Linear Sensor Transfer Function

Formula

Description

Many sensors produce an output voltage that is linearly proportional to the measured physical quantity plus a constant offset. The sensitivity S (also called scale factor or gain) defines how much the output changes per unit change in the measured quantity, while the offset represents the output at zero input. Calibration involves determining both S and offset from measurements at two or more known reference points. This linear model applies to accelerometers, pressure sensors, current sensors, temperature sensors (LM35, TMP36), and many other transducers within their specified operating range.

Variables

• Vout — Sensor output voltage (V)
• S — Sensitivity or scale factor (V per unit of measurement)
• measured_value — Physical quantity being measured
• offset — Output voltage at zero input (V)

Practical Notes

The TMP36 temperature sensor, for example, has S = 10 mV/°C and offset = 500 mV (0.5V at 0°C). An ADXL345 accelerometer has S = 3.9 mg/LSB. For ratiometric sensors (output proportional to supply voltage), sensitivity is specified as a fraction of Vcc. Two-point calibration determines S and offset; more calibration points can reveal and correct nonlinearity.