Current, Power and Temperature Rise
Inductors are not typically rated by power, however anapproximation of the power-handling capability of an aircore or ceramic core chip inductor can be estimated usingthe data sheet specifications for current and resistance.Example: 1 μH, chip inductor hasan Irms rating of 480 mA and a maximum DCR rating of1.2 Ohms. The Irms rating corresponds to a 15°C tempera-ture rise above ambient. The maximum allowed ambienttemperature is 125°C, so the 15°C temperature rise allowsfor a maximum part temperature of ~(125 + 15) = 140°C.To estimate the power capability, calculate Irms2 × DCR. Ifwe assume that the nominal DCR is 80% of the maximumDCR specified, the calculation is:(0.48 A)2 × (0.8 × 1.2 Ohms) = 0.221 W = 221 mW.Therefore, approximately 221 mW of power causes thetemperature of this inductor to rise ~15°C.At RF frequencies, the ESR is much higher than the DCR.Therefore, the amount of current that causes the sametemperature rise is significantly reduced. For example,if the RF signal is 100 MHz, the ESR of the inductor is8.14 Ohms (almost seven times the DC resistance) sothe Irms AC current that corresponds to the same power(and thus temperature rise) is only ~161 mA as opposedto the 480 mA rating at DC. This estimate may be in errorif there are current-dependent losses in the inductor orother loss mechanisms at higher frequency that are notpart of the low-current ESR measurement.
Power dissipated by the inductor
The purpose of the inductor in a bias tee, as shown in thefigure below, is to provide a DC bias to the amplifier whileblocking the high frequency RF signal from entering theDC source. Ideally, any RF signal applied to the bias lineis filtered out by the series inductor. For this discussion, weassume a lossless (e.g. air core or ceramic core) induc-tor for which only (AC and DC) copper losses exist – nocore losses.
The total DC power dissipated by the inductor is:Pdc = Idc2 × DCRThe total AC power dissipated by the inductor is:Pac = Irms2 × ESRwhere:Idc is the DC current through the inductor.Irms is the magnitude of the AC (RF signal) current throughthe inductor (likely low if the inductor is nearly ideal).DCR is the DC resistance of the inductor.ESR is the effective series resistance of the inductor atthe frequency of the RF signal (assuming only a single RFfrequency).The total (DC and AC) power dissipated by the inductor is:Ptotal = Pdc + PacorPtotal = Idc2 × DCR + Irms2 × ESRAs illustrated, in the simplest case of a single frequencyAC signal on the on the RF line, in order to determinethe AC power dissipated by the inductor, the ESR of theinductor at the RF frequency, and the Irms value of theRF current through the inductor, must be known. For morecomplicated multi-frequency noise signals to be filtered,the total AC power dissipated by the inductor is the sumof all Irms2 × ESR contributions, where ESR varies foreach contribution by frequency.
Wideband RF chokes
The broadband performance of wideband RF chokes isthe result of using high permeability core materials such aspowdered iron or ferrite. With RF signals traveling throughthe inductor, frequency-dependent and current-dependentcore losses contribute additional heat to the total producedby the inductor. A simple ESR measurement (typicallymade at very low current) will not capture these losses.Therefore the above estimation method is not applicableand incorrectly predicts a lower temperature rise than willactually result. The inductor will get hotter than expected.The same is true for any inductor that has a high perme-ability (ferrite, powdered iron, composite) core. In thecase of high-perm core products, we suggest making atemperature rise measurement of the inductor under allconditions of frequency and current that may result in yourapplication to determine the worst-case temperature rise.