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Sensor Accuracy Budget

Calculate total sensor error using RSS and worst-case methods. Analyze offset, gain, nonlinearity, resolution, and temperature drift contributions.

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Formula

eRSS=√(e12+e22+...+en2)e_RSS = √(e₁² + e₂² + ... + eₙ²)
e_WC— Worst-case: sum of all errors (% FS)
e_RSS— RSS: root-sum-square (% FS)

How It Works

Sensor accuracy budget calculator computes total system uncertainty by combining multiple error sources using worst-case or RSS methods — essential for instrumentation engineers, calibration technicians, and measurement system designers. A sensor accuracy budget systematically analyzes all error contributions: offset (zero shift), gain/sensitivity error (slope deviation), nonlinearity (deviation from ideal curve), resolution (quantization or noise floor), hysteresis (path-dependent error), and temperature drift (parameter change with temperature). Per NIST Technical Note 1297 (GUM), errors combine two ways: worst-case (algebraic sum of absolute errors) gives guaranteed bounds but is conservative; RSS (root-sum-square: e_total = sqrt(e1^2 + e2^2 + ... + en^2)) treats independent errors statistically and gives typical expected accuracy. ISO/IEC Guide 98-3 recommends RSS for uncorrelated errors with 95% confidence (k=2 coverage factor). Industrial sensors specify Total Error Band (TEB) per IEC 61298, encompassing all errors over the operating temperature range in a single figure (+/-0.1 to +/-1% FS typical).

Worked Example

Problem

Build an accuracy budget for a pressure measurement system. Components: Honeywell sensor (+/-0.25% FS TEB over -40 to +85C), AD7124 ADC (+/-2 ppm INL, +/-1 ppm gain error, +/-0.5 ppm/C drift), signal conditioning (+/-0.05% gain accuracy). Operating temperature is +/-30C from 25C cal point.

Solution
  1. Sensor TEB: e1 = 0.25% FS (includes offset, gain, nonlinearity, temp drift)
  2. ADC INL: e2 = 2 ppm = 0.0002% FS
  3. ADC gain error: e3 = 1 ppm = 0.0001% FS
  4. ADC temp drift: e4 = 0.5 ppm/C * 30C = 15 ppm = 0.0015% FS
  5. Amplifier gain: e5 = 0.05% FS
  6. RSS total: e_RSS = sqrt(0.25^2 + 0.0002^2 + 0.0001^2 + 0.0015^2 + 0.05^2) = sqrt(0.0625 + 0.0025) = sqrt(0.065) = 0.255% FS
  7. Worst-case total: e_WC = 0.25 + 0.0002 + 0.0001 + 0.0015 + 0.05 = 0.302% FS
  8. Dominant error: sensor TEB (0.25%) >> all electronics combined (0.05%)
Result: RSS accuracy is +/-0.26% FS; worst-case is +/-0.30% FS. Sensor TEB dominates; improving ADC or amplifier has negligible effect.

Practical Tips

  • ✓Identify the dominant error term first - reducing it provides the most system improvement; if temperature drift dominates, adding temperature compensation is more effective than upgrading ADC resolution per measurement system design principles
  • ✓System calibration can eliminate offset and gain errors entirely at calibration temperature, leaving only nonlinearity, resolution, and temperature drift in the post-calibration budget; always specify whether accuracy is pre- or post-calibration
  • ✓For datasheet comparisons, confirm whether manufacturer accuracy includes temperature (TEB) or is at 25C only; some quote accuracy without temperature, which underestimates real-world error by 2-5x

Common Mistakes

  • ✗Using worst-case for every analysis: worst-case for 10-term budget may be 3-5x higher than RSS, leading to over-specified, expensive components; reserve worst-case for safety-critical applications per NIST GUM guidelines
  • ✗Forgetting temperature drift as separate term: over +/-50C operating range, 0.01% FS/C drift contributes 1% FS - often the dominant error; always include temperature in the budget per IEC 61298
  • ✗Treating correlated errors as independent in RSS: if offset and gain both drift with temperature from the same physical mechanism, they are correlated and must be added directly, not RSS combined; check error correlation before selecting method

Frequently Asked Questions

Use worst-case for: safety-critical applications (medical devices per IEC 62304, automotive per ISO 26262), type-approval testing requiring guaranteed bounds, and when errors are correlated (e.g., all drift with temperature from common supply). Use RSS for: design trade-off studies where typical performance matters, component selection to meet cost targets, and when errors are truly independent (sensor and ADC from different physical mechanisms). Per NIST Technical Note 1297, RSS with coverage factor k=2 gives 95% confidence interval.
TEB is a single specification encompassing all error sources (offset, gain, nonlinearity, hysteresis, temperature drift) over the full operating temperature range. It is the maximum deviation from ideal output at any temperature and pressure combination - essentially worst-case total error. TEB is the most useful spec for system design because it includes everything; no additional temperature derating is needed. Per IEC 61298, TEB is preferred for industrial pressure transmitters; Honeywell, Sensata, and Bosch specify TEB for automotive and industrial sensors.
% FS (percent of full scale) means the same absolute error at any measurement value; it is the standard for industrial sensors per IEC 61298. % of reading means error scales with measured value (common in DMMs and power analyzers). At 10% of range, a 1% FS sensor has 10% error relative to reading, while a 1% of reading sensor has only 1% error. Conversion: absolute error = (% FS / 100) * full_scale_range. For a 0-1000 kPa sensor, +/-0.5% FS = +/-5 kPa everywhere in range.

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