Concept

Offset drift — where it appears

The rate at which an amplifier's input offset changes with temperature, quoted in microvolts per kelvin. In a bipolar pair whose offset comes from a saturation-current mismatch it is the offset over the absolute temperature, so a trim inside the junction law removes both, and any other share of the offset leaves drift behind.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

What a 5% mismatched pair leaves behind, across 150 K. computed by solving, not by drawing. A saturation-current mismatch of 5.0% appears as an input offset of Vₜ·ln(m) — 1.2613 mV at 300 K — which is proportional to absolute temperature and therefore drifts at 4.2044 µV/K, exactly the offset divided by the temperature. That is 3333 ppm per kelvin at every mismatch on the slider, because the ratio is 1/T and contains nothing about the device. One junction on its own drifts 1.828 mV/K, 435 times harder.

What matching does about temperature

A pair cancels the 1.8 mV/K that broke the previous essay, and what it leaves behind is exact: a saturation-current mismatch of m shows up as an offset of the thermal voltage times ln(m), which is proportional to absolute temperature and therefore drifts in proportion to itself. 3 333 parts per million per kelvin, at every mismatch on the slider, because the ratio is 1/T and contains nothing about the device at all.

semiconductors · Differential pair

A pair with 2.0% saturation-current mismatch, nulled at 300 K: trimmed by a constant it drifts 1.706 µV/K, trimmed by its load ratio 0.000 µV/K. computed by solving, not by drawing, at 31 temperatures — each a Newton solve of both junctions, a bisection for the tail current and a bisection for the input that nulls the output — a bipolar pair at 10 µA a side whose second transistor has 1.02 times the first's saturation current. Untrimmed (grey) it needs 511.9 µV at 300 K and 682.6 µV at 400 K. Trimmed at 300 K by subtracting a constant (dashed) it is zero there and 170.6 µV at 400 K, drifting 1.706 µV/K — the untrimmed offset's drift, untouched. Trimmed at 300 K by making the collector loads 1.02000 to one (solid) it is 0.0 µV at 400 K, drifting 0.000 µV/K. The load ratio acts inside the same logarithm the mismatch does, so it cancels the mismatch at every temperature, not at one.

The trim that takes the drift with it

A bipolar pair's offset from a saturation-current mismatch is proportional to absolute temperature, so trimming it to zero at one temperature can trim its drift to zero too — but only if the trim acts inside the same logarithm the mismatch does. Trimmed by its collector-load ratio, a 2% mismatched pair is zero from 250 to 400 K; trimmed by subtracting a constant after it, it drifts the same 1.706 µV/K it drifted untrimmed. Add 20 kΩ of source resistance and a 10% current-gain mismatch, and a fifth of the offset follows the current gain instead: the load trim now leaves −0.574 µV/K, the constant trim 1.256, and above 34 kΩ the constant trim is the better one. A trim cancels the drift of the share whose temperature law it shares and converts the rest; two knobs, set for value and slope, leave 11 µV of curvature.

semiconductors · Differential pair

Named alongside it

The objects these essays reach for when they reach for this one.

Device matching Differential pair Input offset Thermal voltage Current gain Temperature coefficient

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