How Current and Power
Relates to Losses andTemperature Rise
Losses and Temperature Rise for Inductors and Transformers
Core and winding losses in inductors and transformers
cause a temperature rise whenever current flows througha winding. These losses are limited either by the allowed
total loss for the application (power budget) or the maximum allowable temperature rise.
For example, many Coilcraft products are designed foran 85°C ambient environment and a 40°C temperaturerise implying a maximum part temperature of +125°C. In
general, the maximum allowed part temperature is themaximum ambient temperature plus temperature rise. If
the losses that result in the maximum allowed part temperature meet the power budget limits, the component is
considered acceptable for the application.
The temperature rise created by core and winding losses
is related to the thermal dissipation characteristics of thespecific component. For example, 100 mW of loss might
create a temperature rise of 40°C in one inductor but may
result in only a 30°C rise in another inductor that has better
thermal dissipation (thermal resistance) properties.
Thermal resistance is not specified for Coilcraft inductors
or transformers because they are mostly open framestyle and not solid, homogenous bodies like molded ICpackages. These body styles have a variety of thermal
flow paths and multiple heat sources (winding and core)
as opposed to an IC that may generate heat in a specificjunction and conduct heat consistently throughout thesolid body.
From the datasheet specifications for DCR and Irms,
an approximate thermal resistance (Rth) can calculated.
Dividing the temperature rise due to Irms current (e.g.
40°C rise) by the power required to generate that rise
(Power = DCR × Irms2):
Rth (in °C/W) = 40°C ÷ (DCR × Irms2)
where DCR is in Ohms and Irms is in Amps.

Once a thermal resistance is calculated for a specificcomponent, it is assumed that it is a fixed property of thematerials and construction and does not vary at other operating conditions (temperature, current, frequency, etc.).
Under this assumption, the temperature rise resulting fromany specific power dissipation can be estimated from:
Trise = Rth × P
where:

Trise is the temperature rise
Rth is the thermal resistance in °C/W andP is the dissipated power in Watts

Irms Ratings and Temperature Rise
Coilcraft’s current ratings specify a temperature rise thatresults from applying the rated (Irms) current. The specified temperature rise is allowable at or below the maximum
ambient temperature rating.
The Irms rating is the effective DC (or low-frequency AC)
current that causes the specified temperature rise. The
actual temperature rise will be higher when core and winding losses are involved. Lower current must be applied as
operation approaches the maximum ambient temperature
rating. At lower ambient temperatures, the allowable temperature rise is that which results in the maximum allowed(ambient + temperature rise) part temperature. Core andwinding losses depend on current and frequency, and thespecific component material and construction. Therefore,current derating (based on temperature rise) depends
on the specific losses resulting from the amplitude andfrequency of the AC ripple current.
Core and winding losses, and an estimate of the resulting
temperature rise, can be calculated for Coilcraft’s powerinductors using the web tool at this link:
http://www.coilcraft.com/apps/loss/loss_1.cfm

RF Chip and Air Core Inductors
Note: The following estimate does not account for
current-dependent losses or other large-signal
loss mechanisms at higher frequency that are notpart of the small-signal ESR measurement, suchas with ferrite, iron powder or composite core
constructions.
Frequency-dependent small signal losses for our RF chipand air core spring inductors can be estimated based on
the effective series resistance (ESR).
The ESR of our RF chip and air core spring inductors canbe found using the graphing web tool at this link:
http://www.coilcraft.com/apps/lqz/lqz.cfm
Given the ESR at a specific frequency and the datasheet
ratings, the maximum current the inductor can theoreticallyhandle at that frequency (at maximum ambient temperature) can be estimated.
Example: An 1812CS-102XJL (1 µH) chip inductor has
an Irms rating of 480 mA and a DCR maximum rating of1.2 Ohms. The Irms rating corresponds to a 15°C temperature rise from ambient. The maximum allowed ambient
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temperature is 125°C, so the 15°C temperature rise allows
for a maximum part temperature of ~140°C (125 + 15).
To estimate the power capability at maximum ambient
temperature, calculate:
Irms2 × DCR = (0.48 A) 2 × (0.8 × 1.2 Ohms)= 0.221 W = 221 mW.
Note that this assumes the nominal DCR to be 80% of
the maximum specification. So, approximately 221 mWof power will cause the temperature of this inductor torise ~15°C.
At RF frequencies, the ESR may be much higher than theDCR, therefore the amount of current that causes the sametemperature rise will be significantly reduced. For example,
if the RF signal is 100 MHz, the ESR of the 1812CS inductor in the example above is 8.14 Ohms (almost seventimes the DC resistance) so the Irms AC current that corresponds to the same power (and thus temperature rise)is only 161 mA versus the 480 mA Irms rating.
If the application ambient temperature maximum is lower
than the component data sheet maximum ambient temperature rating, it may be possible to operate at higher
than rated current. Again, as long as the total (applicationmaximum ambient + application component temperaturerise) component temperature does not exceed the data
sheet total (maximum ambient + component temperaturerise due to Irms current) the part can be operated withinsafe limits.
To estimate the temperature rise due to current, use thepower and thermal resistance calculations as describedin the section above.

Ferrite, Iron Powder, or Composite Core
Components
The performance of wideband chokes and transformers isobtained by using high permeability core materials suchas powdered iron or ferrite. As RF signals travel throughthe inductor, frequency-dependent and current-dependent
core losses contribute additional heat to the total producedby the inductor. The ESR measurement (typically made atvery low current) does not capture these losses. Therefore
the above estimation method is not applicable and will
incorrectly predict a lower temperature rise than actuallyresults. The component will get hotter than expected. Thisis true for any component that has a high permeability(ferrite, powdered iron, composite) core. In these cases,
we suggest taking a temperature rise measurement of theinductor under all conditions of frequency and current that
may result in your application to determine the worst-casetemperature rise.

Duty Cycle
The above discussion applies to continuous current waveforms. For pulsed waveforms, the allowable equivalentcurrents can be estimated using the equations describedin the Pulsed Waveforms section of Coilcraft Document
361 (Current and Temperature ratings) found at:
http://www.coilcraft.com/pdf_viewer/showpdf.cfm?f=pdf_
store:Doc361_Current_Temp.pdf
References:
Current and Temperature Ratings, Coilcraft, Inc., Document 361,
October 22, 2008

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