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explains basic measurement concepts like Measurement systems, Static and dynamic characteristics,Units and standards of measurements, Error analysis


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Unit 1 BASIC MEASUREMENT CONCEPTS Measurement systems Static and dynamic characteristics Units and standards of measurements Error analysis Moving coil meters Moving iron meters Multimeters Bridge measurements Maxwell Hay Schering Anderson Wien bridge. R.JhansiRani AP/ECE

Significance Of Measurement : 

Significance Of Measurement Importance of Measurement is simply and eloquently expressed in the following statement of famous physicist Lord Kelvin: “ I often say that when you can measure what you are speaking about and can express it in numbers, you know something about it; when you cannot express in it numbers your knowledge is of meager and unsatisfactory kind ” 3 R.JhansiRani AP/ECE

Introduction : 

Introduction Measurement means, to monitor a process or a operation and using an instrument, express the parameter, quantity or a variable in terms of meaningful numbers. Measurement of a given parameter or quantity is the act or result of a quantitative comparison between a predefined standard and an unknown quantity to be measured. There are 2 basic requirements: The comparison standard is accurately defined and commonly accepted , and The procedure and the instrument used for obtaining the comparison must be provable. R.JhansiRani AP/ECE

Evolution of Instruments.: 

Evolution of Instruments . Mechanical Electrical Electronic Instruments. MECHANICAL: These instruments are very reliable for static and stable conditions. But their disadvantage is that they are unable to respond rapidly to measurements of dynamic and transient conditions. 5 R.JhansiRani AP/ECE


Contd ELECTRICAL: It is faster than mechanical, indicating the output are rapid than mechanical methods. But it depends on the mechanical movement of the meters. The response is 0.5 to 24 seconds. ELECTRONIC: It is more reliable than other system. It uses semiconductor devices and weak signal can also be detected. 6 R.JhansiRani AP/ECE

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Measuring instrument: It is defined as the device for determining the value or magnitude of a quantity or variable. Electronic measurement: It is the one which is based on electronic or electrical principles for its measurement function. R.JhansiRani AP/ECE

Advantages of electronic measurement: 

Advantages of electronic measurement Most of the quantities can be converted by transducers into the electrical or electronic signals. Electronic signals can be amplified, filtered, multiplexed, sampled and measured. Measured signals can be transmitted over long distance through cables or radio links, without any loss of information. Many measurements can be done simultaneously or in rapid succession. Electronic circuits can measure the events of very short duration Higher sensitivity, low power consumption and a higher degree of reliability are the important features of electronic instruments and measurements. R.JhansiRani AP/ECE

Functional elements of an instrument: 

Functional elements of an instrument Primary Sensing element Variable Conversion element Variable manipulation element Data Transmission element Data presentation element Data Storage &playback element Quantity To be measured observer Data conditioning element R.JhansiRani AP/ECE

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Primary Sensing Element: An element of an instrument which makes first contact with the quantity to be measured. In most cases a Transducer follows primary sensing element which converts the measurand into a corresponding electrical signal. Variable Conversion Element: output of the primary sensing element is in electrical form such as Voltage, Frequency….such an o/pt may not be suitable for the actual measurement system. (Ex: A/D converter) R.JhansiRani AP/ECE

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Variable Manipulation Element: The level of the o/pt from the previous stage may not be enough to drive the next stage. Thus variable manipulation element manipulates the signal, preserving the original nature of the signal. Data Transmission Element: When the elements of the system are physically separated, it is necessary to transmit the data from one stage to other. This is achieved by the data transmission element. Data Presentation Element: The data is monitored, for analyzing purpose using data presentation element.(Ex: Visual display) R.JhansiRani AP/ECE

Example : 

Example Moving coil senses current Magnets & coil convert current in coil to force Force is transmitted to pointer through mechanical links Pointer and scale presents the current value R.JhansiRani AP/ECE


Ammeter R.JhansiRani AP/ECE

performance characteristics: 

performance characteristics Static characteristics: The set of criteria defined for the instruments, which are used to measure the quantities which are slowly varying with time or mostly constant, ie ., do not vary with time is called static characteristics Dynamic characteristics: when the quantity under measurement changes rapidly with time, it is necessary to study the dynamic relations existing b/w i /pt and o/pt which is expressed as differential equations The set of criteria defined based on such dynamic differential equation is called dynamic characteristics R.JhansiRani AP/ECE

Calibration : 

Calibration Calibration is the process of making an adjustment or making a scale so that the reading of an instrument agree with the accepted and certified standard. Note: if the device is repaired, aged or modified then recalibration is carried out. R.JhansiRani AP/ECE


STATIC CHARACTERSTICS Accuracy Precision Resolution Error Sensitivity Threshold Reproducibility Zero drift Stability Linearity R.JhansiRani AP/ECE

Accuracy: Degree of closeness which the instrument reading approaches the true value of the quantity to be measured. It indicates the ability of an instrument to indicate true value of the quantity. A) Accuracy as “% of full scale reading”: If the instrument have uniform scale, then accuracy is expressed as % of full scale reading. Accuracy is 0.1% for full scale of 50 units means 0.05 units error is present in any measurement. Accuracy is 0.2% for full scale of 25 units means 0.05 units error Thus as reading decreases error is more and leads misleading.: 

Accuracy: Degree of closeness which the instrument reading approaches the true value of the quantity to be measured. It indicates the ability of an instrument to indicate true value of the quantity . A) Accuracy as “% of full scale reading ”: If the instrument have uniform scale, then accuracy is expressed as % of full scale reading. Accuracy is 0.1% for full scale of 50 units means 0.05 units error is present in any measurement. Accuracy is 0.2% for full scale of 25 units means 0.05 units error Thus as reading decreases error is more and leads misleading. R.JhansiRani AP/ECE

B) Accuracy as “% of True value”:: 

B) Accuracy as “% of True value”: Best method for specifying accuracy. It is specified in terms of true value of the quantity being measured. Eg : ±0.1% of true value. As the reading gets smaller error also gets reduced. Hence accuracy is better. C) Accuracy as “% of scale span”: Maximum point on scale -Minimum point on scale is scale span. For range 25-225, Scale span is 200 If accuracy is 0.2% of span then, error is 0.4 units in any measurement. D) Point Accuracy It is specified at only one point of scale. R.JhansiRani AP/ECE

Precision: : 

Precision: It is the measure of consistency or repeatability of measurement. It denotes the closeness with which individual measurements are departed or distributed about the average of numbers of measured values. High precision may not have high accurate Types: conformity Number of significant figures. R.JhansiRani AP/ECE

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Conformity: Error created due to limitation of scale reading is a precision error. Ex: resistor of value 2385692 Ω is read as 2.4M Ω . Significant figures: Precision is obtained from number of significant figures. Ex: 110 ohms can be specified as 109 or 111 thus 3 significant figures. If it is specified as 110.0 then it may be 110.1 or 109.9 Thus there are 4 significant figures. Greater the significant figure greater is the precision. R.JhansiRani AP/ECE

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Error: The algebraic difference between the indicated value and the true value of the quantity to be measured is called an error. Error of 1 ut is negligible when measure in order of 1000 ut Error of 1 ut is significant when measure in order of 5 ut e = A t – Am , where e – error (or) absolute error Am – measured value of quantity A t – true value of quantity Note: instead of specifying absolute error, the relative or percentage of error is specified. R.JhansiRani AP/ECE

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Relative error: True value absolute error R.JhansiRani AP/ECE

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Sensitivity: The ratio of the change in output of an instrument to a change in the value of the quantity to be measured. Note: if the calibration curve is linear, then sensitivity of the instrument is the slope of the calibration curve. R.JhansiRani AP/ECE

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For manufactures Reciprocal of sensitivity is called inverse sensitivity or deflection factor. unit: sensitivity – mm/ µA, mm/Ω, counts/V etc; Deflection meter - µA/mm, Ω/mm, V/counts etc; Sensitivity should be high, to achieve this the range of the instrument should not exceed the value to be measured. R.JhansiRani AP/ECE

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Resolution means smallest measurable input change. Threshold: If the i/pt is slowly varied from zero, the o/pt does not change until some minimum value of the i/pt is exceeded. This minimum value of the i/pt is called threshold. Threshold is the smallest measurable i/pt. R.JhansiRani AP/ECE

Linearity The closeness to which a curve approximates a straight line. Definition: It is defined as the maximum deviation of the actual calibration curve (o/pt) from the idealized st.line, expressed as a % of full scale reading or a % of the actual reading.: 

Linearity The closeness to which a curve approximates a straight line. Definition: It is defined as the maximum deviation of the actual calibration curve (o/pt) from the idealized st.line , expressed as a % of full scale reading or a % of the actual reading. R.JhansiRani AP/ECE

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Zero drift: The deviation in the instrument output with time from its zero value, when the variable to be measured is a constant. Reproducibility: It is the degree of closeness with which a given value may be repeatedly measured. Reproducibility and repeatability are a measure of the closeness with which a given i/pt may be measured again and again. R.JhansiRani AP/ECE

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Stability: Ability of an instrument to retain its performance throughout its specified operating life and the storage life. Tolerance: The maximum allowable error in the measurement is specified interms of some value which is called tolerance. Bias: The constant error which exists over the full range of measurement of an instrument is called bias. R.JhansiRani AP/ECE

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Hysteresis If the i/pt to the instrument is increased from a negative value, the o/pt also increases : curve 1 If the curve is decreased steadily, the o/pt does not follow the same curve but lags by certain value: curve 2 Difference b/w two curves is called HYSTERESIS. The noncoincidence of loading and unloading curves Dead space: Range of i/pt values were there is no change in o/pt is called dead space. R.JhansiRani AP/ECE

Dynamic characteristics: 

Dynamic characteristics Speed of response Fidelity Lag Dynamic error

Standard variations in i/pt are: 

Standard variations in i /pt are Sudden, instantaneous and finite change in the input. i/pt -> Au(t) R.JhansiRani AP/ECE

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Linear change in i/pt. it changes at a constant rate wrt time. i/pt -> At u(t) R.JhansiRani AP/ECE

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i/pt is proportional to the square of the time & hence represents constant acceleration i/pt -> At 2 u(t) R.JhansiRani AP/ECE

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It exist only at t=0 & zero otherwise Area under it is its magnitude and if its unity it is called delta function δ (t) R.JhansiRani AP/ECE

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i/pt which changes in acco9rdance with a sinusoidal function of constant amplitude. Frequency is the independent variable in this case. R.JhansiRani AP/ECE

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Speed of response : It gives information about how fast the system reacts to the changes in the input. Fidelity: it is defined as the degree to which an instrument indicates the changes in the measured variable without dynamic error. Lag: Delay in the response of a system. retardation lag: response of the system begins immediately after a change in the variable has occurred. time delay: response begins after some time called dead time, after the application of input . Dynamic error 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 R.JhansiRani AP/ECE


units It is necessary to specify type & magnitude for the reading. Where unit represents the type of the physical quantity and reading on the instrument represents its magnitude Different system of units are M.K.S C.G.S S.I (system international units) R.JhansiRani AP/ECE


units The S.I system of units is divided into 3 categories Fundamental units Supplementary units Derived units Fundamental units: units which are independently chosen and not dependent on any other units are called fundamental units or base units Ex: meter (m), kilogram (Kg), second (s), Ampere (A) R.JhansiRani AP/ECE

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Supplementary units: Radian for the plane angle: ( θ , Φ ) Plane angle subtended by an arc of a circle equal in length to the radius of the circle. Steradian for the solid angle: ( θ s, Φ s) Angle subtended at the center of the sphere by the surface whose area is equal to the square of the radius of the sphere. Derived units: These units are derived from fundamental and supplementary units Ex: velocity- m/s, acceleration- m/s 2 , force- Newton(N) R.JhansiRani AP/ECE

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R.JhansiRani AP/ECE

Measurement Standards: 

Measurement Standards A standard of measurement is a physical representation of a unit of measurement. A standard means known accurate measure of physical quantity. ex: unit of mass: Kg Kilogram is defined as the mass of cubic decimeter of water as its temperature of maximum density of 4 degree Celsius R.JhansiRani AP/ECE

Types of Standards: 

Types of Standards 1. International standards 2. Primary standards 3. Secondary standards 4. Working standards R.JhansiRani AP/ECE

International standards: 

International standards These standards are maintained at the international bureau of weights and measures and are periodically evaluated and checked by absolute measurements. These standards are not available for ordinary users for calibration. For accuracy they are replaced by absolute units which are more accurate than international standards. R.JhansiRani AP/ECE

Primary standards : 

Primary standards They are maintained at national standard laboratories in different countries. These standards represents fundamental units as well as electrical and mechanical derived units calibrated by absolute measurements at each national laboratories. used for calibration and verification of secondary standards. R.JhansiRani AP/ECE

Secondary standards : 

Secondary standards Since primary standards are not available for outside users, various industries need some reference. They are used by measurement and calibration laboratories and are maintained by the particular industry to which they belong. Each industry has its own standards. R.JhansiRani AP/ECE

Working standards : 

Working standards These are the basic tools of a measurement laboratory use to check and calibrate for accuracy. ex: resistor industry maintains a standard resistor for checking the values of manufactured resistors. R.JhansiRani AP/ECE



sources of errors: 

sources of errors 1. Faulty design of instrument 2. Insufficient knowledge of quantity and design conditions 3. Improper maintenance of the instrument. 4. Sudden change in the parameter to be measured. 5. Unskilled operator 6. Effects of environmental conditions. R.JhansiRani AP/ECE

Types of errors: 

Types of errors static errors are classified as, 1. Gross error 2. Systematic error 3. Random error R.JhansiRani AP/ECE

Gross error: (personal errors): 

Gross error: (personal errors) Occurs due to carelessness of human while reading, recording and calculating results. Due to incorrect adjustments of instruments. To eliminate error: Take care while reading, recording and calculating results. Take 3 or more readings with 3 or more persons. R.JhansiRani AP/ECE

Systematic error : 

Systematic error A constant uniform deviation of operation in instruments known as systematic error. Due to short comings and characteristics of the material used in instrument like worn parts, ageing effects etc; Types: a) Instrumental error b) Environmental error c) Observational error R.JhansiRani AP/ECE

Instrumental error: 

Instrumental error shortcomings of instrument: Due to mechanical structure of the instruments. Ex: Friction in bearings, Irregular spring tension, variation in air gap. To eliminate error: 1. select proper instrument and select proper procedure. 2. Identify effect of errors and correct it. 3. Calibrate the instrument. R.JhansiRani AP/ECE

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Misuse of instruments: Ex: poor initial adjustments improper zero setting using leads of high resistance Loading effects: Ex: connecting a well calibrated voltmeter across the 2 points of high resistance circuit. R.JhansiRani AP/ECE

Environmental error : 

Environmental error They are due to temperature changes pressure changes thermal e.m.f stray capacitance cross capacitance To eliminate error: 1. proper correction factors given by the manufacturer. 2. make arrangements to keep surrounding constant like using A.C. 3. sealing the components to avoid dust, humidity. 4. providing magnetic or electrostatic shields. R.JhansiRani AP/ECE

Observational error: 

Observational error errors made by observers Ex: parallax error while reading a meter, wrong scale selection To eliminate error: 1. use instruments with mirrors. 2. knife edged pointers. R.JhansiRani AP/ECE

Random error: 

Random error Causes of errors which are unknown are random errors. Due to accumulation of large number of small effects They cannot be corrected by any method. use statistical methods to obtain best approximation of reading . R.JhansiRani AP/ECE



Statistical analysis: 

Statistical analysis Arithmetic mean and median: mean: Median: R.JhansiRani AP/ECE

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Deviation from mean: Average deviation (mean deviation): R.JhansiRani AP/ECE

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Standard deviation: R.JhansiRani AP/ECE

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Variance: mean square deviation R.JhansiRani AP/ECE