Current and Temperature Ratings

Document 361-1

Specifications subject to change without notice. Document 361-1 Revised 05/11/04

IntroductionThis application note describes: How to interpret Coilcraft inductor current and tem-

perature ratings Our current ratings measurement method and per-

formance limit criteria Calculations for estimating power and voltage perfor-

mance limits based on current ratings How to calculate component temperature from the

temperature rating How to estimate component DCR at temperatures

other than 25C. How to calculate performance limits in pulsed wave-

form applications Detailed rms calculations Appendix A Conversion factors for var ious waveforms

Appendix BElectrical ratings are interdependent. The current througha component depends on the applied voltage (wave-form and duty cycle) and the component impedance.The impedance of a component depends on the DCresistance (DCR), the applied signal frequency (for ACresistance), and the component temperature. The tem-perature of a component depends on the thermody-namic (heat transfer) characteristics of the component,the circuit board, the solder connection, the surroundingenvironment, the impedance of the component, and thecurrent through the component. The power dissipation ofa component is a function of all of these variables.The maximum operating rating of a component must begiven in terms of a specific measurement method andperformance limit. For example, the performance limitcould be defined as exceeding a specified temperaturerise or as a total breakdown of the insulation or wire.Different measurement methods and performance limitcriteria lead to different conclusions. By establishing themethod of measurement and the performance limit cri-teria, a baseline is set for evaluating each application.Ultimately, circuit designers attempt to determine maxi-mum operating limits for temperature, current, voltage,and power for each component. Each of these is spe-cific to the application environment.

Coilcraft Inductor Current RatingsDepending on the type of inductor (chip inductor, powerinductor) we may specify an Isat, Irms, or IDC current.

Saturation current (Isat) is the current at which theinductance value drops a specified amount below itsmeasured value with no DC current. The inductancedrop is attributed to core saturation.

rms current (Irms) is the root mean square currentthat causes the temperature of the part to rise a spe-cific amount above 25C ambient. The temperaturerise is attributed to I2R losses.

DC current (IDC) is the current value above which op-eration is not recommended without testing the com-ponent in its intended application.

For some inductors Isat is lower than Irms. The coresaturates before the component temperature reachesthe performance limit. In this case we may specify onlythe Isat as it is the limiting factor. For many inductors,Isat is higher than Irms. In these cases we may specifyonly Irms and the temperature rise above ambient. Inmany cases, we specify both Irms and Isat current toillustrate which measurement is more critical. IDC is speci-fied typically when Irms greatly exceeds Isat.

Coilcraft Measurement Method and PerformanceLimit Criteriarms Current IrmsWe determine Irms by measuring the temperature riseabove 25C ambient caused by the current through arepresentative sample inductor. A low DC bias currentis applied to the inductor, and the temperature of theinductor is allowed to stabilize. This process is repeateduntil the temperature rise reaches the rating limit. Themeasurements are taken with the sample inductor in stillair with no heat sinking. The limit is typically a 15C risefor chip inductors and a 40C rise for power inductors.The actual temperature rise of a component is not con-stant throughout the ambient temperature range. Usethe following equation to calculate the temperature riseof a component:

T

= Td 3.85e3 (234.5 + Ta)where:T is the actual change in temperature of the componentTd is the specified temperature rise from the data sheetTa is the ambient (surrounding environment) temperatureTherefore, the rating criteria are the current level and thetemperature rise limit.

Document 361-2

Specifications subject to change without notice. Document 361-2 Revised 05/11/04

Saturation Current IsatIsat

ratings are established by measuring the inductanceof a representative sample at a specific frequency withno DC current. The DC current level is then graduallyincreased and the inductance is measured.The Isat

rating is the current level at which the induc-tance value drops a specified amount (in percent) be-low its measured value with no DC current.

Power Limit CalculationsTotal or apparent power (PA) consists of a combinationof the average (real) power (Pavg) and the reactive (imagi-nary) power (Pvar). While the purely reactive portion ofpower does not consume energy, there is some lossassociated with its transmission back and forth in thecircuit because transmission lines are not perfect con-ductors.Temperature rise due to the heating effect of currentthrough an inductor is related to the average real powerdissipated by the inductor. The average real power is afunction of the effective series resistance (ESR) of theinductor and the rms current through the inductor, asshown in Equation 1.

Pavg = (Irms)2 ESR (1)where:Pavg = average real power in WattsIrms = rms current in ampsESR = effective series resistance in OhmsEquation 1 can be used to estimate a power limit due toreal losses. The real losses include DC and AC losses,and are described by the ESR of the inductor. The AClosses are frequency-dependent, therefore, we recom-mend using our simulation models to determine the ESRfor calculating the real power dissipation at your specificapplication frequency.The apparent (total) power required by an inductor is afunction of the rms current through the inductor, the rmsvoltage across the inductor, and the phase angle differ-ence between the voltage and current. Equation 2 canbe used to estimate the apparent power required for theinductor.

PA = Irms Vrms cos () (2)where:PA = apparent power in WattsIrms = rms current in ampsVrms = rms potential across inductor in Volts = phase angle in degreesSince the AC behavior of an inductor is frequency-dependent, and Vrms is application-specific, we recom-mend using our simulation models to determine the

apparent power requirements for your specific applica-tion voltage and frequency.

Voltage Limit CalculationsWhile we do not typically specify a maximum voltagerating for our inductors, a limit can be estimated by cal-culating the resulting voltage drop across the inductordue to the maximum current rating (Irms) value. Therms voltage across an inductor is a function of the rmscurrent through the inductor and the complex imped-ance of the inductor, as shown in Equation 3.

Vrms = Irms Z (3)where:Vrms= rms potential across the inductor in VoltsIrms = rms current in ampsZ = complex impedance (R + jX) in OhmsSince the complex impedance is frequency-dependent,we recommend using our simulation models to deter-mine the complex inductor impedance for your specificapplication frequency. Compare the calculated voltagedrop to the dielectric breakdown voltage specified in thedielectric withstanding voltage test. The lower of the twovalues can be used as an estimate of the voltage limit.Our chip inductor qualification standards specify500 Vac for a maximum of one minute as the voltagebreakdown limit of the Dielectric Withstanding Voltagestandard. For some of our power inductors, the break-down voltage of the core material may limit the maxi-mum voltage to a value less than that of the insulationbreakdown voltage.

Operating Temperature RangeOperating temperature is described as a range, such as 40C to +85C. The range describes the recom-mended ambient (surrounding environment) tempera-ture range of operation. It does not describe thetemperature of the component (inductor). The compo-nent temperature is given by the following equation:

Tc = Ta + Tr 3.85e3 (234.5 + Ta)where:Tc is the component temperatureTa is the ambient (surrounding environment) temperatureTr is the temperature rise above ambient due to currentthrough the inductorExample: The operating temperature range for a powerinductor is stated as 40C to +85C, and the Irms israted for a 40C rise above 25C ambient.The worst-case component temperature would be (85C+ 49.2C) = 134.2C at the Irms current.

DC Resistance vs. TemperatureThe following equation can be used to calculate the ap-proximate DC resistance of a component within the op-erating temperature range:

DCRT2 = DCR25 ((1+0.0039 (T225))Where:DCRT2 is the DC resistance at the temperature T2DCR25 is the data sheet value of DC resistance at 25CT2 is the temperature in C at which the DC resistanceis being calculated

Pulsed WaveformsAn ideal pulsed waveform is described by the period(T = 1/ frequency), amplitude, pulse width (Tpw), and dutycycle, as shown in Figure 1. Ideal pulsed waveforms arerectangular. Real pulsed waveforms have rise time, falltime, overshoot, ringing, sag or droop, jitter, and settlingtime characteristics that are not considered in this dis-cussion. We also assume that all pulses in a given appli-cation pulse train have the same amplitude.

The duty cycle (D.C.) is the ratio of the pulse width (timeduration) to the pulse period, as shown in equation 4.

D.C. = Tpw / T (4)where:D.C. = duty cycleTpw = pulse width in seconds, T = period in secondsDuty cycle is typically given as a percent of the period.For example, continuous waves have a 100% duty cycle,since they are on for the whole cycle. Square waveshave a 50% duty cycle: on for a half cycle and off fora half cycle. Duty cycle can also be stated as a ratio. A50% duty cycle is the same as a 0.50 duty cycle ratio.To convert to pulsed power values from the equivalentcontinuous (100% D.C.) waveform estimated power,equate the calculated energy values for a cycle, andsolve the equation for the pulsed power. The calculationuses the definition: energy = power time.

Energy = Pavg T (5)For one cycle of a continuous (100% duty cycle) wave-form, and invoking Equation 1:

Energy = (Irms)2

ESRc Twhere:ESRc = effective series resistance to continuous currentThe ESR is frequency-dependent, and can be obtainedfrom our simulation model of the chosen inductor.For one cycle of a pulsed waveform,

Energy = Ppulsed Tpw (6)Energy = (Ipulsed)2 ESRpulsed Tpw

where:Ppulsed = equivalent pulsed powerTpw = pulse width in secondsESRpulsed = effective series resistance to the pulsedcurrentWhile the pulse width (Tpw) and the pulsed current am-plitude (Ipulsed) are defined for a specific application, theabove logic requires either knowledge of ESRpulsed orthe assumption that it is equivalent to ESRc. For thepurposes of this discussion, we assume that ESR isfrequency-dependent, but not waveform-dependent,therefore ESRpulsed = ESRc. With this assumption, equat-ing the energy terms of Equation 5 and Equation 6, andcanceling the ESR terms:

(Irms)2 T = (Ipulsed)2 Tpw (7)(Irms)2 / (Ipulsed)2 = Tpw / T (8)

and since D.C. is Tpw / T,(Irms)2 / (Ipulsed)2 = D.C.

Solving for the equivalent pulsed current,Ipulsed = ((Irms)2 / D.C.)0.5 (9)

Example: A chip inductor has an Irms rating of 100 mA fora 15C rise above 25C ambient. The duty cycle for aparticular application is calculated using Equation 4 tobe 30%.Using Equation 9,

Ipulsed = ((0.1A)2 / 0.30)0.5Ipulsed = 0.183 A or 183 mA

This calculation predicts an equivalent 15C rise above25C ambient for the 183 mA current pulse at 30% dutycycle.The previous calculations assume that, regardless ofthe pulse amplitude, width, and duration, if the sameamount of energy calculated from the power rating isdelivered to the component over a cycle, the compo-nent will dissipate the energy safely. There may be physi-cal conditions that limit this assumption due to the heat

Document 361-3

Specifications subject to change without notice. Document 361-3 Revised 06/15/04

Time

Am

plitu

de

0 0.5 1.0 1.5 2.0

1.21.00.80.60.40.2

0

Pulsed waveform70% duty cycle

Tpw T

Figure 1

dissipation characteristics of the component, the solderconnection, the circuit board, and the environment.In the previous example, if the duty cycle is reduced to10%, the calculated pulsed current would be 316 mA,which is more than three times the rated rms current,although only applied for 1/10 of a cycle. Our currentratings are based on steady-state measurements, noton pulsed current waveforms. While the duty cycle as-sumption is valid in many cases, we have not verifiedour ratings for pulsed waveforms. Therefore, we recom-mend testing your specific application to determine ifthe calculation assumptions are valid.

Appendix A rms CalculationsFigure 2 shows a typical sinusoidal waveform of alternat-ing current (AC) illustrating the peak and peak-to-peakvalues. The horizontal axis is the phase angle in degrees.The vertical axis is the amplitude. Note that the averagevalue of a sinusoidal waveform over one full 360 cycleis zero.Figure 3 shows the same full sinusoidal waveform ofFigure 2, full-wave rectified. The average rectified andrms values are illustrated for comparison.Calculate the root-mean-square (rms) value by the fol-lowing sequence of calculations: square each ampli-tude value to obtain all positive values; take the meanvalue; and then take the square root.The rms value, sometimes called the effective value, isthe value that results in the same power dissipation (heat-ing) effect as a comparable DC value. This is true of anyrms value, including square, triangular, and sawtoothwaveforms.Some AC meters read average rectified values, andothers read true rms values. As seen from the conver-sion equation in Appendix B, the rms value is approxi-mately 11% higher than the average value for asinusoidal waveform.

Document 361-4

Specifications subject to change without notice. Document 361-4 Revised 06/15/04

0

Peak Peak-to-peak

100 200 300

1.0

1.5

0

-0.5

-1.0

Full sinusoidal waveform

Figure 2

0 100 200 300

1.0

1.5

0

-0.5

-1.0

Rectified sinusoidal waveform

Average = 0.636 rms = 0.707

Figure 3

Appendix B Conversion Factors for Various WaveformsUse the following equations to convert between average, rms, peak, and peak-to-peak values of various waveformsof current or voltage.

Sinusoidal Waveforms

Given an Average Value: Given an rms Value:rms = 1.112 Average Average = 0.899 rmsPeak = 1.572 Average Peak = 2 rms (1.414 rms)Peak-to-Peak = 3.144 Average Peak-to-Peak = 2 2 (2.828 rms)Given a Peak Value: Given a Peak-to-Peak Value:Average = 0.636 Peak Average = 0.318 Peak-to-Peakrms = 1/ 2 Peak (0.707 Peak) rms = 1/ (2 2) Peak-to-Peak (0.354 Peak-to-Peak)Peak-to-Peak = 2 Peak Peak = 0.5 Peak-to-Peak

Squarewave Waveforms

Average = rms = Peak Peak-to-Peak = 2 Peak

Triangular or Sawtooth Waveforms

Given an Average Value: Given an rms Value:rms = 1.15 Average Average = 0.87 rmsPeak = 2 Average Peak = 3 rms (1.73 rms)Peak-to-Peak = 4 Average Peak-to-Peak = 2 3 rms (3.46 rms)Given a Peak Value: Given a Peak-to-Peak Value:Average = 0.5 Peak Average = 0.25 Peak-to-Peakrms = 1/ 3 Peak (0.578 Peak) rms = 1/(2 3) Peak-to-Peak (0.289 Peak-to-Peak)Peak-to-Peak = 2 Peak Peak = 0.5 Peak-to-Peak

Document 361-5

Specifications subject to change without notice. Document 361-5 Revised 05/11/04