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Derating Analysis · Chapter 2

Theoretical Foundations

Definitions, units, models, and the assumptions that bound them.

Derating rests on two facts about parts and one about arithmetic. Parts fail more often the harder they are driven; they fail more often the hotter they are; and a prediction already contains both effects as multiplicative factors, so the design decision and the reliability number are the same decision written twice.

The two axes

The same violation reached two ways. On the left the stress ratio is too high at an unremarkable temperature: a procurement question. On the right every stress ratio is comfortable and the junction is 42 degrees over its cap: a thermal question that the schematic cannot answer.
The same violation reached two ways. On the left the stress ratio is too high at an unremarkable temperature: a procurement question. On the right every stress ratio is comfortable and the junction is 42 degrees over its cap: a thermal question that the schematic cannot answer.

The stress ratio is S = applied / rated, computed per stress type and per part family. A part has several: a MOSFET has a drain-source voltage ratio, a current ratio and a power ratio, and it is derated on all of them at once, against whichever ceiling its family's rule carries. The ratio is a property of the circuit and the part number, and it can be read off a schematic and a parts list.

Temperature is not a ratio. It is the temperature the part itself reaches, which for a semiconductor is its junction:

Tj = Tambient + θja · P , or Tj = Tcase + θjc · P where the case temperature is known

and the rule sets cap it directly, typically well below the part's own maximum. This is the axis that needs the thermal analysis to exist, and the axis on which a part that passes every ratio still fails.

AxisAnswer comes fromFixed by
Stress ratioThe schematic and the parts listA different part number, or a different operating point
TemperatureThe thermal model, at the worst-case environmentLess dissipation, better conduction, or a cooler place on the board

The anatomy of the curve

A rating curve has three parts, and every derating curve inherits them:

FeatureWhat it is
The flat regionUp to the reference temperature, the full rating applies
The kneeThe reference temperature, where the part starts losing capability
The rampA linear fall to zero at the part's maximum temperature

For a resistor rated P₀ at Tknee and zero at Tmax, the manufacturer's curve is

Prated(T) = P₀ for T ≤ Tknee, and P₀ · (Tmax − T)/(Tmax − Tknee) above it

and the programme's allowed power is that multiplied by the policy factor, with the whole curve truncated at the policy's own temperature cap. The worked example's resistor is a quarter watt at 70 °C, and a 50 per cent policy allows it 125 mW to the knee, 103 mW at 85 °C and 44 mW at 125 °C.

Which stresses, per family

Every rule set enumerates the same kind of table: the part family down the side, the stress types across, the ceiling in the cells, and a temperature cap per family. The families are conventional, and so are the stresses that matter:

FamilyStresses that carry the rule
ResistorsPower, and for high values the voltage across the element
Ceramic capacitorsVoltage, and temperature against the dielectric's own limit
Solid tantalum capacitorsVoltage, severely, plus a circuit-impedance condition
Diodes and rectifiersReverse voltage, forward and surge current, junction temperature
Transistors and MOSFETsVoltage, current, power, junction temperature, safe operating area
Integrated circuitsSupply voltage, output current, fan-out, junction temperature, frequency
Relays and switchesContact current by load type, coil voltage, cycles
MagneticsCurrent, hot-spot temperature, voltage per turn
ConnectorsContact current, voltage between adjacent contacts, insertion cycles

Two subtleties in that table are where reviews go wrong. Solid tantalum capacitors are the classic: their voltage derating is the most severe in most rule sets, and several add a series impedance requirement that has nothing to do with a ratio at all. And relay and switch ratings are quoted by load type, so a contact rated 5 A resistive is not rated 5 A into a motor or a lamp.

Application classes

Rule sets grade the application, and the ceilings move with the grade. NASA EEE-INST-002 organises its instructions around part quality Levels 1, 2 and 3; other documents distinguish by mission criticality or by whether the equipment is manned, long-life or expendable. The engineering content of the grade is simple: a part that cannot be replaced, on a mission that cannot be repeated, is derated harder.

The class is a programme decision recorded once, and it belongs beside the rule set's name in the derating policy. Two boards analysed at two different classes cannot be compared, and a report that does not state the class has not stated its result.

What derating buys, in the prediction's own terms

Both curves are the prediction's own. Fixing the capacitor's voltage stress divides its rate by 2.9; moving the regulator's dissipation divides its rate by 3.6. At an activation energy of 0.35 eV, ten degrees costs 33 per cent rather than the doubling the rule of thumb promises.
Both curves are the prediction's own. Fixing the capacitor's voltage stress divides its rate by 2.9; moving the regulator's dissipation divides its rate by 3.6. At an activation energy of 0.35 eV, ten degrees costs 33 per cent rather than the doubling the rule of thumb promises.

A stress ratio enters the prediction as a stress factor. For the solid tantalum family the form is

πV = (S / 0.6)⁵ + 1

which is flat and unremarkable below about half rated voltage and rises steeply above it: at S = 0.5 it is 1.40, at S = 0.75 it is 4.05. Temperature enters as an Arrhenius factor:

πT = exp[ −(Ea / k) · (1/T − 1/Tref) ]

with T in kelvin. At Ea = 0.35 eV a junction at 110 °C carries 20.5 times its 25 °C rate and one at 152 °C carries 58.8.

That last pair is worth holding onto, because it corrects a rule of thumb. "The rate doubles every ten degrees" is a statement about an activation energy near 0.7 eV. At 0.35 eV the same ten degrees costs about a third more at 100 °C, and less than that as the part gets hotter. Both numbers are common in real parts, so the honest version of the rule is that ten degrees is worth somewhere between a third and a doubling, and which one depends on the dominant mechanism.

What derating is not

  • It is not a substitute for margin analysis. Derating checks steady-state stresses against ratings. Inrush, fault currents, transients and single-event effects are separate analyses with their own limits.
  • It is not a wear-out model. A part inside its derating limits can still wear out: electrolytic capacitors dry, connectors fret, solder joints cycle. Derating slows those mechanisms; it does not remove them.
  • It is not free. Derating a part means buying a larger, heavier, costlier one, or spending board area on heat. The trade is real and the prediction is what prices it.
  • It says nothing about whether the circuit works. A part can be beautifully derated and functionally wrong.

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