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Inductor Charging and Discharging: Charge and Discharge Equation

In this article we will introduce the charging and discharging of the inductor in detail. By reading this article you will have a deeper understanding of inductors

Inductor

Catalog

Introduce

What is Inductor Charge?

The Role of Inductor Charging

What is Inductor Discharge?

Application of discharge inductor

Inductor discharge equation

The role of inductance

Introduce

Inductor is an electromagnetic conversion component. Using the electromagnetic induction principle of "electricity generates magnetism" and "magnetism generates electricity", the inductor can convert electrical energy into magnetic energy and store it. The electrical energy stored in the inductor can be converted into electrical energy. At the moment of power-on, the inductor will try to prevent the increase of current, and at the moment of power-off, the inductor will try to prevent the disappearance of current.

The charging and discharging principle of the inductor means that when the inductor is connected to the DC power supply, a magnetic field will be generated inside the inductor and energy will be stored; when the inductor is disconnected from the DC power supply, the stored energy inside the inductor will be released.

What is Inductor Charge?

At the moment when the inductor is connected to the DC power supply, the positive pole of the power supply is connected to the end of the inductor, and current begins to flow through the inductor, creating a changing magnetic field. According to the theory of electromagnetic induction, when the magnetic field changes: an induced drag potential will be generated in the sensor. The direction of this induced electromotive force is opposite to the DC power supply, which hinders the change of current, so the current inside the inductor will slowly increase.

Basic charging and discharging circuit of inductor

Figure 1: Basic charging and discharging circuit of inductor

As time goes by, the current inside the inductor gradually increases, and the magnetic field also strengthens. When the magnetic field inside the inductor reaches saturation, the current inside the inductor also reaches the maximum value, and the charging process is completed.

The Role of Inductor Charging

The charging process of an inductor is fundamental to its role in electronic circuits, particularly in the following applications:

1. Energy Storage

Just as in its discharge, during charging, an inductor stores energy in its magnetic field, which can later be released. This is crucial for energy storage systems that rely on rapid charging and discharging cycles.

2. Filtering and Smoothing

In the charging phase, inductors help to smooth out variations in current, which is vital for filtering applications in power supplies and audio electronics, ensuring steady operation despite fluctuations.

3. Pulse Shaping

In circuits designed to generate specific pulse shapes, the charging characteristics of inductors are used to control the rise time of pulses, which is essential for applications requiring precise timing, such as communication systems.

4. Electromagnetic Interference (EMI) Suppression

The gradual increase in current through an inductor during charging helps suppress sudden changes in current that can cause electromagnetic interference, improving the performance and reliability of electronic devices.

5. Voltage Regulation

In voltage regulation applications, including in switch-mode power supplies, the controlled charging of inductors is used to help maintain a constant output voltage, compensating for variations in input voltage or load.

6.Current Limiting

Inductors are used to limit the inrush current when power is first applied to a circuit, protecting components from damage due to sudden high currents.

What is Inductor Discharge?

When disconnected from the DC power supply, the current inside the inductor cannot stop flowing immediately because the change in current will produce a voltage opposite to the DC power supply. This voltage is called the self-inductance voltage. The self-inductance voltage will cause the current to continue to flow, and the energy stored in the inductor will be gradually released by the reduction of the current within the inductor.

As the current decreases, the magnetic field gradually weakens until it disappears completely. At this point, the discharge process is completed and the energy in the inductor is completely released.

Application of discharge inductor

1. DC-DC Converters

Inductors are used in various types of DC-DC converters, such as buck, boost, and buck-boost converters, to regulate the output voltage. During the discharge phase, the stored energy in the inductor is released to the load, helping to maintain a steady output voltage even when the input voltage or load conditions change.

2. Filters

In LC (inductor-capacitor) filters, the discharge characteristics of inductors are utilized to smooth out the ripple in power supplies or to filter out certain frequencies from a signal. The combination of inductors and capacitors can be designed to allow certain frequencies to pass while blocking others, making them essential for frequency selection in radio receivers and other communication devices.

3. Energy Storage Systems

Inductors can be used in energy storage systems where short-term energy storage is needed. The energy stored in the magnetic field of an inductor can be quickly released, making it useful for applications requiring rapid discharge, such as in pulsed lasers or flash photography.

4. Snubber Circuits

Snubber circuits protect switching components from voltage spikes. When a switch (like a transistor) opens, the inductor tries to maintain the current flow, leading to a potentially damaging voltage spike. A snubber circuit, often incorporating a resistor and a capacitor, safely dissipates the energy stored in the inductor, preventing these spikes.

5. Motor Control

In motor control applications, inductors are used to smooth out the current flow to the motor, providing more stable operation and reducing electrical noise. The discharge characteristics of inductors are crucial for regenerative braking systems in electric vehicles, where the kinetic energy of the vehicle is converted back into electrical energy and stored in the battery.

6. Switch Mode Power Supplies (SMPS)

In SMPS circuits, inductors are essential for both stepping down (buck converters) and stepping up (boost converters) the voltage. The discharge phase of the inductor plays a critical role in transferring energy from the input to the output with high efficiency.

Inductor discharge equation

It can be inferred from Figure 1 that all changes in the inductor voltage from the initial value Vin during the switch turn-on phase are due to the presence of R. Therefore, if R=0, the inductor voltage remains unchanged during the switch conduction phase, and the induced voltage must be equal to the applied voltage. It is easy to draw this conclusion from Kirchhoff's voltage law, because at this time the resistance is zero, the voltage drop across the resistor is also zero, and the external voltage is all applied to both ends of the inductor. If the inductor current continues to change, the inductor can maintain the applied voltage; if there is a voltage across the inductor, the electric wave passing through it must change.

Differentiate both sides of the inductor current equation with time and set R = 0 as shown below.

inductor equation

It can be seen that when the inductor is directly connected to the power supply Vin, the current rises with a fixed slope Vin/L. Derive the general equation for inductance.

General Equations for Inductor Charging and Discharging

The straight line segment of the above equation (inductor voltage V is constant) can also be written as an incremental or decremental equation for a given time period:

inductor equation

The inductance equation applies not only to the charging phase of the inductor, but also to its discharging phase. In addition, the inductance equation is also an important equation for deriving many characteristics of inductors!

The role of inductance

Capacitors have charging and discharging characteristics. By utilizing the mutual conversion of the electric field and magnetic field of the inductor, the inductor and capacitor can be connected in parallel to achieve LC oscillation. When the capacitor discharges and generates current, the inductor will block the passage of the current and convert the electric field into a magnetic field for storage; after the capacitor discharges, the inductor will block the disappearance of the current, and the magnetic field in the inductor will be converted into an electric field, and the generated current will pass through the other electrode of the capacitor. Charging; after charging is completed, the capacitor begins to discharge in reverse direction; forming oscillating energy. If the energy loss is not considered, this oscillation will continue forever.

Electric and magnetic field properties of inductors

The mutual charge and discharge of the electric field and magnetic field of the inductor

By utilizing the mutual conversion (charge and discharge) characteristics of the electric field and magnetic field of the inductor, it is possible to block AC and pass DC. In power supply circuits, we often use inductors to filter to eliminate high-frequency interference signals.

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Frequently Asked Questions

1. How does an inductor discharge?

When an inductor is charged with current and then disconnected from its power source, it begins to discharge. During the discharging process, the inductor's magnetic field collapses, inducing a voltage across its terminals in the opposite polarity to the original voltage that charged it. This induced voltage causes current to continue flowing through the circuit, albeit in the opposite direction, until the magnetic field dissipates completely.

2. How long does it take an inductor to discharge?

Yes, in many cases where fast switching times are required and where the power levels are within the handling capacity of the MOSFET, it can be used to replace a relay. However, relays have advantages in situations requiring high voltage or current handling capabilities or when electrical isolation is needed.

3. What happens if you disconnect a charged inductor?

If you disconnect a charged inductor from its power source, the inductor starts to discharge. The collapsing magnetic field induces a voltage across its terminals, causing current to continue flowing through the circuit in the opposite direction until the stored energy in the magnetic field is dissipated completely. This discharge process can generate a voltage spike, which could potentially damage sensitive components in the circuit if not properly managed, such as through the use of flyback diodes or other protection mechanisms.

4. What is the function of the inductor?

The primary function of an inductor is to store energy in the form of a magnetic field when current flows through it. This stored energy can then be released back into the circuit when the current changes, such as during the discharge process. Inductors are commonly used in electronic circuits for various purposes, including filtering noise, smoothing output voltages, energy storage, and inductive coupling for signal transmission. They are essential components in many electronic devices and systems, including power supplies, filters, transformers, and oscillators.

5. Disadvantages of discharge inductor

Voltage spikes can damage electronics, energy losses reduce efficiency, transient responses cause fluctuations, circuit design complexity increases, and size and weight constraints may arise.

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