Sensors & Signal Conditioning

sensor linearity

Linearity asks a simple question: when the thing you measure doubles, does the sensor's output double too? A perfectly linear sensor draws a straight line — equal steps of input give equal steps of output, all the way across its range. Most real sensors bend that line a little (or a lot), and linearity is the measure of how straight, or how bent, the response really is. A straight sensor is a joy: one slope and one offset turn its reading into a value.

Linearity error is usually quoted as the worst-case deviation from the ideal straight line, as a percentage of full scale. If a sensor is specified as 0.1 percent linearity over a 0 to 10 V range, its output may stray up to 0.01 V from the perfect line at the worst point. Some sensors are beautifully linear (a good RTD, a potentiometer), while others are strongly curved by their physics (a thermistor follows an exponential-like curve; a thermocouple bends; an LDR follows a power law). For a curved sensor you straighten the reading after the fact — in software with the governing equation or a lookup table, or in hardware with a shaping circuit — a step called linearization.

Why this matters: linearity decides how much work it takes to turn a reading into a trustworthy value, and how a single-point calibration behaves away from that point. A linear sensor needs only two calibration points; a curved one needs many, or a model. The honest framing: nonlinearity is not the same as noise or as offset — it is a fixed, repeatable bend, so it can be corrected if you know the curve, unlike random noise which cannot. The danger is assuming a sensor is linear when it is not: a two-point calibration on a curved sensor will be right at the two points and quietly wrong everywhere between them.

Calibrate a thermistor at just 0 °C and 100 °C and draw a straight line between them. At 50 °C the true thermistor response sags well below that line — the reading could be off by several degrees, even though it is dead-on at 0 and 100. Use the Steinhart-Hart curve instead of a straight line and the error vanishes.

A two-point line is exact at the two points and wrong in between for a curved sensor.

Nonlinearity is a fixed, repeatable bend, not random noise, so it can be fully corrected if you know the curve — but only then. Assuming linearity when a sensor is curved gives readings that are perfect at your calibration points and silently wrong everywhere else.

Also called
linearitylinearity error線性度非線性誤差