Temp rise

Power Electronics Technology July 2004 www.powerelectronics.com14

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By calculating core losses and winding losses, transformer temperaturerise may be predicted. Through appropriate core material selection, corelosses may be minimized at the expected operating temperature.

BBBBB y Gy Gy Gy Gy Georeoreoreoreorge G.ge G.ge G.ge G.ge G. Or Or Or Or Orenchak,enchak,enchak,enchak,enchak, General Manager, TSC FerriteInternational, Wadsworth, Ill.

Transformers for power applicationsoften are limited in size by an accept-able temperature rise. An acceptabletemperature rise of a transformer isusually dependent on limitations of the

materials used in the transformer, safety agency regulationsor high-temperature reliability issues associated with othercomponent parts close to the transformer. The tempera-ture rise of a transformer is due to the power loss dissi-pated by the transformer in the form of heat. The powerloss of a transformer consists of core loss and of windingcoil losses, and can be predicted accurately.

Core LossesCore losses significantly contribute to the temperature

rise of a transformer. Hysteresis loss, eddy current loss andresidual loss all contribute to the total core loss. At highflux densities and relatively low frequencies, hysteresislosses are usually dominant.

Hysteresis loss is the amount the magnetization of the

ferrite material lags the magnetizing force because ofmolecular friction. The loss of energy caused by hysteresisloss is proportional to the area of the static or low-frequencyB-H loop. At high frequencies, eddy current losses usuallydominate. Eddy current losses result from a varying induc-tion that produces electromotive forces, which cause acurrent to circulate within a magnetic material.

These eddy currents result in energy loss. Understand-ing the behavior of the combined total core loss as func-tions of flux density and of frequency is most important.FigFigFigFigFig..... 1 1 1 1 1 shows the relationship of core loss versus frequencyfor power-grade ferrite materials. FigFigFigFigFig..... 2 2 2 2 2 shows the relation-ship of core loss versus flux density for power-gradeferrite materials. Manufacturers typically combine andexpand the information on FigFigFigFigFigs.s.s.s.s. 1 1 1 1 1 and 22222 by publishing coreloss as a function of flux density at various frequencies andon logarithmic scales, as shown in FigFigFigFigFig..... 3. 3. 3. 3. 3.

Notice both core loss versus frequency and core lossversus flux density relationships are exponential. Symmetri-cal sine wave, square wave and unidirectional square wave

voltage excitations all result inapproximately the same core loss,providing the frequency and totalflux density excursion remain thesame. Manufacturers typicallypublish core loss, as measured, us-ing symmetrical sinusoidal voltageexcitation.

For the excitation types men-tioned, core loss can be obtainedin a straightforward manner frommanufacturers’ published graphsor calculated from core loss for-

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Fig. 1. Core loss versus frequency at 1000 gauss. Fig. 2. Core loss versus flux density at 100 kHz.


TEMPERATURE RISE

mulas. Non-square wave pulse voltagewaveform excitations (FigFigFigFigFig..... 4 4 4 4 4) need tobe considered differently.

For pulse voltage waveform exci-tation, it’s more accurate to calculatean “apparent frequency” by taking the

these core loss relationships empiri-cally from measured data. The expo-nents and constant are determined bythe use of the following formulas.

At some fixed flux density,x=ln(P

C@1stf/P

C@2ndf)/ln(1stf/2ndf)

At some fixed frequency,y=ln(P

C@1stB/P

C@2ndB)/ln(1stB/2ndB)

k=PC@B&f/(By*fx)

FigFigFigFigFig..... 5 5 5 5 5 shows core loss as functionof temperature for several materialgrades, including a new material(TSF-50ALL Flat Line). Soft ferritematerials were first developed in thelate 1940s for signal applications, andthey had minimum loss densities inthe region of room temperature.Thus, under normal working condi-tions, the loss increased with an in-crease in temperature.

In the 1970s, ferrite manufactur-ers found that losses in ferrite show aminimum at the anisotropy com-pensation temperature. With this dis-covery, manufacturers learned totailor the material composition to

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Fig. 3. Core loss versus flux density.

Fig. 4. Apparent frequency.

inverse of the time period to completeone cycle of flux swing. This resultsin the apparent frequency and ishigher than the switching frequency.Use this apparent frequency to lookup core loss from manufacturers’ pub-lished graphs or to calculate core lossfrom formulas. However, you mustmultiply this result by the duty cycleto obtain a good estimate for core loss.

For a specific material grade, thepower loss at a given temperature canbe expressed by a single formula:P

C = K fx By

Where:P

C = core loss in mW/cm3

K = constant for a specific mate-rial grade (0.08 for TSF-50ALLmaterial)f = frequency in kHzB = flux density in k gaussx = frequency exponent (1.39 for TSF-50ALL)y = flux density exponent (2.91 forTSF-50ALL)

Ferrite manufacturers have derived

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make materials that have minimumcore loss near the expected workingtemperature.

Numerous material grades opti-mized for a specific ideal operatingtemperature now exist. The presentbrings additional discoveries that en-able ferrite manufacturers to developnew material grades that exhibit thesame low core loss over a wider oper-ating temperature range (50 mW/cm3

at 100 kHz, 1000 gauss from roomtemperature to more than 100°C).

This new material grade will contrib-ute to more energy-efficient productsbecause the core loss will be optimizedover the entire operating tempera-ture range. Products made fromthese materials will be safer becausethe chance of thermal runaway willbe less. These new material gradesalso will minimize required core in-ventories because one grade of mate-rial will be optimal for all power ap-plications, regardless of operatingtemperature.

Ferrite Material PropertiesAlthough material properties other

than core loss are unimportant in de-termining temperature rise or coresize of a transformer, other proper-ties are of interest if integrated mag-netics (transformers and inductorswound on a common magnetic core)are being considered.

The magnitude and stability ofTSF-50ALL Flat Line’s initial perme-ability over a wide operating tempera-ture may be advantageous for somelow flux-density signal applications.

Transformer applications requireenough permeability to providea good flux path so flux stays in theintended path and doesn’t stray outof the core. Output power inductorapplications predominantly requirea gapped core. The gap depth sizebecomes a dominant factor while de-termining the component inductanceand the material permeability is rela-tively unimportant.

Transformer core size is often con-strained by the core loss of the core

TEMPERATURE RISE

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Fig. 5. Core loss versus temperature.

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material. However, power inductorcore size is often constrained by thecore material’s saturation propertiesat operating temperatures.

Winding Coil LossesWinding coil losses contribute to

a transformer’s total loss. Copperlosses (I2R losses) are easy to under-stand. Winding coil losses due to skineffect, proximity effect, effect of eddy

currents in the windings, effects fromfringing flux intersecting windingsnear the core gap, edge effects and ex-traneous conductor effects may be sig-nificant and should be considered. Forsimplicity, we’ll ignore these addi-tional winding losses and consideronly I2R copper losses.

The resistance of each winding canbe calculated by multiplying the meanlength turn of the winding by the cop-

per resistance for the appropriate wiresize and by the total turn count.R

P or R

S= MLT * R

CU * N

Where:R

P = primary coil resistance in �

RS = secondary coil resistance in �

MLT = mean length turn in cmR

CU = copper resistance in µ�/cm

N = turn countThe copper losses for each wind-

ing are calculated with the followingformulaP

CU = I2 R

Where:P

CU = copper loss in watts

I = current in ampsR = resistance in �

Sum the primary and all the sec-ondary winding losses to obtain thetotal winding losses, and then sum thetotal winding losses with the corelosses to obtain the total transformerlosses (P�).

Temperature RiseA transformer’s output power is

less than its input power. The differ-ence is the amount of power convertedinto heat by core loss and windinglosses. A combination of radiationand convection dissipate this heatfrom the exposed surfaces of the trans-former. Thus, the heat dissipation isdependent upon the total exposedsurface area of the core and the totalexposed surface area of the windings.

Temperature rise of a transformeris hard to predict with precision. Oneapproach is to lump the winding lossestogether with the core losses and as-sume that the thermal energy is dissi-pated uniformly throughout the sur-face area of the core and winding as-sembly at all ambient temperatures.This isn’t a bad assumption, becausethe majority of the trans-former’s sur-face area is ferrite core area rather thanwinding area, and the thermal conduc-tivity of ferrite (~40 mW/cm/°C) ispoor at any temperature. With theseassumptions, the temperature rise ofa transformer can be estimated by thefollowing formula:�T = (P�/A

T)0.833

Where:�T = temperature rise in °C

TEMPERATURE RISE

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TEMPERATURE RISE

P� = total transformer losses (power lost and dissipated asheat) in mW; A

T = surface area of transformer in cm2.

The exponent (0.833) used in the above formula to es-timate temperature rise has been derived from empiricaldata with the use of the following formula:x=ln(P�@1st�T/P�@2nd�T)/ln(1st�T/2nd�T)

FigFigFigFigFig..... 6 6 6 6 6 shows temperature rise versus power loss for sev-eral different size E core transformers.

The temperature rise of a transformer results in partfrom core loss and in part from winding coil losses. The

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Fig. 6. Temperature rise versus transformer power loss.

core losses and winding losses and temperature rise can beestimated with calculations by making a few assumptions.Because of the assumptions made, it may be necessary toprove the temperature rise empirically by measuring thetransformer using thermal couples. New ferrite materialsthat exhibit consistent core loss over a wide range of oper-ating temperatures will simplify ferrite material selectionand prove valuable to the transformer industry. PETPETPETPETPETe c he c he c he c he c h

References1. Snelling, E.C. “Soft Ferrites Properties and Applications,Second Edition,” Butterworth, 1988.2. McLyman, C. Wm. T. “Magnetic Core Selection for Trans-formers and Inductors,” Marcel Dekker Inc., 1982.3. McLyman, C. Wm. T. “Transformer and Inductor DesignHandbook,” Marcel Dekker Inc., 1978.4. Jamerson, Clifford. “Targeting Switcher Magnetics CoreLoss Calculations,” Power Electronics Technology, February2002, Vol. 28, No. 2.5. Carsten, Bruce. “High Frequency Conductor Losses inSwitchmode Magnetics,” PCIM, November 1986.6. “Soft Ferrites: A User’s Guide,” Magnetic MaterialsProducers Association, MMPA SFG-98, 1998.

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