Q. Enumerate different types of errors in measurement. How can these errors be minimized.
Sol. Types of errors: Errors may arise from different sources and usually classified as under -
(1) Gross Errors (2) systematic Errors (3)
1. Gross Errors: Largely human errors arise due to misreading of instruments, incorrect adjustment , incorrect adjustment and improper application of instruments and computational mistakes, which covers human mistakes in reading or using instruments and in recording and calculating measurement results. As long as human beings are involved, some gross errors will inevitably be committed. Although complete elimination of gross errors is probably impossible , one should try to anticipate and correct them. Some gross errors ae easily detected while others may be very exclusive. One common gross error, frequently committed by beginners ion measurement work, involves the improper use of an instrument. In general, indicating instruments change conditions to some extent when connected into a complete circuit, so that the measured quantity is altered by the method employed. For example, a well calibrated voltmeter may give a misleading reading when connected across two points in a high resistance circuit. The same voltmeter, when connected in a low-resistance circuit, may give a more dependable reading. These examples illustrate that the voltmeter has a "loading effect" on the circuit, altering the original situation by the measurement process.
These errors can be avoided by adopting two means. They are:
(i) Great care should be taken in reading and recording the data.
(ii) Two, three or even more readings should be taken for the quantity
Under measurement, the readings should be taken at a different reading point to avoid re-reading with same error.
2. Systematic Errors: These types of errors are divided into these categories.
(i) Instrumental Errors (ii) Environmental Errors
(iii) Observational Errors
(i) Instrumental Errors: These errors arise due to three main reasons.
Due to inherent shortcoming in the instrument.
Due to misuse of the instruments.
Due to loading effect of instruments
Inherent Shortcomings of Instruments : These errors are inherent in instruments because of their mechanical structure. They may be due to construction, calibration or operation of the instruments or measuring devices. These errors may cause the instrument to read too low or too fast (high).e.g., if the spring of a permanent magnet instrument has become weak, the instrument will always read high. Errors may be caused because of friction, hysteretic or even gear backlash.
While making precision measurements, we must recognize the possibility of such errors as it is often possible to eliminate them, or at least reduce them to a great extent by using the following methods :
(a) The procedure of measurement must be carefully planned. Substitution methods or calibration against standards may be used for the purpose.
(b) Correction factors should be applied after determining the instrumental errors.
(c) The instruments may be re-calibrated carefully.
Misuse of instruments : The errors caused in measurements are due to the fault of the operator than of the instrument. A good instrument used in an unintelligent way may give erroneous results. Like failure to adjust the zero of instruments, using leads of too high resistance etc. Mostly these errors do not cause a permanent damage to the instruments but all the same they cause errors. However, there are certain ill practices like using the instrument contrary to manufacture's instructions and specifications which in addition to producing errors cause permanent damage to the instruments.
Loading Effect : One of the most commo0n errors committed by beginners, is the improper use of an instrument for measurement work. For example, a well calibrated voltmeter may give a misleading voltage reading when connected across a high resistance circuit. The same voltmeter when connected in a low resistance circuit, may give a more dependable reading. So the voltmeter has a loading effect on the circuit, altering the actual circuit conditions by the measurement process.
(ii) Environmental Errors : These errors are due to conditions external to the measuring device including conditions in the area surrounding the instrument. These may be effect of temperature, pressure etc. The corrective measures employed to eliminate or to reduce these undesirable effects are :
1. Arrangements should be made to keep the conditions as nearly as constant as possible. For example, temperature can be kept constant by keeping the equipment in a temperature controlled enclosure.
2. Using equipment which is immune to these effects. For example, variations in resistance with temperature can be minimized by using resistance materials which have a very low resistance temperature coefficient.
3. Employing techniques which eliminate the effects of these distuabces. For example, the effect of humidity, dust etc. can be entirely eliminated by hermetically sealing the equipment.
4. In case it is suspected that external magnetic or electrostatic fields can affect the readings of the instruments, magnetic or electrostatic shields may be provided.
5. Applying computed corrections : Efforts are normally made to avoid the use of application of computed corrections, but where these corrections are needed and are necessaryk they are incorporated for the computations of the results.
(iii) Observational Errors : These are many sources of observational errors. As an example, the pointer of a voltmeter resets slightly above the surface of the scale. Thus an error on account of PARALLAX will be incurred unless the line of vision of the observer is exactly above the pointer. To minimize parallax errors, highly accurate meters are provided with mirrored scales.
When the pointer's image appears hidden by the pointer, observer's eye is directly in line with the pointer. Although a mirrored scale minimizes parallax error, an error is necessarily present though it may be very small. Since the parallax errors arise on account of pointer and the scale not being in the same plane, we can eliminate this error by having the pointer and the scale in the same plane.
There are human factors involved in measurement. The sensing capabilities of individual observers effect the accuracy of measurement. No two persons obseve the same situation in exactly the same way where small details are concerned.
Modern electrical instruments have digital display of loutput which completely eliminates the errors on accounts human observational or sensing powers as the output is in the form of digits.
1. Random (or Accidental or Residual) Errors : It has been consistently found that experimental results show variation from one reading to another, even after all systematic errors have been accounted for. These errors are due to a multitude of small factors which change or fluctuate from one measurement to another and are due surely to chance. The quantity being measured is affected by many happenings throughout the universe. We are aware of and account for some of the factors influencing the measurement, but about the rest we are unaware. The happenings or disturbances about which we are unaware are lumped together and called "Random"or "Residual". Hence the errors caused by these happenings are called Random (or Residual) Errors. Since these errors remain even after the systematic errors have been taken care of, we call these errors as Residual (Random) errors.
The effect of random error is minimized by measuring the given quantity many times under the same conditions and calculating the arithmetical mean of the values obtained. The mean value can be considered as the most probable value of the measured quantity since random errors of equal magnitude but opposite sign are of approximately equal occurrence when making a great number of measurements.
V1 to increase. Since Vx become greater than Vy, current i4 is no longer zero. The magnitude of this current, hence the deflection of the meter is proportional to Vin.
The value of Vin. that cause maximum meter deflection is the basic range of the instrument. This is generally the lowest range on the range switch in non-amplified models. High range can be obtained by using an input attenuator and lower ranges can be obtained by a preamplifier.
The input attenuator in fig (A) is a calibrate front panel control in the form of resistance voltage divider. The full scale voltage appears across the divider so that the voltage at each tap is a progressively lower fraction of the full input voltage.
Bridge balance is obtained by adjustment the zero set potentiometer when Vin is zero full scale calibration is obtained by adjusting the potentiometer marked calibration in series with the ammeter.
The advantages of this meter are
(1) It decreases the amount of power drawn from the circuit under test by increasing the input impedance using an amplifier with unity gain.
(2) The source follower drives am emitter follower. This combination is capable of thousand fold or more increases impedance while maintaining a voltage gain of nearly one.
(3) The input impedance of this meter is 10?, which require a power of .025 µW for a 0.5 V deflection as compared to 25 µ W for an unamplifid meter thereby giving an increased sensitivity of 100 times.
A block diagram of a meter used for measurement of small voltage and currents is shown . the input voltage is amplified and applied to a increased by a like amount. A D.C -coupled amplifier that is an amplifier with no coupling capacitors and having a well controlled D.C, gain, is used to provide dto necessary amplification. An amplifier capable of a fixed DC gain of 10 is not difficult to construct and to keep stable. A simple op-amp plus the required feedback components will do a suitable job for this application.
DC gains of much more than 10 are required to use a standard D Arsonval meter movement to measure very small currents and voltages such as microvolt and nanoampere. To amplify nano ampere to drive a milliampere meter require a gain of 106. This require an op amp and two resistor and a simple circuit. However when gains this large are desired, all the defects of an operational amplifier become significant offset current, offset voltage and biases current become so troublesome that it is practically impossible to achieve acceptable performance with a standard op amp. Many of these defects can be reduced or eliminated by the use of trim adjustments accessible from the front panel in a similar fashion as the calibrate and zero function discussed above.