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Typical Calibration Errors

Recall that the slope-intercept form of a linear equation describes the response of a linear instrument:
y = mx + b

   y = Output

   m = Span adjustment

   x = Input

   b = Zero adjustment

A zero shift calibration error shifts the function vertically on the graph. This error affects all calibration points equally, creating the same percentage of error across the entire range:

A graph showing the effect of a zero shift

A span shift calibration error shifts the slope of the function. This error’s effect is unequal at different points throughout the range:

Graph showing the effect of a span shift

A linearity calibration error causes the function to deviate from a straight line. This type of error does not directly relate to a shift in either zero (b) or span (m) because the slope-intercept equation only describes straight lines. If an instrument does not provide a linearity adjustment, the best you can do for this type of error is “split the error” between high and low extremes, so the maximum absolute error at any point in the range is minimized:


Graph showing the effect of a Linearity Error


A hysteresis calibration error occurs when the instrument responds differently to an increasing input compared to a decreasing input. The only way to detect this type of error is to do an up-down calibration test, checking for instrument response at the same calibration points going down as going up:

Graph showing the effect of a hysteresis error

Hysteresis errors are almost always caused by mechanical friction on some moving element (and/or a loose coupling between mechanical elements) such as bourdon tubes, bellows, diaphragms, pivots, levers, or gear sets. Flexible metal strips called flexures – which are designed to serve as frictionless pivot points in mechanical instruments – may also cause hysteresis errors if cracked or bent.

In practice, most calibration errors are some combination of zero, span, linearity, and hysteresis problems.


As-found and as-left documentation

An important principle in calibration practice is to document every instrument’s calibration as it was found and as it was left after adjustments were made. The purpose for documenting both conditions is to make data available for calculating instrument drift over time. If only one of these conditions is documented during each calibration event, it will be difficult to determine how well an instrument is holding its calibration over long periods of time. Excessive drift is often an indicator of impending failure, which is vital for any program of predictive maintenance or quality control.

Typically, the format for documenting both As-Found and As-Left data is a simple table showing the points of calibration, the ideal instrument responses, the actual instrument responses, and the calculated error at each point. The following table is an example for a pressure transmitter with a range of 0 to 200 PSI over a five-point scale:

 Percent of range   Input pressure 

Output current (ideal) 

 Output current (measured) 

 Error (percent of span) 

0% 0 PSI 4.00 mA    
25% 50 PSI 8.00 mA    
50% 100 PSI 12.00 mA    
75% 150 PSI 16.00 mA    
100% 200 PSI 20.00 mA    


Up-tests and Down-tests

It is not uncommon for calibration tables to show multiple calibration points going up as well as going down, for the purpose of documenting hysteresis and deadband errors. Note the following example, showing a transmitter with a maximum hysteresis of 0.313 % (the offending data points are shown in bold-faced type):

 Percent of range   Input pressure 
 Output current (ideal)   Output current (measured)   Error (percent of span)
 0% 0 PSI 4.00 mA 3.99 mA -0.0625 %
 25% 50 PSI 8.00 mA 7.98 mA -0.125 %
 50% 100 PSI 12.00 mA 11.99 mA -0.0625 %
 75% 150 PSI 16.00 mA 15.99 mA -0.0625 %
 100% 200 PSI 20.00 mA 20.00 mA 0 %
 75% 150 PSI 16.00 mA 16.01 mA +0.0625 %
 50% 100 PSI 12.00 mA 12.02 mA +0.125 %
 25% 50 PSI 8.00 mA 8.03 mA +0.188 %
 0% 0 PSI 4.00 mA 4.01 mA +0.0625 %

In the course of performing such a directional calibration test, it is important not to overshoot any of the test points. If you do happen to overshoot a test point in setting up one of the input conditions for the instrument, simply “back up” the test stimulus and re-approach the test point from the same direction as before. Unless each test point’s value is approached from the proper direction, the data cannot be used to determine hysteresis/deadband error.

Click here to continue reading to the next page,  NIST Traceability and Instrument Turndown

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Comments (4)Add Comment
How can I calculate a pressure transmitter error percent of span
written by John, June 30, 2013
Dear Madam / Sir, please can you explain the maths in simple terms as to how I can calculate for a pressure transmitter the 'error as a percent of span' so I can make and complete a calibration data sheet. In advance I would like to say many thanks for your time & help.
written by Dennis, July 17, 2013
Error % of span can be found by: ((Measured-Ideal)/16)*100%
16 being the span of mA from 4 to 20.
written by bumbay, September 04, 2014
niggaz..woohooooooooo.calibrate mah dick..woohooo
written by MINTO, November 03, 2015
Accuracy = (Deviation / Span ) * 100
Deviation = Expected Value - Actual Value


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