Standard

            All the instruments are calibrated at the time manufacture against a measurement standard. A standard of measurement is a physical representation of a unit of measurement. A standard means known accurate measure of a physical quantity. Other physical quantities are compared with the standards to obtain their values.

          A unit is realized by reference to an arbitrary material standard or to natural phenomenon including physical and atomic constants. For example, the fundamental unit of mass i.e.kilogramme, defined as the mass of a cubic decimeter of water as its temperature of maximum density of 4° C. This unit is represented by material standard i.e. by the mass of international prototype kilogram, consisting of a platinum-iridium alloy cylinder which is preserved at the International Bureau of Weights and measures at Severus, near Paris and is the material representation of the unit kilogram. The unit of length i.e. meters is represented by the distance between two fine lines engraved on gold plugs near the ends of a platinum–iridium   alloy at 0°c and mechanically supported in a prescribed manner. Similarly, for all the units including fundamental and derived units, the different standards have been developed. All these standards have been developed. All these standards are preserved at the International Bureau of Weights and Measures at Severes, near Paris.

      The different types of standards are classified as

1.     International standards

2.    Primary standards

3.    Secondary standards

4.    Working standards

Let us discuss in brief, each of these categories of standards. 

  International standards

     International standards are defined as the international agreement. These standards, as motioned above are mentioned at the International Bureau of Weights and Measures and are periodically evaluated and checked by absolute measurements in terms of fundamental units of physics. These international standards are not available to the ordinary users for the calibration purpose. For the improvements in the accuracy of absolute measurements, the international units replaced by the absolute units in 1948. Absolute units are more accurate than the international units.

Primary standards

                    These are highly accurate standards, which can be used as ultimate reference standards. These primary standards are maintained at National Standard Laboratories in different countries. These standards representing fundamental units as well as some electrical and mechanical derived units are calibrated independently by absolute measurements at each of the national laboratories. These are not available for use, outside the national laboratories.

                    The main function of the primary standards is the calibration and verification of secondary standards.

Secondary standards

                    As mentioned above, the primary standards are not available for the use outside the national laboratories. These various industries need some reference standards. So, to protect highly accurate primary standards the secondary standards are maintained, which are designed and constructed from the absolute standards. These are used by the measurement and calibration laboratories in industries and are maintained by the particular industry to which they belong. Each industry has its own standards.

Working standards

                    These are the basic tools of a measurement laboratory and are used to check and calibrate the instruments used in laboratory for accuracy and the performance. For example, the resistor manufacturing industry maintains a standard resistor in the laboratory for checking the values of the manufactured resistors. The manufacture verifies that the values of the manufactured resistors as well within the specified accuracy limits. Thus, the working standards are somewhat less accurate than the primary standards. Thus the working standards are used to check and calibrate general laboratory instruments for accuracy and performance.

Dynamic characteristics

                    When the instrument is subjected to rapidly varying inputs, the relation between input and output becomes totally different than that in case of static or constant inputs. As the input varies from instant to instant, output also varies from instant to instant. The behaviour of system under such conditions is called dynamic response of the system.

                    The dynamic behaviour of the measuring system is determined by applying some known and predetermined variations of input to the sensing element. The standard variations in the input, used practically to obtain the dynamic behaviour, are as follows:

1.    Step input 

                    This represents sudden, instantaneous and finite change in the input. The step input of magnitude A is denoted as Au (t) and can be indicated as shown in the fig.

Its Laplace transform is given by,

                    F(s) = ……. Laplace of step input.

When A=1 it is called unit step input.

Step

2.    Ramp input

                       This represents linear change in input. The input, i.e. a variable to be measured varies linearly with time. It changes at a constant rate with respect to the time. The ramp input of magnitude A denoted as At u (t) and can be shown in the fig.

The Laplace transform of rape is given by,

                    F(s) =A/S²………..Laplace of ramp input

When A=1, it is called unit ramp input. 

Ramp

3.    Parabolic input  

                     This represents an input signals which is proportional to the square of the time and hence represents constant acceleration. The parabolic input of magnitude A is denoted as u(t) and can be shown in fig.

The Laplace transform of parabola is given by,

                    F(s) = 2A/s³……….Laplace of parabolic input

Parabolic

4.    Impulse input 

                                It exists only at t=o and has zero value at any other time.

f(t) =0  for   t≠ 0

And area under it is its magnitude. If it is unity, it is called delta function denoted as δ (t). It is shown in fig. it shows the concept of impulse input and it shows its representation. It is basically a pulse with its base Δt approaching to zero. The Laplace transform of δ(t) is 1.

                    L (δt) =1……………Laplace of unite impulse input 

Impulse Input

5.    Sinusoidal input  This represents an input which changes in accordance with a Sinusoidal function of constant amplitude. The frequency is the independent variable in this case. For a linear system subjected to Sinusoidal input, the output is also Sinusoidal in steady state, but it differs from input in amplitude and phase. Analyzing the dynamic behaviour includes the study of variation in output amplitude and phase as input is Sinusoidal in nature.

The Sinusoidal input is given by A sinɷt where Ais its amplitude as shown in fig. its Laplace transform is given by,

 F(s)= Aɷ/s²+ɷ²………Laplace of  Sinusoidal input.

The various dynamic characteristics of an instrument are speed of response, fidelity, lag and the dynamic error. 

Sinusoidal Input

Speed of Response 

           It is the rapidity with which the system responds to the changes in the quantity to be measured. It gives the information about how fast the system reacts to the changes in the input. It indicates activeness of the system. 

Fidelity

          It indicates how much faithfully the system reproduces the changes in the input. It is the ability of an instrument to produce a wave shape of input with respect to time.

Lag

       

   Every system takes some time, whatever small it may be, to respond to the changes in the measured variable. This retardation or delay in the response of a system is called lag. The lags are of two types:-

1.    Retardation Lag: In this case, the response of the system begins immediately after a change in the variable has occurred.

2.    Time Delay : In this case,response begins after some time called dead time, after the application of input. Such a delay shifts the response along time axis and hence causes the dynamic error.

Dynamic Error

Dynamic characteristics

          It is the difference between the true value of the variable to be measured, changing with time and the value indicated by the measurement system, assuming zero static error.