General Information on Measuring Accuracy/Measurement Uncertainty

For basic information regarding the explanatory notes below, please refer to chapter “Notes on analog data values” under Continuative documentation for I/O components with analog in and outputs, particularly for full scale value.

This guidance should be read and followed in order to save extra work, time and, presumably, money.

In-depth familiarization with these instructions will make it easy to master this technology and thus facilitate your work.

Basic information on measurement technology:

Measuring devices are used to try to determine the true value of a measured variable, e.g. ambient temperature, with the amount of effort put into this varying. For various practical reasons this cannot be performed conclusively. Depending on the work involved, the measurement/measured value is subject to a random measuring error that cannot be eliminated. With its practically determined specification data, Beckhoff provides an approach that can be used to calculate the residual measurement uncertainty in the individual case. The following paragraphs elucidate this.

General notes

No special maintenance required, although an annual inspection is recommended for the box module.

If a factory calibration certificate is available for the device, a one-year recalibration interval is recommended, unless otherwise specified.

Notes regarding the specification data:

Measurement specifications are usually specified as "% of nominal full scale value" = “% full scale value (%_FSV)”, unless otherwise specified.
With regard to an individual value, "typical" means that on average, this parameter has the specified value. For individual Box modules, the parameter may deviate from the typical value. Current consumption is an example of this.
In the context of a limit (parameter is typically max./min. X) or with two limits (parameter is typically between X and Y), "typical" means that this parameter predominantly between the limits for the individual Box modules. However, deviations may occur: see confidence level. Noise is an example of this. Usually, no measurements are taken, in order to be able to make statements about standard deviations or result frequencies. A typical value is usually indicated with the abbreviation "typ." after the unit.
The confidence level is 95%, unless otherwise specified.

When operating in EMC-disturbed environments, twisted and shielded signal cables which are grounded at one end, at minimum, must be used in order to comply with the specification. The use of Beckhoff shielding accessories ZB8511 or ZS9100-0002 is recommended:

The ZB8520 DIN rail fastening is not recommended with regard to the analog protective effect:

Unless otherwise specified, measurement errors etc. will be stated in electrical DC operation (no use of AC values). During measurement of an AC value, the frequency slope of the analog input influences the measurement itself.

Note on temperature

The internal/external temperature of the device affects the measurement through the electronics. A measuring setup is generally characterized by a temperature dependence, which is specified in the form of a temperature drift, for example. The specifications apply for a constant ambient temperature. Variable conditions (e.g. heating of the control cabinet, sudden temperature drop due to opening of the control cabinet in cold weather) resulting in a temperature change may alter the measured values through dynamic and heterogeneous temperature distribution. To rectify such effects, the internal temperature of the device can be read online from the CoE and used for calculation. Some devices also electrically indicate that they have thermally stabilized; see diagnostic features.

The specification data apply:

after a warm-up time under operating voltage and in fieldbus mode of least 60 minutes at constant ambient temperature

practical note: after power-on, the device generally heats up exponentially such that the major proportion of the heating has occurred within a short period of approximately 10 to 15 minutes, depending on the device,and the measuring properties shift within the specification limits.
for clarification: typical trend of an internal temperature (no significance for a particular device):
some devices display that they are internally thermally stabilized and ∆T within the device is very small in the CoE object 0xF900:02. This can be evaluated by an application,

in horizontal installation position, taking the minimum distances into consideration,
under natural convection (no forced ventilation),
provided the specifications are adhered to.

Under different conditions, user-specific adjustment is required.

Notes on calculation with the specification data:

The independent specification data can be divided into two groups:

the data on offset/gain deviation, non-linearity, and repeatability, whose effect on the measurement cannot be influenced by the user. These are summarized by Beckhoff according to the calculation below, at "basic accuracy at 23°C".
the specification data whose effect on the measurement can be influenced by the user, namely

noise: effect can be influenced by sample rate, filtering and
the temperature: effect can be influenced by control cabinet air conditioning, shielding, cooling, etc.

The independent individual accuracy data are to be added quadratically according to the formula below in order to determine the total measurement accuracy – if there are no special conditions that contraindicate a uniform distribution and thus the quadratic approach (RSS – root sum squared method).

General Information on Measuring Accuracy/Measurement Uncertainty 4:

For measurement ranges where the temperature coefficient is only given as Tc_Terminal:

General Information on Measuring Accuracy/Measurement Uncertainty 5:

E_Offset	:	Offset specification (at 23°C)
E_Gain	:	Gain/scale specification (at 23°C)
E_{Noise, PtP}	:	Noise specification as a peak-to-peak value (applies to all temperatures)
MV	:	Measured value
FSV	:	Full scale value
E_Lin	:	Non-linearity error over the entire measuring range (applies for all temperatures)
E_Rep	:	Repeatability (applies to all temperatures)
Tc_Offset	:	Temperature coefficient offset
Tc_Gain	:	Temperature coefficient gain
Tc_Terminal	:	Temperature coefficient of the box module
ΔT	:	Difference between the ambient temperature and the specified basic temperature (23°C unless otherwise specified)
E_Age	:	Error coefficient for ageing
N_Years	:	Number of years
E_Total	:	Theoretically calculated total error

For example, if the following values are obtained at a determined measured value MV of 8.13 V in the 10 V measurement range (FSV = 10 V) (N_Years = 0):

Gain specification: E_Gain = 60 ppm
Offset specification: E_Offset=70 ppm_FSV
Non-linearity: E_Lin = 25 ppm_FSV
Repeatability: E_Rep = 20 ppm_FSV
Noise (without filtering): E_{Noise, PtP} = 100 ppm_peak-to-peak
Temperature coefficients:

Tc_Gain = 8 ppm/K
Tc_Offset = 5 ppm_FSV/K

then the theoretical possible total measurement accuracy at ΔT = 12K for the basic temperature can be calculated as follows:

General Information on Measuring Accuracy/Measurement Uncertainty 6:

or = ±0.0143.. %_FSV

Remarks:

ppm ≙ 10^-6

% ≙ 10^-2

In general, you can calculate this as follows:

if use at 23°C alone is to be considered:
Total measurement accuracy = basic accuracy & noise according to above formula
If use at 23°C is to be considered with slow measurement (=averaging/filtering):
Total measurement accuracy = basic accuracy
If general use within a known temperature range and incl. noise is to be considered:
Total measurement accuracy = basic accuracy & noise & temperature values according to above formula

Beckhoff usually gives the specification data symmetrically in [±%], i.e. ±0.01% or ±100 ppm. Accordingly, therefore, the unsigned total range would be double this given value. A peak-to-peak specification is a total range specification; the symmetrical value is thus half of it. In the quadratic calculation below, the symmetrical value for "one side" is to be inserted without a sign. Noise is usually specified in peak-to-peak form, therefore the equation for the noise value already contains the division factor 2.

Example:

symmetrical specification: ±0.01% (equivalent to ±100 ppm) e.g. for offset specification
total range: 0.02% (200 ppm)
to be used in the equation: 0.01% (100 ppm)

The total measurement accuracy calculated in this way is also to be considered as a symmetrical maximum value and thus to be provided with ± and ≤ for further use.

Example:

E_Total = 100 ppm
For further use: "≤ ± 100 ppm"

Expressed in words: "The offset of the individual accuracy specifications under the given conditions produced a range of 200 ppm that lies symmetrically around the individual measured value. The measured value specification x thus has an uncertainty of x ±100 ppm; it is thus 95% certain that the true value thus lies in this range".

	The noise component can be omitted The noise component F_Noise can be omitted from the above equation (= 0 ppm) if the average value for a set of samples is used instead of a single sample. The averaging can take place in the PLC, or it can be done by a filter in the analog channel. The output value of a moving average of many samples has a noise component that is almost entirely eliminated. The achievable accuracy thus increases when the noise component is decreased.

Notice

Error coefficient of ageing

If the specification value for aging from Beckhoff has not (yet) been specified, it must be assumed to be 0 ppm when considering measurement uncertainty, as in the above example, even if in reality it can be assumed that the measurement uncertainty of the device under consideration changes over the operating time, or colloquially stated, the measured value "drifts".

Experience has shown that the basic accuracy of the instrument under consideration, provided it is operated according to specifications, can be taken as the order of magnitude for an annual change (10,000 h). This is an informative statement, does not constitute a specification, and exceptions may occur. In general, the change in ageing will be very application-specific. A general ageing specification from Beckhoff is therefore to be regarded as a guideline rather than a guaranteed upper limit, when published.

If the measurement uncertainty consideration in the application shows that aging over the desired operating time can put the measurement accuracy at risk, Beckhoff recommends a cyclical check (recalibration) of the measurement channel, with regard to sensors, cabling and the Beckhoff measurement modules. In this way, potential long-term changes in the measurement chain can be detected early and, in some cases, the trigger (e.g. overtemperature) can even be eliminated. See also Continuative documentation for I/O components with analog in and outputs.

	Basic accuracy, extended basic accuracy, and averaging The basic accuracy will be designated separately to simplify usage. The basic accuracy includes the offset/gain deviation, non-linearity and repeatability, but not the temperature coefficient nor the noise and is thereby a subset of the aforementioned complete calculation. It is possible to increase the measurement accuracy beyond the basic accuracy by means of the offset correction. Note: the ”extended basic accuracy” also includes the temperature behavior across the specified operating temperature range, e.g. 0…60°C, via the temperature coefficient. "Averaging" means that the value has been obtained from the arithmetic average of 100,000 (usually) values to eliminate noise. The averaging function integrated into the box module does not necessarily need to be used. If resources are available, averaging can also be executed within the PLC.

	Measurement accuracy of the measured value (from reading) In several cases, the "Accuracy based on the up-to-date measured value" (percentage of reading), i.e. "Accuracy of value", is sought instead of the "Accuracy related to the full scale value (FSV)" (percentage of range). This value could easily be calculated from the data given by the specification, as the total accuracy consists of a measured value and full scale value dependent component and an exclusively full scale value dependent component, according to the formula: