Chapter 02: Understanding Inductance

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Introduction

Inductance is one of the most important concepts in electrical engineering. Every inductor, transformer, motor winding, and magnetic component relies on inductance to store energy and control current flow.

While many engineers can use inductors successfully, fewer understand what physically creates inductance and why it changes when core materials, air gaps, or winding configurations are modified.

In this chapter, we will explore the physical meaning of inductance and the variables that determine its value.

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What Is Inductance?

Inductance describes the ability of a conductor to store energy in a magnetic field.

When current flows through a wire, a magnetic field forms around that conductor. If the wire is wound into a coil, the magnetic field becomes concentrated and much stronger.

The energy stored within this magnetic field can later be released back into the circuit.

The amount of energy stored depends upon the inductance and the current flowing through the device.

Where:

• E = Stored energy (Joules)
• L = Inductance (Henries)
• I = Current (Amperes)

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The Physical Meaning of Inductance

Inductance is a measure of how effectively current creates magnetic flux.

A commonly used definition is:

Where:

• L = Inductance
• N = Number of turns
• Φ = Magnetic flux
• I = Current

This equation tells us that inductance increases when:

• More turns are added
• More magnetic flux is generated
• The magnetic path becomes more efficient

Inductance decreases when:

• Turns are removed
• Magnetic reluctance increases
• Air gaps are introduced

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How Current Creates Magnetic Flux

One of the most important characteristics of an inductor is that it resists changes in current.

When the current through an inductor attempts to increase or decrease, the magnetic field responds by generating a voltage that opposes that change.

This behavior is fundamental to the operation of switching power supplies, filters, energy storage circuits, and transformers.

The relationship between voltage and changing current is:

Where:

• V = Voltage across the inductor
• L = Inductance
• di/dt = Rate of change of current

This equation explains why larger inductance values produce smaller current ripple in many power converter applications.

Whenever electrical current flows through a conductor, a magnetic field forms around that conductor.Inductors Oppose Changes in Current

A straight wire produces a relatively weak field.

A coil concentrates those magnetic fields into a much smaller region, dramatically increasing magnetic flux density.

This is why coils are used in nearly all practical magnetic components.

The more turns added to a winding, the stronger the resulting magnetic field becomes.

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The Importance of Core Materials

Understanding Magnetic Permeability

The ability of a material to support magnetic flux is described by its permeability.

Materials with high permeability allow magnetic flux to flow more easily than air.

The relationship between material permeability and free-space permeability is:

Where:

• μ = Material permeability
• μ₀ = Permeability of free space
• μᵣ = Relative permeability

Ferrite materials often have relative permeabilities hundreds or thousands of times greater than air, allowing significant increases in inductance with the same winding geometry.

Air-core coils can generate inductance, but magnetic core materials dramatically increase inductance by concentrating magnetic flux.

Common magnetic materials include:

• Ferrite
• Powdered Iron
• Amorphous Metals
• Nanocrystalline Materials

Each material provides different magnetic permeability, loss characteristics, saturation limits, and frequency performance.

Higher permeability generally produces higher inductance for a given number of turns.

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Why Air Gaps Matter

Many power inductors intentionally include an air gap within the magnetic path.

Although adding an air gap reduces inductance, it greatly increases the amount of energy that can be stored before saturation occurs.

This tradeoff is one of the most important concepts in power magnetics design.

A properly designed air gap allows an inductor to:

• Store more energy
• Handle higher currents
• Avoid magnetic saturation

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Factors That Determine Inductance

The Geometry Behind Inductance

The factors discussed above can be combined into a simplified inductance relationship:

Where:

• μ = Core permeability
• N = Number of turns
• A = Core cross-sectional area
• l = Magnetic path length

Although practical magnetic designs often require more advanced calculations, this equation clearly shows the primary variables that influence inductance.

From this relationship we can see:

Longer magnetic paths reduce inductance

More turns increase inductance

Higher permeability increases inductance

Larger core area increases inductance

The primary variables that determine inductance are:

Number of Turns

More turns generally increase inductance.

Core Material

Higher permeability materials increase inductance.

Magnetic Path Length

Longer magnetic paths reduce inductance.

Core Cross-Sectional Area

Larger cores generally increase inductance.

Air Gap Length

Larger gaps reduce inductance but improve energy storage.

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What You’ve Learned

In this chapter you learned:

• What inductance physically represents
• How magnetic fields store energy
• Why coils create magnetic flux
• How core materials influence inductance
• Why air gaps are important
• Which design parameters control inductance

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Continue Reading

Chapter 03: Understanding Magnetic Flux and Flux Density

That sequence creates a very logical engineering progression:

Chapter 01 - Introduction to Inductors
Chapter 02 - Understanding Inductance
Chapter 03 - Magnetic Flux and Flux Density
Chapter 04 - Core Materials
Chapter 05 - Air Gaps
Chapter 06 - Energy Storage
...

which mirrors how magnetics is typically taught while still leading naturally into the design work that SolidMagnetics automates.

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