STATIC CHARACTERISTICS OF MEASUREMENT SYSTEM

STATIC & DYNAMIC CHARACTERISTICS OF MEASUREMENT SYSTEM

Ø  The performance characteristics of an instrument are mainly divided into two categories:

i) Static characteristics

     ii) Dynamic characteristics

Static characteristics

Ø  The set of criteria defined for the instruments, which are used to measure the quantities which are slowly varying with time or mostly constant, i.e., do not vary with time, is called

‘static characteristics’

Ø  The various static characteristics are:

i) Accuracy  ii) Precision  iii) Sensitivity  iv) Linearity   v) Reproducibility  vi) Repeatability  vii) Resolution  viii) Threshold  x) Drift  x) Stability  xi) Tolerance  xii) Range or span

Accuracy:

Ø  It is the degree of closeness with which an instrument reading approaches the true value of the quantity being measured.

Ø  It indicates the ability of the instrument to indicate the true value of quantity.

Ø  The accuracy of a measurement means conformity to truth.

Static error:

Ø  It is the difference between measured value and true value of the quantity.

Obsolute or static error:

 E_s = A_t –A_m 

A_m = measured value of the quantity.

A_t= true value of quantity.

Relative error:

E_r=static  error / true value

Percentage relative error %E_r = E_r x100

Precision:

Ø  It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements. The precision is composed of two characteristics:

a) Conformity:

Consider a resistor having true value as 2385692 , which is being measured by an ohmmeter. But

the reader can read consistently, a value as 2.4 M due to the nonavailability of proper scale. The

error created due to the limitation of the scale reading is a precision error.

b) Number of significant figures:

The precision of the measurement is obtained from the number of significant figures, in which

the reading is expressed. The significant figures convey the actual information about the

magnitude & the measurement precision of the quantity. The precision can be mathematically

expressed as:

Where, P = precision

Xn = Value of nth measurement

Xn = Average value the set of measurement values

Difference between accuracy and precision:

·         An ammeter having high precision which can take readings to 1/150 of an ampere, but has a wrong zero adjustment. Now wecan takereading to 1/150 of an ampere which are consistent and clearly defined since the ammeter is as precise as ever. However, the readings taken with this ammeter are not accurate, since they do not conform the truth because of faulty adjustment of zero.

Sensitivity:

Ø  The sensitivity denotes the smallest change in the measured variable to which the instrument responds.

Ø  It is defined as the ratio of output signal to input signal of measuring system.. Mathematically it is expressed as,

S = change in output / change input

Deflection factor:

Ø  The reciprocal of the sensitivity is called inverse sensitivity or deflection factor.

Ø  Deflection factor = 1 / sensitivity

Resolution or discrimination:

Ø  It is the smallest measurable input change.

Threshold:

Ø  It is the smallest measurable input.

Ø  The minimum value below which no output change when the input of an instrument is increased gradually from zero is called the threshold of the instrument.

Ø  Thus threshold defines minimum value of input which is necessary to cause a detectable change from zero output.

Linearity:

Ø  The ability to reproduce the input characteristics symmetrically is called linearity.

Ø  It is desirable to have an instrument as linear as possible as the accuracy and linearity are closely related to each other

Reproducibility and drift;

Ø  It is the degree of closeness with which a given value may be repeatedly measured.

Ø  Perfect reproducibility means that the instrument has no drift.

Ø  No drift means that given input the measured values do not vary with time.

Range or span:

Ø  The minimum and maximum value of quantity for which an instrument is designed to measure is called its range or span.

Tolerance:

Ø  The maximum allowable error in the measurement is specified in terms of some value which is called tolerance.

Dead space or dead zone:

Ø  For certain range of input values there is no change in output. This range of input is called dead space or dead zone.