Chapter 11: Understanding Copper Losses

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Introduction

While core losses occur within the magnetic material itself, copper losses occur within the winding conductors.

In many power inductors, copper losses are the largest source of heat generation.

Even if a magnetic core is operating efficiently, excessive winding losses can reduce efficiency, increase temperature rise, and limit overall performance.

Understanding copper losses is therefore essential when designing high-performance magnetic components.

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What Are Copper Losses?

Copper losses are the energy dissipated as heat when electrical current flows through a conductor.

Because no conductor has zero resistance, every winding produces some amount of heat.

Copper loss is calculated using:

Where:

• PCu = Copper Loss
• I = Current
• R = Resistance

This equation is sometimes called the I²R loss equation.

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Why Current Is So Important

Notice that current is squared.

This means copper losses increase very rapidly as current increases.

For example:

Current	Relative Copper Loss
1 A	1×
2 A	4×
3 A	9×
4 A	16×

Doubling current results in four times the heating.

This is one reason high-current magnetic components require careful winding design.

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Understanding DC Resistance (DCR)

The resistance of a conductor is determined by:

Where:

• R = Resistance
• ρ = Resistivity
• l = Conductor Length
• A = Cross-Sectional Area

Resistance increases when:

• Wire length increases
• Wire diameter decreases

Resistance decreases when:

• Larger wire is used
• Multiple conductors are placed in parallel

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Why DCR Matters

DCR is often one of the first specifications engineers evaluate.

Lower DCR generally provides:

• Higher efficiency
• Lower temperature rise
• Higher current capability

However, minimizing DCR usually requires:

• More copper
• Larger winding windows
• Larger cores
• Increased cost

The best design balances all of these factors.

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Skin Effect

At low frequencies, current flows uniformly through the conductor.

As frequency increases, current begins concentrating near the outer surface.

This phenomenon is called skin effect.

The effective current penetration depth is known as skin depth.

As frequency increases:

• Skin depth decreases
• Effective conductor area decreases
• AC resistance increases

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Proximity Effect

Skin effect is caused by a conductor’s own magnetic field.

Proximity effect is caused by nearby conductors.

Magnetic fields from adjacent windings force current to crowd into specific regions of a conductor.

This effect increases:

• AC resistance
• Heat generation
• Efficiency loss

In many high-frequency designs, proximity effect contributes more loss than skin effect.

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AC Resistance

At higher frequencies, conductor resistance becomes larger than its DC resistance.

This is called AC resistance.

The ratio between AC resistance and DC resistance depends on:

• Frequency
• Conductor size
• Number of layers
• Winding geometry

As frequency increases, AC resistance can become several times higher than DCR.

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Round Magnet Wire

Round magnet wire remains the most common conductor used in power magnetics.

Advantages:

• Low cost
• Easy winding
• Widely available

Disadvantages:

• Lower fill factor
• Increased AC losses at higher frequencies

Round wire is often the best solution for low- and medium-frequency applications.

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Parallel Conductors

Multiple smaller wires can be connected in parallel.

Advantages:

• Lower resistance
• Better winding flexibility
• Improved fill factor

Parallel conductors are frequently used in:

• High-current inductors
• Automotive electronics
• Industrial power converters

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Litz Wire

Litz wire consists of many individually insulated strands woven together.

The purpose of Litz wire is to reduce:

• Skin effect losses
• Proximity effect losses

Advantages:

• Lower AC resistance
• Improved efficiency
• Better high-frequency performance

Disadvantages:

• Higher cost
• More difficult termination

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Copper Foil Windings

Copper foil can provide excellent current handling capability.

Advantages:

• Low resistance
• Excellent fill factor
• Reduced proximity losses

Disadvantages:

• More complex manufacturing
• Additional insulation requirements

Foil windings are commonly used in high-current transformers and inductors.

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Temperature Rise from Copper Losses

All copper losses eventually become heat.

Higher winding temperatures can:

• Reduce efficiency
• Accelerate insulation aging
• Reduce reliability
• Shorten product life

Thermal performance must always be evaluated alongside electrical performance.

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Methods for Reducing Copper Losses

Engineers commonly reduce copper losses by:

Using Larger Conductors

Lower resistance reduces I²R losses.

Using Parallel Strands

Increases effective conductor area.

Using Litz Wire

Reduces high-frequency AC resistance.

Reducing Mean Length Per Turn

Shorter windings reduce resistance.

Optimizing Winding Layout

Improves current distribution and minimizes AC losses.

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What You’ve Learned

In this chapter you learned:

• What copper losses are
• Why I²R losses generate heat
• How DCR affects efficiency
• What skin effect is
• What proximity effect is
• Why AC resistance increases with frequency
• The advantages of round wire, parallel conductors, Litz wire, and foil windings
• Practical methods for reducing copper losses

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Continue Reading

Chapter 12: Thermal Design of Inductors

Now that we understand both core losses and copper losses, the next step is learning how those losses translate into temperature rise and how engineers design magnetic components that remain reliable under real-world operating conditions.

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