BEEE 106 Lecture Notes PDF

ELECTRICAL MEASUREMENT AND INSTRUMENTATION BEEE 106 Compiled By: Yvonne K. KONKU ASASE HO TECHNICAL UNIVERSITY | ELECTRICAL/ ELECTRONIC ENGINEERING  CHAPTER ONE PHILOSOPHY OF MEASUREMENT INTRODUCTION Measurements are the basic mean...

ELECTRICAL MEASUREMENT AND INSTRUMENTATION BEEE 106 Compiled By: Yvonne K. KONKU ASASE HO TECHNICAL UNIVERSITY | ELECTRICAL/ ELECTRONIC ENGINEERING  CHAPTER ONE PHILOSOPHY OF MEASUREMENT INTRODUCTION Measurements are the basic means of acquiring knowledge about the parameters and variables involved in the operation of a physical system. Measurement generally involves using an instrument as a physical means of determining a quantity or variable. An instrument or a measuring instrument is, therefore, defined as a device for determining the value or magnitude of a quantity or variable. The electrical measuring instrument, as its name implies, is based on electrical principles for its measurement function. These days a number of measuring instruments, both analogue as well as digital ones, are available for the measurement of electrical quantities like voltage, current, power energy, frequency, power factor, etc. Simply, this is done with the aid of instruments (or meters) that indicate the magnitude of quantities either by the position of a pointer moving over a graduated scale (called an analogue instrument) or in the form of a decimal number (called a digital instrument). 1.1 Classification of Instruments The various electrical instruments may be in a broad sense, be divided into (i) Absolute instrument and (ii) Secondary instruments. Absolute instruments are those which give the value of the quantity to be measured, in terms of the constants of the instrument and their deflection only. No previous calibration or comparison is necessary in their case. The example of such an instrument is tangent galvanometer which gives the value of the current in terms of the tangent of deflection produced by the current, the radius and number of turns of wire used and the horizontal component of earth’s field. Secondary instruments are those in which the value of electrical quantity to be measured can be determined from the deflection of the instruments, only if they have been pre-calibrated by comparison with an absolute instrument. Without calibration, the deflection of such instrument is meaningless. It is the secondary instruments, which are most generally used in everyday work; the use of the absolute instruments being merely confined with laboratories, as standardizing instruments. Secondary instruments are widely used and may be classified as indicating, recording, integrating and comparison instruments. (i) Indicating instruments are those which indicate the instantaneous value of the electrical quantity being measured at the time at which it is being measured. Their indications are given by pointers moving over calibrated dials. Ordinary ammeters, voltmeters and wattmeters belong to this class. (ii) Recording instruments are those, which instead of indicating by means of a pointer and a scale the instantaneous value of an electrical quantity; give a continuous record or the variation of such a quantity over a selected period of time. The moving system of the instrument carries an inked pen which rests lightly on a chart or graph, which is moved at a uniform and low speed, 1 in a direction perpendicular to that of the deflection of the pen. The path traced out by the pen presents a continuous record of the variations in the deflection of the instrument. (iii) Integrating instruments are those which measure and register by a set of dials and pointers, either the total quantity of electricity (in amp-hour) or the total amount of electrical energy (in watt-hour or kWh) supplied to a circuit in a given time. This summation gives the product of time and the electrical quantity but gives no direct indication as to the rate at which the quantity or energy is being supplied because their registrations are independent of this rate provided the current flowing through the instrument is sufficient to operate it. Ampere-hour and watt-hour meters fall in this class. (iv) Comparison Instrument: The quantity measured by such an instrument is compared with an appropriate standard value. An example of such instruments is the measuring bridge which makes it possible to compare a resistance to be measured with a standard one. Electrical Principles of Operation All electrical measuring instruments depend for their action on one of the many physical effects of an electric current or potential and are generally classified according to which of these effects is utilized in their operation. The effects generally utilized are: 1. Magnetic effect – for ammeters and voltmeters usually. 2. Electrodynamic effect - for ammeters and voltmeters usually. 3. Electromagnetic effect – for ammeters, voltmeters, wattmeter, and watt-hour meter. 4. Thermal effect - for ammeters and voltmeters. 5. Chemical effect – for d.c. ampere-hour meters. 6. Electrostatic effect – for voltmeters only. Essentials of indicating instruments As defined above, indicating instruments are those which indicate the value of the quantity that is being measured at the time at which it is measured. Such instruments consist essentially of a pointer which moves over a calibrated scale and which is attached to a moving system pivoted in jeweled bearings. The moving system is subjected to the following three torques: 1. A deflecting (or operating) torque. 2. A controlling (or restoring) torque. 3. A damping torque. Deflection torque: The deflecting or operating torque is produced by utilising one or other of the effects of current or voltage. The actual method of producing this torque depends upon the type of instrument. The deflecting torque is required to cause the moving system of the instrument to move from its zero position as well as to bring it to the desired deflection position, representing the magnitude of the quantity under measurement. Controlling torque: The magnitude of the movement of the moving system of an instrument caused by the deflecting torque in most cases may tend to be somewhat indefinite unless some controlling torque is employed to limit the movement. A controlling torque would also ensure that the magnitude of deflection is always the same for a given value of quantity under 2 measurement. Such controlling torque in indicating instruments is almost always obtained either by a spring or gravity. The control torque must increase with the angular deflection of the pointer and this is arranged by using spiral springs or a ribbon suspension. Fig. 1.1 – Controlling torque Spring Control Figure 1.2(a) below shows a spindle free to turn between two pivots. The moving system is attached to the spindle. Two phosphor-bronze hair springs A and B wound in opposite directions are also shown whose inner ends are attached to the spindle. The outer end of spring A is connected to a leaver which is pivoted the adjustment of which gives zero setting. However, the outer end of B is fixed. When the pointer is deflected one spring unwinds itself while the other is twisted. This twist in the spring produces restoring (controlling) torque, which is proportional to the angle of deflection of the moving systems. Let E be the young-modulus for the material of the spring and θ (radians) be the deflection of the moving system to which one end of the spring is attached. Then, the controlling torque developed in the spiral spring is given by 𝐸𝑏𝑡 3 TC = 𝜃 12𝑙 Or TC = 𝑘𝑠 𝜃 Where l = Total length of spring strip (m) b = depth of the strip (m) t = thickness of the strip (m) ks = spring constant In a permanent magnet moving coil type instrument the deflecting torque is proportional to the current passing through them. Thus the operating torque, Td, is directly proportional to the current Td = KI Then for spring control instrument, the controlling torque, Tc, is Tc = KS𝜃 3 The pointer comes to rest when the deflecting torque (Td) and the controlling or restoring torque (Tc) are equal, i.e., Td is equal and opposite to Tc At equilibrium Td = Tc Therefore KI = KS𝜃 𝐾𝑠 𝜃 Hence, I= 𝐾 This equation shows that the current is directly proportional to the deflection (a) (b) Fig. 1.2 – Spring control Springs are made of such material which (i) are non-magnetic (ii) are not subjected to much fatigue (iii) have low specific resistance especially in case where they are used for leading current in or out of the instrument. (iv) have low resistance coefficient 4 Damping torque: A damping torque is also necessary to bring the moving system of an instrument to rest in its deflected position quickly. In the absence of such a torque the pointer may oscillate about its final position for quite sometimes before coming to rest, owing to the inertia of moving system. This causes a problem in taking readings and may also involve wastage of time. However, the damping torque must only be active when the moving system of the instrument is actually moving. The final deflection must not be affected by the damping at all. Depending upon the degree of damping introduced in the moving system, the instrument may have any one of the following conditions as depicted in Fig.1.3. 1. Under damped condition: The response is oscillatory 2. Over damped condition: The response is sluggish and it rises very slowly from its zero position to final position. 3. Critically damped condition: When the response settles quickly without any oscillation, the system is said to be critically damped. In practice, the best response is slightly obtained when the damping is below the critical value i.e., the instrument is slightly under damped. Fig. 1.3 – Damping Curves Eddy Current Damping This is the most effective way of providing damping. It is based on the faraday’s law and Lenz’s law. When a conductor moves in a magnetic field cutting the flux, emf gets induced in it and direction of the emf is so as to oppose the cause producing it. In this method aluminum disc is connected to the spindle. The arrangement of disc is such that when it rotates it cuts the magnetic flux lines of a permanent magnet. The arrangement is shown in the fig. below. When the pointer oscillates, the aluminum disc rotates under the influence of magnetic field of damping magnet. So, the disc cuts the flux which causes an induce emf in the disc. The disc is a closed path hence induced e.m.f. circulates current through the disc called eddy current. The direction of such eddy current is so as to oppose the cause producing it. The cause is relative motion between disc and field. Thus, it produces an opposing torque so as to 5 reduce the oscillation of pointer. This brings pointer to rest quickly. This is most effective and efficient method of damping. Damping Magnet N Aluminium disc S Spindle Fig. 1.4 - Eddy Current Damping Fluid Friction Damping Fluid friction damping may be used in same instruments. The method is similar to air friction damping, only air is replaced by working fluid. The friction between the disc and fluid is used for opposing motion. Damping force due to fluid is greater than that of air due to more viscosity. The disc is also called vane. The arrangement is shown in the fig. below. It consists of a vane attached to the spindle which is completely dipped in the oil. The frictional force between oil and the vane is used to produce the damping torque, which opposes the oscillating behavior of the pointer. Spindle rotation Damping oil Vane or disc Fig. 1.5 - Fluid Friction Damping 6 Advantages 1. Due to more viscosity of fluid more damping is provided. 2. The oil can also be used for insulation purposes. 3. Due to the thrust of oil, the load on the bearings is reduced, thus reducing the frictional error Disadvantages 1. This can only be used for the instruments which are in vertical position. 2. Due to oil leakage, the instruments cannot be kept clean. Analogue instruments may be divided into three groups: (a) Electromechanical instruments; (b) Electronic instruments which are often constructed by the addition of electronic circuits to electromechanical indicators thus increasing their sensitivity and input impedances; and (c) Graphical instruments which are electromechanical and electronic instruments having a modified display arrangement so that a graphical trace, that is, a display of instantaneous values against time. Analogue Multimeters An analogue multimeter is a (usually) moving-coil instrument that can measure both d.c. and a.c. currents and voltages, together with resistance. Because of their versatility, multimeters are far more widely-used in the field than separate ammeters, voltmeters, and ohmmeters, which are mainly found in laboratories. Some multimeters can measure other quantities, too. Reading Analogue Instruments A good-quality analogue instrument is a very accurate instrument —certainly more accurate than an inexpensive ‘consumer-level’ digital instrument, but probably somewhat less-accurate than a professional digital multimeter. Analogue instruments, however, are undoubtedly more difficult to read accurately, compared with digital instruments, and a certain amount of preparation is necessary in order to use them properly. You should develop a habit of following these guidelines: 1. Firstly, all analogue instruments are designed to give accurate readings when placed in a particular (usually horizontal) position, so they should never be propped-up at an angle, placed vertically, or held in the hands —where gravitational forces will act on the pointer to give an inaccurate reading. 2. Before measuring current or voltage, the pointer should be always checked to ensure it is pointing exactly at zero. If it isn’t, then it must be mechanically adjusted, using a small screwdriver, by means of the zero-adjust screw, located just below the instrument’s scale. Don’t confuse this with the zero-ohms adjustment. 3. All multimeters, offer different ranges (e.g. voltage ranges offered might be 0 V – 125 V, 0 V – 250 V, 0 V – 500 V). The highest range should always be selected first, but whichever scale then provides the greatest deflection, should always be used when taking a reading. This is 7 because the accuracy of any instrument is highest at its full-scale deflection, and the accuracy decreases towards the lower-end of the scale! 4. Multimeters usually have several scales, corresponding to the different functions and ranges available, and to whether we are measuring a.c. or d.c. values. It’s important to ensure we use the correct scale —i.e. the scale that corresponds to the function- and range-switch settings. Digital Multimeters Digital multimeters have now largely replaced analogue multimeters. In fact, with very few exceptions, analogue instruments are no longer being manufactured. The term, ‘digital’ applies, not only to an instrument’s readout, but also to the technology it employs. Analogue instruments have long-reached the limits of their development —the accuracy of their movements and an ease of reading have become about as good as they can possibly get. Digital instruments have now overtaken analogue instruments in terms of their robustness, potential accuracy, and the elimination of reading errors. Some digital multimeters can also measure additional quantities, such as frequency, capacitance, etc. So, let’s briefly compare digital multimeters with analogue multimeters: 1. Analogue multimeters have several scales for measuring current, voltage, and resistance and, often, separate scales for measuring a.c. and d.c. They are, therefore, relatively difficult to read, require practice and, therefore, are prone to mistakes by the user: such as reading the wrong scale or misinterpreting a particular reading. 2. Digital multimeters, on the other hand, have a single, simple, digital, readout (often with automatic range adjustment) which is very easy to read with virtually no chance of making a reading error. 3. Analogue multimeters movements are relatively delicate and must be treated with care to prevent them from becoming miscalibrated or their movement damaged. 4. Digital multimeters, however, are tough and robust, and are far less likely to become damaged. Even relatively-severe external physical damage is unlikely to affect their accuracy. 5. Analogue multimeters require a careful set-up routine prior to taking a measurement, as explained in the previous Section. 6. Digital multimeters must be set to the appropriate function setting (current, voltage, or resistance), but many types will then automatically select the most appropriate range within that function, will compensate for an aging battery, and all will automatically self-zero when set to measure resistance. 7. Analogue multimeters require a battery only to measure resistance, and will read current and voltage without a battery. 8. Digital multimeters, though, require a battery for all their functions, and will not operate at all once its battery is exhausted. 8 Features of a Digital Multimeter There is an enormous range of digital multimeters available from a great many manufacturers: from inexpensive consumer-level models to very expensive professional models. They all measure d.c. and a.c. voltages and currents, as well as resistance, but many will also have additional features, enabling them to measure frequency, capacitance, inductance, etc., and to test electronic components such as diodes and transistors. Measuring Current: Ammeters To measure current, the circuit must be broken at the point where we want that current to be measured, and the ammeter inserted at that point. In other words, an ammeter must be connected in series with the load under test. Fig. 1.6 – Measuring current As it’s very important that the insertion of the ammeter into a circuit has little effect on the circuit’s existing resistance and, thus, alter the current normally flowing in the circuit, ammeters are manufactured with very low values of internal resistance. Because ammeters have a very low internal resistance, it is vitally important that they are never inadvertently connected in parallel with any circuit component —and especially with the supply. Failure to do so will result in a short-circuit current flowing through the instrument which may damage the ammeter (although most ammeters are fused) or even result in personal injury. NOTE: Ammeters have a very low internal resistance, and must always be connected in series in a circuit. Measuring Voltage: Voltmeters To measure potential-difference, or voltage, a voltmeter must be connected between two points at different potentials. In other words, a voltmeter must always be connected in parallel with the part of the circuit under test. Fig. 1.7 – Measuring voltage 9 In order to operate, a voltmeter must, of course, draw some current from the circuit under test, and this can lead to inaccurate results because it can interfere with the normal condition of the circuit. We call this the ‘loading effect’ and, to minimize this ‘loading effect’ (and, therefore, improve the accuracy of a reading), this operating current must be as small as possible and, for this reason, voltmeters are manufactured with a very high value of internal resistance —usually many mega-ohms. NOTE: Voltmeters must always be connected in parallel in a circuit, and have a very high internal resistance. Measuring Resistance: Ohmmeters To measure the resistance of a circuit or of a circuit component, we use an instrument called an ohmmeter. Ohmmeters also provide a convenient way in which to check continuity —that is, to find out whether there are any breaks in a circuit. When checking continuity, we are usually only interested in observing a deflection, and not necessarily the value of the resistance reading. An ohmmeter works by using its internal battery to pass a small test current through the unknown resistance, and measuring the value of that current: the higher the resulting current, of course, the lower the resistance and vice-versa. Its scale, of course, is graduated in ohms and kilohms. When using an ohmmeter, we must always observe the following rules: 1. Never connect an ohmmeter to a live circuit —a failure to do so will likely result in a burnt- out of the instrument, and may cause harm. 2. Beware of measuring resistance of any component that may be connected in parallel with other components (this is not necessarily obvious), as you’ll end up measuring the combined resistance of all those components! It may be necessary to remove at least one of the component’s connections (e.g. disconnect one end of the resistor from the circuit). 3. When using a multimeter to measure resistance (or to check continuity), it is important to switch the instrument from its resistance setting when the measurement has been completed. Failure to do so might result in the battery becoming discharged should the test-leads accidentally short circuit during storage. Methods of Measurement Methods of measurement can be classified as: Direct comparison methods and indirect comparison methods. Direct Comparison Methods: In direct measurement methods, the unknown quantity is measured directly. Direct methods of measurement are of two types, namely, deflection methods and comparison methods. In deflection methods, the value of the unknown quantity is measured with an instrument having a calibrated scale, indicating the quantity directly (eg. Current by ammeter). In comparison methods, the value of the unknown quantity is determined by direct comparison with a standard of the given quantity (eg. emf, compared with std. cell). Comparison methods are classified as null methods, differential methods 10 Indirect Comparison Methods: In indirect measurement methods, the comparison is done with a standard through the use of a calibrated system. These methods for measurement are used in cases where the desired parameter to be measured is difficult to be measured directly, but the parameter has some relation with some other related parameter which can be easily measured. There is a need to establish an empirical relation between the actual measured quantity and desired parameter. The different methods of measurement are summarised with the aid of a tree diagram in Fig. 1.8. Fig. 1.8 – Different methods of measurement Measurement System and Its Elements A measurement system may be defined as a systematic arrangement for the measurement or determination of an unknown quantity and analysis of instrumentation. The generalized measurement system and its different components/elements are shown in Fig. 1.9. The operation of a measurement system can be explained in terms of functional elements of the system. Every instrument and measurement system is composed of one or more of these functional elements and each functional element is made of distinct components or groups of components which performs required and definite steps in measurement. Fig. 1.9 – The generalized measurement system 11 Primary Sensing Elements: It is an element that is sensitive to the measured variable. The physical quantity under measurement, called the measurand, makes its first contact with the primary sensing element of a measurement system. The measurand is always disturbed by the act of the measurement, but good instruments are designed to minimise this effect. Primary sensing elements may have a non-electrical input and output such as a spring, manometer or may have an electrical input and output such as a rectifier. In case the primary sensing element has a non-electrical input and output, then it is converted into an electrical signal by means of a transducer. The transducer is defined as a device, which when actuated by one form of energy, is capable of converting it into another form of energy. More often, certain operations are performed on the signal before its further transmission so that interfering sources are removed, in order that the signal may not get distorted. The process may be linear such as amplification, attenuation, integration, differentiation, addition and subtraction, or nonlinear such as modulation, detection, sampling, filtering, chopping and clipping, etc. The process is called signal conditioning. So a signal conditioner follows the primary sensing element or transducer, as the case may be. The sensing element senses the condition, state or value of the process variable by extracting a small part of energy from the measurand, and then produces an output which reflects this condition, state or value of the measurand. Variable conversion Elements: After passing through the primary sensing element, the output is in the form of an electrical signal, such as voltage, current, or frequency, which may or may not be accepted to the system. To perform the desired operation, it may be necessary to convert this output to some other suitable form while retaining the information content of the original signal. For example, if the output is in analogue form and the next step of the system accepts only digital signals, then an analogue-to-digital converter (ADC) will be employed. Many instruments do not require any variable conversion unit, while some others require more than one element. Manipulation Elements: Sometimes, the signal level needs to be changed without altering the information contained in it, for the acceptance of the instrument. The function of the variable manipulation unit is to manipulate the presented signal, while preserving the original nature of the signal. Example is an electronic amplifier that converts a small low voltage input signal into a high voltage output signal. Thus, the voltage amplifier acts as a variable manipulation unit. Some instruments may require this function while some may not. Data Transmission Elements: The data transmission elements are required to transmit the data containing the information of the signal from one system to another. For example, satellites are physically separated from the earth where the control stations guiding their movement are located. Data Presentation Elements: These elements provide an indication or recording in a form that can be evaluated by an unaided human sense or by a controller. The information regarding the measurand is to be conveyed to the personnel handling the instrument or the system for monitoring, controlling or analysis. Such a device may be in the form of analogue or digital format. The simplest form of a display device is the common panel meter with some kind of calibrated scale and pointer. In case the data is to be recorded, recorders like magnetic tapes or magnetic discs may be used. For control and analysis purpose, computers may be used. 12 The stages of a typical measurement system are summarized in Fig. 1.10. Fig. 1.10 – Steps of a typical measurement system The various types of instruments 1. Ammeters and voltmeters  Moving –iron type (for both D.C/A.C) a. The attraction type b. The repulsion type  Moving–coil type a. Permanent magnet type (for D.C. only) b. Electrodynamic or dynamometer type (for D.C./A.C.) 2. Wattmeter  Dynamometer type (for both D.C. /A.C)  Induction type (for A.C. only)  Electrostatic type (for D.C only) 3. Energy Meter  Electrolytic type (for D.C. only)  Motor Meters a. Mercury Motor Meter; For d.c. work only. Can be used as amp-hour or watt-hour meter. b. Commutator Motor Meter; Used on D.C. /A.C. can be used as Ah or Wh meter c. Induction type; For A.C. only Moving – iron Ammeters and Voltmeters There are two basic forms of these instruments i.e. the attraction type and the repulsion type. The operation of the attraction type depends on the attraction of a single piece of soft iron into a 13 magnetic field and that of repulsion type depends on the repulsion of two adjacent pieces of iron magnetized by the same magnetic field. For both types of these instruments, the necessary magnetic field is produced by the ampere-turns of a current-carrying coil. In case the instrument is to be used as an ammeter, the coil has comparatively fewer turns of thick wire so that the ammeter has low resistance because it is connected in series with the circuit. In case it is to be used as a voltmeter, the coil has high impedance so as to draw as small a current as possible since it is connected in parallel with the circuit. As the current through the coil is small, it has large number of turns in order to produce sufficient ampere-turns. The attraction type of moving iron instruments The attraction type of moving iron instruments utilizes the force of attraction which a solenoid exerts on an iron core. The coil C is shaped as shown in the figure below and the attraction iron B is made of sheaths metal specially shaped to give a scale as nearly uniform as possible. When current flows in the coil, the iron is attracted into the coil, causing the spindle S and the pointer to rotate, the exact calculation of the deflecting torque is even more difficult than in the case of repulsion type and the design of the shape of the iron is largely by trial, such instruments, normally have spring control and pneumatic damping, in general it may be said that attraction type instrument possess advantages and are subjected to the limitations described for the repulsion type. An attraction instruments will usually have a lower inductance than the corresponding repulsion instruments and volt-meters will therefore be accurate over a wider range of frequency and there is a greater possibility of using shunt with ammeters. The repulsion type of the moving-iron instruments The deflecting torque in any moving-iron instrument is due to forces on a small piece of magnetically soft iron, which is magnetized by a coil carrying the operating current. In the repulsion type shown below, there are two irons, thus A and B, A is fixed and the other B mounted on a short arm fixed to the instrument spindle. The two irons lies in the magnetic field produced by the coil C which consist of only a few turns if the instrument is an ammeter, or of many turns if the instrument is a voltmeter. The simplest type of construction uses two iron bars and it will be seen that they will be magnetize with like polarity for either current direction in the coil. The instrument will therefore deflect up-scale for either polarity of connection to d.c. circuit and also for a.c. flowing. The control torque is normally provided by the spiral spring and the balancing weight, pointer, pivots and jeweled bearing are in general similar to those described for moving coil instrument. The advantages of moving-iron instruments are: (i) Robust construction (ii) Relatively cheap (iii) Can be used to measure direct and alternating currents and voltages. The disadvantage of moving-iron instruments are: (i) Affected by stray magnetic fields. Error due to this cause is minimize by the use of a magnetic screen such as an iron casing. 14 (ii) Liable to hysteresis error when used in a d.c. circuit; i.e. for a given current, the instrument reads higher with decreasing than with increasing values of current. This error is reduce by making the iron strips of nickel-iron alloy such as Mumetal (iii) Owing to the inductance of the solenoid, the reading on moving-iron voltmeters may be appreciably affected by variation of frequency. This error is reduced by arranging for the resistance of the voltmeter to be large compared with the reactance of the solenoid. (iv) Moving-iron voltmeters are liable to a temperature error owing to the solenoid being wound with copper wire. This error is minimized by connecting in series with the solenoid a resistor of a material, such as manganin, having a negligible temperature coefficient of resistance. Fig. 1.11 – Moving iron instruments Moving-Coil Instruments Generally, moving coil instruments can be divided into two types these are Permanent magnet type and Electrodynamic or dynamometer type. The principles of operation of moving coil instrument  The moving part of the meter is a coil wound on an aluminium former or frame which is free to rotate around a cylindrical soft iron core.  The moving coil is situated in the magnetic field produced by a permanent magnet  The function of the soft iron core is to ensure that the magnetic field is uniformly distributed. 15   The current, I enter the moving coil from the positive terminal through spiral hairspring. It is the hairspring which provides the controlling force of the instrument.  When current flows in the coil, the reaction between each current carrying conductor and the magnetic field produces a mechanical force on the conductor, this is the deflecting force of the meter.  This force causes the pointer to be deflecting and as it does so the movement is opposed by the hairspring which carries current into the meter until finally the system is damped. Permanent-Magnetic Type Instruments The operation of a permanent magnetic moving coil type instrument is based upon the principle that when a current-carrying conductor is placed in magnetic field, it is acted upon by a force which tends to move it to one side and out of a field. pointer Pointer Non-magnetic fixing screw material Hair spring Moving coil N S Permanent Permanent Magnet magnet soft-iron Soft-iron core core Aluminium former Terminals Terminalsmarking marking Fig. 1.12 Permanent-magnet type moving coil instrument Construction As the name indicates, the instrument consists of a permanent magnet and a rectangular coil of many turns wound on a light aluminium or copper former inside which is an iron core. Between the magnetic poles is fixed a soft iron cylinder whose function is (i) to make the field radial and uniform and (ii) to decrease the reluctance of the air path between the poles and hence increase the magnetic flux. Surrounding the core is a rectangular coil of many turns wound on a light aluminium frame which is supported by delicate bearings and to which is attached a light pointer. The aluminium frame not only provides support for the coil but also provides damping by eddy 16 current induced in it. The sides of the coil are free to move in the two air-gaps between the poles and core. Control of the movement is affected by the two phosphor bronze hair springs, one above and one below, which additionally serve the purpose of lending the current in and out of the coil. The two springs are spiraled in opposite directions in order to neutralize the effects to temperature changes. Advantages and Disadvantages The permanent-magnet moving-coil (PMMC) type instruments have the following advantages and disadvantages: Advantages 1. They have low power consumption. 2. Their scales are uniform and designed to extend over an arc of 170o. 3. They possess high (torque/weight) ratio. 4. They can be modified with the help of shunts and resistances to cover a wide range of currents and voltages. 5. They have no hysteresis loss. 6. They have very effective and efficient eddy-current damping. 7. Since the operating fields of such instruments are very strong, they are not much affected by stray magnetic fields. Disadvantages 1. Due to delicate construction and the necessary accurate machining and assembly of various parts, such instruments are somewhat costlier as compared to moving – iron instrument 2. Some errors set in due to the aging of control springs and the permanent magnets. 3. Such instruments are mainly used for d.c. work only, but they have been sometimes used in conjunction with rectifiers or thermo-junctions for a.c. measurements over a wide range of frequencies. Extension of Range Shunts are used for the extension of range of Ammeters. So, a good shunt should have the following properties: 1. The temperature coefficient of the shunt should be low. 2. Resistance of shunt should not vary with time. 3. They should carry current without excessive temperature rise. 4. They should have thermal electromotive force with copper. Ammeter: PMMC is used as an indicating device. The current capacity of PMMC is small. It is impractical to construct a PMMC coil, which can carry a current greater than 100 mA. A shunt is therefore required for measurement of large currents. Rm = Internal resistance of movement (coil) in Ω Rsh = Resistance of shunt in Ω Im = Ifs = Full scale deflection current of movement in Amperes Ish = Shunt current in Amperes 17 I = Current to be measured in Amperes Since the shunt resistance is in parallel with the meter movement, the voltage drop across shunt and movement must be same. Fig. 1.13 – Shunt connection 𝐼𝑠ℎ 𝑅𝑠ℎ = 𝐼𝑚 𝑅𝑚 𝐼𝑚 𝑅𝑚 𝑅𝑠ℎ = ⁄𝐼 𝑠ℎ 𝐼𝑠ℎ = 𝐼 − 𝐼𝑚 𝐼𝑚 𝑅𝑚 ∴ 𝑊𝑒 𝑐𝑎𝑛 𝑤𝑟𝑖𝑡𝑒 𝑅𝑠ℎ = (𝐼 − 𝐼𝑚 ) 𝐼 𝑅𝑚 − 1= 𝐼𝑚 𝑅𝑠ℎ 𝐼 𝑅𝑚 = 1+ 𝐼𝑚 𝑅𝑠ℎ 𝐼 = 𝑚 𝑖𝑠 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 multiplying power 𝑜𝑓 𝑠ℎ𝑢𝑛𝑡 𝐼𝑚 𝑅𝑚 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑠ℎ𝑢𝑛𝑡 𝑅𝑠ℎ = (𝑚 − 1) Fig. 1.14 – Multi-range ammeter 18 Multi Range Ammeter: Let m1, m2, m3, m4 be the shunt multiplying powers for current I1, I2, I3, I4. 𝑅𝑚 𝐼𝑚 𝑅𝑚 𝑅𝑠ℎ1 = = (𝑚1 − 1) (𝐼1 − 𝐼𝑚 ) 𝑅𝑚 𝐼𝑚 𝑅𝑚 𝑅𝑠ℎ2 = = (𝑚2 − 1) (𝐼2 − 𝐼𝑚 ) 𝑅𝑚 𝐼𝑚 𝑅𝑚 𝑅𝑠ℎ3 = = (𝑚3 − 1) (𝐼3 − 𝐼𝑚 ) 𝑅𝑚 𝐼𝑚 𝑅𝑚 𝑅𝑠ℎ4 = = (𝑚4 − 1) (𝐼4 − 𝐼𝑚 ) Voltmeter: For measurement of voltage, a series resistor or a multiplier is required for extension of range. Im = Deflection current of movement Rm = Internal resistance of movement Rs = Multiplier resistance V = Full range voltage of instrument 𝑉 = 𝐼𝑚 (𝑅𝑠 + 𝑅𝑚 ) 𝑉 − 𝐼𝑚 𝑅𝑚 𝑉 𝑅𝑠 = = − 𝑅𝑚 𝐼𝑚 𝐼𝑚 For more than 500V, the multiplier is mounted outside the case. Fig. 1.15 – Multiplier connection Multi Range Voltmeter: 19 Fig. 1.16– Multi-range voltmeter 𝑉1 𝑅𝑠1 = − 𝑅𝑚 𝐼𝑚 𝑉2 𝑅𝑠2 = − 𝑅𝑚 𝐼𝑚 𝑉3 𝑅𝑠3 = − 𝑅𝑚 𝐼𝑚 𝑉4 𝑅𝑠4 = − 𝑅𝑚 𝐼𝑚 The moving-coil instrument is a very sensitive instrument. It is, therefore, widely used for measuring current and voltage. The coil of the instrument may require a small amount of current (in the range of μA) for full-scale deflection. The sensitivity is sometimes expressed in ohm/volt. The sensitivity of a voltmeter is given by: 𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑡𝑚𝑒𝑡𝑒𝑟 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑖𝑛 𝑜ℎ𝑚) 𝑅𝑚 1 𝑆= = = Ω/v 𝐹𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 (𝑖𝑛 𝑣𝑜𝑙𝑡) 𝑉 𝐼𝑓𝑠 Work Examples Example 1: The full-scale deflection current of an ammeter is 1 mA and its internal resistance is 100 ohms. If this meter is to have scale deflection at 5 A, what is the value of shunt resistance to be used. [Answer: 𝑅𝑠ℎ = 0.020004Ω]. Example 2: The full-scale deflection current of a meter is 1 mA and its internal resistance is 100 . If this meter is to have full-scale deflection when 100 V is measured. What should be the value of series resistance? [Answer: 𝑅𝑠 = 99,900Ω]. Example 3: A PMMC instrument gives full-scale reading of 25 mA when a potential difference across its terminals is 75 mV. Show how it can be used (a) as an ammeter for the range of 0-100 A (b) as a voltmeter for the range of 0-750 V. Also find the multiplying factor of shunt and voltage amplification. [Answer: (a) 𝑅𝑠ℎ = 0.75𝑚Ω, (𝑏) 𝑅𝑠 = 29,997Ω 𝑎𝑛𝑑 10000]. Example 4: A moving coil instrument gives full scale deflection of 10 mA and potential difference across its terminals is 100 mV. Calculate (a) shunt resistance for full-scale deflection 20 corresponding to 200 A (b) Series resistance for full reading corresponding to 1000 V. [Answer: (𝑎)𝑅𝑠ℎ = 5.00025𝑥10−4 Ω (b) 𝑅𝑠 = 99,990Ω ]. Example 5: A moving coil instrument has a resistance of 2and it reads up to 250 V when a resistance of 5000 is connected in series with it. Find the current range of the instrument when it is used as ammeter with the coil connected across a shunt resistance of 2 m. [Answer: 50𝐴]. Characteristics of Measurement System Performance  Static Characteristics: Some applications involve the measurement of quantities that are either constant or varies slowly with time. Under these circumstances it is possible to define a set of criteria that gives a meaningful description of quality of measurement without interfering with dynamic descriptions that involve the use of differential equations. These criteria are called static characteristics.  Dynamic Characteristics: Many measurements are concerned with rapidly varying quantities and therefore, for such cases we must examine the dynamic relations which exist between the output and the input. This is normally done with the help of differential equations. Performance criteria based upon dynamic relations constitute the dynamic characteristics. Static characteristics: 1. Accuracy: The accuracy of an instrument is defined as the degree of closeness of the measured value to its true value. Accuracy is usually expressed in term of percentage error with respect to full scale reading. 2. Precision/repeatability/reproducibility: Precision is a term that describes an instrument’s degree of freedom from random errors. If a large number of readings are taken of the same quantity by a high precision instrument, then the spread of readings will be very small. Precision is often, though incorrectly, confused with accuracy. High precision does not imply anything about measurement accuracy. A high precision instrument may have a low accuracy. Low accuracy measurements from a high precision instrument are normally caused by a bias in the measurements, which is removable by recalibration. The terms repeatability and reproducibility mean approximately the same but are applied in different contexts as given below. Repeatability describes the closeness of output readings when the same input is applied repetitively over a short period of time, with the same measurement conditions, same instrument and observer, same location and same conditions of use maintained throughout. Reproducibility describes the closeness of output readings for the same input when there are changes in the method of measurement, observer, measuring instrument, location, conditions of use and time of measurement 3. Tolerance: Tolerance is a term that is closely related to accuracy and defines the maximum error that is to be expected in some value. When used correctly, tolerance describes the maximum deviation of a manufactured component from some specified value. For instance, crankshafts are machined with a diameter tolerance quoted as so many microns (10-6m), and electric circuit components such as resistors have tolerances of perhaps 5%. 21  One resistor chosen at random from a batch having a nominal value 1000W and tolerance 5% might have an actual value anywhere between 950W and 1050 W. 4. Range or span: The range or span of an instrument defines the minimum and maximum values of a quantity that the instrument is designed to measure. 5. Linearity: It is normally desirable that the output reading of an instrument is linearly proportional to the quantity being measured. The Xs marked on the figure show a plot of the typical output readings of an instrument when a sequence of input quantities is applied to it. Normal procedure is to draw a good fit straight line through the Xs, as shown below. Fig. 1.17 The non-linearity is then defined as the maximum deviation of any of the output readings marked X from this straight line. Non-linearity is usually expressed as a percentage of full-scale reading. 6. Sensitivity: The sensitivity of measurement is a measure of the change in instrument output that occurs when the quantity being measured changes by a given amount. Thus, sensitivity is the ratio: 𝑆𝑐𝑎𝑙𝑒 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑛𝑑 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑛𝑔 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 The sensitivity of measurement is therefore the slope of the straight line drawn on. If, for example, a pressure of 2 bar produces a deflection of 10 degrees in a pressure transducer, the sensitivity of the instrument is 5 degrees/bar (assuming that the deflection is zero with zero pressure applied). 7. Threshold: If the input to an instrument is gradually increased from zero, the input will have to reach a certain minimum level before the change in the instrument output reading is of a large enough magnitude to be detectable. This minimum level of input is known as the threshold of the instrument. Manufacturers vary in the way that they specify threshold for instruments. Some quote absolute values, whereas others quote threshold as a percentage of full-scale readings. As an illustration, a car speedometer typically has a threshold of about 15 km/h. This means that, if the vehicle starts from rest and accelerates, no output reading is observed on the speedometer until the speed reaches 15 km/h. 8. Resolution: When an instrument is showing a particular output reading, there is a lower limit on the magnitude of the change in the input measured quantity that produces an 22  observable change in the instrument output. Like threshold, resolution is sometimes specified as an absolute value and sometimes as a percentage of f. s. deflection. One of the major factors influencing the resolution of an instrument is how finely its output scale is divided into subdivisions. Using a car speedometer as an example again, this has subdivisions of typically 20 km/h. This means that when the needle is between the scale markings, we cannot estimate speed more accurately than to the nearest 5 km/h. This figure of 5 km/h thus represents the resolution of the instrument. 9. Drift: The drift is the gradual shift of the instrument indication, over an extended period during which the value of the input variable does not change. The Zero Drift is defined as the deviation in the instrument output with time, from its zero value, when the variable to be measured is constant. The whole instrument calibration may gradually shift by the same amount. If there exists a proportional change in the indication, all along the upward scale then the drift from nominal characteristics is called sensitivity drift. 10. Dead Space: In some instruments it is possible that till input increases beyond certain value, the output does not change. So, for a certain range of input values there is no change in output. This range of input is called dead space. Dynamic Characteristics: The static characteristics of measuring instruments are concerned only with the steady state reading that the instrument settles down to, such as the accuracy of the reading etc. The dynamic characteristics of a measuring instrument describe its behaviour between the time a measured quantity changes value and the time when the instrument output attains a steady value in response. In any linear, time-invariant measuring system, the following general relation can be written between input and output for time t > 0: Where qi is the measured quantity, q0 is the output reading and a0... an, b0... bm are constants. The major point of importance is to have a practical appreciation of the manner in which various different types of instruments respond when the measurand applied to them varies. If we limit consideration to that of step changes in the measured quantity only, then equation (1) reduces to: Further simplification can be made by taking certain special cases of equation (2), which collectively apply to nearly all measurement systems. 1. Speed of response: It is the rapidity with which the system responds to the changes in the quantity to be measured. It gives the information about how fast the system reacts to the changes in the input. It indicates activeness of the system. 23  2. Fidelity: It indicates how much faithfully the system reproduces the changes in the input. It is the ability of an instrument to produce a wave shape identical to wave shape of input w.r.t time. 3. Lag: Every system takes some time, whatever small it may be, to respond to the changes in the measured variable. This retardation or delay in the response of a system is called as lag. The lags are of two types: i. Retardation lag: In this case, the response of the system begins immediately after a change in the variable has occurred. ii. Time delay: In this case, response begins after some time called dead time, after the application of input. Such a delay shifts the response along time axis and hence, causes the dynamic error. Dynamic Error: It is the 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. Errors in Measurement Through measurement, we try to obtain the value of an unknown parameter. However, this measured value cannot be the actual or true value. If the measured value is very close to the true value, we have very accurate measuring system. But before using the measured data for further use, one must have some idea how accurate is the measured data. So error analysis is an integral part of measurement. We should also have a clear idea what the sources of error are, how they can be reduced by properly designing the measurement methodology and also by repetitive measurements. These issues have been dwelt upon in this lesson. Besides, for maintaining accuracy, the readings of the measuring instrument are to be frequently compared and adjusted with the reading of another standard instrument. This process is known as calibration. We will also discuss about calibration in details. Error Analysis The term error in a measurement is defined as: Error = Instrument reading – true reading. Error is often expressed in percentage as 𝐼𝑛𝑠𝑡𝑟𝑢𝑚𝑒𝑛𝑡 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 − 𝑡𝑟𝑢𝑒 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 % 𝐸𝑟𝑟𝑜𝑟 = 𝑥 100 𝑡𝑟𝑢𝑒 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 Absolute error may be defined as the difference between the expected value of the variable and the measured value of the variable, or 𝑒 = 𝑋𝑛 − 𝑌𝑛 where 𝑒 = absolute error 𝑌𝑛 = expected value 𝑋𝑛 = measured value 24  𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑒𝑟𝑟𝑜𝑟 Therefore % Error = × 100 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑒 = × 100 𝑌𝑛 𝑋𝑛 −𝑌𝑛 Therefore % Error = ( ) × 100 𝑌𝑛 It is more frequently expressed as accuracy rather than error. 𝑋𝑛 −𝑌𝑛 Therefore 𝐴 = 1 − | | 𝑌𝑛 Where, A is the relative accuracy. Accuracy is expressed as % accuracy a = 100% - % error a = A × 100% where a is the % accuracy. EXAMPLE 1: The expected value of the voltage across a resistor is 80V. However, the measurement gives a value of 79 V. Calculate (i) absolute error, (ii) % error, (iii) relative accuracy, and (iv) % accuracy. Solution: i. 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑒𝑟𝑟𝑜𝑟 𝑒 = 𝑋𝑛 − 𝑌𝑛 = 79 − 80 = −1𝑉 𝑋𝑛 −𝑌𝑛 79−80 ii. % 𝑒𝑟𝑟𝑜𝑟 = × 100 = × 100 = −1.25% 𝑌𝑛 80 𝑋𝑛 −𝑌𝑛 79−80 1 iii. Relative accuracy 𝐴 = 1 − | |= 1−| | = 1 − 80 = 0.9875 𝑌𝑛 80 iv. % 𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦 𝑎 = 𝐴 × 100% = 0.9875 × 100% = 98.75% If a measurement is accurate, it must also be precise, i.e. Accuracy means precision. However, a precision measurement may not be accurate. (The precision of a measurement is a quantitative or numerical indication of the closeness with which a repeated set of measurement of the same variable agree with the average set of measurements.) Precision can also be expressed 𝑋𝑛 −𝑋̅𝑛 mathematically as 𝑃 = 1 − | | 𝑋̅𝑛 Where 𝑋𝑛 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑡ℎ 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡, 𝑋̅𝑛 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓 𝑠𝑒𝑡 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 Example 2: Table 1 gives the set of 10 measurements that were recorded in the laboratory. Calculate the precision of the 6th measurement. 25 Table 1 Measurement number Measurement value Xn 1 98 2 101 3 102 4 97 5 101 6 100 7 103 8 98 9 106 10 99 The accuracy and precision of measurements depend not only on the quality of the measuring instrument but also on the person using it. However, whatever the quality of the instrument and the case exercised by the user, there is always some error present in the measurement of physical quantities. Types of Static Error The static error of a measuring instrument is the numerical difference between the true value of a quantity and its value as obtained by measurement, i.e. repeated measurement of the same quantity gives different indications. Static errors are categorised as gross errors or human errors. Systematic error, and random errors. Gross Errors: These errors are mainly due to human mistakes in reading or in using instruments or errors in recording observations. Errors may also occur due to incorrect adjustment of instruments and computational mistakes. These errors cannot be treated mathematically. The complete elimination of gross errors is not possible, but one can minimise them. Some errors are easily detected while others may be elusive. One of the basic gross errors that occur frequently is the improper use of an instrument. The error can be minimized by taking proper care in reading and recording the measurement parameter. In general, indicating instruments change ambient conditions to some extent when connected into a complete circuit. (One should 26 therefore not be completely dependent on one reading only; at least three separate readings should be taken, preferably under conditions in which instruments are switched off and on.) Systematic Error: These errors occur due to shortcomings of the instrument, such as defective or worn-out parts, or ageing or effects of the environment on the instrument. These errors are sometimes referred to as bias, and they influence all measurements of a quantity alike. A constant uniform deviation of the operation of an instrument is known as a systematic error. There are basically three types of systematic errors: (i) Instrumental (ii) Environmental and (iii) Observational. (i) Instrumental Errors: Instrumental errors are inherent in measuring instruments, because of their mechanical structure. For example, in the D’Arsonval movement, friction in the bearings of various moving components, irregular spring tensions, stretching of the spring or reduction in tension due to improper handling or overloading of the instrument. Instrumental errors can be avoided by o Selecting a suitable instrument for the particular measurement applications o Applying correction factors after determining the amount of instrumental error. o Calibrating the instrument against a standard. (ii) Environmental Errors: Environmental errors are due to conditions external to the measuring device, including conditions in the area surrounding the instrument, such as the effects of change in temperature, humidity, barometric pressure or of magnetic or electrostatic fields. These errors can also be avoided by (i) air conditioning, (ii) hermetically sealing certain components in the instruments, and (iii) using magnetic shields. (iii) Observational Errors: Observational errors are errors introduced by the observer. The most common error is the parallax error introduced in reading a meter scale, and the error of estimation when obtaining a reading from a meter scale. These errors are caused by the habits of individual observers. For example, an observer may always introduce an error by consistently holding his head too far to the left while reading a needle and scale reading. In general, systematic errors can also be subdivided into static and dynamic errors. Static errors are caused by limitations of the measuring device or the physical laws governing its behaviour. Dynamic errors are caused by the instrument not responding fast enough to follow the changes in a measured variable. Example 3(a): A voltmeter having a sensitivity of 1kΩ/V is connected across an unknown resistance in series with a milliammeter reading 80V on 150V scale. When the milliammeter reads 10 mA, calculate the (i) Apparent resistance of the unknown resistance, (ii) Actual resistance of the unknown resistance, and (iii) Error due to the loading effect of the voltmeter. 27 Example 3(b) Referring to Ex. 3.3 (a), if the milliamrnetcr reads 600 mA and the voltmeter reads 30 V on a 150 V scale, calculate the following: (i) Apparent, resistance of the unknown resistance. (ii) Actual resistance of the Unknown resistance. (iii) Error due to loading effect of the voltmeter Comment on the loading effect due to the voltmeter for both Examples 1.3 (a) and (b). (Voltmeter sensitivity given 1000 Ω/V.) 28 In Example 3(a), a well calibrated voltmeter may give a misleading resistance when connected across two points in a high resistance circuit. The same voltmeter, when connected in a low resistance circuit (Example 3(b)) may give a more dependable reading. This shows that voltmeters have a loading effect in the circuit during measurement. Random Errors: These are errors that remain after gross and systematic errors have been substantially reduced or at least accounted for. Random errors are generally an accumulation of a large number of small effects and may be of real concern only in measurements requiring a high degree of accuracy. Such errors can be analyzed statistically. These errors are due to unknown causes, not determinable in the ordinary process of making measurements. Such errors are normally small and follow the laws of probability. Random errors can thus be treated mathematically. For example, suppose a voltage is being monitored by a voltmeter which is read at 15 minutes intervals. Although the instrument operates under ideal environmental conditions and is accurately calibrated before measurement, it still gives readings that vary slightly over the period of observation. This variation cannot be corrected by any method of calibration or any other known method of control. Sources of Error The sources of error, other than the inability of a piece of hardware to provide a true measurement, are as follows: 1. Insufficient knowledge of process parameters and design conditions 2. Poor design 3. Change in process parameters, irregularities, upsets, etc. 4. Poor maintenance 5. Errors caused by person operating the instrument or equipment 6. Certain design limitations 29  CHAPTER TWO ANALOGUE MEASUREMENT OF ELECTRICAL QUANTITIES Electrostatic Instruments In electrostatic instruments, the deflecting torque is produced by action of electric field on charged conductors. Such instruments are essentially voltmeters, but they may be used with the help of external components to measure current and power. Their greatest use in the laboratory is for measurement of high voltages. The electrostatic force acts in two ways:  Two oppositely charged electrodes; one fixed and the other moveable. Due to force of attraction, the moveable electrode is drawn towards the fixed one.  There is force of attraction or repulsion between the electrodes which causes rotary motion of the moving electrode In both cases, the operating mechanism resembles a variable capacitor, and the force is due to the fact that the mechanism moves the electrode to such a position where the energy stored is maximum. 1. Linear Motion: From Fig. 2.1, plate A is fixed and B is moveable. The plates are oppositely charged and restrained by a spring connected to a fixed point. Let a potential difference of V volt be applied to the plates; then a force of attraction F Newton exists between them. Plate B moves towards A until the force is balanced by the spring. The capacitance between the plates is then C farad and the stored energy is ½ CV2 joules. Fig. 2.1 – Linear motion of electrostatic instruments Let there be a small increment dV in the applied voltage, then plate B moves a small distance dx towards A. When voltage is being increased, a capacitive current flows. 𝑑𝑞 𝑑 𝑑𝑉 𝑑𝐶 This is given by 𝑖 = = 𝑑𝑡 (𝐶𝑉) = 𝐶 𝑑𝑡 + 𝑉 𝑑𝑡 𝑑𝑡 The input energy is 𝑉𝑖𝑑𝑡 = 𝑉 2 𝑑𝐶 + 𝐶𝑉𝑑𝑉 1 1 1 Change in stored energy = 2 (𝐶 + 𝑑𝐶)(𝑉 + 𝑑𝑉)2 − 2 𝐶𝑉 2 = 2 𝑉 2 𝑑𝐶 + 𝐶𝑉𝑑𝑉 From energy conservation principles, input electrical energy = increase in stored energy + mechanical work done 1 𝑉 2 𝑑𝐶 + 𝐶𝑉𝑑𝑉 = 𝑉 2 𝑑𝐶 + 𝐶𝑉𝑑𝑉 + Fdx 2 1 2 𝑑𝐶 ∴𝐹= 𝑉 2 𝑑𝑥 30 2. Rotational Motion: The forgoing treatment can be applied to the rotational motion by writing an angular displacement θ in place of linear displacement x and deflecting torque Td instead of force F. Fig. 2.2 – Rotary motion of electrostatic instruments 1 𝑑𝐶 Deflecting torque 𝑇𝑑 = 2 𝑉 2 𝑑𝜃 If the instrument is spring-controlled or has a suspension, then the controlling torque 𝑇𝑐 = 𝑘𝜃, where k = spring constant, and θ = deflection 1 𝑉 2 𝑑𝐶 ∴𝜃= 2 𝑘 𝑑𝜃 Since deflection is proportional to square of voltage to be measured, the instrument can be used on both ac and dc. The instrument exhibits a square law response; hence the scale is non-uniform. Advantages of Electrostatic Instruments They may be used on both ac and dc They draw negligible amount of power from the mains They have no frequency and waveform errors as the deflection is proportional to the square of voltage, and there is no hysteresis They are suitable for high voltage There are no errors caused by stray magnetic fields as the instrument works on electrostatic principles Disadvantages of Electrostatic Instruments These instruments are expensive, large and not robust in construction Their scale is not uniform Their use is limited to certain special applications, particularly in ac circuits of relatively high voltage, where the current drawn by other instruments would result in erroneous indication. A protective resistor is generally used in series with the instrument in order to limit the current in case of a short circuit between plates. The operating force is small Rectifier-Type Instruments A rectifier-type instrument is to measure ac quantities, where the ac signal is first converted to dc with the help of the rectifier. The dc signal is then measured by the PMMC meter. The multiplier resistance, Rs, is used to limit the value of the current so that it doesn’t exceed the current rating of the PMMC meter. These instruments are used for light current work where 31 voltage is low and resistance is high. The basic arrangement of a rectifier type of instrument using a full-wave rectifier circuit is shown in Fig. 2.3. Fig. 2.3 – Rectifier-type instrument Sensitivity of Rectifier-Type Instruments 1 The dc sensitivity of a rectifier-type instrument is given by 𝑆𝑑𝑐 = 𝐼 𝛺/𝑣 where 𝐼𝑓𝑠 is the current 𝑓𝑠 required to produce full-scale deflection. Sensitivity of a Half-Wave Rectifier Circuit: The average value of voltage/ current for a half- wave rectifier, 𝜋 1 𝑉𝑚 𝑉𝑎𝑣 = ∫ 𝑉𝑚 sin 𝜔𝑡 𝑑𝜔𝑡 = = 0.318𝑉𝑚 = 0.45𝑉 2𝜋 𝜋 0 Hence, the sensitivity of a half-wave rectifier instrument with ac is 0.45 times its sensitivity with dc, and the deflection is 0.45 times that produced with dc of equal magnitude V 𝑆𝑎𝑐 = 0.45𝑆𝑑𝑐 Fig. 2.4 – Half-wave rectifier circuit Sensitivity of a Full-Wave Rectifier Circuit: The average value of voltage/ current for a full- wave rectifier, 𝜋 1 2𝑉𝑚 𝑉𝑎𝑣 = ∫ 𝑉𝑚 sin 𝜔𝑡 𝑑𝜔𝑡 = = 0.636𝑉𝑚 = 0.9𝑉 𝜋 𝜋 0 Hence, the deflection is 0.9 times in a full-wave rectifier with an ac than that produced with dc of equal magnitude V 𝑆𝑎𝑐 = 0.9𝑆𝑑𝑐 32 Fig. 2.5 – Full-wave rectifier circuit Extension of Range of Rectifier Instrument as Voltmeter: To extend the range of a rectifier instrument which uses a PMMC instrument with a dc sensitivity of 𝑆𝑑𝑐 , let v = voltage drop across PMMC instrument, V = applied voltage. For dc operation, the value of series resistance required can be calculated as 𝑉 = 𝑅𝑠. 𝐼𝑓𝑠 + 𝑅𝑑. 𝐼𝑓𝑠 + 𝑅𝑚. 𝐼𝑓𝑠 𝑉 𝑅𝑠 = ( ) − 𝑅𝑚 − 𝑅𝑑 𝐼𝑓𝑠 = 𝑆𝑑𝑐 𝑉 − 𝑅𝑚 − 𝑅𝑑 (for half-wave rectification) = 𝑆𝑑𝑐 𝑉 − 𝑅𝑚 − 2𝑅𝑑 (for full-wave rectification) For ac voltmeter, 𝑅𝑠 = 𝑆𝑎𝑐 𝑉 − 𝑅𝑚 − 𝑅𝑑 = 0.45𝑆𝑑𝑐 𝑉 − 𝑅𝑚 − 𝑅𝑑 (for half-wave) = 𝑆𝑎𝑐 𝑉 − 𝑅𝑚 − 2𝑅𝑑 = 0.9𝑆𝑑𝑐 𝑉 − 𝑅𝑚 − 𝑅𝑑 (for full-wave) Fig. 2.6 – Extension of range of rectifier instrument Limitations They are only accurate on the waveforms on which they are calibrated; the presence of harmonics gives erroneous readings The rectifier is temperature-sensitive, hence the instrument readings are affected by large temperature variations Applications The instrument is very suitable for measuring alternating voltages in the range of 50 – 250 V They are mainly used for measurement in high-impedance circuits at low audio frequencies. They are commonly used in communications circuits because of their high sensitivity and low power consumption They may be used as micrometer or low milliammeter (up to 10 – 15 mA); it’s not suitable for measuring large currents 33 ELECTRODYNAMIC INSTRUMENTS The stationary part consists of two fixed coils connected in series as shown above, so that they can carry the same current. The moving system consists of a coil mounted on the spindle which is free to rotate in the space between the two fixed coils. The coil is made up of thin copper wire and is air cored to avoid hysteresis. The control torque is provided by two spiral springs. They also act as connecting leads for the moving coil. The pointer is mounted on the spindle. A mirror is provided to avoid parallax error. Damping is provided by air friction damping. I F F Fixed Coil (F) b a I I I Moving Coil (M) Fig. 2.7 – Electrodynamic instrument Working Principles: When the current to be measured is passed through the two stationary coils which are connected in series, it forms a magnetic field. Current to be measured is also passed through the moving coil through control springs. Now current carrying moving coil is placed in a magnetic field. And according to Fleming’s left-hand rule, force is experienced on the moving coil, which then brings about the deflection of the pointer. Advantages 1. They can be used for a.c. as well as d.c. measurements 2. They can be used as ammeter, voltmeter and wattmeter 3. They are useful as transfer type and calibration/ standard instruments 4. They are free from eddy current and hysteresis error 34 Disadvantages 1. Low torque/weight ratio 2. They are more expensive than PMMC instruments 3. Weak magnetic field 4. The scale is non-uniform 5. Power consumption is comparably high because of their construction Electrodynamic Ammeter: The fixed and moving coils are connected in series, as shown in Fig. 2.8. The fixed coils are made up of thick conductors to carry the load current. A shunt is connected across (in parallel) the moving coil for limiting the current. Fig. 2.8 – Electrodynamic ammeter Electrodynamic Voltmeter: The electrodynamic instrument can be used as a voltmeter by connecting a large non-inductive resistance (R) of low temperature coefficient in series with the instrument coil. All coils are made from a conductor with smaller cross-section. Fig. 2.9 – Electrodynamic voltmeter Electrodynamic Wattmeter: The electrodynamic wattmeter consists of two fixed coils ‘a’ and ‘b’, which are placed symmetrical to each other and produce a uniform magnetic field. They are connected in series with the load and are called the Current Coils (CC). The two fixed coils can be connected in series or parallel to give two different current ratings. The current coils carry the full-load current or a fraction of full load current. Thus, the current in the current coils is 35 proportional to the load current. The moving coil ‘c’, in series with a high non inductive resistance Rv, is connected across the supply. Thus, the current flowing in the moving coil is proportional to, and practically in phase with the supply voltage. The moving coil is also called the voltage coil or Pressure Coil (PC). The voltage coil is carried on a pivoted spindle which carries the pointer, which moves over a calibrated scale. The fixed coils are made of thick copper wire and moving coil with thin conductors. Fig. 2.10 – Electrodynamic wattmeter Wattmeter Power may be defined as the rate at which energy is transformed or made available. The power in a circuit at any instant is equal to the product of the current in the circuit and the voltage across its terminals at that instant. In d. c. circuit, if the current and voltage are constant, P = IV so that it is necessary only to determine the current and voltage and to take their product in order to obtain the value of the power in the circuit. In the case of a. c. circuits, the instantaneous power varies continuously as the current and voltage which go through a cycle of values. If the voltage and current are both sinusoidal the average power over cycle is given by the expression P = VI cos𝜃 watts. Construction and Working Principle of Electrodynamometer Type Wattmeter: There are two types of coils present in the electrodynamometer; moving coil and fixed coil. (a) Moving coil: the moving coil moves the pointer with the help of spring control instrument. A limited amount of current flows through the moving coils so as to avoid heating. So in order to limit the current we have connected the high value resistor in series with the moving coil. The moving coil is air cored and is mounted on a pivoted spindle and can move freely. In the electrodynamometer type wattmeter, moving coil works as pressure coil. Hence moving coil is connected across the voltage and thus the current flowing through this coil is always proportional to the voltage. (b) Fixed coil: the fixed coil is divided into two equal parts and connected in series with the load, therefore the load current will flow through these coils. Now the reason is very obvious of using two fixed coils instead of one, so that it can be constructed to carry considerable amount of electric current. These coils are called the current coils of electrodynamometer type wattmeter. 36 Control System: Out of two controlling system only spring-controlled systems are used in this type of wattmeter. Damping System: Air friction damping is used because eddy current damping will distort the weak operating magnetic field and it may lead to error. Derivation of Expressions for Controlling and Damping Torque Current coil 𝐼2 𝐼1 Load Supply Resistance Pressure coil Fig. 2.11 - The instantaneous torque in electrodynamic type instrument is directly proportional to product of instantaneous values of current flowing through both the coils and the rate of change of flux linked with the circuit. Let 𝐼1 𝑎𝑛𝑑 𝐼2 𝑏𝑒 the instantaneous values of currents in pressure and current coil respectively. 𝑑𝑀 Hence Torque, T = 𝐼1 𝑥 𝐼2 𝑥 where x is the angle 𝑑𝑥 Let the applied value of voltage across the pressure coil be 𝑉 = √2 𝑣𝑆𝑖𝑛𝜔𝑡 Assuming that, the electrical resistance of the pressure coil be very high hence we can neglect reactance with respect to its resistance. In this the impedance is equal to its electrical resistance therefore it is purely resistive. The expression for instantaneous current can be written as 𝐼1 = 𝑉 ⁄𝑅𝑝 𝑤ℎ𝑒𝑟𝑒 𝑅𝑝 𝑖𝑠 𝑡ℎ𝑒 𝑉𝑆𝑖𝑛𝜔𝑡 resistance of pressure coil 𝐼1 = √2 𝑋 𝑅𝑝 If there is phase difference between voltage and current, then expression for instantaneous current through current coil can be written as 𝐼2 = 𝐼(𝑡) = √2 𝐼𝑆𝑖𝑛(𝜔𝑡 − 𝜃) As current through the pressure coil is very small compared to current through current coil hence current through the current coil can be considered as equal to total load current. Hence the instantaneous value of torque can be written as 37  𝑉𝑆𝑖𝑛𝜔𝑡 𝑑𝑀 √2 𝑋 𝑋 √2 𝑋 𝐼 𝑋 𝑆𝑖𝑛(𝜔𝑡 − 𝜃) 𝑋 𝑅𝑝 𝑑𝑥 Average value of deflecting torque can be obtained by integrating the instantaneous torque from 0 to T, where T is the time period of the cycle. 𝑉𝐼 𝑑𝑀 𝑇𝑑 = 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑡𝑜𝑟𝑞𝑢𝑒 = 𝐶𝑜𝑠𝜃 𝑋 𝑅𝑝 𝑑𝑥 Controlling torque is given by 𝑇𝑐 = 𝐾𝑥 𝑤ℎ𝑒𝑟𝑒 𝐾 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑎𝑛𝑑 𝑥 𝑖𝑠 𝑡ℎ𝑒 𝑓𝑖𝑛𝑎𝑙 𝑠𝑡𝑒𝑎𝑑𝑦 𝑠𝑡𝑎𝑡𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛. Advantages of electrodynamometer type wattmeter 1. The scale is uniform up to a certain limit. 2. They can be used for measuring both ac as well as dc quantities as the scale is calibrated for both. Errors in Electrodynamometer type wattmeter 1. Errors in the pressure coil inductance. 2. Errors may be due to pressure coil capacitance. 3. Errors may be due to mutual inductance effects. 4. Errors may be due to connections (ie pressure coil is connected after current coil). 5. Errors may be due to eddy currents. 6. Error caused by vibration of moving system. 7. Temperature error. 8. Errors due to stray magnetic field. POWER MEASUREMENT IN POLYPHASE SYSTEMS Blondel’s Theorem states that ‘in an n-phase network, the total power can be obtained by taking summation of the n wattmeters so connected that the current elements of the wattmeters are each in one of the n lines, and the corresponding voltage element is connected between that line and a common point’. Power in Three-Phase Systems: Three-Wattmeter Method Consider the case of measuring power using three wattmeters in a 3-phase, 3-wire system as shown in Fig. 1.12. Current coils of the three wattmeters, W1, W2 and W3 are connected to the three lines R, Y, and B. Potential coils of the three wattmeters are connected to the common point C. The potential at the point C may be different from the neutral point (N) potential of load. Power consumed by load 𝑃 = (𝑉𝑅𝑁 × 𝐼𝑅 ) + (𝑉𝑌𝑁 × 𝐼𝑌 ) + (𝑉𝐵𝑁 × 𝐼𝐵 ) Reading of wattmeter W1, 𝑃1 = 𝑉𝑅𝐶 × 𝐼𝑅 Reading of wattmeter W2, 𝑃2 = 𝑉𝑌𝐶 × 𝐼𝑌 Reading of wattmeter W3, 𝑃3 = 𝑉𝐵𝐶 × 𝐼𝐵 38 Fig. 2.12 – Power measurement in a 3-phase 3-wire system If the voltage difference between the nodes C and N is taken as 𝑉𝐶𝑁 = 𝑉𝐶 − 𝑉𝑁 then we can have 𝑉𝑅𝑁 = 𝑉𝑅 − 𝑉𝑁 = 𝑉𝑅 − 𝑉𝐶 + 𝑉𝐶 − 𝑉𝑁 = 𝑉𝑅𝐶 + 𝑉𝐶𝑁 𝑉𝑌𝑁 = 𝑉𝑌 − 𝑉𝑁 = 𝑉𝑌 − 𝑉𝐶 + 𝑉𝐶 − 𝑉𝑁 = 𝑉𝑌𝐶 + 𝑉𝐶𝑁 𝑉𝐵𝑁 = 𝑉𝐵 − 𝑉𝑁 = 𝑉𝐵 − 𝑉𝐶 + 𝑉𝐶 − 𝑉𝑁 = 𝑉𝐵𝐶 + 𝑉𝐶𝑁 The sum of the three wattmeter readings can be combined as 𝑃1 + 𝑃2 + 𝑃3 = 𝐼𝑅 (𝑉𝑅𝑁 − 𝑉𝐶𝑁 ) + 𝐼𝑌 (𝑉𝑌𝑁 − 𝑉𝐶𝑁 ) + 𝐼𝐵 (𝑉𝐵𝑁 − 𝑉𝐶𝑁 ) = 𝐼𝑅 𝑉𝑅𝑁 + 𝐼𝑌 𝑉𝑌𝑁 + 𝐼𝐵 𝑉𝐵𝑁 − 𝑉𝐶𝑁 (𝐼𝑅 + 𝐼𝑌 + 𝐼𝐵 ) Applying Kirchhoff’s current law at node N, 𝐼𝑅 + 𝐼𝑌 + 𝐼𝐵 = 0 ∴ 𝑃1 + 𝑃2 + 𝑃3 = 𝐼𝑅 𝑉𝑅𝑁 + 𝐼𝑌 𝑉𝑌𝑁 + 𝐼𝐵 𝑉𝐵𝑁 It can be observed that the sum of the three individual wattmeter readings indicate the total power consumed by the load Wattmeter connections for measurement of power in a 3-phase 4-wire system are shown in Fig. 1.13. The common point of the three pressure coils coincides with the neutral N of the system. Voltage across each potential coil is thus, effectively the per-phase voltages of the corresponding phases. Current through current coils of the three wattmeters are nothing but the phase currents of the corresponding phases. Fig. 2.13 – Power measurement in a 3-phase 4-wire system The sum of the three wattmeter readings in this case will be 𝑃1 + 𝑃2 + 𝑃3 = 𝐼𝑅 𝑉𝑅𝑁 + 𝐼𝑌 𝑉𝑌𝑁 + 𝐼𝐵 𝑉𝐵𝑁 39 This is exactly the same as the power consumed by the load. Therefore, summation of the three wattmeter readings display the total power consumed by the load Power in Three-Phase Systems: Two-Wattmeter Method This is the most common of measuring three-phase power. It is very useful when the load is unbalanced 1. Star-Connected System: The current coils of the wattmeters are connected in lines R and B, and their voltage coils are connected between lines R and Y, and B and Y respectively. Fig. 2.14 – Two-wattmeter method for star-connected load Power consumed by load 𝑃 = 𝐼𝑅 𝑉𝑅𝑁 + 𝐼𝑌 𝑉𝑌𝑁 + 𝐼𝐵 𝑉𝐵𝑁 Reading of wattmeter W1, 𝑃1 = 𝐼𝑅 𝑉𝑅𝑌 = 𝐼𝑅 (𝑉𝑅𝑁 − 𝑉𝑌𝑁 ) Reading of wattmeter W2, 𝑃2 = 𝐼𝐵 𝑉𝐵𝑌 = 𝐼𝐵 (𝑉𝐵𝑁 − 𝑉𝑌𝑁 ) Summation of the two wattmeter readings: 𝑃1 + 𝑃2 = 𝐼𝑅 (𝑉𝑅𝑁 − 𝑉𝑌𝑁 ) + 𝐼𝐵 (𝑉𝐵𝑁 − 𝑉𝑌𝑁 ) = 𝐼𝑅 𝑉𝑅𝑁 + 𝐼𝐵 𝑉𝐵𝑁 − 𝑉𝑌𝑁 (𝐼𝑅 + 𝐼𝐵 ) From Kirchhoff’s law, summation of currents at node N must be zero 𝐼𝑅 + 𝐼𝑌 + 𝐼𝐵 = 0, ∴ 𝐼𝑅 + 𝐼𝐵 = −𝐼𝑌 Hence, 𝑃1 + 𝑃2 = 𝐼𝑅 𝑉𝑅𝑁 + 𝐼𝑌 𝑉𝑌𝑁 + 𝐼𝐵 𝑉𝐵𝑁 Therefore, the sum of the two wattmeter readings is equal to total power consumed by the load, whether it is balanced or not. 2. Delta-Connected System: The current coils of the wattmeters are connected in lines R and B, and their voltage coils are connected between lines R and Y, and B and Y respectively. Fig. 2.15 – Two-wattmeter method for delta-connected load 40 Power consumed by load 𝑃 = 𝑖𝑅 𝑉𝑅𝐵 + 𝑖𝑌 𝑉𝑌𝐵 + 𝑖𝐵 𝑉𝑅𝑌 Reading of wattmeter W1, 𝑃1 = −𝑉𝑅𝑌 (𝑖𝑅 − 𝑖𝑌 ) Reading of wattmeter W2, 𝑃2 = 𝑉𝐵𝑌 (𝑖𝐵 − 𝑖𝑅 ) Summation of the two wattmeter readings: 𝑃1 + 𝑃2 = −𝑉𝑅𝑌 (𝑖𝑅 − 𝑖𝑌 ) + 𝑉𝐵𝑌 (𝑖𝐵 − 𝑖𝑅 ) = 𝑖𝑌 𝑉𝑅𝑌 + 𝑖𝐵 𝑉𝐵𝑌 − 𝑖𝑅 (𝑉𝑅𝑌 + 𝑉𝐵𝑌 ) From Kirchhoff’s voltage law, summation of voltage drops across a closed loop is zero 𝑉𝑅𝑌 + 𝑉𝐵𝑌 + 𝑉𝑅𝐵 = 0 𝑉𝑅𝑌 + 𝑉𝐵𝑌 = −𝑉𝑅𝐵 Therefore 𝑃1 + 𝑃2 = 𝑖𝑌 𝑉𝑅𝑌 + 𝑖𝐵 𝑉𝐵𝑌 + 𝑖𝑅 𝑉𝑅𝐵 Therefore, the sum of the two wattmeter readings is equal to total power consumed by the load, whether it is balanced or not. SINGLE PHASE INDUCTION TYPE ENERGY METER OR WATT-HOUR METER Introduction: An instrument that is used to measure either quantity of electricity or energy, over a period of time is known as energy meter or watt-hour meter. In other words, energy is the total power delivered or consumed over an interval of time t may be expressed as: 𝑡 𝑊 = ∫ 𝑣(𝑡) 𝑖(𝑡) 𝑑𝑡 0 If v (t) is expressed in volts, i (t) in amperes and t in seconds, the unit of energy is joule or watt second. The commercial unit of electrical energy is kilowatt hour (KWh). For measurement of energy in a.c. circuit, the meter used is based on “electro-magnetic induction” principle. They are known as induction type instruments. The measurement of energy based on the induction principle is particularly suitable for industrial or domestic meters on the account of lightness and robustness of the rotating element. Moreover, because of smallness of the variations of voltage and frequency in supply voltage, the accuracy of the induction meter is unaffected by such variations. If the waveform of the supply is badly distorted, the accuracy, however, is affected. Fig. 2.16 – Single-phase induction type energy meter 41 Basically, the induction energy meter may be derived from the induction watt-meter by substituting for the spring control and pointer an eddy current brake and a counting train, respectively. For the meter to read correctly, the speed of the moving system must be proportional to the power in the circuit in which the meter is connected. Construction of induction type energy meter Induction type energy meter essentially consists of following components: (a) Driving system (b) Moving system (c) Braking system and (d) Registering system. Driving system: The construction of the electro magnet system is shown in the figure below. It consists of two electromagnets, called “shunt” magnet and “series” magnet, of laminated construction. Fig. 2.17 – Driving system A coil having large number of turns of fine wire is wound on the middle limb of the shunt magnet. This coil is known as “pressure or voltage” coil and is connected across the supply mains. This voltage coil has many turns and is arranged to be as highly inductive as possible. In other words, the voltage coil produces a high ratio of inductance to resistance. This causes the current, and therefore the flux, to lag the supply voltage by nearly 900. Adjustable copper shading rings are provided on the central limb of the shunt magnet, to make the phase angle displacement between the magnetic field set up by shunt magnet and supply voltage to be approximately 90 0. The copper shading bands are also called the power factor compensator or compensating loop. The series electromagnet is energized by a coil, known as “current” coil which is connected in series with the load so that it carries the load current. The flux produced by this magnet is proportional to, and in phase with the load current. Moving system: The moving system essentially consists of a light rotating aluminium disk mounted on a vertical spindle or shaft. The shaft that supports the aluminium disk is connected by a gear arrangement to the clock mechanism on the front of the meter to provide information on the energy consumed by the load. The time varying (sinusoidal) fluxes produced by shunt and series magnet induce eddy currents in the aluminium disc. The interaction between these two magnetic fields and eddy currents set up a driving torque in the disc. The number of rotations of the disk is therefore proportional to the energy consumed by the load in a certain time interval and is commonly measured in kilowatt-hours (Kwh). 42 Braking system: Damping of the disk is provided by a small permanent magnet, located diametrically opposite to the a.c magnets. The disk passes between the magnet gaps. The movement of rotating disc through the magnetic field crossing the air gap sets up eddy currents in the disc that reacts with the magnetic field and exerts a braking torque. By changing the position of the brake magnet or diverting some of the flux, the speed of the rotating disc can be controlled. Fig. 2.18 – Braking system Registering or counting system: The registering or counting system essentially consists of gear train, driven either by worm or pinion gear on the disc shaft, which turns pointers that indicate on dials the number of times the disc has turned. The energy meter thus determines and adds together or integrates all the instantaneous power values so that total energy used over a period is thus known. Therefore, this type of meter is also called an “integrating” meter. Fig. 2.19 – Registering system Basic operation Induction instruments operate in alternating-current circuits and they are useful only when the frequency and the supply voltage are approximately constant. The most commonly used technique is the shaded pole induction watt-hour meter, as shown in Fig. 2.20 below. The rotating element is an aluminium disc, and the torque is produced by the interaction of eddy currents generated in the disc with the imposed magnetic fields that are produced by the voltage and current coils of the energy meter. 43 Fig. 2.20 – Shaded pole induction watt-hour meter Errors in Induction Type Energy Meter Phase angle error Error due to friction at light loads Creeping error Error due to change in temperature Error due to overload Error due to voltage variations THERMOCOUPLE INSTRUMENTS These instruments also employ a technique which enables the moving coil instrument to be used for the measurement of a. c. quantities. The conversion from a. c. to d. c. is in this case performed by using the alternating current to heat a small element, the temperature of which is converted to a direct current by a thermocouple attached to it. A thermocouple circuit is the term applied to two lengths of dissimilar electric conductor, joined at the ends to form a closed loop. If the junctions of the dissimilar metals are maintained at different temperatures a current which may be measured by a sensitive moving coil instrument flows in the loop. evacuated glass cold junction Terminal block alternating current envelope room temperature heater d.c. moving coil heater thermocouple microammeter terminals hot junction Fig. 2.21 – Thermocouple instrument 44 Principle of the Thermocouple Instrument: Since this current is approximately proportional to the temperature difference between the hot and cold junctions, and if the cold junction is maintained at a constant temperature, the current in the moving coil instrument will be proportional to the temperature of the heater, which in turn is dependent on the r.m.s. or heating effect of the current in the heater. In many instruments of this type the terminals of the moving coil instrument will form the cold junction as shown in the figure above and will be subject to the variations in ambient temperature. However, these variations are generally insignificant (say 10 to 25 OC) compared with the temperatures of the heater which may be of the order of 1000 O C for the heater current corresponding to full scale deflection. It should be noted that if a thermocouple is being used to measure the temperature of an object it is often more satisfactory to open circuit; the dissimilar metal loop and measure, using an instrument with a high input impedance, the voltage that appears across the open circuit. Properties (a) Measures true r.m.s. value of an alternating current irrespective of its waveshape. (b) Wide frequency range. May be used from d.c. up to the megahertz range, but pointer vibrations may be experienced at low frequencies (less than 10 Hz). (c) Fragile, having a low overload capacity. Normally exceeding a 50 per cent overload will melt the heater element. (d) May have a higher impedance than moving-iron or electrodynamic instruments. (e) Nonlinear scale. The temperature of the heater will be proportional to current squared, also the temperature/voltage characteristic of a thermo-couple is slightly nonlinear. Applications: The main use is as an r.m.s. sensing milliammeter, and consequently when used with a series resistor it becomes a voltmeter. However, if it is intended that the instrument shall be used at high frequencies, it is important for the series resistance to be 'pure', that is, nonreactive, or its impedance, and hence the current in the heater will change with frequency. The thermocouple instrument is one of the few methods of determining the true r.m.s. value of an a.c. waveform. For precise measurement, the heater/hot junction and the cold junction are situated in an evacuated container and the d.c. output measured by a good quality digital voltmeter or potentiometer. By this technique the a.c. to d.c. conversion may be performed with an error of less than 0.05 per cent over a range of frequencies from 20 Hz to 1 MHz. It also applies for higher frequencies (50 MHz), but with reduced accuracy. LOADING EFFECT ON MEASURING INSTRUMENT Under ideal conditions, an element used for signal sensing, conditioning, transmission and detection should not change/distort the original signal. The sensing element should not use any energy or take least energy from the process so as not to change the parameter being measured. However, under practical conditions, it has been observed that the introduction of any element in a system results invariably in extraction of the energy from the system, thereby distorting the original signal. This distortion may take the form of attenuation, waveform distortion, phase shift, etc., and consequently, the ideal measurements become impossible. 45 The incapability of the system to faithfully measure the input signal in undistorted form is called loading effect. This results in loading error. The loading effects, in a measurement system, not only occur in the detector–transducer stage but also occur in signal conditioning and signal presentation stages as well. The loading problem is carried right down to the basic elements themselves.