Inductance and Energy Storage
5. Practical Inductance Applications
Learning outcomes
- I can identify devices that use inductors.
- I can explain the role of inductors in electrical circuits.
- I can describe how inductors reduce electrical noise.
- I can explain how inductors are used in power supplies.
- I can evaluate the advantages of inductors in modern electronics.
Practical Inductance Applications
Inductors are used throughout modern electrical and electronic systems because they oppose rapid changes in current and store energy in magnetic fields.
An inductor is usually made from a coil of conducting wire. Many inductors also contain a magnetic core to increase their inductance.
Their behaviour is based on self-induction:
changing current → changing magnetic field → self-induced EMF
The induced EMF opposes the change in current according to Lenz's law.
This simple effect allows inductors to perform several important jobs:
- storing and transferring energy
- smoothing changing currents
- reducing electrical noise
- filtering signals
- converting voltages efficiently
- controlling current in motors and other devices
Inductors in Everyday Electronics
Inductors are found in many familiar devices, including:
- phone chargers
- laptop power supplies
- televisions
- radios
- computers
- Wi-Fi equipment
- LED lighting
- electric vehicles
- electric motors
- audio equipment
- solar power systems
Some inductors are large coils that are easy to recognize.
Others are extremely small components mounted directly onto circuit boards.
Why Inductors Are Useful
The key property of an inductor is that it opposes changes in current.
The induced EMF is related to:
|ε| = L|ΔI/Δt|
where:
- ε = induced EMF
- L = inductance
- ΔI/Δt = rate of current change
Rapid current changes therefore produce larger inductive effects.
This makes inductors particularly useful in circuits containing rapidly changing or switching currents.
Inductors and Steady DC
An ideal inductor behaves differently depending on whether the current is changing.
When DC current is changing:
- the magnetic field changes
- self-induced EMF occurs
- the inductor opposes the current change
When the current becomes steady:
ΔI/Δt = 0
so:
ε = 0
An ideal inductor therefore has zero induced voltage once steady DC conditions are reached.
A real inductor still has some resistance in its wire.
Energy Storage
An inductor stores energy in its magnetic field.
The stored energy is:
E = ½LI²
where:
- E = energy in joules
- L = inductance in henries
- I = current in amperes
When current increases, magnetic energy increases.
When current decreases, the magnetic field can return energy to the circuit.
This temporary energy storage is extremely important in modern power electronics.
Inductors in Power Supplies
One of the most important applications of inductors is in power supplies.
Electronic devices often require a different voltage from the available power source.
For example:
- a battery voltage may need to be reduced
- a battery voltage may need to be increased
- an AC supply may need to be converted to controlled DC
- a varying input may need to produce a stable output
Inductors help accomplish these tasks efficiently.
Switching Power Supplies
Modern electronics commonly use switch-mode power supplies.
Instead of continuously wasting excess electrical energy as heat, electronic switches turn on and off rapidly.
Inductors repeatedly:
store magnetic energy → release magnetic energy
during each switching cycle.
This allows electrical energy to be transferred and converted efficiently.
Why Switching Works
Imagine a switch connected to an inductor.
When the switch is turned on:
- current increases
- magnetic field strengthens
- energy is stored
When the circuit switches configuration:
- current begins changing
- magnetic field changes
- the inductor produces an induced voltage
- stored energy is transferred elsewhere in the circuit
This process may occur thousands or millions of times each second in modern electronics.
Buck Converters
A buck converter reduces DC voltage.
For example, a circuit might convert:
12 V → 5 V
The inductor helps maintain a relatively smooth output current while an electronic switch rapidly turns on and off.
During part of the switching cycle, energy is stored in the magnetic field.
During another part, the stored energy is delivered to the load.
This allows efficient voltage reduction.
Boost Converters
A boost converter increases DC voltage.
For example:
5 V → 12 V
During one part of the cycle:
- current increases through the inductor
- magnetic energy is stored
During another part:
- the magnetic field collapses
- the inductor produces an induced voltage
- its voltage contributes to the output
This can produce an output voltage greater than the input voltage.
Buck-Boost Converters
A buck-boost converter can increase or decrease voltage depending on its design and operating conditions.
Inductive energy storage allows energy to be transferred between different parts of the circuit.
Buck-boost systems are useful when battery voltage changes during operation but the electronics require a controlled output.
Phone and Laptop Chargers
Modern chargers commonly contain inductive components as part of their switching power supplies.
Their functions can include:
- temporary energy storage
- voltage conversion
- current smoothing
- noise filtering
- electromagnetic interference reduction
Efficient switching designs allow chargers to be much smaller than older power supplies while still handling significant electrical power.
Smoothing Current
Switching circuits naturally produce rapid variations in current.
Many electronic devices require a much smoother electrical supply.
An inductor resists rapid current changes.
Therefore, it can reduce the size of these fluctuations.
The result is:
rapidly varying current → inductor → smoother current
This is often called current smoothing.
Current Ripple
Small repeated variations around the desired current are often called ripple.
For example, instead of remaining perfectly constant, current might repeatedly rise and fall slightly.
An inductor helps reduce current ripple because:
rapid current change → larger self-induced EMF
The inductor therefore opposes the rapid increase and decrease.
Inductors as Electrical Filters
Inductors can also help separate unwanted high-frequency signals from useful lower-frequency signals.
For sinusoidal AC, the opposition provided by an ideal inductor is described by inductive reactance:
X_L = 2πfL
where:
- X_L = inductive reactance in ohms
- f = frequency in hertz
- L = inductance in henries
As frequency increases:
X_L increases
Therefore, an inductor has a stronger effect on higher-frequency current variations.
Worked Example: Inductive Reactance
An inductor has:
L = 0.020 H
At:
f = 50 Hz
X_L = 2πfL
X_L = 2π(50)(0.020)
X_L ≈ 6.3 Ω
At:
f = 5000 Hz
X_L = 2π(5000)(0.020)
X_L ≈ 628 Ω
The same inductor provides much greater opposition to the higher-frequency signal.
Reducing Electrical Noise
Electronic circuits can contain unwanted rapidly changing signals called electrical noise.
Noise can come from:
- switching circuits
- motors
- radio-frequency signals
- digital electronics
- power lines
- nearby electronic equipment
Because many forms of unwanted noise contain high-frequency components, inductors can help reduce them.
Chokes
An inductor designed mainly to reduce unwanted AC or high-frequency signals is often called a choke.
A choke can allow desired DC current to pass while providing greater opposition to rapidly changing current.
Therefore:
desired DC → passes relatively easily
while:
high-frequency noise → strongly opposed
Chokes are widely used in power supplies and communication equipment.
Filtering Power-Supply Noise
A DC power supply may contain:
- useful DC
- unwanted AC ripple
- high-frequency switching noise
An inductor can help separate these components.
The DC component is steady and therefore produces little inductive opposition.
Rapid variations produce larger inductive effects.
This allows an inductor to help create a cleaner DC supply.
Inductors and Capacitors Together
Inductors are often combined with capacitors.
They have complementary behaviour:
Inductor: opposes rapid changes in current.
Capacitor: opposes rapid changes in voltage.
Together, they can form powerful filtering circuits.
LC Filters
An LC filter contains:
- an inductor, L
- a capacitor, C
The inductor helps smooth current.
The capacitor helps smooth voltage.
Together, they can reduce unwanted variations more effectively than either component alone.
LC filters are common in:
- power supplies
- audio systems
- radio circuits
- communication equipment
- motor controllers
Common-Mode Chokes
Some cables carry unwanted high-frequency noise that appears in similar ways on multiple conductors.
A common-mode choke uses coupled windings to strongly oppose this unwanted noise while allowing the intended current or signal to pass.
Common-mode chokes are often found in:
- computer equipment
- power adapters
- communication systems
- USB and other data interfaces
- industrial electronics
They help reduce electromagnetic interference (EMI).
Electromagnetic Interference
Electromagnetic interference, or EMI, is unwanted electromagnetic energy that interferes with the operation of electrical equipment.
EMI can cause:
- distorted signals
- communication errors
- audio noise
- unstable electronics
- interference with nearby devices
Inductive filters help prevent unwanted high-frequency currents from travelling through wires and cables.
Ferrite Components
Ferrite is a magnetic ceramic material commonly used in high-frequency inductive components.
You may have seen a cylindrical or enlarged section near the end of a computer or display cable.
Some of these devices contain ferrite material that helps reduce high-frequency interference.
Ferrite components are useful because they can provide strong magnetic effects while limiting unwanted eddy-current losses at high frequencies.
Inductors in Radio Circuits
Inductors are important in radio-frequency circuits.
When combined with capacitors, they can form resonant circuits that respond strongly to particular frequencies.
This allows circuits to:
- select radio frequencies
- reject unwanted frequencies
- tune transmitters
- tune receivers
- filter communication signals
The ability to select frequencies is fundamental to radio and wireless communication.
LC Resonance
In an LC circuit, energy can move between:
- the capacitor's electric field
- the inductor's magnetic field
The capacitor stores energy as:
E_C = ½CV²
The inductor stores energy as:
E_L = ½LI²
This exchange can produce electrical oscillations.
The resonant frequency of an ideal LC circuit is:
f = 1/(2π√(LC))
Example: Radio Tuning
Suppose a radio receives many frequencies simultaneously.
A carefully chosen combination of L and C can have a resonant frequency corresponding to the desired station.
The circuit responds strongly near that frequency while responding less strongly to many other frequencies.
Changing L or C changes the resonant frequency.
This allows the circuit to be tuned.
Inductors in Audio Systems
Inductors can also be used in audio crossover networks.
Different speakers are designed for different frequency ranges.
For example:
- woofers reproduce lower frequencies
- tweeters reproduce higher frequencies
Inductors and capacitors can help direct appropriate frequency ranges to different speakers.
Inductors in Electric Motors
Motor windings are coils and therefore have inductance.
Their inductance affects:
- how quickly current changes
- motor starting behaviour
- current ripple
- electromagnetic torque
- electronic motor control
Modern motor controllers must account for the inductance of the motor windings.
Motor Current Smoothing
Electronic motor controllers often switch voltage rapidly.
Without inductance, current could change very rapidly.
Motor winding inductance helps smooth these changes.
This is especially important in:
- electric vehicles
- drones
- robots
- industrial machines
- computer cooling fans
Relays and Solenoids
Relays and electromagnetic solenoids contain coils.
When current flows:
- a magnetic field develops
- magnetic energy is stored
- magnetic forces can move mechanical components
Examples include:
- electrical switches
- valves
- door locks
- automotive actuators
Because these coils have inductance, switching them off can produce large induced voltages.
Flyback Protection
When current through a coil is suddenly interrupted:
|ε| = L|ΔI/Δt|
If Δt is very small, the induced voltage can become very large.
A flyback diode can provide a temporary path for current when a DC inductive load is switched off.
The stored magnetic energy is then released more safely.
This protects components such as transistors and switches.
Transformers
Transformers contain inductive windings.
Alternating current in the primary produces changing magnetic flux.
Mutual induction produces an EMF in the secondary.
Transformers can:
- increase voltage
- decrease voltage
- provide electrical isolation
- transfer signals
- transfer electrical power
Inductance is therefore central to transformer operation.
Wireless Charging
Wireless charging also uses inductive effects.
An alternating current passes through a transmitter coil.
The changing magnetic field reaches a receiver coil.
Mutual induction produces an EMF in the receiver.
Energy can therefore be transferred without exposed electrical contacts.
Applications include:
- smartphones
- smartwatches
- electric toothbrushes
- some medical devices
- some electric vehicle charging systems
Inductive Sensors
Inductors can be used as sensors because nearby materials can affect their magnetic fields.
Applications include:
- proximity sensors
- position sensors
- metal detectors
- vehicle detection systems
- industrial automation
A nearby conducting or magnetic object changes the electromagnetic behaviour of the sensor coil, allowing the electronics to detect its presence.
Induction Heating
Changing magnetic fields can induce currents in nearby conducting materials.
These currents can produce heating.
Induction heating is used in:
- induction cooktops
- industrial metal heating
- metal treatment
- manufacturing
The coil itself creates the changing magnetic field responsible for the induction process.
Energy Storage in Power Electronics
Inductors are particularly useful because they can store and release energy extremely quickly.
Suppose an inductor has:
L = 0.50 H
and carries:
I = 4.0 A
Stored energy:
E = ½LI²
E = ½(0.50)(4.0²)
E = 4.0 J
If current changes, this energy can be transferred elsewhere in the circuit.
Worked Example: Power-Supply Inductor
A power-supply inductor has:
L = 5.0 mH
and carries:
I = 3.0 A
Convert:
5.0 mH = 0.0050 H
Then:
E = ½LI²
E = ½(0.0050)(3.0²)
E = 0.0025(9)
E = 0.0225 J
Although this is a relatively small amount of energy, the inductor may store and release energy thousands of times per second.
The rate of energy transfer can therefore be significant.
Advantages of Inductors
Inductors provide several important advantages.
They can:
- store energy without relying on chemical reactions
- release stored energy very rapidly
- smooth current
- reduce ripple
- suppress high-frequency noise
- help filter signals
- enable efficient switching power supplies
- support voltage conversion
- provide frequency selection
- operate reliably for very large numbers of cycles
These properties make them extremely valuable in modern electronics.
High Efficiency
An ideal inductor does not dissipate energy.
Instead:
electrical energy → magnetic energy → electrical energy
Real inductors do have losses, but efficient designs can transfer a large fraction of their stored energy back into the circuit.
This makes inductors particularly useful in efficient power-conversion systems.
Fast Response
Magnetic energy can be stored and released quickly.
Unlike chemical energy storage, no chemical reaction is required.
This makes inductors suitable for circuits switching at high frequencies.
Modern power converters can therefore repeatedly store and release energy many thousands or millions of times per second.
Reliability
Inductors are often simple components with no moving parts.
This can provide:
- long operating life
- high reliability
- large numbers of operating cycles
This is especially useful in power electronics and industrial equipment.
Limitations of Inductors
Inductors also have disadvantages.
Real inductors can:
- occupy significant circuit-board space
- be relatively heavy
- have wire resistance
- generate heat
- produce electromagnetic interference
- experience magnetic-core losses
- saturate at high currents
- be more expensive than simple resistors
Engineering design involves balancing these disadvantages against the benefits.
Copper Losses
The wire used to make an inductor has resistance.
Therefore:
P = I²R
describes power converted into thermal energy in the winding.
Large currents can therefore cause significant heating.
Using lower-resistance conductors can reduce these losses.
Core Losses
Magnetic cores can experience energy losses.
Two important mechanisms are:
- eddy currents
- magnetic hysteresis
Core materials and construction are selected to reduce these effects.
For example:
- laminated cores can reduce eddy currents
- ferrite materials are useful at higher frequencies
Magnetic Saturation
Magnetic cores cannot always respond proportionally to indefinitely increasing current.
At sufficiently strong magnetic fields, a core may approach magnetic saturation.
When this occurs:
- effective inductance can decrease
- current may increase rapidly
- losses and heating can increase
- circuit performance may deteriorate
Engineers therefore choose inductors with suitable current ratings.
Size and Energy Storage
Storing significant magnetic energy generally requires:
- sufficient inductance
- sufficient current capability
- adequate magnetic core volume
- suitable conductor size
This is one reason high-power inductors can be physically large.
Miniaturizing inductors while maintaining efficiency and current capacity is an important engineering challenge.
Inductors vs Resistors
| Inductor | Resistor |
|---|---|
| Stores magnetic energy | Mainly dissipates energy as heat |
| Opposes changes in current | Opposes current |
| Ideal component can return stored energy | Does not return dissipated thermal energy |
| Frequency-dependent behaviour | Ideal resistance largely frequency-independent |
| Important in filters and power conversion | Important in current and voltage control |
Inductors vs Capacitors
| Inductor | Capacitor |
|---|---|
| Stores magnetic field energy | Stores electric field energy |
| Energy = ½LI² | Energy = ½CV² |
| Opposes rapid current changes | Opposes rapid voltage changes |
| Current cannot change instantly in ideal model | Voltage cannot change instantly in ideal model |
| Useful for current smoothing | Useful for voltage smoothing |
Inductors and capacitors are often used together because their properties complement each other.
Choosing an Inductor
Engineers may consider:
- inductance
- maximum current
- resistance
- core material
- physical size
- operating frequency
- saturation current
- energy-storage capacity
- heat generation
- electromagnetic interference
The "largest inductance" is therefore not automatically the best choice.
A successful design balances several requirements.
Evaluating Inductors in Modern Electronics
Inductors remain extremely useful because modern electronics increasingly relies on rapid switching.
Switching is used to control energy efficiently rather than continuously dissipating excess energy.
Inductors are well suited to this because they can:
store energy during one part of a switching cycle
and:
release energy during another part
This allows efficient control of electrical power.
Electric Vehicles
Electric vehicles contain numerous inductive components.
They can appear in:
- motor windings
- DC-DC converters
- onboard chargers
- electromagnetic interference filters
- power-conditioning systems
Inductance helps control the very large electrical currents involved in vehicle operation.
Renewable Energy
Solar panels and wind turbines often produce electrical power that must be converted before it can be used or supplied to a grid.
Power-electronic converters use inductors to:
- store energy temporarily
- smooth current
- filter switching noise
- control power flow
Inductors therefore contribute to efficient renewable-energy systems.
Computers and Digital Electronics
Computer processors and other digital components can require low voltages and very large currents.
Voltage-regulator circuits commonly use inductors to convert and control electrical power efficiently.
You may see several small power inductors close to a computer processor or graphics chip.
Their job includes helping deliver stable power despite rapidly changing electrical demand.
A Complete Application Example
Consider a computer power circuit that must convert:
12 V → lower controlled voltage
for a processor.
A switching transistor rapidly connects and disconnects the input.
The inductor:
- stores magnetic energy when current increases
- opposes sudden current changes
- releases energy when the switching state changes
- helps maintain continuous current
- reduces current ripple
A capacitor can simultaneously help stabilize voltage.
Together, the switching components, inductor, and capacitor provide efficient power conversion.
Common Mistakes
Thinking inductors simply block electricity
Inductors oppose changes in current, not current itself.
Thinking an inductor always has a large voltage across it
The induced voltage depends on how rapidly the current changes.
Thinking inductors only work with AC
Inductors also affect DC circuits whenever the DC current changes, such as during switching.
Thinking inductors destroy unwanted electrical energy
Filtering often redirects, stores, releases, or dissipates unwanted variations through a combination of circuit components.
Thinking all noise has the same frequency
Electrical noise can contain many different frequencies, so filters must be designed for the particular application.
Thinking an ideal inductor consumes power continuously
An ideal inductor stores and returns energy. Real inductors have resistance and other losses.
Ignoring saturation
Real magnetic cores have limits to how strongly they can be magnetized.
Thinking larger inductance is always better
Greater inductance may also mean greater size, resistance, cost, or slower current response.
Key Terms
Inductor — component that stores energy in a magnetic field and opposes changes in current.
Inductance — measure of the ability of a circuit to produce self-induced EMF when current changes.
Self-induction — production of an induced EMF caused by a circuit's own changing current.
Magnetic energy — energy associated with the magnetic field of an inductor.
Switch-mode power supply — power supply that uses rapid electronic switching to control and convert electrical energy efficiently.
Buck converter — circuit that reduces DC voltage using switching and energy-storage components.
Boost converter — circuit that increases DC voltage using switching and energy-storage components.
Buck-boost converter — switching converter capable of producing an output voltage above or below its input under appropriate operation.
Ripple — unwanted repeated variation in voltage or current.
Choke — inductor designed to oppose unwanted changing currents or high-frequency signals.
Inductive reactance — opposition an ideal inductor provides to sinusoidal alternating current, given by X_L = 2πfL.
Electrical noise — unwanted electrical variations that interfere with desired signals or power.
Electromagnetic interference (EMI) — unwanted electromagnetic disturbance affecting electrical equipment.
LC filter — filter containing an inductor and capacitor.
Ferrite — magnetic ceramic material commonly used in high-frequency inductive components.
Magnetic saturation — condition in which a magnetic core can no longer respond proportionally to increasing magnetizing influence.
Flyback diode — component used to provide a safe current path when a DC inductive load is switched off.
Key Takeaways
- Inductors are used extensively in modern electrical and electronic devices.
- Their key property is opposition to changes in current.
- Changing current produces self-induced EMF.
- Inductors store energy in magnetic fields.
- Stored magnetic energy is given by E = ½LI².
- Inductors can store and release energy repeatedly and rapidly.
- Switching power supplies use inductors for efficient energy transfer.
- Buck converters use inductors while reducing DC voltage.
- Boost converters use inductors while increasing DC voltage.
- Inductors help smooth current and reduce ripple.
- High-frequency signals experience greater inductive reactance because X_L = 2πfL.
- Chokes use inductance to suppress unwanted changing currents and electrical noise.
- Inductors and capacitors are frequently combined to form filters.
- Common-mode chokes can help reduce electromagnetic interference.
- Inductors are important in radios, audio systems, motors, transformers, sensors, wireless chargers, and power converters.
- Motor windings and electromagnetic coils naturally possess inductance.
- Real inductors experience resistance, heating, core losses, and possible saturation.
- Inductors can improve efficiency because energy can be temporarily stored rather than simply dissipated.
- Their disadvantages can include size, weight, resistance, cost, and magnetic interference.
- Modern electronics depends heavily on inductors for efficient power conversion, current control, noise suppression, and signal filtering.
Check Your Understanding
- Identify five common devices or systems that use inductors.
- Explain why an inductor opposes rapid changes in current.
- Explain how an inductor can store energy and later return it to a circuit.
- Why can an inductor allow steady DC while strongly opposing high-frequency current variations?
- Calculate the inductive reactance of a 0.050 H inductor at 60 Hz.
- The same 0.050 H inductor is used at 6000 Hz. Calculate its inductive reactance and compare it with your answer to Question 5.
- Explain how an inductor can help reduce high-frequency electrical noise.
- What is a choke, and why is it useful in electronic equipment?
- Explain why inductors and capacitors are often used together in power-supply filters.
- Describe the role of an inductor in a buck converter.
- Describe how magnetic energy stored in an inductor can help a boost converter produce a higher output voltage.
- A 20 mH power inductor carries 5.0 A. Calculate the energy stored in its magnetic field.
- Explain why switching off a relay or solenoid can produce a large voltage and how a flyback diode can help protect the circuit.
- Evaluate two advantages and two disadvantages of using inductors in modern electronic devices.
- A designer needs a circuit that efficiently converts voltage, reduces current ripple, and suppresses high-frequency noise. Explain why inductors would be useful and identify other components that could be combined with them.