Determining Inductor Power Losses

Core, DCR and ACR Losses

Abstract

As power supply output current requirements continue to increase, it is important for the design engineer to pay close attention to inductor power losses and their affect on overall power supply efficiency. This paper introduces the basic formulas to determine the approximate inductor power losses.

Introduction

The demand for an improvement in power supply efficiency, and therefore, inductor efficiency has increased quite rapidly. This demand has come as a result of an increase in power supply output current. At the same time, there has been a renewed effort to reduce the amount of heat that power supplies have to dissipate, which has a direct effect on overall power supply efficiency. The reduction in heat creation is especially important to laptop users. Since heat creation and inductor power loss are directly related, it is extremely important to reduce inductor power losses. To reduce these losses, it is necessary to understand where the they come from.

Inductor Power Loss

The power loss of an inductor is defined by the basic formula:

P_lossInductor = P_core + P_dcr + P_acr

Each component of this formula is discussed below.

P_core

The calculated and/or measured core loss is often directly provided by the inductor supplier. If not, a formula can be used to calculate the core loss. Measuring core loss and getting repeatable results can be a tedious task depending on the test frequency. A general form of the core loss formula for ferrite cores is:

P_core (mW) = K₁f^xB^y × V_e

Where:
K₁ = Constant for core material
f = Frequency in kHz
B = Peak Flux Density in kGauss
x = Frequency exponent
y = Flux Density exponent
V_e = Effective core volume (cm³)

The core loss can be calculated by entering the K₁ coefficient and the frequency and flux density exponents, which are unique to each core material.

P_dcr

The wire loss caused by dc resistance is easy to calculate. It is defined by this basic formula:

P_dcr (W) = I_rms² × DCR

Where:
I_rms = The rms value of the peak current applied to the inductor
DCR = The dc resistance of the inductor

P_acr

The wire loss caused by ac resistance is more difficult to calculate since ac winding resistance values are not always readily available from magnetics vendors. P_acr is defined by the following formula:

P_acr (W) = I_rms² × ACR

Where:
I_rms = The rms value of the peak-peak ripple current applied to the inductor
ACR = The ac resistance of the inductor

The inductor power loss information can be often be provided by inductor suppliers for most of their products. In an effort to speed up the design process for engineers using inductors, Coilcraft has developed a calculator for estimating inductor core and winding loss. The calculator is based on the formula:

P_lossInductor = P_core + P_dcr + P_acr

Conclusion

This paper has introduced the basic formulas used in determining inductor power loss. It also discussed the importance of knowing where inductor power losses come from in order to reduce heat creation and thus improve overall efficiency.

For a more thorough discussion on ac losses refer to:
Document 1400, titled Choosing Inductors for Energy Efficient Power Applications.

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Determining Inductor Power Losses

Core, DCR and ACR Losses

Abstract

Introduction

Inductor Power Loss

P_core

P_dcr

P_acr

Conclusion

Questions or Concerns?

General Applications

Handling and Processing

RF Inductors

Power Conversion

EMI/RFI Filtering

Special Applications

Warehouses

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Determining Inductor Power Losses

Core, DCR and ACR Losses

Abstract

Introduction

Inductor Power Loss

Pcore

Pdcr

Pacr

Conclusion

Questions or Concerns?

General Applications

Handling and Processing

RF Inductors

Power Conversion

EMI/RFI Filtering

Special Applications

Warning

P_core

P_dcr

P_acr