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Resolution of a measuring instrument
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Resolution of a measuring instrument
In metrology, the resolution of a measuring instrument is the ability to detect the smallest change in the value of a physical property that an instrument can detect. It also represents a static characteristic of an instrument. The resolution of an instrument can also be defined as the minimum incremental value of the input signal that is required to cause a detectable change in the output. Resolution is also defined in terms of percentage as:
\[\textrm{Resolution}=\dfrac{\Delta I}{I_{max}-I_{min}}\times 100\]
The quotient between the measuring range and resolution is often expressed as a dynamic range and is defined as:
\[\textrm{Dynamic range}=\dfrac{\textrm{measurement range}}{\textrm{resolution}}\]
And is expressed in terms of dB. The dynamic range of an n-bit ADC comes out to be approximately \(6n\) dB.
The resolution is actually the lower limit of subdivision of the measurement scale within which it still makes sense to define a reading value. Example: you can say that you have read 10.5 V with a measuring system having a resolution of 0.1 V (or 0.5 V); it does not make sense to say that you have read 10.5 V with a measuring system having a resolution of 1 V.
In common usage, the resolution is defined as the value of the measuring instrument’s format unit (the smallest graduation of a scale). Example: A 20 cm ruler with notches in 1 mm increments is commonly referred to as a ruler with a resolution of 1 mm. This easy approximation is not acceptable in metrology, where the distinction is not only conceptual, but also practical. Wanting to forcefully apply this approximation can lead to significant errors.
A still very common error (and much more serious) in everyday life is to consider the accuracy of the measure equal to the value of the resolution of the instrument, where “resolution” still means the unit of format of the instrument. The precision of a measurement depends on a multiplicity of factors, of which the resolution is only one element.
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