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Scale Factor Non-Linearity
Deviation Measure
A performance metric describes the variation in a sensor’s sensitivity across its entire operating range. This scale factor non-linearity is the difference between the actual output of the instrument and the ideal linear response expected for a given input. It is usually expressed as a percentage of the full scale output or in parts per million of the reading.
The metric quantifies how much the conversion from a physical quantity to an electrical signal deviates from a straight line. This measurement defines the accuracy of the sensor in applications where the input varies significantly. The analysis stops at the saturation point of the sensor where the output no longer changes with the input.
Linearity Logic
Calculation of this value involves taking measurements at multiple points throughout the sensor’s range and comparing them to a best fit line. When assessing scale factor non-linearity, the technician uses a least squares regression or a zero based line to establish the reference. The residuals between the measured points and the line represent the non linearity of the device.
This characteristic is often caused by mechanical stresses in the sensing element or limitations in the analog electronics. In some cases, the non linearity follows a predictable curve that can be modeled and compensated for in software. Calibration involves verifying the output at the extremes and the midpoint of the range to capture any bowing or S shaped deviation.
Drift in the component values over time can alter the linearity and require re calibration of the instrument. Verification of the performance is essential for high precision sensors used in industrial control.
Error Sources
Challenges in maintaining a linear response arise from environmental factors such as temperature and mechanical packaging. For a sensor experiencing scale factor non-linearity, the thermal expansion of the housing can introduce non linear stresses on the sensing element. The interference from external magnetic or electric fields can also distort the response curve in certain regions of the operating range.
Calibration certificates for these sensors specify the maximum deviation and the method used to calculate it. The drift in the linearity is monitored through periodic testing to ensure that the sensor remains within its specified tolerance. Technicians verify the linearity by using a high precision reference that is at least ten times more accurate than the sensor under test.
This verification ensures that the error recorded is a true representation of the sensor’s behavior.
Resolution Boundary
Performance limits are reached when the non linearity of the sensor exceeds the required accuracy for the application. Although scale factor non-linearity can be compensated, the complexity of the compensation model is limited by the processing power of the embedded system. Integration into a control loop requires that the remaining error after compensation be smaller than the noise floor of the system.
The tolerance for this deviation is set by the system designers based on the total error budget for the measurement. Final qualification of the sensor involves testing the linearity across the full temperature range and for different load conditions. This ensures that the instrument provides a consistent and predictable response regardless of the operating environment.
Proper characterization of the linearity allows for the high fidelity measurement of complex physical phenomena.
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