* fundamental of measurement:-
purpose of measurement and significance of measurement:
purpose of measurement: the measurement of a given quantity is essentially an act or the result of a quantitative comparison between the quantity and a predefined standard. since two quantities are compared, the result is expressed in numerical values. in fact, measurement process by which one can convert physical parameters to meaningful numbers. The measuring process is one in which the property of an object or system under consideration is compared to an accepted
standard unit. the number of times the unit standard fit into the quantity being measured is the numerical measure. The numerical measure is meaningless unless followed by a unit used, since it identifies the characteristic measured. Phenomena and relationships are discovered and these advances make new types ot measurements
imperative. new discoveries are not of any practical utility unless the results are backed by actual measurements. this results in an unending chain which leads to new discoveries that required more,
new and sophisticated measurement techniques.
significance of measurement: the advancement of science and technology is dependent upon a parallel process in measurement techniques. as science and technology move ahead, new 2 definition and brief explanation of :
range & span: range of an instrument 1st defined as the largest and smallest reading and span is defined as the difference between largest and smallest reading. eg. a thermocouple calibrated between 200°c to 500c, the range is 200'c to 500°c but span is 500-200=300c.
Sensitivity: sensitivity of an instrument is the ratio of the magnitude of the output signal or
response to the magnitude of the input signal or the quantity being measured. its units are mm/ma, counts per volt etc. depending upon the input and output True & indicated value: the true value of quantity to be measured may be defined as the average
of an infinite number of measured values when the average deviation due to the various contributing factors tends to zero. such an ideal situation is impossible to realise in practice and hence it is not possible to determine the "true value" of a quantity by experimental method.
in practice, the thru value refer to a value that would be obtained if the quantity under
consideration were measured by a method agreed upon by experts as being accurate for the purpose to which the data will ultimately be put to use. Indicated value is the value of a quantity actually indicated or provided by a measuring instrument or measuring device.
static error: it is defined as the difference between the measured (indicated) value and the true value of the quantity.
da = am - at
where, da = error
Am= indicated or measured value of quality.
a = true value of quantity.
da is also called the absolute static error of quantity a. T
he absolute value of da does not indicate precisely the accuracy of measurement
error of +_2a is negligible when the current being measured is of the order of 1000a while the same
error of +_2a may be regarded as intolerable when the current under measurement is 10A or so. Resolution:- If the input is slowly increased from some arbitrary input value, it will be found that output does not change at all until a certain increment is exceeded.This increment is called resolution of the instrument. Thus the smallest increment in input which can be detected by
If a voltmeter has a uniform scale with 100 divisions, full scale reading is 200V and 1/10 of a scale division can be estimated with a fair degree of certainty. Then I scale division = 200/100 = 2V And resolution = 1/10 scale division = (1/10) x 2 =0.2V Accuracy: It is the closeness with which an instrument reading approaches the true value of the quantity being measured. Thus accuracy of a measurement means conformity to truth.
Precision: t is a measure of reproducibility of the measurement, ie., given a fixed value of a
quantity, precision is a measure of the degree of agreement within a group of measurements. Let a voltage of 100V measured by a voltmeter. Five readings are taken, and the indicated values are 104, 103, 105, 103 and 105V. From these values it is seen that accuracy is 5% (5V in this case) while precision is of +1% is indicated since the maximum deviation from the mean
reading of 104V is only 1.0V. Efficiency: It is defined as the ratio of the measured quantity and the power absorbed by the instrument at full scale. 1.3 classification of institutions:The various electrical measuring instruments are broadly divided into two classes (1) Absolute
Instruments (2) Secondary Instruments. Secondary Instruments are also classified into three groups.
1) Indicating Instruments (2) Recording Instruments and (3) Integrating Instruments.
Absolute instruments: These instruments give the magnitude of the quantity under measurement in terms o physical constant of the instrument. The examples of this class of instruments are
Tangent Galvanometer and realised Current.
Secondary Instruments: These instruments are so constructed that the quantity being measured can also be measured by observing the output indicated by the instrument. These instruments are
calibrated by comparison with an absolute instrument or another secondary instrument which has already been calibrated against an absolute instrument. Voltmeter, ammeter and glass
thermometer are typical example of secondary instruments.
(1)Indicating Instruments: Indicating instruments are those instruments which indicate the magnitude of a quantity being measured. They generally make use of the dial and pointer tor this purpose. Ordinary voltmeters, ammeters and belong to this category.
(2)Recording Instruments: These instruments give continuous records of the quantity being measured over a specified period. The variations of the quantity being measured are recorded by a pen (attached to the moving system of the instrument) on a sheet of paper fixed or moving. For example we may have a recording voltmeter in a sub station keeps record of the variations of supply voltage during a day. (3) Integrating Instruments: These instruments totalize the events over a specified period of time. The summation, which they give, is the product of time and an electrical quantity. Ampere hour and watt hour (energy) meters are examples of this category. The integration is generally given by a register consisting of a set of a pointer and dials. Electrical measuring instruments can also be classified as Analog Instruments and Digital Instruments.
Analog Instruments: An analog instrument is one in which the output or display is a continuous function of time and bears a constant relation to its input. The analog instruments may be divided
into two groups - (1) Electromechanical instruments (2) Electronic instruments.
Digital Instruments: Digital instruments provide a digital display of the measured. A fixed number ot pulses proportional to the measured are entered in a digital counter and the counter actuates the digital display. Digital instruments are becoming more and more popular because of their inherent advantages over analog instruments, such a, greater speed, increased accuracy, better resolution, reduction in operation errors, and the ability to provide automatic measurements in system application. 1.4 Basic Requirements for Measurements:
Three types of torques are needed for satisfactory operation of indicating instrument. These are (1)Deflecting Torque, (2) Controlling Torque and (3) Damping Torque
!1) Deflecting torque: Deflecting torque is produced by making use of one of the magnetic, heating, chemical, electrostatics and electromagnetic induction effect of
Current or voltage and causes the moving system ot instrument to move irom its zero
position when the instrument is connected to an electric circuit to measure the electrical quantity. The method of producing this torque depends upon the type of instrument The deflecting system of most of the commercial instruments is mounted on a
pivoted spindle, the quantity being measured producing a deflecting torque proportional
to its magnitude.
(2) Controlling torque: The controlling torque opposes the deflecting torque and increases
in deflection of the moving system, thus limits the movement and ensures the magnitude of is always the same tor a given value of quantity to be measured. In absence of the controlling torque, the pointer will shoot beyond the final steady position for any magnitude of current and thus the deflection will be infinite. It also brings the moving system back to zero position when the force causing the instrument moving system to deflect is removed. Controlling System: There are two types of control systems which are used for indicating instruments (a) Spring Control (b) Gravity Control
(a) Spring control:
The spring control system is illustrated in fig.1. The phosphor bronze spiral hair springs A and B coiled in opposite directions and acting one against the other are used in spring control. One end of each spring is attached to the spindle. The Outer end of spring A is attached to the lever at point C, pivoted at P while that of B is fixed. Under the influence of deflecting torque when the pointer moves, one of the springs unwinds itself while the other gets twisted. The twist in fact produces controlling torque which is directly proportional to the angle of deflection of the moving system. When the deflecting torque Td and controlling torque Tc are equal, the pointer comes to rest
in its final deflected position. Since Tc is directly proportional to the angle of twist "Q" and deflecting torque Td is proportional to the current flowing through it, as in case of P.M.M.C type instruments, and in final deflecting position Tc= Td Therefore, Deflection "Q" is directly proportional to I, the current flowing through the instrument. Since in spring controlled instruments the deflection is directly proportional to the
current, therefore, these instruments have uniform scale.
(b) Controlling torque:
In gravity control instrument a small weight is attached to moving system in such a way that it produced a controlling torque, when the moving system is in deflected position. The controlling torque cab be varied either by adjusting the position of the controlling weight upon the arm. The usual arrangement in fig.2.
In zero position of the pointer the control weight is vertical. When the pointer is deflected through an angle "Q" from its zero position, the control weight will be in position shown dotted in the figure. In deflected position Tc will be "Q" where W is the control weight, 1 is the distance from the axis of rotation and "Q" is angle of deflection. Therefore, Tc directly please to sin"Q"
Since, Td directly proportional to "I"
Then, in final deflected position Td=Tc
Or, "I" directly proportional to sin "Q"
Or, I=k sin "Q" (say),
Then, "Q"= sin^-1(1/k)
Hence in gravity control instruments scales are not uniform but are crowded in the
beginning.
ii) Damping torque: Damping torque is necessary to avoid oscillations of the moving system about its final deflected position. In absence of damping the moving system of
an instrument would oscillate about the position at which the deflecting torque and
controlling torque are equal. If the instrument is under damped the moving system will oscillate about its final position and take some time to come to rest in its steady position. If the instrument is Over damped, the moving system will become slow and lethargic and when the degree of damping is such that the pointer rises quickly to its final deflected position without oscillations, the damping. Is said to be critical and the instrument is said to be "dead beat". In practice to obtain the best result the damping is adjusted to the value slightly less than the critical value.
The various methods of obtaining damping are (a) Air Friction Damping (b) Fluid Friction
(a) air friction Damping:
Two types of air friction damping are shown in fig. (a) & (b). In first type of air friction
damping system a light aluminium piston is attached to the moving system. The piston moves in a fixed air chamber closed at one end. The clearance between the piston and chamber walls is uniform and very small. When there are oscillations the piston moves into and out of an air chamber. When piston moves into the chamber, the air inside it is compressed and pressure of air opposes the motion of piston and hence whole of the moving system. When piston moves out of the air chamber, pressure in the closed space falls and pressure on open side of piston is greater than on the other side. Thus there is again an opposition to motion.The arrangement of fig.(b) consists of an aluminium vane mounted on a spindle which
moves in a quadrant (sector) shaped air chamber. The aluminium piston should be carefully fitted so that it does not touch the wall otherwise a serious error will be caused in reading.
(b) fluid friction Damping:
In fig.(a) a number of vanes are attached to the spindle. These vanes are submerged in oil and move in a vertical plane. This arrangement gives a greater damping torque.In fig.(b) a disc is attached to the moving system, this disc dips into an oil pot and is
completely submerged in oil. When the moving system moves, the disc moves in oil and a frictional drag is produced. This frictional drag always opposes the motion
(c) Eddy current damping:
Eddy current damping is the most efficient method of damping. When a conductor moves in a magnetic field an e.m.f is induced in it and if a closed path is
provided, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the strength of magnetic field and current produced. This current is proportional to e.m.f which in turn is proportional to velocity of conductor. Thus if strength of magnetic fiel is constant (if it is produced by a permanent magnet), the torque is proportional to the velocity of the conductor.
There are two method of providing eddy current damping - In first method a disc or vane of conducting but non- magnetic material like copper or aluminium is mounted on the spindle carrying
the moving system and the pointer as shown in fig.6(a) & 6(b). The disc or vane is positioned so that its edges rotate between the poles of a permanent magnet. In the second method of eddy current damping, as used in P.M.M.C instruments, the coil is
wound on a light metal former in which eddy currents are produced due to movement of the coil in the field of a permanent magnet, as shown in fig.6(c).
Written by
Abhishek Singh.(E.E)
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