DAQ Offset + Gain Error

Turn a two-point calibration into offset and gain-error terms, then correct any raw DAQ reading.

Inputmeasured = gain·applied + offset , gain = (Hₘ − Lₘ)/(Hᵣ − Lᵣ) , offset = Lₘ − gain·Lᵣ , corrected = (raw − offset)/gain

Low reference (applied) (V)Low reading (measured) (V)High reference (applied) (V)High reading (measured) (V)Raw reading to correct (V) — optional

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The engineering

Every real DAQ channel departs from the ideal straight line in two ways: it can read a fixed amount high or low everywhere (offset), and its slope can be a hair off unity (gain error). Apply two known references — usually a shorted-input zero and a near-full-scale value — read what the card reports, and this card solves the two-point line so you can back the errors out of live data.

Offset dominates near zero; gain error dominates near full scale — which is why NI specs quote them separately and why a single midscale check hides both. Rule of thumb: correct offset first (it's stable and easy to null with a shorted input), then trust gain error to a fresh cal only if the channel drifts more than its published ppm/°C times your ambient swing.

Where this math comes from

The offset-and-gain decomposition predates digital DAQ — it's the classic linear-fit error model bench techs applied to analog bridge amplifiers and strip-chart recorders, where a zero knob and a span knob physically set the two terms this card computes. When ADCs arrived the same two adjustments moved into firmware calibration coefficients.

National Instruments codified the language for a generation of test engineers: its multifunction DAQ manuals from the 1990s onward spell out absolute accuracy as a sum of gain error (a percent of reading) plus offset error (a fixed voltage) plus noise, and ship every board with factory cal constants stored in EEPROM. This card is the field-cal version of that same two-point routine.

1930Instrumentation practiceZero-and-span adjustment established as the standard two-knob calibration for analog meters and bridges.
1965Bernard Gordon / early ADC makersOffset and gain error become the dominant specified nonidealities of successive-approximation converters.
1995National InstrumentsMultifunction DAQ manuals define absolute accuracy = gain error + offset error + noise, with EEPROM cal constants.

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