# Common Errors in Calibration of Measuring Instruments: Zero, Span, Linearity, and Hysteresis.

Instrument calibration is a procedure that certifies the measurement obtained by an instrument is compatible with what is expected and is suitable for use, to avoid deviations in the analysis processes and reduce costs.

In general, it comprises comparing the results obtained by the instruments with those obtained by standards, under pre-established and controlled conditions.

During calibration, a technician encounters certain errors that are classified to understand and rectify.

Actually, the most common calibration errors are a combination of zero, span, linearity, and hysteresis problems.

The equation below describes the response of any linear instrument, that is

y = mx +b

Where

y = instrument output signal

m = Span value

x = Instrument input signal

b = value of zero

Zero-offset error in calibration

A zero-offset error in a calibration causes a vertical offset or displacement of the graph of the equation, which is equivalent to modifying the value of b of the equation.

This error affects all the calibration points or values, in the same way, causing the same error percentage within all the points or values of the instrument’s range.

If a transmitter has a zero-calibration error, that error can be corrected by carefully adjusting the “zero” until reaching the ideal response, essentially altering the value of b from the linear equation.

Span-offset error in calibration

A span offset error in a calibration causes the slope of the function to change, which is equivalent to changing the value of m in the linear equation. This error affects unequally at different values or points through the range of the instrument.

Transmitters with span calibration errors can be corrected by carefully adjusting the span until an ideal response is achieved, essentially altering the value of m.

Linearity error in calibration

A linearity error in a calibration causes the response function of the instrument to stop being a straight line. This kind of error is not directly related to zero (b) or span (m) offsets because the above equation only describes straight lines.

Some instruments provide the possibility of adjusting the linearity response, in this case, this parameter must be modified with extreme care. The behavior of the linearity adjustment is unique for each instrument model, therefore we must consult the manufacturer’s documentation to know the details of

How this parameter works exactly? If the instrument does not provide the possibility of modifying its linearity, the best we can do when faced with this type of error is to “divide or split the error” between the high and low ends of the range, therefore the absolute maximum error at any point in the range will be minimized.

Hysteresis error in calibration

A hysteresis error in calibration occurs when the response of the instrument at certain points or values is different when increasing the input signal that when decreasing the input signal.

The only way to detect this type of error is to do an up-down test in the calibration, that is, to take note of the determined values when the input signal increases and compare them with the same values but decreasing the input signal.

They are almost always caused by mechanical friction of the sensor elements such as bourdon tubes, bellows, diaphragms, pivots, etc. The friction always acts in the opposite direction to that of the relative motion-usually faulty components must be replaced or coupling problems in the instrument mechanism corrected.

In practice, the most common calibration errors are a combination of zero, span, linearity, and hysteresis problem.