes and careful circuit design. Practical implementations often necessitate simulations and prototyping to refine performance based on specific applications and operational conditions.

3.3 Load Regulation

In the realm of charge-pump circuits, achieving stability and reliability under varying load conditions is paramount. This stability is quantitatively measured through a parameter known as load regulation. Load regulation defines how well a circuit maintains its output voltage in response to changes in the output load current. Essentially, it is critical for ensuring that the output voltage remains within specified limits as the load varies.

Load regulation can be mathematically expressed through the formula:

$$ \text{Load Regulation} = \frac{\Delta V_{out}}{\Delta I_{load}} $$

Here, $ \Delta V_{out} $ represents the change in output voltage when varying the load current $ \Delta I_{load} $. This relationship highlights that a smaller variation in output voltage for a given change in load current reflects better performance in terms of load regulation.

Understanding the Factors Influencing Load Regulation

Several factors contribute to the load regulation performance of charge-pump circuits. Key elements include:

Capacitance: The output capacitor significantly affects the transient response to load changes. Larger capacitance values generally provide improved load regulation but may add bulk and reduce the circuit's speed of response.
Topological Design: Different charge-pump topologies, such as voltage doubling or inverting configurations, may exhibit distinct load regulation characteristics due to varying internal resistances and output configurations.
Switching Frequency: The operating frequency and efficiency of the switching elements during charge and discharge phases influence the overall impedance presented to the load, thus affecting load regulation.
Control Mechanisms: Implementing feedback control systems can significantly enhance load regulation by adjusting the charge-pump's operation based on real-time output voltage measurements.

Practical Relevance of Load Regulation

In practice, excellent load regulation is crucial for applications where stable voltage is essential, such as in precision analog circuits, radio frequency systems, and battery-powered devices. For instance, inconsistent output voltage can lead to performance degradation, increased noise, or even component failure in sensitive equipment. Case studies illustrate how improved load regulation directly correlates with enhanced device performance and lifespan.

As an example, consider a handheld device powered by a charge-pump circuit. If the load regulation is poor, diverse loads during operation (such as display backlighting or signal processing tasks) could lead to voltage dips, which may affect functionality or reduce signal integrity. Consequently, engineers carefully consider load regulation during design and simulation phases to ensure adherence to performance standards.

Overall, understanding and optimizing load regulation in charge-pump circuits not only enhances device reliability but also boosts overall efficiency in power management systems. Therefore, ongoing research and refinement in this area remain pivotal as electronic devices continue to evolve and demand more stringent performance criteria.

Diagram Description: The diagram would illustrate the relationship between output voltage and load current, visually representing the concept of load regulation through a graph or curve showing variations in voltage against changing loads. Additionally, it could show the impact of different factors like capacitance and switching frequency on load regulation.

4. Voltage Doublers and Inverters

4.1 Voltage Doublers and Inverters

Charge-pump circuits are essential in modern electronics, especially for applications requiring voltage conversion without bulky transformers. Within this realm, voltage doublers and inverters are fundamental designs that help achieve specific voltage levels effectively.

Understanding Voltage Doublers

A voltage doubler is a simple yet effective circuit that converts an input AC or pulsating DC voltage to a higher DC voltage, typically double that of the input. This capability is particularly useful in battery-powered devices where space is limited and efficiency is critical.

There are various implementations of voltage doublers, the Greinacher circuit being one of the most common due to its simplicity and ease of integration. This circuit typically employs two capacitors and two diodes to achieve the voltage doubling effect.

To derive the output voltage of a simple voltage doubler, consider the circuit where the diodes conduct during alternating cycles. Assuming an ideal diode and perfect capacitors, we can state:

$$ V_{out} = 2 \cdot V_{in} $$

Where V_out is the output voltage, and V_in is the input voltage. The charging and discharging of capacitors during each phase create the higher output voltage.

Exploring Inverters

On the other hand, voltage inverters serve to convert a lower DC voltage to a higher DC voltage, essentially performing the inverse function of a voltage doubler. This is particularly useful in applications where a boost in voltage is required, such as in powering devices from low-voltage batteries.

Similar to voltage doublers, inverters utilize capacitors and diodes but are designed to alternate the charge direction to achieve the required voltage boost. The boost converter configuration is often employed in inverter designs, characterized by its capability to produce an output voltage greater than its input.

The basic operation of a boost converter can be derived using the principle of energy conservation. During the 'on' phase, energy is stored in the inductor, while in the 'off' phase, this stored energy is released to attain a higher output voltage. The voltage relationship can be expressed as:

$$ V_{out} = \frac{V_{in}}{1 - D} $$

Here, D is the duty cycle of the switching device. This relationship highlights that the output voltage can be significantly increased with a suitably tuned duty cycle.

Applications and Practical Relevance

Both voltage doublers and inverters have extensive applications in consumer electronics, battery management systems, and renewable energy technologies. They play a crucial role in systems where efficient power management is necessary:

Power supply circuits for portable devices.
Photovoltaic energy systems to regulate output voltage levels.
DC-DC converters in electric vehicles for powering peripheral systems.

In advanced applications, even microcontrollers and low-power RF circuits utilize these charge-pump configurations to enhance performance while minimizing size and complexity.

Conclusion

Understanding voltage doublers and inverters within charge-pump circuits is fundamental for anyone working in the fields of electronics and electrical engineering. These mechanisms not only provide higher voltages but also optimize circuit performance and enhance device functionality in various applications.

Diagram Description: The diagram would illustrate the configuration of the voltage doubler and inverter circuits, showing the arrangement of components like diodes and capacitors. It would help visualize the operational principles of these circuits, including the flow of current and voltage levels during different phases of operation.

4.2 Battery Management Systems

Battery management systems (BMS) are critical components in modern electronic devices that utilize rechargeable battery packs. Their primary function is to monitor and manage battery performance, ensuring efficiency, extending lifespan, and enhancing safety. Given the increasing complexity of applications ranging from electric vehicles to portable electronics, integrating charge-pump circuits within BMS has become a focal point for optimizing energy management.

Understanding the role of charge-pump circuits in BMS requires a grasp of voltage regulation and power conversion, both of which are essential for maintaining the operational integrity of battery cells. Charge pumps are simple DC-DC converters that handle small to moderate power supplies, converting lower voltages into higher voltages via capacitive storage. This feature is particularly useful in BMS where precise voltage levels dictate the charging and discharging processes.

Charge-Pump Functionality in Battery Management

At their core, charge pumps operate on the principle of displacement of charge, typically utilizing capacitive elements. The basic operation involves charging a capacitor to a certain voltage and subsequently transferring this charge to another capacitor, thus achieving a voltage boost. The effectiveness of this mechanism in a BMS can be broken down into several key applications:

Voltage Regulation: Charge pumps help in fine-tuning the output voltage necessary for different cells within a pack, allowing for uniform charging and discharging.
Cell Balancing: Unequal charging among cells can lead to reduced performance. Charge pumps can facilitate active balancing by moving charge between cells, thus optimizing battery lifecycle.
Protection Mechanisms: Implementing charge pumps effectively allows for fail-safes like over-voltage protection by quickly adjusting output in response to sensed conditions.

The reliability of charge pumps in BMS applications lies in low quiescent current and minimized electromagnetic interference (EMI), making them ideal for battery-powered devices where energy efficiency is paramount.

Mathematical Description of Charge-Pump Performance

To understand the behavior of charge pumps in a BMS context, we can derive the output voltage ($V_{out}$) from the input voltage ($V_{in}$) based on a typical flying capacitor architecture. The output voltage can be approximated by the formula:

$$ V_{out} = V_{in} \cdot (1 + D) $$

In this equation, $D$ is the duty cycle of the switching action, defined as the ratio of the time the switch is on to the total period of the cycle. This relationship illustrates that by controlling the duty cycle, the output voltage can be systematically adjusted.

Real-World Applications

As the demand for lightweight and efficient BMS continues to rise, charge-pump circuits are becoming increasingly integrated into various technologies. In electric vehicles, for instance, they play an essential role in battery pack management, ensuring that each cell remains within optimal operational limits. Furthermore, in consumer electronics, optimizing power supply to sensors and microcontrollers expands battery life and enhances user experience.

Incorporating charge-pump circuits into BMS not only augments performance but also influences the cost-effectiveness of battery solutions by minimizing overall component counts and enhancing thermal management. As we move toward a future dominated by smart energy systems, the synergy between charge-pump circuits and advanced battery management will undoubtedly shape the next generation of electronic devices.

Diagram Description: The diagram would illustrate the basic operation of a charge pump, showcasing how capacitors charge and transfer energy to achieve a higher output voltage. This visual representation will clarify the voltage transformation process that is difficult to convey effectively through text alone.

4.3 Power Management Integrated Circuits

Introduction to Charge-Pump Circuits in Power Management

Charge-pump circuits have emerged as invaluable tools in the realm of Power Management Integrated Circuits (PMICs), playing a critical role in voltage regulation and conversion. These circuits utilize capacitive elements to generate higher or lower voltages without the need for inductors, thus simplifying circuit designs and enhancing reliability. In this section, we will delve into the operational principles of charge-pump circuits as they relate to PMICs, discussing configurations, efficiency considerations, and practical applications.

Operating Principles of Charge-Pump Circuits

At their core, charge-pump circuits employ a series of switches (typically MOSFETs) and capacitors to transfer charge and achieve the desired voltage change. The basic operational mechanism involves two main phases: the charging phase and the discharging phase. In the charging phase, input voltage is applied to a capacitor, which collects charge. During the discharging phase, the charge is redirected either to a load or another capacitor arranged in a way that facilitates voltage multiplication (in a voltage-doubler configuration, for example).

The fundamental equation governing the charge transfer can be derived from the principle of conservation of charge. Assuming ideal conditions, the output voltage $ V_{out} $ of a basic charge pump can be expressed as:

$$ V_{out} = n \cdot V_{in} $$

Here, $ n $ represents the multiplication factor determined by the configuration of the circuit—specifically, the number of capacitors and the switching methodology used. If the circuit is designed as a voltage-doubler, $ n $ would equal 2, thus yielding $ V_{out} = 2 \cdot V_{in} $.

Configuration Types

Charge pumps can be broadly categorized into two types: voltage doublers and voltage inverters. Voltage doublers convert a lower input voltage into a higher output voltage, which is beneficial in applications requiring increased voltage for component operation or sensor excitation. Conversely, voltage inverters, or negative voltage charge pumps, convert a positive input voltage to a negative output voltage, presenting unique utility in biasing operations for analog components, particularly in operational amplifiers and similar configurations.

Efficiency Considerations

While charge pumps offer many advantages, such as simplicity and small size, efficiency remains a pivotal consideration in their application within PMICs. Parameters such as load current, switching frequency, and capacitor sizes can significantly influence efficiency. It's common for charge pumps to achieve efficiencies ranging from 70% to 95%, depending largely on the operating conditions and design choices. Engineers must balance the capacitive values and switching speed to minimize losses associated with capacitance charging and discharging, in addition to ensuring minimal switching losses.

A practical approach for improving efficiency involves the implementation of a low-resistance path for the current flow within the circuit, reducing power dissipation. Furthermore, using low on-resistance MOSFETs can significantly enhance performance by mitigating the losses during the switches’ transitional states.

Real-World Applications

Charge pumps are frequently utilized in various applications spanning from consumer electronics to automotive systems. Common uses include:

Battery-powered devices: Ensuring proper voltage levels for integrated circuits in compact formats.
LED drivers: Providing sufficient voltages for efficient LED illumination.
RFID tags: Generating voltages necessary for signal transmission.
Microcontrollers: Supplying core and peripheral voltages in embedded systems.

As systems continue to demand higher performance while minimizing space and cost, the relevance of charge pumps in PMICs is expected to grow, supporting innovations across diverse fields of electronics.

Diagram Description: The diagram would illustrate the operation of a charge-pump circuit, showing the charging and discharging phases, along with the voltage transformation. It would depict both voltage doubler and inverter configurations to enhance understanding of their distinct operations.

5. Common Issues and Symptoms

5.1 Common Issues and Symptoms

Charge-pump circuits serve a crucial role in various electronic applications, from portable devices to sophisticated communication systems. However, like any electronic device, they can encounter issues that may affect their performance. Recognizing these common problems and their symptoms is essential for diagnosing and troubleshooting effectively.

Understanding Common Issues

Charge-pump circuits typically generate higher voltage levels than the input supply, using capacitors and diodes to transfer charge efficiently. The signaling performance and voltage output can be hindered due to several factors. Here are some prevalent issues:

Capacitor Quality: The type and quality of capacitors used in charge-pump circuits directly impact performance. Low ESR (equivalent series resistance) capacitors are essential to minimize energy loss during the charge transfer process. Use of subpar capacitors may result in increased ripple voltage and reduced output stability.
Switching Frequency: The operating frequency is pivotal to the efficiency and output voltage of the charge pump. Frequencies too low may lead to inadequate charge transfer, while excessively high frequencies can introduce noise and increase electromagnetic interference (EMI), affecting the circuit's reliability.
Load Conditions: Variability in the load resistance can alter the performance of the charge pump significantly. Heavy loading may cause voltage drop, while a light load can result in over-voltage conditions, potentially damaging sensitive components downstream.

Diagnostic Symptoms

When a charge pump circuit underperforms, several symptoms emerge, often indicating issues highlighted previously. Identifying these signs is crucial for timely intervention:

Insufficient Output Voltage: If the output voltage is lower than expected, it may indicate capacitor failure or an incorrect switching frequency. Typical solutions involve testing the capacitors and adjusting the frequency to the optimal range.
Excessive Ripple Voltage: A significant fluctuation in output voltage may hint at inadequate filtering due to poor capacitor performance. Observing the output with an oscilloscope can reveal the extent of ripple, guiding further action such as capacitor replacement or circuit redesign.
Overheating Components: If components are getting excessively hot, this might be a sign of a short circuit or an inefficient design leading to high current draw. A systematic approach is necessary to identify the source of overheating.

Real-World Applications and Importance

Charge pumps are frequently employed in portable electronics, where efficient voltage conversion is paramount. Examples include smartphones, battery management systems, and various other consumer electronics. Thus, understanding and addressing common issues in charge-pump circuits is not only an academic exercise but a practical necessity that directly affects device reliability and user experience.

Mastering the challenges associated with charge-pump systems enhances one's ability to design and implement more robust and efficient voltage conversion circuits, ensuring that engineers and researchers remain at the forefront of technological advancements.

Diagram Description: The diagram would illustrate the charge-pump circuit's operation, showcasing the interaction between capacitors and diodes in transferring charge, as well as depict the voltage waveforms at different points in the circuit. This visual representation would clarify the key operational concepts that may be challenging to grasp purely from text.

5.2 Diagnostic Techniques

In the realm of charge-pump circuits, diagnostic techniques are crucial for both the development and troubleshooting stages. These circuits, often employed for voltage conversion, require reliable performance in energy transfer, efficiency, and voltage regulation. Understanding the diagnostic strategies can vastly improve the efficacy and longevity of these circuits in practical applications, such as power supply circuitry, RF circuits, and portable devices.

Understanding Performance Metrics

Before diving into specific diagnostic techniques, it's essential to grasp the key performance metrics of charge-pump circuits. The most critical parameters include:

Voltage Conversion Ratio (VCR): The ratio of output voltage to input voltage.
Efficiency (η): Defined as the ratio of output power to input power, calculated as:

$$ \eta = \frac{P_{out}}{P_{in}} \times 100\% $$

Load Regulation: The change in output voltage resulting from a change in load current.
Line Regulation: The sensitivity of the output voltage to variations in input voltage.

These metrics provide an initial framework for assessing the health and effectiveness of charge-pump circuits, directing us toward appropriate diagnostic methods.

Diagnostic Techniques

Identifying issues within charge-pump circuits often entails employing a combination of analytical and experimental techniques. Here are several diagnostic methodologies commonly used:

1. Voltage Probing

One of the first methods for diagnosing charge-pump circuits involves probing the various nodes in the circuit with an oscilloscope or a multimeter. By measuring the voltages at critical junctions, engineers can determine if the circuit is achieving the desired outputs and if there are any unexpected voltage drops.

2. Waveform Analysis

An oscilloscope is a powerful tool for visualizing the waveforms generated by charge pumps, particularly in switching configurations. Examining the waveform not only helps identify issues related to oscillation frequency but also provides information about noise and ripple, which could indicate problems with filtering or capacitance. It is important to assess both the clock signal and the output voltage waveform. Discrepancies in these signals may lead to identifying faulty components, inadequate loop compensation, or mismatched switching devices.

3. Load Testing

Load testing is essential for validating whether a charge pump can handle specified load conditions. By connecting variable resistive loads and measuring changes in output voltage, engineers can assess the load regulation specifications. Instantaneous load changes can be simulated to evaluate the circuit’s transient response, providing insights into stability and performance.

4. Thermal Imaging

Overheating components often signify underlying issues such as overloading or inadequate cooling. Using a thermal imaging camera can allow for non-intrusive inspection, making it easier to pinpoint hotspots that may indicate failing components or poor thermal contact.

5. Component Testing

As charge pumps typically employ various semiconductor devices, integrity checks of components, such as diodes and capacitors, are critical. Utilizing a component tester can help identify faulty switches or rectifying devices, which may lead to circuit malfunctions. Additionally, electrolytic capacitors can degrade over time, and testing capacitance with a dedicated meter can reveal aging components in need of replacement.

6. Simulation and Modeling

Before deployment, charge-pump circuits can be modeled using simulation tools (e.g., SPICE). These models can provide insights into expected performance and allow engineers to iterate designs efficiently. Comparing real-world measurements against simulated predictions can yield clues about discrepancies in expected behavior.

Conclusion

Effective diagnostics for charge-pump circuits combine multiple techniques to ensure optimal performance and longevity. By employing methods such as voltage probing, waveform analysis, and load testing, engineers can identify potential failures early, saving time and resources during development and production phases. As we continue to advance our methodologies and adopt new diagnostic tools, our ability to manage the complexities of charge-pump circuits will only improve, bolstering their applications in the technological landscape. Additionally, these diagnostic strategies emphasize the importance of staying proactive, not only in fault detection but in ensuring the continual optimization of charge-pump circuit performance.

Diagram Description: The diagram would illustrate the voltage waveforms at critical points in a charge-pump circuit, showcasing how different inputs affect the output and highlighting transient responses under varying load conditions.

5.3 Solutions and Preventive Measures

When dealing with charge-pump circuits, understanding potential issues is critical for maintaining performance and reliability. This section aims to offer advanced-level readers insights into various challenges faced during operation, along with effective solutions and preventive measures to mitigate these risks.

Identifying Common Issues

Charge-pump circuits can encounter several issues, including voltage droop, ripple voltage, and inefficiencies in conversion ratios. These problems may stem from design imperfections, component mismatches, or external conditions such as temperature fluctuations. Focusing on these core challenges will lead to a better grasp of how to enhance circuit performance. 1. Voltage Droop: This represents a drop in output voltage under load, commonly influenced by parasitic capacitances and resistance in the circuit layout. Moreover, the output capacitor value and the load current can exacerbate this issue. 2. Ripple Voltage: Ripple voltage appears as an AC component on the output DC voltage. This might stem from insufficient filtering or incorrect capacitor sizing, which can lead to undesirable behavior in sensitive electronics. 3. Efficiency Losses: Low conversion efficiency can occur due to fundamental design constraints, such as inappropriate selection of switches and diodes, leading to significant heat generation and reliability issues.

Solutions to Voltage Droop and Ripple Voltage

Effective solutions to mitigate voltage droop and ripple voltage can be approached through careful analysis and circuit design: - Decoupling Capacitors: Incorporating high-frequency decoupling capacitors in parallel with the output capacitor can effectively reduce voltage droop during transient loading. Selecting capacitors with low Equivalent Series Resistance (ESR) ensures minimal voltage drop during heavy load conditions. - Optimized Output Capacitor Selection: Careful calculation of capacitance value based on load specifications ensures that ripple voltage stays within acceptable limits. The capacitance required can be assessed using the formula:

$$ C_{min} = \frac{I_{load}}{f_{sw} \Delta V_{out}} $$

where $ I_{load} $ is the load current, $ f_{sw} $ is the switching frequency, and $ \Delta V_{out} $ the allowable output voltage ripple.

Increasing Efficiency

To tackle inefficiencies, the following strategies may be employed: - Switch Selection: Utilizing low on-resistance transistors for switching applications minimizes conduction losses, contributing to higher efficiency. It’s advisable to adopt synchronous rectification techniques, effectively enhancing performance by reducing reverse recovery losses. - Optimized Layout: A well-planned PCB layout can reduce the parasitic inductance and capacitance. Employing short trace lengths, minimizing loop areas for high-frequency paths, and placing decoupling capacitors physically close to the switching devices can greatly enhance circuit performance.

Preventive Measures

Implementing preventive measures is paramount in maintaining circuit integrity under various operating conditions. Some crucial strategies include: - Thermal Management: Proper thermal management techniques, such as heat sinks and thermal pads, can alleviate overheating issues and improve component longevity. - Testing Under Load Conditions: Pre-deployment testing of the charge-pump circuit under various load scenarios is essential to ascertain robustness. Simulations can serve as valuable tools in this regard. - Component Quality Assurance: Utilizing high-quality components with appropriate ratings and tolerances helps mitigate failures, especially in critical applications where reliability is essential. By recognizing potential problems, implementing solutions, and applying preventive measures, the reliability and efficiency of charge-pump circuits can be significantly enhanced, ensuring they meet demanding specifications in advanced applications.

Diagram Description: The diagram would illustrate the relationships between decoupling capacitors, output capacitors, and load conditions, highlighting how they affect voltage droop and ripple voltage. Additionally, a layout image showing optimum PCB design to minimize parasitic effects would clarify spatial arrangements critical for effective circuit performance.

6. Recommended Textbooks

6.1 Recommended Textbooks

Design of Analog CMOS Integrated Circuits by Behzad Razavi — Explores comprehensive design methods for CMOS ICs, a vital resource for understanding charge-pump circuits. The book emphasizes design principles and real-world applications in analog and mixed-signal circuits.
Microelectronics: Circuit Analysis and Design by Donald A. Neamen — This textbook provides an in-depth view of microelectronics, including extensive coverage of charge-pump circuits. It combines theoretical framework with practical techniques and real-life examples.
CMOS Circuit Design for RF Sensors by Gunnar Gudnason and Martin Vesterager — Offers insights into the design of CMOS circuits for RF sensors, covering fundamental concepts and tailored approaches to circuit design, including charge-pump applications.
Analog Integrated Circuit Design by Tony Chan Carusone, David Johns, and Kenneth W. Martin — A comprehensive guide focusing on modern analog circuit design, covering topics such as CMOS technology and circuit techniques for charge-pumps.
Digital Integrated Circuits: A Design Perspective by Jan M. Rabaey — Though primarily focusing on digital circuits, this book includes essential insights and techniques in integrated circuit design, offering valuable context for high-efficiency charge-pump circuits.
Power Management Integrated Circuits by Mona M. Hella and Patrick P. Mercier — Focuses on the design of power management circuits, especially essential for the optimization of charge-pump circuits in low-power applications.
Switching Power Supplies A to Z by Sanjaya Maniktala — Offers an extensive exploration of switching power supplies, crucial for understanding the design and operation of charge-pump circuits in power supply applications.
Charge Pump Circuits: An Overview and Step-by-Step Design by Johan Henselmans and Enrico Santarelli — Specifically focuses on charge pump circuits, providing both the theoretical basis and practical design tips to implement these components effectively in integrated circuits.

Charge-Pump Circuits - Relevant Research Papers

6.2 Relevant Research Papers

A Charge-Pump Design with Low Output Voltage Ripple — This IEEE paper presents a novel charge-pump design aimed at reducing output voltage ripple. The paper offers detailed insights into the methodology and experimental results supporting the design's performance.
Design Challenges and Solutions for High Power Efficiency Charge Pumps — This article reviews various design challenges associated with improving the power efficiency of charge pumps and provides technological solutions based on experimental studies.
Optimal Sizing for Charge-Pump Circuits Using Convex Optimization — This research discusses the application of convex optimization in determining the optimal sizing of charge-pump circuits, enhancing their overall performance and reliability.
Analysis of Charge-Pump Circuit Efficiency Improvement Techniques — It presents an analytical study on various techniques used for enhancing the efficiency of charge-pump circuits, supported by simulation and experimental data.
Energy Consumption Reduction in Charge-Pump Circuits — This paper investigates methodologies to reduce energy consumption in charge-pump circuits, offering a comparative evaluation of different approaches to achieve energy efficiency.
Advancements in Multi-Stage Charge-Pump Design — A comprehensive exploration of advancements in multi-stage charge-pump design, providing insights into their benefits and limitations through practical case studies and simulations.
New Approaches to Minimize Charge-Pump Circuit Losses — This study analyzes innovative approaches to minimizing loss in charge-pump circuits, including a detailed discussion on implementation and expected improvements.
Mathematical Modeling of Charge-Pump Performance — Focuses on novel mathematical modeling techniques to predict and enhance the performance parameters of charge-pump circuits, a resourceful guide for researchers aiming to design efficient systems.

6.3 Online Resources and Tools

Design and Analysis of Charge Pump Circuits — Texas Instruments — A detailed application note from Texas Instruments on designing charge-pump circuits, including practical usage scenarios, components, and analysis techniques.
Understanding Charge Pump Circuits — Analog Devices — This article explains the principles and applications of charge-pump circuits, focusing on their operation and real-world use cases.
Charge Pump Circuit Design and Simulation — Cadence — Cadence provides insight into simulation environments for charge-pump circuits, detailing tools and methods to accurately analyze performance.
Charge Pump Voltage Regulators — EEWeb — A comprehensive overview of voltage regulation using charge-pump circuits, including design considerations and performance factors.
Understanding and Choosing the Best Charge Pumps — EE Times — This article discusses factors influencing the choice of charge-pump circuits and covers industry standards and advancements in technology.
Charge Pump Design Help — All About Circuits Forum — A community forum post that provides interactive discussions on troubleshooting and improving charge-pump circuit designs.
AN201: Charge Pump Circuits — Silicon Labs — A PDF guide by Silicon Labs that elaborates on the necessary calculations, examples, applications, and efficiency optimization for charge-pump circuits.