Module 10 Measuring Instruents
Lesson 42 Study of DC-AC Measuring Instruents
Objectives To understand the basic construction of a peranent agnet oving coil (PMMC) instruent and its operation. Sketch and explain circuit diagras for electroechanical dc aeters and volteters. To understand how a single instruent ay be used for ulti-range aeters and volteters. To study the advantage and liitation of PMMC instruents. To understand the basic construction of Moving-iron Instruent and its principle operation. To study the advantage and errors involved in oving-iron instruents. L.42.1 Introduction Measuring instruents are classified according to both the quantity easured by the instruent and the principle of operation. Three general principles of operation are available: (i) electroagnetic, which utilizes the agnetic effects of electric currents; (ii) electrostatic, which utilizes the forces between electrically-charged conductors; (iii) electro-theric, which utilizes the heating effect. Electric easuring instruents and eters are used to indicate directly the value of current, voltage, power or energy. In this lesson, we will consider an electroechanical eter (input is as an electrical signal results echanical force or torque as an output) that can be connected with additional suitable coponents in order to act as an aeters and a volteter. The ost coon analogue instruent or eter is the peranent agnet oving coil instruent and it is used for easuring a dc current or voltage of a electric circuit. On the other hand, the indications of alternating current aeters and volteters ust represent the RMS values of the current, or voltage, respectively, applied to the instruent. L.42.1.1 Various forces/torques required in easuring instruents Deflecting torque/force: The defection of any instruent is deterined by the cobined effect of the deflecting torque/force, control torque/force and daping torque/force. The value of deflecting torque ust depend on the electrical signal to be easured; this torque/force causes the instruent oveent to rotate fro its zero position. Controlling torque/force: This torque/force ust act in the opposite sense to the deflecting torque/force, and the oveent will take up an equilibriu or definite position when the deflecting and controlling torque are equal in agnitude. Spiral springs or gravity usually provides the controlling torque. Daping torque/force: A daping force is required to act in a direction opposite to the oveent of the oving syste. This brings the oving syste to rest at the deflected position reasonably quickly without any oscillation or very sall oscillation. This is provided by i) air friction ii) fluid friction iii) eddy current. It should be pointed out that any daping force shall not influence the steady state deflection produced by a given deflecting force or torque. Daping force
increases with the angular velocity of the oving syste, so that its effect is greatest when the rotation is rapid and zero when the syste rotation is zero. Details of atheatical expressions for the above torques are considered in the description of various types of instruents. L.42.2 General Theory Peranent Magnet Moving Coil (PMMC) Instruents The general theory of oving-coil instruents ay be dealt with considering a rectangular coil of N turns, free to rotate about a vertical axis. Fig. 42.1(a) shows the basic construction of a PMMC instruent. A oving coil instruent consists basically of a peranent agnet to provide a agnetic field and a sall lightweight coil is wound on a rectangular soft iron core that is free to rotate around
its vertical axis. When a current is passed through the coil windings, a torque is developed on the coil by the interaction of the agnetic field and the field set up by the current in the coil. The aluinu pointer attached to rotating coil and the pointer oves around the calibrated scale indicates the deflection of the coil. To reduce parallax error a irror is usually placed along with the scale. A balance weight is also attached to the pointer to counteract its weight (see Fig. 42.1(b)). To use PMMC device as a eter, two probles ust be solved. First, a way ust be found to return the coil to its original position when there is no current through the coil. Second, a ethod is needed to indicate the aount of coil oveent. The first proble is solved by the use of hairsprings attached to each end of the coil as shown in Fig. 42.1(a). These hairsprings are not only supplying a restoring torque but also provide an electric connection to the rotating coil. With the use of hairsprings, the coil will return to its initial position when no current is flowing though the coil. The springs will also resist the oveent of coil when there is current through coil. When the developing force between the agnetic fields (fro peranent agnet and electro agnet) is exactly equal to the force of the springs, the coil rotation will stop. The coil set up is supported on jeweled bearings in order to achieve free oveent. Two other features are considered to increase the accuracy and efficiency of this eter oveent. First, an iron core is placed inside the coil to concentrate the agnetic fields. Second, the curved pole faces ensure the turning force on the coil increases as the current increases. It is assued that the coil sides are situated in a unifor radial agnetic field of 2 flux density B wb /, let the length of a coil side (within the agnetic field) be l (eter), and the distance fro each coil side to the axis be r (eter). Principle of operation It has been entioned that the interaction between the induced field and the field produced by the peranent agnet causes a deflecting torque, which results in rotation of the coil. The deflecting torque produced is described below in atheatical for: Deflecting Torque: If the coil is carrying a current of iap., the force on a coil side = B iln (newton, N). (42.1) Torque due to both coil sides =( 2 r) ( BilN ) ( N ) = Gi ( N) (42.2) where G is the Galvanoeter constant and it is expressed as G= 2rBlN ( N / ap.) = NBA ( N / a p.). (note A = 2rl = area of the coil.) N = no. of turns of the coil. 2 B = flux density in Wb / Wb/ 2. l = length of the vertical side of the coil,. 2 r = breadth of the coil, i = current in apere. A= 2rl= area, 2 Truly speaking, the equation (42.2) is valid while the iron core is cylindrical and the air gap between the coil and pole faces of the peranent agnet is unifor. This result the
flux density B is constant and the torque is proportional to the coil current and instruent scale is linear. Controlling Torque: The value of control torque depends on the echanical design of the control device. For spiral springs and strip suspensions, the controlling torque is directly proportional to the angle of deflection of the coil. ie.., Control torque =Cθ (42.3) where, θ = deflection angle in radians and C = spring constant N / rad. Daping Torque: It is provided by the induced currents in a etal forer or core on which the coil is wound or in the circuit of the coil itself. As the coil oves in the field of the peranent agnet, eddy currents are set up in the etal forer or core. The agnetic field produced by the eddy currents opposes the otion of the coil. The pointer will therefore swing ore slowly to its proper position and coe to rest quickly with very little oscillation. Electroagnetic daping is caused by the induced effects in the oving coil as it rotates in agnetic field, provided the coil fors part of closed electric circuit. dθ Let the velocity of the coil is ω () t = rad./sec., and let the resistance of the dt dθ coil circuit with N turns be R Ω. Then the velocity of a coil side vt () = r ( /sec.) dt dθ E..f induced in each turn of the coil = 2Blv = 2Blr volt. (note both the sides of dt the coil having sae e..fs but they are additive in nature). 2BlN r dθ G dθ Induced current across N turns of coil = = aps. ( R = resistance of R dt R dt coil) 2 Gdθ G dθ dθ By Lenz s Law, torque produced = Gi= G = = D (N)= opposing R dt R dt dt 2 G torque. Note, D = is the daping constant for the induced currents in the coil due to R its otion. This daping torque is active when the coil posses a change in deflection. A etal forer or core ay be considered as a single-turn coil and if its diensions are landr 1 1 and its resistance R 1. Siilarly, daping torque for the forer or core can be coputed as dθ Daping torque (for the core or forer) = D1 (N) where D 1 = daping constant dt due to induced currents in the core or forer. In addition to the induced current daping, dθ there will be a sall daping torque due to air friction. Air daping torque ( D2 ) dt ay be assued to be proportional to the angular velocity of the coil.
Equation of otion: The resulting torque in a coil or otion of a coil in a agnetic field is due to the cobined effect of deflecting torque ( T ), controlling torque (Cθ ), daping dθ torque ( D ) and it is expressed atheatically as dt d θ θ θ θ J = Gi C D J + D + Cθ = Gi 2 2 d d d d θ 2 2 dt dt dt dt where J is the oent of inertia of the oving parts. One can easily study the dynaic behavior of the above second order syste by solving the differential equation. Rearks: When the oving syste reached at steady state i.e. at final deflected position, the controlling torque becoes equal and opposite to the deflecting torque. The deflecting angle is directly proportional to the current in the ovable coil (see eq. 42.2). For this reason, the scale of the oving coil instruent is calibrated linearly. L.42.3 A ulti-range aeters and volteters An aeter is required to easure the current in a circuit and it therefore connected in series with the coponents carrying the current. If the aeter resistance is not very uch saller than the load resistance, the load current can be substantially altered by the inclusion of the aeter in the circuit. To operate a oving coil instruent around a current level 50a is ipractical owing to the bulk and weight of the coil that would be required. So, it is necessary to extend the eter-range shunts (in case of aeters) and ultipliers (in case of volt eters) are used in the following anner. For higher range aeters a low resistance ade up of anganin (low teperature coefficient of resistance) is connected in parallel to the oving coil (see Fig.42.2 (a)) and instruent ay be calibrated to read directly to the total current. They are called shunts. The oveent of PMMC instruent is not inherently insensitive to teperature, but it ay be teperature-copensated by the appropriate use of series and shunt resistors of copper and anganin. Both the agnetic field strength and springtension decrease with an increase in teperature. On other side, the coil resistance
increases with an increase in teperature. These changes lead to ake the pointer read low for a given current with respect to agnetic field strength and coil resistance. Use of anganin resistance (known as swaping resistance which has a teperature coefficient practically zero) in series with the coil resistance can reduce the error due to the variation of resistance of the oving coil. The swaping resistance ( r ) is usually three ties that of coil thereby reducing a possible error of, say, 4% to 1%. A ultirange aeter can be constructed siple by eploying several values of shunt resistances, with a rotary switch to select the desired range. Fig. 42.2(b) shows the circuit arrangeent. When an instruent is used in this fashion, care ust be taken to ensure shunt does not becoe open-circuited, even for a very short instant. When the switch is oved fro position B to C or oved to any positions, the shunt resistance will reain opencircuited for a fraction of tie, resulting a very large current ay flow through the aeter and daage the instruent. To avoid such situation, one ay use the akebefore-break switch as shown in Fig.42.(c). The wide-ended oving contact connected to the next terinal to which it is being oved before it loses contact with the previous terinals. Thus, during the switching
tie there are two resistances are parallel with the instruent and finally the required shunt only will coe in parallel to the instruent. Exaple- L42.1 A PMMC instruent has a coil resistance of 100Ω and gives a fullscale deflection (FSD) for a current of 500 μ A. Deterine the value of shunt resistance required if the instruent is to be eployed as an aeter with a FSD of 5 A. Solution: Let current flowing through the shunt is I s. Fro the circuit shown in Fig.42.3, one can the following expression using the parallel divided rule. I Rsh = R + R sh I (42.4) where Rsh = shunt resis tan ce, R = aeter resis tan ce = 100Ω, I = aeter full scale deflection current = 500 μ A and I = desired range of aeter = 5 A. Fro the above expression (42.4) we get, 6 Rsh 500 10 = 5 R sh = 0.01Ω R + 100 sh Multi-range volteter: A dc volteter is constructed by a connecting a resistor in series with a PMMC instruent. Unlike an aeter, a volteter should have a very high resistance R se and it is norally connected in parallel with the circuit where the voltage is to be easured (see Fig.42.4). To iniize volteter loading, the volteter operating current should be very sall i.e., the resistance connected in series with the coil should be high.
The oving coil instruents can be suitably odified to act either as an aeter or as a volteter. For ulti-range volteters the arrangeent is as follows: In Fig.42.5 any one of several ultiplier resistors is selected by eans of a rotary switch. Unlike the case of the aeter, the rotary switch used with the volteter should be a break-before ake type, that is, oving contact should disconnect fro one terinal before connecting to the next terinal. Exaple-42.2 A PMMC eter with a coil resistance 100Ω and a full scale deflection current of 100 μ A is to be used in the volteter circuit as shown in Fig.42.6. The volteter ranges are to be 50 V, 100 V, and 150V. Deterine the required value of resistances for each range.
Solution: Fro the circuit shown in Fig.42.6, one can write the expression for the 50 V range as V V I = RS = R (42.5) R + R I s 6 Now for (i) V = 50 V, I = 100μ A = 100 10 A, and R = 100Ω, the value of series resistance ( R ) = 0. 4999 M Ω. s1 6 (ii) V = 100 V, I = 100μ A = 100 10 A, and R = 100Ω, the required value of resistance ( R s2 ) = 0.9999 M Ω 6 (iii) V = 150 V, I = 100μ A= 100 10 A, and R = 100Ω, the required series resistance ( R ) = 1.4999 M Ω. s3 L.42.4 Advantages, Liitations and sources of errors Advantages: G The scale is uniforly divided (see at steady state, θ = I s ). C The power consuption can be ade very low ( 25 μw to 200 μ W ). The torque-weight ratio can be ade high with a view to achieve high accuracy. A single instruent can be used for ulti range aeters and volteters. Error due to stray agnetic field is very sall. Liitations: They are suitable for direct current only. The instruent cost is high. Variation of agnet strength with tie. The Errors are due to: i) Frictional error, ii) Magnetic decay, iii) Thero electric error, iv) Teperature error. Errors can be reduced by following the steps given below:
Proper pivoting and balancing weight ay reduce the frictional error. Suitable aging can reduce the agnetic decay. Use of anganin resistance in series (swaping resistance) can nullify the effect of variation of resistance of the instruent circuit due to teperature variation. The stiffness of spring, pereability of agnetic core (Magnetic core is the core of electroagnet or inductor which is typically ade by winding a coil of wire around a ferroagnetic aterial) decreases with increases in teperature. Aeter Sensitivity: Aeter sensitivity is deterined by the aount of current required by the eter coil to produce full-scale deflection of the pointer. The saller the aount of current required producing this deflection, the greater the sensitivity of the eter. A eter oveent that requires only 100 icroaperes for full- scale deflection has a greater sensitivity than a eter oveent that requires 1 A for the sae deflection. Volteter Sensitivity: The sensitivity of a volteter is given in ohs per volt. It is deterined by dividing the su of the resistance of the eter (R ), plus the series resistance (R s ), by the full-scale reading in volts. In equation for, sensitivity is expressed as follows: R Sensitivity = This is the sae as saying the sensitivity is equal to the reciprocal of the full-scale deflection current. In equation for, this is expressed as follows: + E ohs 1 1 sensitivy = volt = volt = apere ohs Therefore, the sensitivity of a 100-icroapere oveent is the reciprocal of 0.0001 apere, or 10,000 ohs per volt. R s 1 1 sensitivy = 10, 000 ohs per volt apere = 0.0001 = L.42.5 Construction and Basic principle operation of Moving-iron Instruents We have entioned earlier that the instruents are classified according to the principles of operation. Furtherore, each class ay be subdivided according to the nature of the ovable syste and ethod by which the operating torque is produced. Specifically, the electroagnetic instruents are sub-classes as (i) oving-iron instruents (ii) electro-dynaic or dynaoeter instruents, (iii) induction instruents. In this section, we will discuss briefly the basic principle of oving-iron instruents that are generally used to easure alternating voltages and currents. In oving iron instruents the ovable syste consists of one or ore pieces of specially-shaped soft iron, which are so pivoted as to be acted upon by the agnetic field produced by the current in coil. There are two general types of oving-iron instruents naely (i)
Repulsion (or double iron) type (ii) Attraction (or single-iron) type. The brief description of different coponents of a oving-iron instruent is given below. Moving eleent: a sall piece of soft iron in the for of a vane or rod Coil: to produce the agnetic field due to current flowing through it and also to agnetize the iron pieces. In repulsion type, a fixed vane or rod is also used and agnetized with the sae polarity. Control torque is provided by spring or weight (gravity) Daping torque is norally pneuatic, the daping device consisting of an air chaber and a oving vane attached to the instruent spindle. Deflecting torque produces a oveent on an aluinu pointer over a graduated scale. L.42.5.1 Construction of Moving-iron Instruents The deflecting torque in any oving-iron instruent is due to forces on a sall piece of agnetically soft iron that is agnetized by a coil carrying the operating current. In repulsion (Fig.42.7) type oving iron instruent consists of two cylindrical soft iron vanes ounted within a fixed current-carrying coil. One iron vane is held fixed to the coil frae and other is free to rotate, carrying with it the pointer shaft. Two irons lie in the agnetic field produced by the coil that consists of only few turns if the instruent is an aeter or of any turns if the instruent is a volteter. Current in the coil induces both vanes to becoe agnetized and repulsion between the siilarly agnetized vanes produces a proportional rotation. The deflecting torque is proportional to the square of the current in the coil, aking the instruent reading is a true RMS quantity Rotation is opposed by a hairspring that produces the restoring torque. Only the fixed coil carries load current, and it is constructed so as to withstand high transient current. Moving iron instruents having scales that are nonlinear and soewhat crowded in the lower range of calibration. Another type of instruent that is usually classed with the attractive types of instruent is shown in Fig.42.8.
This instruent consists of a few soft iron discs ( B ) that are fixed to the spindle ( D ), pivoted in jeweled bearings. The spindle ( D ) also carries a pointer ( P ), a balance weight ( W1 ), a controlling weight ( W2 ) and a daping piston ( E ), which oves in a curved fixed cylinder ( F ). The special shape of the oving-iron discs is for obtaining a scale of suitable for. Reark: Moving-iron vanes instruents ay be used for DC current and voltage easureents and they are subject to inor frequency errors only. The instruents ay
be effectively shielded fro the influence of external agnetic fields by enclosing the working parts, except the pointer, in a lainated iron cylinder with lainated iron end covers. Torque Expressions: Torque expression ay be obtained in ters of the inductance of the instruent. Suppose the initial current is I, the instruent inductance L and the deflection θ. Then let I change to I + di, di being a sall change of current; as a result let θ changes to( θ + dθ), and L to ( L+ dl). In order to get an increental change in current di there ust be an increase in the applied voltage across the coil. d( LI) dl di Applied voltage v= = I +L (42.6) dt dt dt The electric energy supplied to the coil in dt is 2 v I dt = I dl + IL di (42.7) 1 2 1 2 Increase in energy stored in the agnetic field = ( I + di ) ( L + dl) I L 2 2 1 2 ILdI + I dl 2 (neglecting second and higher ters in sall quantities) If T is the value of the control torque corresponding to deflection θ, the extra energy stored in the control due to the change dθ is Tdθ. Then, the stored increase in stored 1 2 energy = ILdI + I dl+t dθ (42.8) 2 Fro principle of the conservation of energy, one can write the following expression Electric energy drawn fro the supply = increase in stored energy + echanical work done 2 1 2 I dl + IL di = IL DI + I dl + T dθ 2 1 2 dl T ( torque) = I (N) (42.9) 2 dθ Controlling torque: i Spring control: Ts = Ksθ where K S is the spring constant. ii Gravity control: Tg = Kg sinθ. Where K g = gl
At equilibriu i.e. for steady deflection, Deflecting torque = Controlling torque. If the instruent is gravity controlled T = T D C 1 K KI = K g sinθ θ = sin I (42.10) K L.42.5.2 Ranges of Aeters and Volteters g For a given oving-iron instruent the apere-turns necessary to produce fullscale deflection are constant. One can alter the range of aeters by providing a shunt coil with the oving coil. L.42.5.2.1 Shunts and Multipliers for MI instruents For oving-iron aeters: For the circuit shown in Fig.42.9, let R and L are respectively the resistance and inductance of the coil and Rshand L sh the corresponding values for shunt. The ratio of currents in two parallel branches is
ωl R 1+ R 2 2 R + ( ωl Ish ) = = 2 2 I 2 R sh + ( ωlsh ) ωlsh Rsh 1+ R sh The above ratio will be independent of frequency ω provided that the tie constants of L Ls h the two parallel branches are sae i.e = R Rs h Ish R Lsh L In other words, = if = I R h R R s sh Now, R R I= I sh +I = I +I = I 1+ R sh R sh R Multipliers for the shunt = 1+ R. It is difficult to design a shunt with the appropriate sh inductance, and shunts are rarely incorporated in oving iron aeters. Thus the ultiple ranges can effectively be obtained by winding the instruent coil in sections which ay be connected in series, parallel or series-parallel cobination which in turn changing the total apere-turns in the agnetizing coil. For oving-iron volteters: Volteter range ay be altered connecting a resistance in series with the coil. Hence the sae coil winding specification ay be eployed for a nuber of ranges. Let us consider a high resistance R se is connected in series with the oving coil and it is shown below. 2 ( ) 2 2 v=i R + ωl ( ) 2 2 V=I (R +R ) + ωl se Multiplier = V = = ( R se +R ) + ( ωl ) 2 2 ( ) v R + ωl 2 2. (42.11) Note: An ordinary arrangeent with a non-inductive resistance in series with the fixed coil results in error that increases as the frequency increases. The change of ipedance
of the instruent with change of frequency introduces error in signal easureents. In order to copensate the frequency error, the ultiplier ay be easily shunted by the capacitor. Advantages: The instruents are suitable for use in a.c and d.c circuits. The instruents are robust, owing to the siple construction of the oving parts. The stationary parts of the instruents are also siple. Instruent is low cost copared to oving coil instruent. Torque/weight ration is high, thus less frictional error. Errors: i. Errors due to teperature variation. ii. Errors due to friction is quite sall as torque-weight ratio is high in oving-iron instruents. iii. Stray fields cause relatively low values of agnetizing force produced by the coil. Efficient agnetic screening is essential to reduce this effect. iv. Error due to variation of frequency causes change of reactance of the coil and also changes the eddy currents induced in neighboring etal. v. Deflecting torque is not exactly proportional to the square of the current due to non-linear characteristics of iron aterial. L.42.6 Test your understanding (Marks: 40) T.42.1 Sketch the circuit of an electro-echanical aeter, and briefly explain its operation. Coent on the resistance of an aeter. [10] T.42.2 Fig.42.11 shows a PMMC instruent has a coil resistance of 200 Ω and gives a FSD (full-scale deflection) for a current 200 μ A. Calculate the value of shunt resistance required to convert the instruent into a 500 A aeter. [5] (Ans. 0. 08Ω )
T.42.3 A PMMC instruent has a resistance of 100Ω and FSD for a current of 400 μ A. A shunt arrangeent is shown in Fig.42.12 in order to have an ulti-range aeters. Deterine the various ranges to which the aeter ay be switch. (Assue R1= R2= R3= R4 = 0.001Ω) (Ans. 10 A, 13.32 A, 20 A, and 40 A) [9] T.42.4 Fig.42.13 shows a PMMC instruent with a resistance of 75Ω and FSD current of 100 μ A is to be used as a volteter with 200 V, 300 V, and 500V ranges. Deterine the required value of ultiplier resistor of each range. (Ans. 2.0 M Ω, 3.0 M Ω, and 5.0M Ω) [8]
T.42.5 Two resistors are connected in series across a 200V dc supply. The resistor values are R1 = 300kΩ and R2 = 200kΩ. The volteter FSD is 250V and its sensitivity is 10 kω / V. Deterine the voltage across the resistance R2 : (i) without volteter in the circuit. (ii) with volteter connected. Meter resis tan ce + resis tan ce of ultiplier (Volteter sensitivity = ) Range of volteter (Ans. 80 V,76.33V ) [8]