IEC TR 62967 — Methods for Calculating Static Performance Indicators of Transducers and Transmitters

The performance of industrial transducers and transmitters is fundamental to the reliability of process measurement and control systems. IEC TR 62967 provides a unified mathematical framework for calculating the static performance indicators of transducers and transmitters, including span, resolution, sensitivity, hysteresis, repeatability, linearity, conformity, and drift. This Technical Report consolidates methodologies that were previously scattered across multiple standards and manufacturer-specific documents, offering engineers a single authoritative reference for quantifying and comparing instrument performance.

1. Scope and Fundamental Concepts

IEC TR 62967 applies to all types of transducers and transmitters used in industrial measurement and control systems, covering pressure, temperature, flow, level, force, displacement, and analytical measurements. The report is organised around the static calibration characteristic — the relationship between the input measurand and the output signal under steady-state conditions. It defines standard terminology and calculation methods that enable consistent performance specification across instrument types and manufacturers.

IEC TR 62967 is a Technical Report, meaning it provides guidance rather than mandatory requirements. However, its methodologies are widely referenced in product standards (e.g., IEC 60770 for process transmitters) and are considered the industry baseline for transducer performance specification.

2. Individual Static Performance Indicators

2.1 Span and Full-Span Output

The span (xFS) is defined as the algebraic difference between the upper and lower limits of the specified input range. For example, a pressure transmitter with an input range of 0 to 100 bar has a span of 100 bar. The full-span output (YFS) is the corresponding difference in the output signal (e.g., 16 mA for a 4–20 mA transmitter). These two parameters establish the coordinate system within which all other performance indicators are evaluated.

2.2 Resolution and Sensitivity

Resolution (Rx) is defined as the smallest change in the input measurand that produces a detectable change in the output signal. The standard distinguishes between absolute resolution (expressed in input units) and relative resolution (expressed as a percentage of span). Sensitivity (Si) is the ratio of the change in output signal to the change in input that produces it, calculated as the derivative dY/dX of the static calibration characteristic at any given point. For an ideal linear transducer, sensitivity is constant across the entire span; for non-linear devices, sensitivity must be specified at multiple operating points.

Indicator	Symbol	Definition	Typical Expression
Span	xFS	x_max − x_min	100 bar
Full-span output	YFS	y_max − y_min	16 mA
Resolution	Rx	Smallest detectable input change	0.1 % of span
Sensitivity	Si	dY/dX	0.16 mA/bar
Hysteresis	H	Maximum output difference for same input (up vs. down)	0.05 % of span
Repeatability	R	±t × s (coverage factor × std dev)	±0.03 % of span

3. Linearity and Conformity

3.1 Types of Linearity

One of the most valuable contributions of IEC TR 62967 is the comprehensive classification of linearity definitions. The report defines eight distinct types of linearity, each representing a different reference line against which deviations are measured:

Absolute linearity (L,ab): Deviation from a straight line passing through the true zero point, useful for absolute measurement systems.
Terminal-based linearity (L,te): Deviation from the straight line connecting the actual endpoints of the calibration curve. This is the most commonly specified linearity in product datasheets.
Shifted-terminal-based linearity (L,s,te): Terminal-based linearity with parallel shift to minimise maximum deviation.
Zero-based linearity (L,ze): Similar to terminal-based but the line is forced through the true zero point.
Front-terminal-based linearity (L,f,te): Uses only the first portion of the range for the reference line.
Independent linearity (L,in): Devation from the best-fit straight line with no constraints, the most optimistic linearity specification.
Least-squares linearity (L,ls): Based on the linear regression line minimising the sum of squared deviations.

Engineers must be extremely cautious when comparing linearity specifications from different manufacturers. A transmitter specified with “±0.1 % independent linearity” may have actual deviation twice as large when measured using the terminal-based method. Always verify which linearity definition is used before making procurement comparisons. IEC TR 62967 recommends that datasheets clearly state the linearity type using the standard symbols (e.g., L,te for terminal-based).

3.2 Conformity

Conformity (C) extends the linearity concept to non-linear transfer functions. It quantifies the deviation of the actual calibration curve from a specified nominal characteristic (which may be logarithmic, square-root, exponential, or any other defined function). This is particularly important for transducers with inherent non-linearities, such as differential pressure flowmeters (square-root characteristic) and thermocouples (polynomial characteristic). The same classification used for linearity (absolute, terminal-based, independent, least-squares) applies to conformity.

4. Drift and Shift

The standard defines several types of temporal performance degradation:

Zero drift (D0): The change in output at zero input over a specified time period.
Sensitivity drift (DS): The change in sensitivity over time, altering the slope of the calibration characteristic.
Zero shift (S0): An abrupt, non-recoverable change in zero output (as opposed to gradual drift).
Span shift (SFS): An abrupt change in the full-span output value.

A practical approach to managing drift in industrial applications is the “3-6-12” calibration interval strategy: new instruments are verified after 3 months, if drift is within ±0.1 % the interval is extended to 6 months, and if still within tolerance the interval is extended to 12 months. This adaptive approach, based on the drift indicators defined in IEC TR 62967, optimises maintenance resources while ensuring measurement integrity.

5. Engineering Design Insights

Calibration Point Selection: The standard recommends a minimum of 5 calibration points equally distributed across the span for linearity determination, with 11 points preferred for full characterisation. Bi-directional (up-scale and down-scale) measurements at each point are required for hysteresis calculation.
Temperature Effect Separation: Static performance indicators should be evaluated at reference conditions (typically 23 °C ± 2 °C). Additional temperature coefficients (zero thermal error and sensitivity thermal error) are specified separately and should not be conflated with the basic static indicators.
Digital vs. Analogue Transmitters: For digital transmitters with internal signal processing (filtering, averaging, linearisation), the static performance indicators may depend on the configuration settings. The standard recommends that performance be verified with factory-default settings and with application-specific settings.
Uncertainty Budget: The overall measurement uncertainty of a transducer chain should be calculated as the root-sum-square (RSS) combination of individual performance indicators, accounting for their statistical independence. The standard’s clear definitions facilitate rigorous uncertainty budgeting.

One of the most overlooked aspects in transducer specification is the interaction between hysteresis and repeatability. A transducer with moderate hysteresis but excellent repeatability can be compensated through software correction (using a bi-directional calibration model). However, a transducer with poor repeatability cannot be compensated by any correction algorithm. When selecting transducers for high-accuracy applications, prioritise repeatability over linearity, as repeatability fundamentally limits the achievable uncertainty regardless of correction.

6. Frequently Asked Questions

Q: What is the difference between accuracy, error, and uncertainty in the context of this standard?
A: IEC TR 62967 follows the vocabulary of the International Vocabulary of Metrology (VIM). Accuracy is a qualitative concept indicating closeness of agreement. Error is the quantitative difference between measured and true values. Uncertainty is the dispersion of values that could reasonably be attributed to the measurand, expressed as a range with a coverage factor (typically k=2 for 95 % confidence).

Q: How should dead band be handled in performance calculations?
A: Dead band (the range of input values that produce no change in output) is treated as a separate indicator. If dead band exceeds the specified resolution, it must be reported. Dead band can be determined by applying small input changes in both directions and measuring the output response.

Q: Does this standard address digital communication protocol effects on performance?
A: No. The static performance indicators defined in IEC TR 62967 apply to the analogue measurement path. Digital communication effects (update rate, resolution limits of digital transmissions, protocol latency) are outside the scope and are covered by the respective communication standard (e.g., HART, PROFIBUS, Foundation Fieldbus).

Q: What is the recommended calibration interval for re-evaluating static performance?
A: The report does not prescribe specific intervals, as these depend on the application criticality, environmental conditions, and the transducer’s demonstrated stability. However, it recommends that after any repair, re-range, or firmware update that affects the measurement path, the static performance indicators be re-evaluated through a full calibration cycle.