- 1. Unit V Bridges & Measurement Of Physical Parameters -BY GVNSK SRAVYA ASST. PROFESSOR ECE DEPT.
- 2. Contents Bridges: Wheat stone Bridge, Kelvin Bridge, and Maxwell Bridge Measurement of Physical Parameters: Flow measurement Displacement meters Liquid level measurement Temperature Measurement Measurement of Humidity and Moisture Velocity Measurement Force Measurement Pressure- High pressure Vacuum level Measurement Data acquisition systems 2
- 3. Bridges Bridge circuit is an instrument to measure resistance, capacitance, inductance and impedance. In simplest form it consists of four arms network. They use Comparison measurement technique and null- indication principle. This means the indication is independent of the calibration of the indicating device or any characteristics of it. Unknown components value is calculated when the bridge is balanced. 3
- 4. Advantages of Bridge Circuits Balance equation is independent of the magnitude of the input voltage or the source impedance. High measurement accuracy since measurement is based on comparison. Accuracy depends on components values and not on the characteristics of the null detector. 4
- 5. Contd… Balance equation is independent of the sensitivity of the null detector. Balance condition transparent to the interchange of source and detector positions. Can be used in the control circuits. 5
- 6. Types of Bridges Two types of bridges are used in the measurement based on the voltage signal with which those can be operated. • DC Bridges- Wheatstone Bridge, Kelvin Bridge • AC Bridges- Maxwell Bridge 6
- 7. DC Bridges If the bridge circuit can be operated with only DC voltage signal, then it is a DC bridge circuit or simply DC bridge. DC bridges are used to measure the value of unknown resistance. The circuit diagram of DC bridge looks like as shown in below figure. 7
- 8. Contd… The DC bridge has four arms and each arm consists of a resistor. Among which, two resistors have fixed resistance values, one resistor is a variable resistor and the other one has an unknown resistance value. The above DC bridge circuit can be excited with a DC voltage source by placing it in one diagonal. The galvanometer is placed in other diagonal of DC bridge. It shows some deflection as long as the bridge is unbalanced. 8
- 9. Contd… Vary the resistance value of variable resistor until the galvanometer shows null (zero) deflection. Now, the above DC bridge is said to be a balanced one. So, we can find the value of unknown resistance by using nodal equations. DC bridges can be operated with only DC voltage signal. DC bridges are useful for measuring the value of unknown resistance, which is present in the bridge. Wheatstone’s Bridge & Kelvin Bridge are examples of DC bridge. 9
- 10. Wheatstone Bridge Wheatstone’s bridge is a simple DC bridge, which is mainly having four arms. These four arms form a rhombus or square shape and each arm consists of one resistor. To find the value of unknown resistance, we need the galvanometer and DC voltage source. Hence, one of these two are placed in one diagonal of Wheatstone’s bridge and the other one is placed in another diagonal of Wheatstone’s bridge. It measures resistance from 1 ohm to 1megaohm. 10
- 11. Contd… Wheatstone’s bridge is used to measure the value of medium resistance. The circuit diagram of Wheatstone’s bridge is shown in below figure. 11
- 12. Contd… R3 is a standard resistor and R4 is unknown resistor which is to be measured. Bridge can be balanced by varying the value of R3 resistor. The above bridge circuit is balanced when no current flows through the diagonal arm, DB. That means, there is no deflection in the galvanometer, when the bridge is balanced. 12
- 13. Contd… The bridge will be balanced, when the following two conditions are satisfied. 13
- 14. Contd… As galvanometer current is zero, 14
- 15. Contd… 15
- 16. Sensitivity of Wheatstone Bridge When the bridge is in unbalanced condition, current flows through the galvanometer causing deflection of the pointer. The amount of deflection is the function of sensitivity of the galvanometer. The sensitivity can be expressed as amount of deflection per unit current(mm/µA, radians/µA or degrees/µA). Greater the sensitivity of the galvanometer, greater its deflection. 16
- 17. Unbalanced Wheatstone bridge By using Thevenin's theorem, the current through the galvanometer can be determined. 17
- 21. Applications 1. It is a DC bridge which is used to measure the resistance from 1ohm to low mega ohm. 2. A Wheatstone bridge may be used to measure the dc resistance of various types of wire, either for the purpose of quality control of the wire itself, or of some assembly in which it is used. 3. For example, the resistance of motor windings, transformers, solenoids, and relay coils can be measured. 4. Wheatstone Bridge Circuit is also used extensively by telephone companies and others to locate cable faults. 5. The fault may be two lines shorted together, or a single line shorted to ground. 21
- 22. Limitations 1. For low resistance measurement, the resistance of the leads and contacts becomes significant and introduces an error. This can be eliminated by Kelvin’s Double bridge. 2. For high resistance measurements, the resistance presented by the bridge becomes so large that the galvanometer is insensitive to imbalance. Therefore, a power supply has to replace the battery and a dc VTVM replaces the galvanometer. In the case of high resistance measurements in mega ohms, the Wheatstone's bridge cannot be used. 3. Another difficulty in Wheatstone Bridge Circuit is the change in resistance of the bridge arms due to the heating effect of current through the resistance. The rise in temperature causes a change in the value of the resistance, and excessive current may cause a permanent change in value. 22
- 23. Problems 1. Wheatstone bridge consists of the following parameters, R1=10K ohm, R2=15K ohm and R3=40K ohm. Find the unknown resistance Rx. Solution: R1R4 = R2R3 R1Rx=R2R3 Rx= R2R3/R1 = (15K X 40K)/10K = 60K ohms 23
- 24. Problems 2. An unbalanced Wheatstone bridge consists of the following parameters, R1=1K ohm, R2=2.5K ohm, R3=3.5K ohm, R4 = 10K ohm and Rg=300 ohms and DC source is of 6V. Find the current through the galvanometer. 24
- 25. Problems Solution: Eth = 0.312V Rth = 2.778K ohms Ig= 42.88 micro amperes 25
- 26. Kelvin’s Bridge When the resistance to be measured is of the order of magnitude of bridge contact and lead resistance, a modified form of Wheatstone’s bridge, the Kelvins Bridge theory is employed. Kelvins Bridge theory is a modification of Wheatstone’s bridge and is used to measure values of resistance below 1 Ω. In low resistance measurement, the resistance of the leads connecting the unknown resistance to the terminal of the bridge circuit may affect the measurement. 26
- 27. Contd… 27
- 28. Contd… Ry represents the resistance of the connecting leads from R3 to Rx (unknown resistance). The galvanometer can be connected either to point c or to point a. When it is connected to point a, the resistance Ry, of the connecting lead is added to the unknown resistance Rx, resulting in too high indication for Rx. When the connection is made to point c, R3, is added to the bridge arm R3 and resulting measurement of Rx is lower than the actual value, because now the actual value of R3 is higher than its nominal value by the resistance Ry. 28
- 29. Contd… If the galvanometer is connected to point b, in between points c and a, in such a way that the ratio of the resistance from c to b and that from a to b equals the ratio of resistances R1 and R2, then 29 and the usual balance equations for the bridge give the relationship.
- 30. Contd… 30
- 31. Contd… 31
- 32. Contd… 32
- 33. Contd… 33 Equation (11.8) is the usual Wheatstone’s balance equation and it indicates that the effect of the resistance of the connecting leads from point a to point c has been eliminated by connecting the galvanometer to an intermediate position, b. The above principle forms the basis of the construction of Kelvin’s Double Bridge, popularly known as Kelvin’s Bridge. It is a Double bridge because it incorporates a second set of ratio arms. Figure 11.11 shows a schematic diagram of Kelvin’s double bridge.
- 34. Kelvins double bridge 34
- 35. Contd… 35 The second set of arms, a and b, connect the galvanometer to a point c at the appropriate potential between m and n connection, i.e. Ry. The ratio of the resistances of arms a and b is the same as the ratio of R1 and R2. The galvanometer indication is zero when the potentials at k and c are equal.
- 36. Contd… 36
- 37. Contd… 37
- 38. Contd… 38 This is the usual equation for Kelvins Bridge theory. It indicates that the resistance of the connecting lead has no effect on the measurement, provided that the ratios of the resistances of the two sets of ratio arms are equal. In a typical Kelvins Bridge theory the range of a resistance covered is 1 — 0.00001 Ω (10 μ ohm) with an accuracy of ± 0.05% to ± 0.2%.
- 39. Advantages 39 It can measure the resistance value in the range of 0.1 µohms to 1.0 ohm. Power consumption is less Simple in construction Sensitivity is high.
- 40. Disadvantages 40 For knowing whether the bridge is balanced or not, the sensitive galvanometer is used. To obtain good sensitivity of the device, a high current is required. Manual adjustments are to made periodically when required.
- 41. Problems 41 In the figure below the ratio of Ra to Rb is 1000 ohm, R1 is 5 ohm and R1 is 0.5R2, What is the value of Rx.
- 42. Problems 42
- 43. Problems 43
- 44. Problems 44
- 45. Problems 45
- 46. AC Bridges 46 An AC Bridge, In its simplest form consists of 4 arms, a source of excitation and a balance detector. Each arm consists of impedance. The source is an ac supply which supplies ac voltages at required frequency. For low frequencies, powerline itself can act as source of supply. For high frequencies, the electronic oscillators are used as source. A typical oscillator has a range of 50 Hz to 125kHz with a power output of around 7 W. Commonly used balanced detectors are head phones, tunable amplifiers or vibration galvanometers.
- 47. Contd… 47 The headphones are used as detectors at frequencies of 250Hz. to 3 to 4KHz. For single frequency a tuned detector is most sensitive detector at frequency range is from 10Hz to 100Hz. For low audio frequencies vibration galvanometers are used at 5Hz to 1000Hz, commonly used below 200Hz.
- 48. Contd… 48 Impedances at AF or RF are commonly determined by means of an ac Wheatstone bridge. This bridge is similar to a dc bridge, except that the bridge arms are impedances. The bridge is excited by an ac source rather than dc and the galvanometer is replaced by a detector, such as a pair of headphones, for detecting ac.
- 49. AC Bridge 49
- 50. Contd… 50 When the bridge is balanced, where Z1, Z2, Z3 and Z4 are the impedances of the arms, and are vector complex quantities that possess phase angles. It is thus necessary to adjust both the magnitude and phase angles of the impedance arms to achieve balance, i.e. the bridge must be balanced for both the reactance and the resistive component.
- 51. Maxwell’s Bridge 51 It is an Maxwell Inductance Capacitance bridge developed by Maxwell. It measures an unknown inductance in terms of a known capacitance.
- 52. Contd… 52
- 53. Contd… 53 The use of standard arm offers the advantage of compactness and easy shielding. The capacitor is almost a loss-less component. One arm has a resistance R1 in parallel with C1, and hence it is easier to write the balance equation using the admittance of arm 1 instead of the impedance.
- 54. Contd… 54 The general equation for bridge balance is
- 55. Contd… 55
- 56. Contd… 56 Maxwell Bridge Theory is limited to the measurement of low Q values (1 — 10). The measurement is independent of the excitation frequency. The scale of the resistance can be calibrated to read inductance directly.
- 57. Maxwell Bridge Advantages and Disadvantages 57 Advantages The frequency does not appear in the final expression of both equations, hence it is independent of frequency. Maxwell’s inductor capacitance bridge is very useful for the wide range of measurement of inductor at audio frequencies.
- 58. Contd… 58 The bridge is particularly suited for inductances measurements, since comparison with a capacitor is more ideal than with another inductance. Commercial bridges measure from 1 — 1000 H, with ± 2% error. (If the Q is very large, R1 becomes excessively large and it is impractical to obtain a satisfactory variable standard resistance in the range of values required).
- 59. Contd… 59 Disadvantages 1. The variable standard capacitor is very expensive. 2. Inductance cannot be measured over a wide range, since Q is proportional to inductance. 3. The bridge is limited to measurement of low quality coils (1 < Q < 10) and it is also unsuitable for low value of Q (i.e. Q < 1) from this we conclude that a Maxwell bridge is used suitable only for medium Q coils.
- 60. Problems 60 In Maxwell’s Bridge, as shown in the figure below, Determine the values of the resistance R1 and inductance L1 of a coil after the bridge is balanced with capacitance of 0.5 µF.
- 61. Contd… 61 Solution: R1=(R2R3)/R4 R1= 375 Ω. L1= C1R2R3 L1 = 0.5µ x 2000 x 750 = 75mH
- 62. Contd… 62 A maxwell bridge is used to measure inductive impedance. The bridge constants at balance are C1=0.01 µF, R1=470KΩ, R2=5.1KΩ and R3=100KΩ. Find the series equialent of the unknown impedance.
- 63. Contd… 63
- 64. Measurement of Physical Parameters 64 Flow measurement Displacement meters Liquid level measurement Temperature Measurement Measurement of Humidity and Moisture Velocity Measurement Force Measurement Pressure- High pressure Vacuum level Measurement Data acquisition systems
- 65. Flow Measurement 65 In many process industries, measurement of flow is an important aspect. Depending on the quantity flowing such as Solid, Liquid and gaseous appropriate method of flow rate measurement is used. Incase of solids, rate of mass flow rate is measured while in case of liquids and gases flow interms of volume flow rate is measured.
- 67. Contd… 67 The volume flow rate is used for finding flow of materials in liquids, gases and semi liquid forms. Devices used for measurement are of 2 types 1. Mechanical type flow meters 2. Electrical type flow meters
- 68. Contd… 68 Different instruments are used for measurement of flow rate. 1. Head type flowmeters (based on differential pressure measurement) 2. Variable area meters (Rotameters) 3. Mechanical Flow meters (Turbine flow meter) 4. Electromagnetic Flow meter 5. Anemometer 6. Ultrasonic Flow meter 7. Vertex Flow meter
- 69. Variable Area Flowmeter(Rotameter) 69 It gives visual indication of flow. Advantages 1. Reliable and inexpensive. 2. It gives direct visual indication on linear scale. 3. It can measure flow rate in the range of 1m3/sec to 0.1m3/sec. 4. Accuracy is 0.5 to 3% of full scale range. Disadvantages 1. It must be mounted vertically. 2. Bubbles in the fluid results in oscillations of float.
- 71. Contd… 71 Advantages 1. Reliable & less rugged. 2. High accuracy. 3. Lighter. Disadvantages 1. Large permanent pressure losses as bearing wears out. Applications 1. Used in oil industries, for low viscosity and high flow measurements.
- 72. Electromagnetic Flowmeter Volume flow rates of electrically conductive fluids can be measured. According to Faraday’s law of electromagnetic induction, voltage V induced across length l of flowing fluid with velocity v in the magnetic flux density B is given by V=B.l.v 72
- 73. Contd… 73 Advantages 1. Simple construction & rugged with no moving parts. 2. No obstruction in flow is required. 3. Output is independent of temperature, viscosity & Pressure. 4. Good accuracy & highly reliable. 5. Bidirectional flow measurements are possible. 6. It can measure flow in any size of tube because magnetic fields can be generated easily.
- 74. Contd… 74 Disadvantages 1. Meter is expensive. 2. Conductivity of the fluid should not be less than 10µΩ/m. 3. The output signal is of very low level usually micro volts, therefore, high amplification is required. 4. The system requires to generate magnetic field, which is bulky and requires more floor space.
- 75. Liquid Level Measurement 75 In modern manufacturing plants, various methods are used to measure levels of liquids, solvents chemicals required for processing and sometimes solids which are in the form of powders or small particles. It is used in industries not only for monitoring but also for measuring liquid contents in tanks, reservoirs etc.,
- 76. Contd… Two methods are used for measurement Direct method • Dip stick • Bob and tape method • Hook Gauge • Float Gauge Indirect method • Hydraulic method • Mechanical method • Pneumatic method • Electrical method • Ultrasonic method • Nucleonic method 76
- 77. Ultrasonic Method for Level Measurement It is used to measure liquid level in a tank. It is based on principle of sound echo. This principle is also used for measurement of thickness of a given material. 77
- 78. Contd… 78 Advantages 1. This is a non disturbance technique i.e., it does not involve placing sensor in the material. 2. Installation is easy. 3. It is used for liquids as well as solids measurements. Disadvantages 1. System is costly. 2. The electronic circuit required for detection, amplification, synchronization makes it a complex circuit.
- 79. Pneumatic Method This method Is also called Bubbler method or Purge method. It is suitable for liquid measurements and also for corrosive liquids, liquids containing solids. 79
- 80. Temperature Measurement 80 Based on the principle of operation of thermal expansion, different temperature measurement instruments are used. 1. Bimetallic Strip 2. Liquid in gas thermometer 3. Pressure thermometer
- 81. Bimetallic Strip 81 Flat type Bimetallic Strip Curved Bimetallic strip Spiral Bimetallic Strip
- 82. Liquid in gas thermometer 82 It is used to measure temperature from -200 degree centigrade to 1000 degree centigrade range.
- 83. Velocity Measurement 83 Velocity transducers are used for measurement of Linear velocity as well as Angular velocity. Linear Velocity Measurement Based on the electromagnetic induction mechanical vibrations are converted in to alternating voltages. Hence, called electromagnetic transducers. There are 2 types of EM transducers 1. Moving Coil type 2. Moving Magnet type
- 84. Moving Magnet type Velocity Transducer Advantages 1. There are no mechanical surfaces or contacts, hence the maintenance required is negligible. 2. Robust and less expensive. 3. Output voltage is linearly proportional to the velocity. Disadvantages 1. Limited frequency response. 2. The stray magnetic fields affects the performance of these transducers. 84
- 85. Angular Velocity Measurement The main disadvantage of linear velocity measurement is that for large distance travel it is very difficult to detect with fixed reference. In such cases, Angular velocity transducers are used by converting linear velocity in to angular velocity. The measurement of speed can be done with the help of Tachogenerator. 85
- 86. Contd… Tachogenerators are of 2 types 1. Electrical type tachogenerator 2. Mechanical type tachogenerator Electrical type are preferred over mechanical type. 86
- 87. Electrical type of Tachogenerator DC Tachogenerator 87
- 88. Contd… Advantages 1. Output voltage is small enough to measure it with DC Voltmeters. 2. Polarity of output directly indicates direction of rotation. Disadvantages 1. Because of variation in contact resistances, considerable error is introduced in the output voltage. Hence, the maintenance of commutator is required. 2. Non linearity in output occurs because of distortions in permanent magnetic field due to large armature currents. Hence, input resistor should be very high as compared to output resistor of generator. 88
- 89. AC Tachogenerator It is used to measure speed in only one direction. The emf induced in quadrature coil is directly proportional to the rotor speed and is in phase with applied voltage to the reference coil. 89
- 90. Contd… Advantages 1. Output can be calibrated in terms of amplitude and frequency of induced voltage. 2. Commutator contact resistance problems are eliminated as the coil is wounded on the stator. Disadvantages 1. For low speed rotation, frequency of induced voltage is very low thus ripples in output increases. 2. At high speeds frequency is very high, coil impedance increases. This effects linearity of output. 90
- 91. Digital methods of measurement of angular velocity Electro mechanical methods are used for angular velocity measurement effectively for speeds of 10,000rpm or less. For higher speeds, electromechanical transducers are not suitable. The main advantage of digital method is that there is no physical contact between shaft whose speed is to be measured and measuring device, thus loading of shaft is avoided. 91
- 92. Contd… There are two methods 1. Photo Electric type Tachometer 2. Inductive type Tachometer 92
- 93. Photo Electric Tachometer Advantages 1. Output is Pulsated output, i.e., output is in digital form. So no additional ADC is required. 2. Amplitude of pulses is constant, hence complex electronic circuit is not required. Disadvantages 1. Life time of light source is drawback, typical life time of light source is 50,000 to 60,000 hours. Hence necessary to replace light source. 2. Accuracy depends on error represented by one pulse. 93
- 94. Inductive type Tachometer It is also called as Toothed rotor variable reluctance tachometer. Advantages 1. Simple and rugged in construction. 2. Maintenance free tachometer. 3. Calibration of tachometer is simple. 4. The transmission of output of tachometer is easy. 94 Speed = n = pulses per second/number of teeth n= P/N rps
- 95. Measurement of Moisture There are two types of moisture measurement techniques. 1. Laboratory Techniques 2. Industrial Techniques 95
- 96. Laboratory Techniques for Moisture Measurement It gives better accurate measurement, but requires longer time for measurement. Different methods of Moisture measurement are 1. Water Separation Method 2. Gravimetric Methods 3. Phase Change Method 4. Equilibrium Relative Humidity Measurement 96
- 97. Industrial Techniques for Moisture Measurement These techniques are based on the change of physical property of the material with moisture. Different methods of Moisture measurement are 1. Electrical Methods 2. Neutron Moderation 97
- 98. Measurement of Humidity The amount of water vapour in surrounding air is called Humidity. Three separate terms are used to represent the Humidity. Absolute Humidity HA It is defined as mass of water vapour in unit volume of a moist air. Relative Humidity HR It is defined as ratio of moisture content of the gas to the maximum moisture of gas at a temperature i.e., saturated gas. Generally it is expressed in percentage. The relative humidity of dry air is zero, while that of air with all moisture is 100%. 98
- 99. Contd… Specific Humidity Hs It is defined as mass of water in a unit mass of a moist air. Dew Point It is defined as the saturation temperature of the mixture at the corresponding vapour pressure. It is expressed in degree centigrade. 99
- 100. Contd… The instruments used for measurement of relative humidity are called HYGROMETERS. Some of the important types of Hygrometers are 1. Electrical Hygrometer 2. Psychrometer (Wet and dry bulb Hygrometer) 3. Hair Hygrometer 4. Dew Point Meter 100
- 101. Electrical Hygrometer – Resistive Hygrometer (Humistor) 101
- 102. Contd… 102 Advantages 1. Simple in construction. 2. High response time. 3. High sensitivity. 4. Digital readout is possible. 5. 1% variation in relative humidity can be detected. Disadvantages 1. Constant temperature environment is necessary. 2. Cannot measure extreme changes in humidity as scale becomes non linear. 3. Hygrometer gets damaged in 100% humid environment.
- 103. Displacement Measurement 103 Displacement is classified as 1. Translational Displacement 2. Rotational Displacement Some of the translational displacement transducers are 1. Resistive potentiometers 2. Strain gauges 3. LVDT 4. Variable inductance transducers Some of the angular displacement transducers are 1. Capacitive transducers 2. Synchros
- 104. Translational Displacement Transducers 104 Resistive potential Displacement Transducer
- 105. Rotational Displacement Transducers 105 Incremental shaft encoder for Clockwise and anti clockwise direction
- 106. Force Measurement 106 According to Newton’s Law, F= m.a Different methods are used for the measurement of Force. 1. Force measurement using Accelerometer 2. Force measurement using Vibrating wire sensor 3. Force measurement using Load cell
- 107. Force Measurement using Vibrating Wire Sensor The resonant frequency is given by 107
- 108. Force Measurement using Load Cell 108 Some force measuring devices using Load cell are 1. Cantilever Beam type load cell 2. Column type load cell
- 109. Cantilever Beam type load cell 109
- 110. Column type load cell 110
- 111. Pressure Measurement 111 Pressure is a non electrical, physical quantity defined as force acting per unit area measured at a given point over a surface. Classification of Pressure
- 112. Pressure Measurement by U tube Manometer P – Pref = ρ. g. h P- pressure field Pref – reference pressure source g- gravitational constant h- difference in heights of liquid levels in 2 columns 112
- 113. Pressure Measurement by Well type Manometer Pressure measurement using well type manometer is given as, 113
- 114. High Pressure Measurement When the pressure exceeds 10,000 psi high pressure measurement techniques are used. Bulk modulus resistance pressure gauge is used for high pressure measurement. 114
- 115. Bulk modulus resistance pressure gauge 115
- 116. Vaccum Measurement 116 Pressure below atmospheric pressure is defined as Vacuum pressure. Vaccum ranges are
- 117. Contd… 117 Different instruments used for vaccum measurement are 1. Mc Leod Gauge 2. Thermal Conductive Gauge 1. Pirani Gauge 2. Thermo couple Gauge 3. Ionization Gauge
- 118. Pirani Gauge Advantages 1. Easy to operate 2. Simple design Limitations 1. Scale is non linear 2. Calibration of pirani gauge is dependent on nature of gas. 118
- 119. Data Acquisition Systems (DAS) The system used for data processing, data conversion, data transmission, data storage is called DAS. DAS can be classified as follows 1. Analog DAS 2. Digital DAS 119
- 120. Data Acquisition Systems (DAS) A schematic block diagram of a General of DAS is shown below. 120