Mathematical Correction
Polynomial equations used to model sensor behavior include non-linear terms to account for curved response profiles. These mathematical multipliers, called second order coefficients, represent the parabolic curvature of the sensor output in relation to the physical input. While linear approximations are sufficient for rough measurements, high-precision systems require these higher-order terms to minimize residual errors.
This refinement is critical for sensors that exhibit non-linear physical characteristics.
Sensor Calibration
Determining these polynomial parameters involves measuring the sensor output at multiple calibrated reference points. For a system utilizing second order coefficients, at least three distinct test conditions are required to fit the quadratic equation. Automated calibration systems execute these measurements and calculate the coefficients using a least-squares regression algorithm.
These calculated values are then programmed into the non-volatile memory of the device.
Temperature Compensation
Thermistors and silicon bandgap sensors exhibit non-linear outputs that vary significantly with changes in ambient temperature. Applying second order coefficients to the temperature-correction formula allows the system to maintain stable readings across a wide operating range. This compensation cancels the characteristic curve of the sensor, which would otherwise introduce substantial measurement errors at the temperature extremes.
This process guarantees that the corrected reading reflects only the actual target variable.
Computation Execution
Low-power microcontrollers process these quadratic calculations using fixed-point arithmetic to save processing cycles. The firmware multiplies the raw digitized sensor value by the stored second order coefficients and adds the linear and offset terms. This arithmetic sequence must be optimized to prevent round-off errors that could degrade the precision of the output.
In high-speed data acquisition boards, dedicated hardware multipliers execute these equations within the analog-to-digital converter cycle, ensuring real-time compensation with zero latency for downstream control loops.
