Silicon Die Stress Transduction Mechanics under Packaging Temperature Changes
Packaging thermal expansion mismatch generates die stress that converts to electrical offset drift via piezoresistive coupling and polymer viscoelastic creep.
Multi-Point Temperature Trimming
Thermal Calibration
Sensor compensation uses the measurement and correction of sensor outputs at multiple temperature setpoints to minimize thermal drift. The process of multi-point temperature trimming calculates polynomial coefficients that adjust the sensor response across the entire operational range. This calibration ensures high measurement accuracy in environments subject to fluctuating ambient temperatures.
Compensation Coefficient
Thermal errors are modeled using high-order mathematical equations to correct the non-linear drift of silicon strain gauges. A microprocessor uses the calculated coefficients to adjust the digital output of the sensor in real time. The coefficients are stored in non-volatile memory during the factory calibration phase.
Polynomial Correction
Instrument calibration utilizes an environmental chamber to expose sensors to a sequence of controlled temperature steps. At each stable point, the raw output of the sensor is recorded alongside a reference thermometer reading. A regression algorithm then computes the correction curve to align the sensor output with the reference values.
This multi-point approach outperforms simple two-point span and offset adjustments by addressing the second-order and third-order non-linear thermal behaviors. The resulting calibration decreases the residual temperature coefficient of sensitivity to extremely low levels, permitting use in demanding aerospace and industrial applications.
Sensor Linearity
Precision performance requires that the temperature sensor used for compensation is co-located with the sensing element to prevent thermal lag. If a temperature gradient exists between the two elements, the compensation algorithm introduces localized correction errors. The final assembly undergoes a verification cycle to guarantee that the compensated output remains within specified tolerance limits.