Document 486 Revised 12/20/05

AbstractAs power supply output current requirements continueto increase, it is important for the design engineer topay close attention to inductor power losses and theiraffect on overall power supply efficiency. This paperintroduces the basic formulas to determine the approxi-mate inductor power losses.

IntroductionThe demand for an improvement in power supply effi-ciency, and therefore, inductor efficiency has increasedquite rapidly. This demand has come as a result of anincrease in power supply output current. At the sametime, there has been a renewed effort to reduce theamount of heat that power supplies have to dissipate,which has a direct effect on overall power supply effi-ciency. The reduction in heat creation is especiallyimportant to laptop users. Since heat creation andinductor power loss are directly related, it is extremelyimportant to reduce inductor power losses. To reducethese losses, it is necessary to understand where thethey come from.

Inductor Power LossThe power loss of an inductor is defined by the basicformula:

PlossInductor = Pcore + Pdcr + Pacr

Each component of this formula is discussed below.

PcoreThe calculated and/or measured core loss is oftendirectly provided by the inductor supplier. If not, aformula can be used to calculate the core loss. Measur-ing core loss and getting repeatable results can be atedious task depending on the test frequency. A gen-eral form of the core loss formula for ferrite cores is:

Pcore (mW) = K1fxBy × Ve

Where:K1 = Constant for core material

f = Frequency in kHzB = Peak Flux Density in kGaussx = Frequency exponenty = Flux Density exponent

Ve = Effective core volume (cm3)

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

PdcrThe wire loss caused by dc resistance is easy to calcu-late. It is defined by this basic formula:

Pdcr (W) = Irms2 × DCRWhere:Irms = The rms value of the peak current applied to

the inductorDCR = The dc resistance of the inductor

PacrThe wire loss caused by ac resistance is more difficultto calculate since ac winding resistance values are notalways readily available from magnetics vendors. Pacr isdefined by the following formula:

Pacr (W) = Irms2 × ACRWhere:Irms = The rms value of the peak-peak ripple current

applied to the inductorACR = The ac resistance of the inductor

The inductor power loss information can be often beprovided by inductor suppliers for most of their prod-ucts. In an effort to speed up the design process forengineers using inductors, Coilcraft has developed acalculator for calculating inductor core and dcr loss.Currently, the calculator is based on the formula:

PlossInductor = Pcore + Pdcr

The calculator will eventually also account for Pacr. Inmany cases Pacr is a small percentage of the overallinductor power loss.

ConclusionThis paper has introduced the basic formulas used indetermining inductor power loss. It also discussed theimportance of knowing where inductor power lossescome from in order to reduce heat creation and thusimprove overall efficiency.For a more thorough discussion on ac losses refer to:Document 470-1, titled Inductor Performance in HighFrequency DC-DC Converters: Understanding AClosses.

Determining InductorPower LossesNelson GarciaCoilcraft

Core, DCR and ACR Losses