Measurement Terminology

Range, Span, and Turndown Ratio (Rangeability)

Precision measurement requires standardized terminology defined by the International Society of Automation (ISA) under standard ISA-51.1 (Process Instrumentation Terminology).

Range, LRV, and URV

• Range: The region bounded by the limits within which a quantity is measured, received, or transmitted. Range is expressed by stating the lower and upper limits.
• Lower Range Value (LRV): The lowest value of the measured variable that the device is calibrated to measure (corresponds to 0% signal or 4.00mA).
• Upper Range Value (URV): The highest value of the measured variable that the device is calibrated to measure (corresponds to 100% signal or 20.00mA).

  [ -50 °C ] ----------------------- [ +150 °C ]   --> RANGE: -50 °C to +150 °C
     (LRV)                               (URV)
      4mA                                 20mA

  |<----------------- SPAN = 200 °C ----------------->|

Span Calculation

Span is the algebraic difference between the Upper Range Value (URV) and the Lower Range Value (LRV):

$\text{Span} = \text{URV} - \text{LRV}$

Examples of Span Calculations:

1. Standard Positive Range: Range = $0\text{ to } 250\text{ psig}$ $\text{Span} = 250 - 0 = 250\text{ psi}$
2. Suppressed Zero Range: Range = $100\text{ to } 300\text{ }^\circ\text{F}$ $\text{Span} = 300 - 100 = 200\text{ }^\circ\text{F}$
3. Elevated Zero (Negative) Range: Range = $-50\text{ to } +50\text{ inH}_2\text{O}$ $\text{Span} = 50 - (-50) = 50 + 50 = 100\text{ inH}_2\text{O}$
4. Full Vacuum to Positive Pressure Compound Range: Range = $-14.7\text{ to } +30.0\text{ psig}$ $\text{Span} = 30.0 - (-14.7) = 44.7\text{ psi}$

Upper Range Limit (URL) vs. Lower Range Limit (LRL)

• Upper Range Limit (URL): The maximum process value that an instrument is physically capable of measuring based on sensor hardware construction.
• Lower Range Limit (LRL): The minimum process value that the instrument hardware can physically measure.

Turndown Ratio / Rangeability

Turndown Ratio (also called Rangeability) is the ratio of the maximum calibrated span (or URL) to the minimum calibrated span that the instrument can be adjusted to measure without acceptable accuracy degradation:

$\text{Turndown Ratio} = \frac{\text{Maximum Calibrated Span (or URL)}}{\text{Minimum Calibrated Span}}$

$\text{Turndown Ratio} = \frac{\text{URL}}{\text{Calibrated Span}}$

Worked Example: Smart DP Transmitter Turndown

Scenario: A high-precision differential pressure transmitter has an Upper Range Limit (URL) of $400.0\text{ inH}_2\text{O}$. A technician calibrates the transmitter for a flow measurement application with a span of $16.0\text{ inH}_2\text{O}$. Calculate the turndown ratio.

$\text{Turndown Ratio} = \frac{400.0\text{ inH}_2\text{O}}{16.0\text{ inH}_2\text{O}} = 25$

This is expressed as a 25:1 Turndown Ratio.

Technical Impact: While modern digital transmitters offer turndown ratios up to 100:1, operating at extreme turndown amplifies ambient temperature drift and thermal noise relative to the calibrated span, degrading overall percent-of-span accuracy.

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Accuracy Statements: Percent of Span vs. Percent of Reading

Accuracy defines how close an instrument's measured value comes to the true value of the process variable. Manufacturers specify accuracy using two distinct mathematical foundations.

Percent of Span (% of Span)

When accuracy is specified as a percentage of calibrated span, the absolute measurement error band remains constant across the entire measuring range.

$\text{Absolute Error Limit} = \pm \left( \frac{\text{Accuracy Statement (\%)}}{100} \right) \times \text{Calibrated Span}$

Percent of Reading (% of Reading)

When accuracy is specified as a percentage of actual reading, the absolute measurement error band scales proportionally with the magnitude of the measured process variable.

$\text{Absolute Error Limit at Value } X = \pm \left( \frac{\text{Accuracy Statement (\%)}}{100} \right) \times X$

Comparative Worked Example: Flow Meter Selection

Scenario: An industrial process requires measuring oil flow between $10\text{ GPM}$ and $100\text{ GPM}$ (Calibrated Span = $100\text{ GPM}$). Two meters are evaluated:

• Meter A (DP Meter): Rated at $\pm 0.5%$ of Span.
• Meter B (Coriolis Mass Meter): Rated at $\pm 0.5%$ of Reading.

Calculate the absolute error and relative percent error of both meters at $100\text{ GPM}$ (full scale) and at $10\text{ GPM}$ (10% flow).

+-----------------------------------------------------------------------------------------+
|                         ACCURACY COMPARISON MATRIX                                      |
|                                                                                         |
| Flow Rate   Meter A (+/-0.5% Span)                      Meter B (+/-0.5% Reading)       |
| ---------   -----------------------------------------   ------------------------------- |
| 100 GPM     Error = +/- (0.005 * 100) = +/- 0.50 GPM    Error = +/- (0.005 * 100) = 0.50|
|             % of Reading Error = 0.5%                   % of Reading Error = 0.5%       |
|                                                                                         |
| 10 GPM      Error = +/- (0.005 * 100) = +/- 0.50 GPM    Error = +/- (0.005 * 10) = 0.05 |
|             % of Reading Error = (0.50 / 10) = 5.0% !   % of Reading Error = 0.5%       |
+-----------------------------------------------------------------------------------------+

Analysis:

• At 100 GPM, both meters deliver identical absolute accuracy ($\pm 0.50\text{ GPM}$).
• At 10 GPM, Meter A's absolute error remains fixed at $\pm 0.50\text{ GPM}$, representing a massive $\pm 5.0%$ error of actual flow! Meter B's absolute error scales down to $\pm 0.05\text{ GPM}$, maintaining a true $\pm 0.5%$ error.
• Key Takeaway for CCST Exam: % of Span meters exhibit severe low-end accuracy degradation. Applications with wide turndowns require % of Reading flow meters (Coriolis, Ultrasonic, Magnetic).

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Linearity, Repeatability, Hysteresis, and Deadband

Linearity

Linearity is the closeness with which an instrument's calibration curve approximates a specified straight line.

• Independent Linearity: The maximum deviation of any calibration point from a straight line positioned to minimize maximum deviation.
• Zero-Based Linearity: Deviation from a straight line passing through the actual zero point.
• Terminal-Based Linearity: Deviation from a straight line passing through actual LRV (0%) and URV (100%) output points.

Repeatability

Repeatability is the closeness of agreement among consecutive measurements of the same input process value under identical operating conditions, approaching from the same direction.

$\text{Repeatability Error} = \text{Maximum Output Deviation between Consecutive Identical Runs}$

Note: High repeatability does NOT guarantee high accuracy. An instrument can be highly repeatable (always giving the exact same output) while suffering from a large zero shift error.

Hysteresis

Hysteresis is the maximum difference in output reading for a given input process value when approached from increasing (upscale) direction versus decreasing (downscale) direction across a full-scale calibration cycle.

  Output
    ^
100%|                        /  (Downscale Curve)
    |                       / /
    |                      / /   <-- Hysteresis Gap
    |                     / /
    |                    / /  (Upscale Curve)
  0%|-------------------/---------------------> Input Process Variable
    0%                                   100%

• Causes of Hysteresis: Mechanical backlash in gear trains, friction in valve packing, magnetic remanence in inductive cores, or elastic deformation in Bourdon tubes.

Deadband

Deadband is the range through which an input process variable can be varied without initiating a measurable change in instrument output response.

$\text{Deadband} = \text{Input Change Required to Produce Output Movement}$

• Deadband vs. Hysteresis: Hysteresis refers to output deviation for a given input depending on direction of approach. Deadband refers to the physical threshold of input change required to overcome internal mechanical friction or digital rounding before any output reaction occurs.

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Classification of Calibration Errors

When evaluating calibration curves, CCST technicians must diagnose four distinct error signatures:

1. ZERO SHIFT ERROR             2. SPAN (GAIN) ERROR            3. NON-LINEARITY ERROR
   Output                          Output                          Output
   ^   / (Actual)                  ^   / (Actual)                  ^    /---
   |  /                            |  /                            |  /    /
   | / / (Ideal)                   | /-- (Ideal)                   | / (Ideal)
   |/ /                            |/                              |/
   +----------> Input              +----------> Input              +----------> Input
   (Parallel Offset)               (Slope Difference)              (Mid-Scale Bowing)

1. Zero Shift Error (Offset Error)

• Characteristics: The actual output differs from the ideal output by a constant amount across the entire range. The calibration curve shifts up or down in a parallel line.
• Cause: Mounting position changes, static pressure effects, sensor zero drift.
• Correction: Adjust the Zero screw or perform a digital Zero Trim.

2. Span Error (Gain / Multiplication Error)

• Characteristics: Zero error is negligible at 0% (LRV), but output error increases progressively, reaching maximum magnitude at 100% (URV). The slope of the calibration curve changes.
• Cause: Incorrect lever arm linkage ratios, span resistor resistance changes, incorrect electronic gain settings.
• Correction: Adjust the Span screw or perform a digital Span Trim.

3. Non-Linearity Error

• Characteristics: Output agrees with ideal output at 0% (LRV) and 100% (URV), but deviates in the middle of the scale, reaching maximum error near 50% span.
• Cause: Diaphragm stiffness non-linearities, uncompensated sensor non-linearities.
• Correction: Perform multi-point digital characterization or linearization trim.

4. Hysteresis Error

• Characteristics: Upscale and downscale calibration curves diverge, forming a closed loop.
• Cause: Mechanical friction, loose mechanical linkages, packing drag.
• Correction: Replace worn mechanical gears, adjust packing torque, clean or overhaul internal linkages.

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5-Point Calibration Methodology and Error Analysis

To detect all four types of calibration errors, a standard 5-point calibration test is conducted by applying accurate test standards at 0%, 25%, 50%, 75%, 100%, and returning down through 75%, 50%, 25%, 0%.

Standard 5-Point Calibration Reference Values

Percent Error Calculation Formula

$\text{Percent Error (\% of Span)} = \left( \frac{\text{Actual Output} - \text{Ideal Output}}{\text{Output Span}} \right) \times 100$

$\text{Percent Error (mA)} = \left( \frac{\text{Actual mA} - \text{Ideal mA}}{16.000\text{ mA}} \right) \times 100$

Worked Example: Evaluating Field Calibration Data

Scenario: A technician tests a pressure transmitter calibrated for $0\text{ to } 100\text{ psig}$ ($4-20\text{mA}$ output). The manufacturer's tolerance is $\pm 0.50%$ of span ($\pm 0.080\text{ mA}$). The following test data is recorded:

+-----------------------------------------------------------------------------------------+
|                           5-POINT CALIBRATION TEST DATA                                 |
|                                                                                         |
| Point (%)  Input (psig)  Upscale (mA)   Downscale (mA)  Max Error (mA)  % of Span Error |
| ---------  ------------  ------------   --------------  --------------  --------------- |
| 0 %        0.00          4.080          4.082           +0.082 mA       +0.512 %        |
| 25 %       25.00         8.081          8.083           +0.083 mA       +0.512 %        |
| 50 %       50.00         12.080         12.084          +0.084 mA       +0.525 %        |
| 75 %       75.00         16.079         16.082          +0.082 mA       +0.512 %        |
| 100 %      100.00        20.080         20.080          +0.080 mA       +0.500 %        |
+-----------------------------------------------------------------------------------------+

Diagnostic Analysis:

1. Error Classification: Notice that at every test point, the actual output is approximately $+0.080\text{ mA}$ higher than the ideal output across both upscale and downscale sweeps. The slope is unchanged and hysteresis is negligible ($< 0.004\text{ mA}$).
2. Diagnosis: This represents a pure Zero Shift Error (+0.080 mA parallel offset).
3. Corrective Action: The technician performs a Zero Calibration Adjustment (or Zero Trim) to lower the output by $0.080\text{ mA}$, bringing all points to within $\pm 0.005\text{ mA}$ ($0.03%$ of span), fully restoring instrument compliance.