DISPLACEMENT MEASUREMENT CAPACITIVE TRANSDUCER Capacitive transducer consists of two or more metal plate conductors separated by an insulator. As voltage is applied across the plates, equal and opposite charges are generated on plates. The capacitance of a parallel plate capacitor is given by the equation, Where, C = Area of each plate, in m 2

d = Distance between two plates, in m e0 = 9.85 x 1CT12 F/m K = Dielectric constant Since the capacitance is inversely proportional to the spacing of plates, any variation in distance’d’ causes a corresponding variation in capacitance. This principle is applied in capacitive transducer. Change in distance between two plates can be measured by resultant change in capacitance with an a.c. bridge, but it is usually measured with an oscillator circuit. Advantages of Capacitive Transducer: 1. Excellent frequency response. 2. Can measure either static or dynamic phenomenon. 3. Easy to fabricate. 4. Good linearity. 5. Relatively low initial and maintenance cost. Disadvantage of Capacitive Transducer:

1. Sensitivity to temperature variation and possibility of erratic or distorted signals POTENTIOMETER: Potentiometer is passive transducer, since it requires external power for its operation. Basically a resistance potentiometer consists of resistance element provided with a sliding contact. This sliding contact is known as wiper. The motion of the sliding contact may be translatory or rotational. Some have combination of both motions with resistive element in the form of helix so called as heliport. Translatory or Linear Type Potentiometer: The translatory resistive elements are straight or linear device used for measurement of linear displacement. Rotational type potentiometer: The rotational resistive elements are circular in shape and used for measurement of angular displacement.

Helipot type potentiometer: The helical resistive elements are multi-turn rotational device, which can be used for the measurement of either linear or angular motion.

Working principle: Positioning of the slider by external force varies the resistance in potentiometer or a bridge circuit. Operation: Consider a translatory or linear potentiometer as shown in Fig. Let, e, and e0 = Input and output voltages. Xt = Total length of linear pot in meter. X| = Displacement of wiper from its zero position in meter. Rp = Total resistance of potentiometer. The movement is linear, so resistance per unit length is IgTi .-. Output voltage is, ^Resistance at the output t e r m i n a l _ . .. _ e° = I Resistance at the input terminals J x I n P u t v o l t a g e

x Xi Rp~x e i

_ Xi 4

~ x t x e i

Under Ideal circumstances, the output voltage varies linearly with displacement as shown in Fig. Material used for potentiometer may be of two types: 1. Wire wound potentiometer: Wire wound potentiometers are platinum, chromium, nickel, copper wire wound on pot. It carries large current at high temperature. Its temperature coefficient is small. It is used to low frequencies. 2. Non-wire wound potentiometer: The materials used are cermet, hot moulded carbon, carbon film and thin metal films. Non-wire pots are more sensitive to temperature changes and have higher wiper contact Resolution of Potentiometer: It is smallest detectable change and for potentiometer it is defined as 'the potentiometer difference between adjacent turns of wire on the former divided by the input potential difference to the potentiometer as whole'. The slider can only make contact with the wire at certain points; the variation in resistance proceeds in small steps as the contact moves from one turn to the next. Obviously the o/p potential difference forms the potentiometer or change only in steps. Resolution can be improved by: (a) Reducing the diameter wire. (b) By using thin strip of resistance material rather than a coil.

(c) By use of carbon film or conductive plastic resistive elements. Noise in Potentiometer: Noise in potentiometer refers to spurious output voltage fluctuations due to slider contact bounce, dirt and contact wear, and variation in voltage drop across the contacts and includes the effect of resolution. This noise or output smoothness of a potentiometer is expressed as percentage of total applied potential difference under specified conditions of use. Advantages of Potentiometer: 1. They are inexpensive. 2. Simple to operate. 3. Useful for measurement of large amplitudes of displacement. 4. Electrical efficiency is very high and provides sufficient output to allow control operation. Disadvantages of Potentiometer: 1. For linear potentiometer, a large force is required to move the sliding contact. 2. The sliding contacts can wear out, become misaligned and so generate noise. LINEAR VARIABLE DIFFERENTIAL TRANSDUCER (LVDT) LVDT is used for measurement of displacement, which works on the principle of mutual induction phenomenon in which flux linking to coil depends on position of magnetic core or armature. Construction of LVDT: Above the Fig. shows schematic diagram of LVDT in which it consists of an insulating hollow cylinder made up of Bakelite or other insulating material. On the insulating cylinder, two windings are wound called as primary and secondary. Equivalent Circuit of LVDT: Primary winding is wound at the center of insulating cylinder and on either side of primary winding two secondary windings Si and S 2 having equal number of turn are wound. The direction of secondary windings Si and S 2 are exactly opposite to each other. Inside the insulating cylinder magnetic core or armature is placed, which is free to move in either of direction. When AC supply is given to primary of LVDT, it produces magnetic flux, which completes its path through secondary windings S1 and S2. While completing the path flux produced by primary of LVDT links to the number of conductors of the secondary windings. Therefore according to the Faraday's Law of electromagnetic induction, e.m.f is induced in secondary windings. When core is at central position of insulating cylinder, magnetic flux linking to coil S1 and S2 has same value. Therefore e.m.f. induced in coil St and S 2 are also equal. So that output measured between two secondary terminals is zero.( E0 = I

When core is moved towards left side then, flux linking to coil S1 will increase at the same time, flux linking to coil S 2 decreases. Hence e.m.f induced in coil S1 is greater than that of S2. As a result of which output measured between secondary terminals is in phase with primary voltage. When core is moved towards the right side, then flux linking to coil S2 is more as compared to coil S1 that is e.m.f. induced in S 2 is greater than e.m.f. in S1. Hence output measured between secondary terminals is out of phase with primary voltage. Thus, output measured between two secondary terminals of LVDT is directly proportional to the displacement of magnetic core. Advantages of LVDT: 1. It has infinite resolution. 2. High sensitivity. 3. Good accuracy. 4. Linear output characteristics for 5 mm core displacement. 5. Simple and easy to design. 6. It has electrical isolation. 7. It has range of 1.2 mm to 25 mm. 8. Low hysterics therefore it has good repeatability. 9. Low power consumption. Disadvantages of LVDT: 1. The performance is affected by temperature variation. 2. Sensitive to stray magnetic field. 3. Its performance is affected due to vibration of magnetic core. 4. It requires external power of A.C. source. Advantages of LVDT as Pressure Transducer: 1. Sensitivity of pressure gauge using LVDT is good. 2. Frequency response is good. 3. Due to small displacement, linear characteristic. Disadvantages of LVDT as Pressure Transducer: 1. Response is linear only for small range of displacement. 2. Due to mass of core, dynamic response is limited. RVDT Fig. shows the constructional details of RVDT. The basic operating principle and its construction are similar to that of the LVDT. But it is used for measurement of angular displacement It consists of two secondary windings having same number of turns but wound in opposite direction and the primary winding connected across single phase A.C. supply. Magnetic core or armature is placed in air gap such that it will be freely able to move either in direction depending on angular displacement of shaft.

When single phase A.C. supply is switched on, it produces magnetic flux completes their path through secondary winding. Therefore, according to Faraday’s Law of electro-magnetic induction emf will induce in the secondary winding. When displacement of armature core is zero i.e. core is at central position, then emf measured across the secondary is>zero. When displacement of armature core takes place in either of direction i.e. clockwise or anti-clockwise, due to unequal flux distribution emf will be measured between two secondary terminals so that emf measure is directly calibrated in terms of quantity being measured.