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# Instruments - Static Characteristics

The static characteristics of instruments are attributes that changes slowly with time. Static characteristics can be divided in to desirable and undesirable.

Desirable characteristics - what we want to achieve - are

• Accuracy
• Sensitivity
• Repeatability
• Reproducibility

Undesirable characteristics - what we want to avoid - are

• Drift
• Threshold
• Hystersis
• Creep
• Resolution
• Static error
.

### Desirable Characteristics

#### Accuracy

Accuracy is

• the closeness of a measurement to the true value

Relative accuracy can be expressed as

ar = (ymax - x) / x                                       (1)

where

ar = relative accuracy (unit/unit)

x = input true value (unit)

y = instrument output (unit)

##### Example - Accuracy

The true length of a steel beam is 6 m. Three repeated readings with a laser meter indicates a length of 6.01 m, 6.0095 and 6.015 m. The accuracy based on maximum difference can be calculated as

an absolute value like

aa = 6.015 m - 6 m

= 0.015 m

or as a relative value

ar = (6.015 m - 6 m) / 6 m

= 0.0025 m/m

or as relative value in percentage

a% = ((6.015 m - 6 m) / 6 m) 100%

= 0.25 %

The accuracy of an instrument can be related to

• maximum measured value possible for the instrument
• maximum range for the instrument
• actual output from the instrument

Two terms commonly used in connection with accuracy are precision, trueness and calibration.

##### Precision
• Precision is the closeness of agreement among a set of results

Example - for the steel beam above all measurements are within ±0.01 m - and we could say that the precision is good.

##### Trueness
• Trueness is the closeness of the mean of a set of measurement results to the actual (true) value

Example - for the steel beam above the mean value of the set of measurements is 6.01 m - and we could say that the trueness could have been better.

##### Calibration

The precision of the laser meter used in the example above is good and the accuracy of the meter can be improved with calibration as

calibration = 6.01 m - 6 m

= 0.01 m

#### Sensitivity

Sensitivity is the increment of the output signal (or response) to the increment of the input measured signal - and can be expressed as

s = dy / dx                           (2)

where

s = sensitivity  (output unit / input unit)

dy = change instrument output value (output unit)

dx = change in input true value (input unit)

##### Example - Temperature measurement with a Pt100 Platinum Resistance Thermometer

When temperature is changed from 0oC to 50oC - the resistance in a Pt100 thermometer changes from 100 ohm to 119.4 ohm. The sensitivity for this range can be calculated as

s = (119.4 ohm - 100 ohm) / (50oC - 0oC)

=  0.388 ohm/oC

#### Repeatability

Repeatability is the variation in measurements taken on the same item under the same conditions.

#### Reproducibility

Reproducibility is the ability of a measurement to be duplicated, either by the same person or by someone else under changed conditions.

.

### Undesirable Characteristics

#### Drift

Drift is the change in instrument output over time - when the true value is constant.

Dead zone errors are created by

##### Threshold

Threshold is when a minimum input is required to generate change in output.

##### Hystersis

An example can be a nut that is screwed a number of turns on a threaded rod. When turned back the same number of turns the nut will not be in the exact the same position as at the start. This is a typical a problem that must be adressed in applications like cnc machines and 3d printers.

##### Creep

Creep is caused by the time an instrument need to adapt to change in aplied input.

##### Resolution

Depending on the instrument - but minimum change in input may required for change in output.

### Significant Figures

Uncertainty in measurements or calculated values is indicated by the number of significant figures.

• Significant figures are the digits of a number known with certain certainty

The last digit in a number is taken as uncertain while the other digits are regarded as certain.

#### Example - Significant Figures

For the number 31.2 we regard the two first digits 30 as certain and the last digit 6 as uncertain. Unless otherwise stated an uncertainity of ±1 is assumed for the last digit.

## Related Topics

### • Measurements and Instrumentation

Measurement and instrumentation strategies.

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