UNIT II-ELECTRICAL AND ELECTRONICS INSTRUMENTS

OBJECTIVES:

We shall learn

Types of analog and digital voltmeters

Types of analog and digital ammeters, multimeters

Principle of analog and digital voltmeters, ammeters, multimeters

Principle of analog and digital ammeters, multimeters

Single and three phase wattmeter’s and energy meters

HISTORY: Among the earliest length measures was the foot, which varied from place to place There were two

common sizes for a "foot" - the foot of 246 to 252 mm based on a man's bare foot - the foot of 330 to

335 mm based on two hand measurements. The first calibrated foot ruler was invented in 1675 by an

unknown inventor. Weights and measures were among the earliest tools invented by man. Primitive

societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate

size and shape, fashioning clothing, or bartering food or raw materials. This provides a summary of

most of the units of measurement to be found in use around the world today (and a few of historical

interest), together with the appropriate conversion.

We know that for as long as history has been recorded there have been standards of length defined.

Three different Greek standards are known. The Doric foot, the Attic foot and the Simian foot. The

makers and markers of gauges, rules, squares & tapes An instrument which measures vertical

distance with respect to a reference level. Louis Paul Cailletet was the French physicist who

invented the altimeter. The invention of the quartz watch, mechanical clocks, timekeeping devices,

time. An instrument used to construct and measure plane angles. The simple protractor looks like a

semicircular disk marked with degrees, from 0º to 180º. The simple protractor is an ancient device.

The first complex protractor was created for plotting the position of a boat on navigational charts.

Called a three-arm protractor or station pointer, it was invented in 1801, by Joseph Huddart, a U.S.

naval captain. The center arm is fixed, while the outer two are Rota table, capable of being set at any

angle relative to the center one. Because electrical devices and measurements are so pervasive,

some knowledge of them is essential to all technical disciplines. In this experiment we will introduce

several instruments and use them to measure the electrical characteristics of some common

components and circuits.

INTRODUCTION: The measurement of a given quantity is the result of comparison between the quantity to be

measured and a definite standard. The instruments which are used for such measurements are called

measuring instruments. The three basic quantities in the electrical measurement are current, voltage

and power. The measurement of these quantities is important as it is used for obtaining

measurement of some other quantity or used to test the performance of some electronic circuits or

components etc.

The necessary requirements for any measuring instruments are

1. With the introduction of the instrument in the circuit, the circuit condition conditions

should not be altered .Thus the quantity to be measured should not get affected due to the

instrument used.

2. The power consumed by the instruments for their operation should be as small as possible.

The instrument which measures the current flowing in the circuit is called ammeter while the

instrument which measures the voltage across any two points of a circuit is called voltmeter. Thus all

the analog ammeters and voltmeters are basically current measuring devices .The instruments which

are used to measure the power are called power meters are wattmeters.

Classification of Measuring Instruments:

Instruments

Primary (or) Secondary Instruments Absolute Instruments According to the nature of reading According to the Principle Given by the instrument (or) Effects utilized Indicating instruments Recording Instruments Integrating Instruments Magnetic effect Heating effect Electro static Effect Induction Effect Hall Effect TYPES OF ANALOG VOLTMETER AND AMMETER

Classification Operating Principle

AMMETERS DC

VOLTMETERS Moving Coil Type

AMMETERS

VOLTMETERS Moving Iron type

AMMETERS AC

VOLTMETERS Rectifier Type

Essential Requirements of an Instrument: 1. Deflecting system produced Deflecting Torque Td 2. Controlling system produced controlling Torque Tc 3. Damping system produced damping Torque. Common Errors in Ammeter and Voltmeter: 1. Friction Error

2. Error due to temperature rise

3. Error due to unbalancing moving System

4. Error due to magnetic field

5. Error due to spiring

PERMANENT-MAGNET MOVING-COIL INSTRUMENT:

The compass and conducting wire meter can be considered a fixed-conductor moving-magnet

device since the compass is, in reality, a magnet that is allowed to move. The basic principle of this

device is the interaction of magnetic fields-the field of the compass (a permanent magnet) and the

field around the conductor (a simple electromagnet).

A permanent-magnet moving-coil movement is based upon a fixed permanent magnet and a coil of

wire which is able to move, as in figure 1-4.

When the switch is closed, causing current through the coil, the coil will have a magnetic field which

will react to the magnetic field of the permanent magnet. The bottom portion of the coil in figure 1-4

will be the north pole of this electromagnet. Since opposite poles attract, the coil will move to the

position shown in figure 1-5.

Figure 1-4. - A movable coil in a magnetic field (no current).

Figure 1-5. - A movable coil in a magnetic field (current).

The coil of wire is wound on an aluminum frame, or bobbin, and the bobbin is supported by jeweled

bearings which allow it to move freely. This is shown in figure 1-6.

Figure 1-6. - A basic coil arrangement.

To use this permanent-magnet moving-coil device as a meter, two problems must be solved. First, a

way must be found to return the coil to its original position when there is no current through the coil.

Second, a method is needed to indicate the amount of coil movement.

The first problem is solved by the use of hairsprings attached to each end of the coil as shown in

figure 1-7. These hairsprings can also be used to make the electrical connections to the coil.

With the use of hairsprings, the coil will return to its initial position when there is no current. The

springs will also tend to resist the movement of the coil when there is current through the coil.

When the attraction between the magnetic fields (from the permanent magnet and the coil) is

exactly equal to the force of the hairsprings, the coil will stop moving toward the magnet.

Figure 1-7. - Coil and hairsprings.

As the current through the coil increases, the magnetic field generated around the coil also

increases. The stronger the magnetic field around the coil, the farther the coil will move. This is a

good basis for a meter.

But, how will you know how far the coil moves? If a pointer is attached to the coil and extended out

to a scale, the pointer will move as the coil moves, and the scale can be marked to indicate the

amount of current through the coil. This is shown in figure 1-8.

Figure 1-8. - A complete coil.

Two other features are used to increase the accuracy and efficiency of this meter movement. First,

an iron core is placed inside the coil to concentrate the magnetic fields. Second, curved pole pieces

are attached to the magnet to ensure that the turning force on the coil increases steadily as the

current increases.

The meter movement as it appears when fully assembled is shown in figure 1-9.

Figure 1-9. - Assembled meter movement.

This permanent-magnet moving-coil meter movement is the basic movement in most measuring

instruments. It is commonly called the d'Arsonval movement because it was first employed by the

Frenchman d'Arsonval in making electrical measurements. Figure 1-10 is a view of the d'Arsonval

meter movement used in a meter.

Figure 1-10. - A meter using d'Arsonval movement.

Key point:

1. Thus the deflection is directly proportional to the current passing through the coil.

2. The PMMC is the most accurate type for measurements.

3. It measures only D.C

Questions For Discussion: 1 .What type of meter movement is the d'Arsonval meter movement? 2. What is the effect of current flow through the coil in a d'Arsonval meter movement? 3. What are three functions of the hairsprings in a d'Arsonval meter movement?

1

PRINCIPLE AND TYPES OF ANALOG AND DIGITAL VOLTMETER

AC voltmeters and ammeters:

AC electromechanical meter movements come in two basic arrangements: those based on DC movement designs, and those engineered specifically for AC use. Permanent-magnet moving coil (PMMC) meter movements will not work correctly if directly connected to alternating current, because the direction of needle movement will change with each half-cycle of the AC. (Figure below) Permanent-magnet meter movements, like permanent-magnet motors, are devices whose motion depends on the polarity of the applied voltage (or, you can think of it in terms of the direction of the current).

Passing AC through this D'Arsonval meter movement causes useless flutter of the needle.

In order to use a DC-style meter movement such as the D'Arsonval design, the alternating current must be rectified into DC. This is most easily accomplished through the use of devices called diodes. We saw diodes used in an example circuit demonstrating the creation of harmonic frequencies from a distorted (or rectified) sine wave. Without going into elaborate detail over how and why diodes work as they do, just remember that they each act like a one-way valve for electrons to flow: acting as a conductor for one polarity and an insulator for another. Oddly enough, the arrowhead in each diode symbol points against the permitted direction of electron flow rather than with it as one might expect. Arranged in a bridge, four diodes will serve to steer AC through the meter movement in a constant direction throughout all portions of the AC cycle: (Figure below)

Passing AC through this Rectified AC meter movement will drive it in one direction.

Another strategy for a practical AC meter movement is to redesign the movement without the inherent polarity sensitivity of the DC types. This means avoiding the use of permanent magnets. Probably the simplest design is to use a non magnetized iron vane to move the needle against spring tension, the vane being attracted toward a stationary coil of wire energized by the AC quantity to be measured as in Figure below.

Iron-vane electromechanical meter movement.

Electrostatic attraction between two metal plates separated by an air gap is an alternative mechanism for generating a needle-moving force proportional to applied voltage. This works just as well for AC as it does for DC, or should I say, just as poorly! The forces involved are very small, much smaller

than the magnetic attraction between an energized coil and an iron vane, and as such these “electrostatic” meter movements tend to be fragile and easily disturbed by physical movement. But, for some high-voltage AC applications, the electrostatic movement is an elegant technology. If nothing else, this technology possesses the advantage of extremely high input impedance, meaning that no current need be drawn from the circuit under test. Also, electrostatic meter movements are capable of measuring very high voltages without need for range resistors or other, external apparatus.

When a sensitive meter movement needs to be re-ranged to function as an AC voltmeter, series-connected “multiplier” resistors and/or resistive voltage dividers may be employed just as in DC meter design: (Figure below)

Multiplier resistor (a) or resistive divider (b) scales the range of the basic meter movement.

Capacitors may be used instead of resistors, though, to make voltmeter divider circuits. This strategy has the advantage of being non-dissipative (no true power consumed and no heat produced): (Figure below)

AC voltmeter with capacitive divider.

If the meter movement is electrostatic, and thus inherently capacitive in nature, a single “multiplier” capacitor may be connected in series to give it a greater voltage measuring range, just as a series-connected multiplier resistor gives a moving-coil (inherently resistive) meter movement a greater voltage range: (Figure below)

An electrostatic meter movement may use a capacitive multiplier to multiply the scale of the basic meter movement..

The Cathode Ray Tube (CRT) mentioned in the DC metering chapter is ideally suited for measuring AC voltages, especially if the electron beam is swept side-to-side across the screen of the tube while the measured AC voltage drives the beam up and down. A graphical representation of the AC wave shape and not just a measurement of magnitude can easily be had with such a device. However, CRT's have the disadvantages of weight; size, significant power consumption, and fragility (being made of evacuated glass) working against them. For these reasons, electromechanical AC meter movements still have a place in practical usage.

With some of the advantages and disadvantages of these meter movement technologies having been discussed already, there is another factor crucially important for the designer and user of AC metering instruments to be aware of. This is the issue of RMS measurement. As we already know, AC measurements are often cast in a scale of DC power equivalence, called RMS (Root-Mean-Square) for the sake of meaningful comparisons with DC and with other AC waveforms of varying shape. None of the meter movement technologies so far discussed inherently measure the RMS value of an AC quantity. Meter movements relying on the motion of a mechanical needle (“rectified” D'Arsonval, iron-vane, and electrostatic) all tend to mechanically average the instantaneous values into an overall average value for the waveform. This average value is not necessarily the same as RMS, although many times it is mistaken as such. Average and RMS values rate against each other as such for these three common waveform shapes: (Figure below)

RMS, Average, and Peak-to-Peak values for sine, square, and triangle waves.

Since RMS seems to be the kind of measurement most people are interested

A voltmeter is an instrument used for measuring the electrical potential difference between two points in an electric circuit. Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit; digital voltmeters give a numerical display of voltage by use of an analog to digital converter.

Voltmeters are made in a wide range of styles. Instruments permanently mounted in a panel are used to monitor generators or other fixed apparatus. Portable instruments, usually equipped to also measure current and resistance in the form of a multimeter, are standard test instruments used in electrical and electronics work. Any measurement that can be converted to a voltage can be displayed on a meter that is suitably calibrated; for example, pressure, temperature, flow or level in a chemical process plant.

General purpose analog voltmeters may have an accuracy of a few per cent of full scale, and are used with voltages from a fraction of a volt to several thousand volts. Digital meters can be made with high accuracy, typically better than 1%. Specially calibrated test instruments have higher accuracies, with laboratory instruments capable of measuring to accuracies of a few parts per million. Meters using amplifiers can measure tiny voltages of microvolts or less.

Part of the problem of making an accurate voltmeter is that of calibration to check its accuracy. In laboratories, the Weston Cell is used as a standard voltage for precision work. Precision voltage references are available based on electronic circuits.

Analog voltmeter

A moving coil galvanometer of the d'Arsonval type. The red wire carries the current to be measured.

The restoring spring is shown in green.N and S are the north and south poles of the magnet.

A moving coil galvanometer can be used as a voltmeter by inserting a resistor in series with the instrument. It employs a small coil of fine wire suspended in a strong magnetic field. When an electrical current is applied, the galvanometer's indicator rotates and compresses a small spring. The angular rotation is proportional to the current through the coil. For use as a voltmeter, a series resistance is added so that the angular rotation becomes proportional to the applied voltage.

One of the design objectives of the instrument is to disturb the circuit as little as possible and so the instrument should draw a minimum of current to operate. This is achieved by using a sensitive ammeter or microammeter in series with a high resistance.

The sensitivity of such a meter can be expressed as "ohms per volt", the number of ohms resistance in the meter circuit divided by the full scale measured value. For example a meter with a sensitivity of 1000 ohms per volt would draw 1 milliampere at full scale voltage; if the full scale was 200 volts, the resistance at the instrument's terminals would be 200,000 ohms and at full scale the meter would draw 1 milliampere from the circuit under test. For multi-range instruments, the input resistance varies as the instrument is switched to different ranges.

Moving-coil instruments with a permanent-magnet field respond only to direct current. Measurement of AC voltage requires a rectifier in the circuit so that the coil deflects in only one direction. Moving-coil instruments are also made with the zero position in the middle of the scale instead of at one end; these are useful if the voltage reverses its polarity.

Voltmeters operating on the electrostatic principle use the mutual repulsion between two charged plates to deflect a pointer attached to a spring. Meters of this type draw negligible current but are sensitive to voltages over about 100 volts and work with either alternating or direct current.

Vacuum Tube Voltmeter (VTVM)

The sensitivity and input resistance of a voltmeter can be increased if the current required to deflect the meter pointer is supplied by an amplifier instead of the circuit under test. A once-popular form of voltmeter of this type was the vacuum tube voltmeter, frequently referred to as a VTVM. Today these instruments use a solid-state amplifier using field-effect transistors. The electronic amplifier between input and meter gives two benefits; a rugged moving coil instrument can be used, since its sensitivity need not be high, and the input resistance can be made high, reducing the current drawn from the circuit under test. Amplified voltmeters often have an input resistance of 1, 10, or 20 megohms which is independent of the range selected.

Digital voltmeters (DVM)

Two digital voltmeters. Note the 40 microvolt difference between the two measurements, an offset of 34 parts per million.

The first digital voltmeter was invented and produced by Andrew Kay of Non-Linear Systems (and later founder of Kaypro) in 1954.

Digital voltmeters are usually designed around a special type of analog-to-digital converter called an integrating converter. Voltmeter accuracy is affected by many factors, including temperature and supply voltage variations. To ensure that a digital voltmeter's reading is within the manufacturer's specified tolerances, they should be periodically calibrated against a voltage standard such as the Weston cell.

Digital voltmeters necessarily have input amplifiers, and, like vacuum tube voltmeters, generally have a constant input resistance of 10 meg ohms regardless of set measurement range.

The voltmeter symbol is seen in this example circuit diagram. A voltmeter (V) and an ammeter (A) are shown measuring a voltage and a current respectively, in a simple series circuit.

Key point:

1. In the MI instruments deflection is proportional to the square of the current through the coil.

2.Moving Iron instruments used to measure both A.C and D.C

Questions for Practice: Choose the Best answer: 1. For absolute measurement of current the method commonly used is a) Electro – dynamometer method b) Tangent galvanometer method c) Rayleigh current balance method d) Lorenz method 2. The moving iron voltmeters are likely a) To indicate the same value on ac as on dc b) to indicate higher value on ac than on dc c) to indicate lower value on ac than on dc d) the moving iron voltmeter cannot be used for dc measurement at all 3. The term artificial aging in instrument is associated with a) springs b) permanent magnets c) controlling torques d) damping 4. In PMMC instruments the scale is a) Non - linear b) logarithmic c) exponential d) informally divided 5. In PMMC meter can measure a) Only ac quantities b) only dc quantities c) both ac and dc quantities d)only very high frequency quantities 6. PMMC instrument gives uniform scale be cause a) it uses spring control b)it uses eddy current damping c) the deflesting torque is proportional to the instrument current d) both A and B and C Answer:

1. (c) 2. (c) 3. (b) 4 (d) 5(b) 6. (d)

Fill in the Blanks: 7. The PMMC instruments give ----------------- scale

8. The range of a dc ammeter is increased by using a -------------

9. The shunt resistance in an ammeter is usually -------------instrument

Resistance `

10. A dynamometer type wattmeter has ------------scale

11. Most commonly used wattmeter is-----------

Answer: 7. Linear 8. Shunt 9. Smaller than 10. Linear 11.electro-dynamic type

True (or) False: 12. Secondary instruments are widely used in practice

13. D’ Arsonval Galvanometer is an absolute instrument

14. Gravity controlled instruments have uniforms scales

15. Damping torque in indicating instruments is usually reduced electro statically

16. Eddy current damping can be provided in instruments having metallic parts

Answer: 12. True 13. False 14. False 15. False 16.False

Digital Voltmeter:-

It is generally referred as DVM, convert the analog signal into digital and display

the voltage to be measured as discrete numericals instead of pointer deflection on the digital display.

Such voltmeter can be used to measure ac & dc voltages. By using the proper transducer & signal conditioning circuit for the measurement

of pressure, temp, stree etc.in the output of these given to the voltmeter and output are displayed in the form of digital ratings.

Advantages of DVM:- 1) The human reading errors, interpolation error and parallax error are

reduced by the digital display 2) They have input range from 1.00v to 1000v with the automatic range

section and the overload indication 3) The accuracy is high up to ± 0.005% of the reading the input impedance is

very high as 10MΩ , and also reading speed is high. 4) It is mostly used in computerized control and the outputs are directly

recorded 5) The inclusion of additional circuitry make them suitable for measurement

of qualites like current impedance, capacitance, tem, pressure etc. Varieties of DVM:- The several varieties of DVM differed in the following ways

1) Number of measurement ranges 2) Number of digits in readout 3) Accuracy 4) Speed of reading 5) Normal mode Noise rejection 6) Common mode noise rejection 7) Digital output of several types

Classifiction of DVM:- The classification is mainly based technique method analog to digital conversion technique method. 1. Non Integrating type:- (a) Potentiometric type

1) Servo potentiometric type 2) Successive approximation type 3)Null balance type

b) Ramp type 1)Linear type 2)Stair case type

2.Integrating type:- a) Voltage to frequency converter type b) Potentiometeic type c) Dual slope integrating type Servo Potentiometric Type DVM :

In the potentiometric type voltmeters internal reference voltage is provided. The reference voltage is denoted as Vref.

The voltage to be measured is the input voltage and is denoted asVin. A voltage comparison technique is used to measure the input voltage.

The unknown voltage is compared with the reference voltage with the help of the setting of the calibrated potentiometer ie. Potential divider.

The arm of the potentiometer is varied to obtain the null condition i.e. balancing condition . The internal reference voltage is present at the two terminals of the potentiometer.

When the null condition is obtained, the value of the unknown voltage is indicated by the dial setting of the potentiometer. The basic principle of potentiometer voltmeter

The 25. shows the Basic principle of potentiometric DVM Principle of potentiometric DVM:

Practically, the null balancing is not obtained manually but is obtained automatically. Such a voltmeter is called self balancing potentiometric type DVM.

The servomotor is used to vary the arm of the potentiometer hence it is also called servo balancing potentiometer type DVM. The block diagram of servo potentiometer type DVM is shown in the Fig. 26.

Fig.26. block diagram

The input voltage to be measures is applied to one side of mechanical chopper type comparator after filtering and attenuating to suitable level.

The reference voltage is applied at the two terminals of the potentiometer. The position of the sliding contact decides the value of the feedback voltage, which is used as the second input to the comparator.

The comparator which is an error detector, compares the unknown voltage and the feedback voltage.

The output of the comparator is a square wave signal whose amplitude is a function of the difference in the two voltages connected to its two ends i.e. error voltage.

This output signal from comparator is amplified and to its two ends i.e error voltage. This output signal from comparator is amplified and then fed to power amplifier.

The power amplifier output is given to the servomotor which acts as a potentiometer adjustment device.

The servomotor moves the sliding contact depends on the sign of the error i.e whether the feedback voltage is larger or smaller than the unknown input voltage.

When the feeback voltage is same as the input voltage, the eror is zero and therefore servomotor will not receive any signal, which will stop the movement of the sliding contact. Thus the sliding contact will attain a stable position.

The servomotor also derives the mechanical readout. The voltage corresponding to the stable position of the sliding contact is indicated in the numerical form on the digital display.

The relation between the unknown input voltage and the reference voltage can be mathematically expressed as,

Vin = Vref. Where Vin = voltage to be measured

Vref = reference voltage x = fraction depends on the position of slider.

The voltage to be measured depends on the reference voltage as the maximum value of the fraction x is 1.

The reference voltage source used in such DVMs must be extremely stable and generally a standard cell or zener diode is used as a reference voltage source.

This DVM uses the principle of balancing, instead of sampling because of mechanical movement.

Successive Approximation Type DVM

The potentiometer used in the servo balancing type DVM is a linear divider but in successive approximation type a digital divider is used. The digital divider is nothing but a digital to analog (D/A) converter. The servomotor is replaced by an electronic logic.

The basic principle of measurement by this method is similar to the simple example of determination of weight of the object.

The object is placed on one side of the balance and the approximate weight is placed on other side. If weight placed is more, the weight is removed and smaller weight is placed.

If this weight is smaller than the object, another small weight is added, to the weight present. If now the total weight is higher than the object, the added weight is removed and smaller

weight is added. Thus by such successive procedure of adding and removing the weight of the object is

determined. The successive approximation type DVM works exactly on the same principle. In successive approximation type DVM, the comparator compares the output of digital to

analog converter with the unknown voltage. Accordingly, the comparator provides logic high or low signals. The digital to analog

converter successively generates the set pattern of signals. The procedure continues till the output of the digital to analog converter becomes equal to

the unknown voltage. The Fig 27 shows the block diagram of successive approximation type DVM.

Fig.27. block diagram

The capacitor is connected a the input of the comparator. The output of the digital to analog

converter is compared with the unknown voltage, by the comparator.

The output of the comparator is given to the logic control and sequencer. This unit generates the sequence of code which is applied to digital to analog converter.

The position 2 of the switch S1 receives the output from digital to analog converter. The unknown voltage is available at the position 1 of the switch S1. The logic control also

drives the clock which is used to alternate the switch S1 between the position 1 and 2, as per the requirement.

Consider the voltage to be measured is 3.7924 V. The set pattern of digital to analog converter is say 8-4-2-1. at the start, the converter generates 8V and switch is at the position 2.

The capacitor C1 charges to 8V. The clock used to change the switch position. So during next time interval, switch position is 1 and unknown input is applied to the capacitor.

As capacitor is charged to 8V which is more than the input voltage 3.7924 V, the comparator sends HIGH signal to the logic control and sequencer circuit.

This HIGH signal resets the digital to analog converter which generates its next step of 4V. This again generates HIGH signal.

This again resets the converter to generate the next step of 2V. Now 2V is less than the input voltage. The comparator generates LOW signal and sends it to

logic control and sequence circuit. During the generation of LOW signal the generated signal by the converter is retained. Thus the total voltage level becomes, stored 2+ generated 1 i.e 3V. This is again less than the

input and generates LOW signal. Due to low signal, this gets stored. After this 0.8 V step is generated for the second digit

approximation. Thus the process of successive approximation continues till the converter generates 3.7924 V.

This voltage is then displayed on the digital display. At each low signal there is an incremental change in the output of the digital to analog

converter. This output voltage approaches the value of the unknown voltage. The limit to how close this

output can approach to the unknown voltage, depends on the level of noise at the input of comparator and the stability of the input switch.

To reduce the nose, filters may be used but it reduces the speed of measurement. These limiting factors usually determine the number of digits of resolution of an instrument. The general range of digits is 3 to5.

The speed depends upon the type of switches used in digital to analog converter and comparator circuitry.

If solid state switches are used, the high speed can be obtained. For electromechanical switches, the speed is few readings per second.

The accuracy depends on the internal reference supply associated with the digital to analog converter and the necessary of the converter itself.

The noise can cause incorrect reading due to incorrect decisions made by the comparator circuitry.

But inexpensive method of analog to digital conversion and resolution upto 5 significant digits are the advantages of the successive approximation type DVM. The technique is used for the speed of the order of 100 readings per second.

Ramp Type DVM

It uses a linear ramp technique or staircase ramp technique. The staircase ramp technique is simpler than the linear ramp technique. Let us discuss both the techniques.

Linear Ramp Technique

The basic principle of such measurement is based the measurement of the time taken by a linear ramp to rise from oV to the level of the input voltage or to decrease from the level of the input voltage to zero.

This time is measured with the help of electronic time interval counter and the count is displayed in the numeric form with the help of a digital display.

Basically it consists of a linear ramp which is positive going or negative going. The range of the ramp is± 10V.

The conversion going. The range of the ramp is± 12V while the base range is ± 10V. The conversion from a voltage to a time interval is shown in the Fig. 28.

Fig.28.

At the start of measurement, a ramp voltage is initiated which is continuously compared with

the input voltage. When these two voltage are same, the comparator generates a pulse which opens a gate i.e

the input comparator generates a start pulse. The ramp continues to decrease and finally reaches to 0V or ground potential. This is sensed

by the second comparator or ground comparator. At exactly oV, this comparator producesa stop pulse which closes the gate. The number of

clock pulses are measured by the counter. Thus the time duration for which the gate is opened, is proportional to the input voltage. In

the time interval between start and stop pulses, the gate remains open and the oscillator circuit drives the counter.

The magnitude of the count indicates the magnitude of the input voltage, which is displayed by the display. The block diagram of linear ramp DVM is shown in the fig. 29..

Fig.29. block diagram

Properly attenuated input signal is applied as one input to the input comparator. The ramp

generator generates the proper linear ramp signal which is applied to both the comparators. Initially the logic circuit sends a reset signal to the counter and the readout. The comparators

are designed in such a way that when both the input signals of comparator are equal then only the comparator changes its state.

The input comparator is used to send the start pulse while the ground comparator is used to send the stop pulse.

When the input and ramp are applied to the input comparator, and at the point when negative going ramp becomes equal to input voltage the comparator sends start pulse, due to which gate opens.

The oscillator drives the counter. The counter starts counting the pulse received from the oscillator.

Now the same ramp is applied to the ground comparator and it is decreasing. Thus when ramp becomes zero, both the inputs of ground comparator becomes zero (grounded) i.e.equal and it sends a stop pulse to the gate due to which gate closed. Thus the counter stops receiving the pulses from the local oscillator.

A definite number of pulse will be counted by the counter, during the start and stop pulse which is measured of the input voltage. This is displayed by the digital readout.

The sample rate multivibrator determines the rate at which the measurement cycles are initiated. The oscillation of this multivibrator is usually adjusted by a front panel control named, rate, from few cycles per second to as high as 1000 or more cycles per second.

The typical value is 5 measuring cycles / second with an accuracy of ± 0.005% of the reading. The sample rate provides an initiating pulse to the ramp generator to start its next ramp voltage. At the same time, a reset pulse is also generated which resets the counter to the zero state.

Advantages

1. The circuit is easy to design. 2. The cost is low. 3. The output pulse can be transferred over long feeder lines without loss of information. 4. The input signal is converted to time, which is easy to digitize. 5. By adding external logic, the polarity of the input also can be displayed. 6. The resolution of the readout is directly proportional to the frequency of the local oscillator. So adjusting the frequency of the local oscillator better resolution can be obtained.

Disadvantages

1. The ramp requires excellent characters regarding its linearity. 2. The accuracy depends on slope of the ramp and stability of the local oscillator. 3. Large errors are possible if noise is superimposed on the input signal. 4. The offsets and drifts in the two comparators may cause errors. 5. The speed of measurement is low. 6. The swing of the ramp is ± 12V, this limits the base of measurement to ± 10 V.

Stair Case Ramp Technique

In this type of DVM, instead of linear ramp, the staircase ramp is used. The staircase ramp is generated by the digital to analog converter. The block diagram of staircase ramp type DVM is shown in the Fig. 30..

Fig.30. block diagram The technique of using staircase ramp is also called null balance technique. The input voltage

is properly attenuated and is applied to a null detector.

The input to null detector is the staircase ramp generated by digital to analog converter. The ramp is continuously compared with the input signal.

Initially the logical control circuit sends a reset signal. This signal resets the counter. The digital to analog converter is also resetted by same signal.

At the start of the measurement, the logic control circuit sends a starting pulse which opens the gate. The counter starts counting the pulse generated by the local oscillator.

The output of counter is given to the digital to analog converter which generates the ramp signal. At every count there is an incremental change in the ramp generated.

Thus the staircase ramp is generated at the output of the digital to analog converter. This is given as the second input of the null detector. The increase in ramp continues till achieves the voltage equal to output voltage.

When the two voltage are equal, the null detector generates a signal which in turn initiates the logic control circuit. Thus logic control circuit sends a stop pulse, which closes the gate and the counter stops counting

At the same time, the logic control circuit generates a transfer signal due to which the counter information is transferred to the readout. The readout shows the digital result of the count.

Advantages

1. The greater accuracy is obtained than the linear ramp technique. 2. The overall design is more simple hence economical. 3. The input impedance of the digital to analog converter is high when the Compensation is reached.

Disadvantages

1. Though accuracy is higher than linear ramp, it is dependent on the accuracy digital to analog converter and its internal reference. 2. The speed is limited upto 10 readings per second.

Voltage to Frequency Converter Type Integrating DVM.

In case of ramp type DVM, the voltage is converted to time. The time and frequency are related to each other.

Thus the voltage can be converted to frequency for the measurement purpose. A train of pulses, whose frequency depends upon the voltage being measured, is generated.

Then the number of pulses appearing in a definite interval of time is counted. Since the frequency of these pulses is a function of the unknown voltage, the number of pulses counted in that period of time is the indication of the unknown input voltage.

The heart of such integrating type of DVM is the operational amplifier used as an integrator. The input voltage is integrated for a fixed interval.

An integration of a constant input voltage results a ramp at the output, the slope of which is proportional to the input voltage.

If the input is positive, the output of op-amp is negative going ramp. After some time, the capacitor is discharged to 0, thus output returns back to zero and the next cycle begins.

Hence the waveform at the output is a saw tooth waveform as shown in the Fig.31.

Fig.31. If the input signal is doubled, the number of teeth in the output signal per unit time will be

also doubled. Thus the frequency of the output will be doubled. Thus the frequency of the output is proportional to the input voltage. This is nothing but the voltage to frequency conversion.

The saw tooth pulses are finally enter into a reversible counter. The measured value by the reversible counter is finally displayed with the help of digital readout.

The block diagram of voltage to frequency converter type integrating DVM is shosn in the Fig. 32..

Initially output of an integer is adjusted to zero voltage. When the input voltage Vin is applied, the charging current Vin /R1 flows, which starts the charging of the capacitor C. This produces a ramp at the output.

When input voltage is positive, the output ramp is negative going. This ramp is given as one input of a comparator. A-V volts are given as a reference to the second input terminal of a comparator. When the ramp reaches to – V volts reference is compared by the comparator.

The negative going ramp –V volts reference are compared by the comparator. When the ramp reaches to – V volts the comparator output changes its state. This signal triggers the pulse generator.

The function the output changes its state. This signal triggers the pulse generator. The function of the pulse generator is to produce a pulse of precision charge content.

The polarity of this charge is opposite to that of capacitor charge. Thus the pulse generated by the pulse generator rapidly discharges the capacitor. Hence the output of the op-amp again becomes rapidly discharges the capacitor.

Hence the output of the op-amp again becomes zero. This process continues so as to get a saw tooth waveform at the output of op-amp.

The frequency of such waveform is directly proportional to the applied input voltage. Thus if the input voltage increases, the number of teeth per unit in the saw tooth waveform also increase i.e. the frequency increases.

Fig.32. block diagram

Each teeth produces a pulse at the output of the pulse generator so number of pulses is directly related to the number of teeth ie. The frequency.

These pulses are allowed to pass through the pulse transformer. These 'are applied at one input of the gate. Gate length control signal is applied at the other input. The gate length may be 0.1 sec, I sec, 20 msec etc. The gate remains open for this much time period.

When the gate is open, the pulses are counted by the reversible counter. After gate length

period, when the gate is closed, the count measured by the counter is transferred to the digital readout.

Accuracy: The accuracy of voltage to frequency conversion technique depends on the

magnitude and stability of the charge produced by the pulse generator. Thus the accuracy depends on the precision of the charge feedback in every pulse and also on the linearity between voltage and frequency. To obtain the better accuracy the rate of pulses generated by the pulse generator is kept equal to, i) the voltage time integration of the input signal ii) the total voltage time areas of the feedback pulses There are two techniques to design the pulse generator for the better B,CCV,CB,C~

i) Using a precision capacitor: The precision capacitor is placed between the pulse generator and the summing junction of

op-amp. The capacitor is allowed to charge upto precise voltage level and then this charge can be transferred to the summing junction of op-amp.

ii) Using a transformer The transformer can be placed between the pulse generator and the summing junction of up-

amp. The primary of the transformer is connected to the pulse generator. The secondary is

connected to the Summing junction of op-amp. The transformer material has a square type hysteresis loop characteristics. Due to this, there

is excursion around the B-H loop of transformer. This excursion can produce precise amount of charge at the summing junction of op-amp.

The purpose of the reversible counter is to sense the polarity of input voltage and count the pulses accordingly. If the input signal changes its polarity during a measuring period then the pulses received by the counter after the reversal of polarity must be subtracted from the previous count.

For this purpose, the counter used is a reversible counter. If a reversible counter is not used, then the counter will keep on adding the number of pulses and total count will keep on increasing though actually the input polarity is reversed. This will give the incorrect reading.

This type of situations may occur while measuring the low voltage of the order of mV in presence of a large amount of superimposed noise signal. When the reversible counting scheme is used, there are four conditions of counting are possible which are,

i) Positive up-counting ii) Positive down-counting iii) Negative up-counting iv) Negative down-counting

For the measurement of bipolar voltages, one more set of comparator and the pulse generator is necessary to add.

The second comparator produces positive going pulse for the negative input signal. A +V volts reference is used at the second input terminal of this comparator. The only important thing is that, both the pulse generators should produce same amount of feedback charge at the summing point of the op-amp.

Let us study the waveforms at various stages of the DVM when a complex input waveform is applied to it.

The input voltage has positive polarity for the period to t0 t1 and negative polarity for the period t2 to t4. For the periods t1 to t2 and t4 to t5, the voltage level is zero. The gate should be open for the entire time interval t0 to t6. This is shown in the waveform Fig. 33(d).

When input voltage polarity is positive i.e. for the periods t0 to t1 and t5 to t6’ the output of the pulse generator is high. For other time period it is low. This is shown in the Fig.33 (b).

When the input voltage polarity is negative i.e. for the period t2 to t4 the output of the pulse generator is high. This is due to other pulse generator used for the bipolar voltages. This is shown in the Fig. 33 (c).

For the period t0 to t1, it is positive counting up. For the period t2 to t3 it is positive counting down. For t3 to t4 negative counting up while for the period t5 to t6 it is negative counting down.

Transfer characteristics. The transfer characteristics show the relation between the input voltage and the output frequency. This should be as linear as possible. It remains linear upto a frequency called saturation frequency. This is shown in the Fig.34.

The slope of both the positive and negative voltage characteristics must be same.

To increase the operating speed of this type of DVM, the upper frequency can be increased i.e. increasing V/f conversion rate.

But this results into reduced accuracy and design cost of such circuit is also very high.Hence another method in which 5 digit resolution is available, is used to increase the speed of operation. This is the modified version of V/f integrating type DVM and is called interpolating integrating DVM.

Interpolating Integrating DVM

The block diagram of interpolating integrating DVM is shown in the Fig. 35. This is a modified version of V/f integrating DVM. A zero comparator is the additional circuitry in the DVM. The zero comparator ensures that the charge on the capacitor is zero.

During first 20 m sec, the operation is exactly similar to the normal V/f integrating DVM. However during this time the pulses are directed to the 100 s decade. Here each pulse is equivalent to the 100 counts.

Fig.35. block diagram

After 20 msec, the switch S1 is moved from position 1 to 2 and Vref of opposite polarity is offered. Some charge is still present on the capacitor.

The opposite polarity Vref helps to remove the remaining charge at a constant rate. When the charge reaches zero, the zero comparator provides a pulse to the control logic.

When the switch is moved from position 1 to 2, at the same time gate G2 is also opened. Hence the pulses from 50 kHz oscillator can reach to ls decade.

When the zero comparator provides a pulse, the gate G2 is closed. This completes the reading operation.

Potentiometric integrating Type DVM

The block diagram of potentiometric integrating type DVM is shown in the Fig 36. it uses a potentiometer at the input side and each measurement consists of two sample periods t1 and t2 as decided by the control logic.

During the first sampling periods t1, the output of digital to analog converter is zero. Hence the voltage to be measured is directly applied to V/I converter and then I/f converter.

Thus the voltage to frequency conversion takes place during the period t1. The pulse produced by the pulse transformer are fed into 100 s decade of the reversible counter.

Fig.36. block diagram

The reversible counter counts these pulse which are proportional to the input voltage. This count is then transferred to digital to analog converter. The digital to analog converter produces a voltage corresponding to the counts. During the process of transfer, the count is retained in the counter.

The input to V/f converter is now the difference between the input voltage and the voltage produced by digital to analog converter. Due to the small errors and reduced resolution, the output of digital to analog converter is not exactly equal to the input voltage.

Hence there exists a small voltage at the input of V/f converter, which is the difference between input voltage and output of digital to analog converter.

Now the second sampling period t2 starts. During this period the V/f converter generates a train of pulses, the frequency of which is proportional to the difference between the input and the output of digital to analog converter.

These pulse are given to the 1s decade of the reversible counter. The carry is generated when each hundredth pulse is generated.

This is then passed to 100 s decade. At the end of the period t2, the reading operation ends. The count is then transferred to the digital readout.

Advantages

1. The accuracy is very high. It depends on the digital to analog converter and its reference. The accuracy of V/f converter is of reduced importance. 2. The rejection of noise signals superimposed on input signal to be measured. While the high cost and less speed of operation are the two major limitations of this DVM.

Dual Slop Integrating Type DVM :

This is the most popular method of analog to digital conversion. In the ramp techniques, the noise can cause large errors but in dual slope method the noise is averaged out by the positive and negative ramps using the process of integration.

The basic principle of this method is that the input signal is integrated for a fixed interval of time. And then the same integrator is used to integrate the reference voltage with reverse slope. Hence the name given to the technique is dual slope integration technique.

The block diagram of dual slope integrating type DVM is shown in the Fig. 37.. It consists of five blocks, an op-amp used as an integrator, a zero comparator, clock pulse generator, a set of decimal counters and a block of control logic.

Fig.37. block diagram

When the switch S1 is in position 1, the capacitor C starts charging from zero level. The rate of

charging is proportional to the input voltage level. The output of the op-amp is given by

Vout = ∫1t

0

in

1

dtVCR

1

∴ Vout = CR

tV

1

1in …..(1)

Where t1 = Time for which capacitor is charged. Vin =Input voltage R1 = Series resistance C = Capacitor in feedback path

After the interval t1, the input voltage is disconnected and a negative voltage –Vref is connected by throwing the switch S1 in position 2. In this position, the output

Vout = ∫2t

0

ref

1

dtVCR

1

∴ Vout = CR

tV

1

2ref …..(2)

Subtracting (1) from (2),

Vout – Vout = 0=

−−

−

CR

tV

CR

tV

1

1in

1

2ref

∴CR

tV

1

2ref =CR

tV

1

1in

∴Vref t2 = Vin t1 .

∴Vin = Vref. 1

2

t

t …(3)

Thus the input voltage is dependent on the time periods t1 and t2 and not on the values of R1 and C.

This basic principle of this method is shown in the Fig.38..

Fig.38.

At the start of the measurement, the counter is resetted to zero. The output of the filp- flop is also zero. This is given to the control logic.

This control sends a signal so as to close an electronic switch to position 1 and integration of the input voltage starts. It continues till the time period t1. As the output of the integrator changes from its zero value, the zero comparator output changes its state.

This provides a signal to control logic which inturn opens the gate and the counting of the clock pulses starts.

The counter counts the pulses and when it reaches to 9999, it generates a carry pulse and all digits go to zero. The filp output gets activated to the logic level ‘1’. This activates the control logic.

This sends a signal which changes the switch S1 position from 1 to 2. Thus –Vref gets connected to op- amp. As Vref polarity is opposite, the capacitor starts discharging.

The integrator output will have constant negative slope as shown in the Fig. 38. The output will have constant negative slope as shown in the Fi. 38. The output will have constant negative slope as shown in the Fig. 2.78. The output decreases linearly and after the interval t2, attains zero value, when the capacitor C gets fully discharged.

At this instant, the output of zero comparator changes its state. This inturn sends a signal to the control logic and the gate gets closed. Thus gate remains open for the period t1+t2. The counting operation stops at this instant.

The pulses counted by the counter thus have a direct relation with the input voltage. The counts are then transferred to the readout. From equation (3) we can write,

Vin = Vref .1

2

t

t

Let time period of clock oscillator be T and digital counter has counted the counts n1 and n2 during the period t1 and t2 respectively.

Vin = Vref . Tn

Tn

1

2 = Vref. 1

2

n

n

Thus the unknown voltage measurement is not dependent on the clock frequency, but dependent on the counts measured by the counter.

Advantages :

i. Excellent noise rejection as noise and superimposed a.c are average out during the process of

integration. ii. The RC time constant does not affect the input voltage measurement. iii. The capacitor is connected via an electronic switch. This capacitor is an auto zero capacitor

and avoids the effects of offset of voltage. iv. The integrator responds to the average value of the input hence sample and hold circuit is not

necessary. v. The accuracy is high and can be readily varied according to the specific requirements. vi. The only disadvantage of this type of DVM is its slow speed.

Comparison of Various Techniques:

2.12.9

.-

2

1and

4-

2

1Dig

it T

he resolution of digital meters depends on the number of digits used in the display. The three digit display for 0-1 V range can indicate the value from 0 to 999 mV with te smallest increment of 1mV.

S.No Technique Operating speed

Noise effect

Circuit complexity

Accuracy Stability

1 Successive approximation

Very high Very much High High Poor

2 V/f conversion Moderate Minimum Low Moderate Moderate 3 Single slope V/t

conversion Slow High Low Low Poor

4 Dual slope Moderate Minimum Moderate High High 5 Delta modulation Moderate Minimum Moderate High High

Fig.39.

Practically one more digit which can display only 0 or 1 is added. This digit is called half digit

and display is called 3-2

1 digit display. This is shown in the Fig. 39..

In such a display the meter can read the values above 999 upto 1999, to give the overlap between the ranges for convenience. This process is called over-ranging.

In case of 4-2

1digit display, there are 4 full digits and 1 half digit. The number obtained is from

0 to 19999. For this operation the time period required for counting operation should be reduced.

This can be achieved by changing the frequency of the clock signal. The wave shaping and

amplifier circuitry should be more accurate for 42

1 digit display.

It is necessary to add one more BCD counter, latch, BCD to 7 segment decoder and 7

segment display unit. The resolution of 42

1digit display is better than 3-

2

1digit display while

the accuracy is 10 times better.

Digital Multimeters (DMM)

The digital multimeter is an instrument which is capable of measuring a.c. voltages, d.c. voltages, a.c. and d.c. currents and resistances over several ranges. The basic circuit of a digital multimeter is always a d.c. voltmeter as shown in the Fig. 40.

Fig.40. digital multimeter The current is converted to voltage by passing it through low shunt resistance. The a.c.

quantities are converted to d.c. by employing various rectifier and filtering circuits. While for the resistance measurements the meter consists of a precision low current source

that is applied across the unknown resistance while gives d.c. voltage. All the quantities are digitized using analog to digital converter and displayed in the digital

form on the display. The analog multi meters require no power supply and they suffer less from electric noise and isolation problems but still the digital multi meters have following advantages over analog multi meters :

i. The accuracy is very high. ii. The input impedance is very high hence there is no loading effect. iii. An unambiguous reading at greater viewing distances is obtained. iv. The output available is electrical which can be used for interfacing with external equipment. v. Due to improvement in the integrated technology, the prices are going down. vi. These are available in very small size. The requirement of power supply, electric noise and isolation problems are the two limitations.

The basic building blocks of digital multimeter are several A/D converters, counting circuitry and an attenuation circuit.

Generally dual slope integration type ADC is preferred in the multimeters. The single attenuator circuit is used for both a.c. and d.c. measurements in many commercial multimeters. The block diagram of a digital multimeter is shown in the Fig.41

Fig.41. block diagram As mentioned above basically it is a d.c. voltmeter. In order to measure unknown currents,

current to voltage converter circuit is implemented. This is shown in the Fig.42.

Fig.42. current to voltage converter

The unknown current is applied to the summing junction ∑ i at the input of op- amp. As

input current of op-amp is almost zero, the current IR is almost same as Ii, This current IR causes a voltage drop, which is proportional to the current to be measured.

This voltage drop is the analog input to the analog to digital converter, .thus providing a reading that is proportional to the unknown current.

In order to measure the resistances, a constant current source is used. The known current is passed through the unknown resistance.

The voltage drop across the resistance is applied to analog to digital converter hence providing the display of the value of the unknown resistance.

To measure the a.c. voltages, the rectifiers and filters are used. The a.c. is converted to d.c and then applied to tlle analog to digital converter.

In addition to the visual display, the output from the digital multimeters can also be used to interface with some other equipments.

Specifications of Digital Multimeter

The important specifications of a digital multimeter are as follows : i)D.C. Voltage

There are five ranges available from ± 200 mV to ± 1000 V. The resolution is 10 µ V on the lowest range.

The accuracy is ± 0.03 % of the reading + two digits ii) A.C.Voltage

There are five ranges from 200 mV to 750 V The resolution is 10 µ V on the lowest range.

The accuracy is frequency dependent but the best accuracy is 0.5% + 10 digits between 45 Hz and 1kHz on all the ranges.

Single Phase Energy Meter

Induction type instruments are most commonly used as energy meters. Energy meter is an integrating instrument which measures quantity of electricity. Induction type of energy meters are universally used for domestic and industrial applications. These meters record the energy in kilo-watt-hours (kWh).

The Fig 19 shows the induction type single phase energy meter. It works on the principle of induction i.e. on the production of eddy currents in the moving system by the alternating fluxes. These eddy currents induced in the moving system interact with each other to produce a driving torque due to which disc rotates to record the energy.

In the energy meter there is no controlling torque and thus due to driving torque only, a continuous rotation of the disc is produced. To have constant speed of rotation braking magnet is provided.

Construction

There are four main parts of operating mechanism 1) Driving system 2) Moving system 3) Braking system 4) Registering system.

1. Driving system: It consists of two electromagnets whose core is made up of silicon steel laminations. The coil

of one of the electromagnets, called current coil, is excited by load current which produces flux further.

The coil of another electromagnet is connected across the supply and it carries current proportional to supply voltage. This coil is called pressure coil. These two electromagnets are called series and shunt magnets respectively.

The flux produced by shunt magnet is brought in exact quadrature with supply voltage with the help of copper shading bands whose position is adjustable.

2. Moving system:

Light aluminum disc mounted in a light alloy shaft is the main part of moving system. This disc is positioned in between series and shunt magnets.

It is supported between jewel bearings. The moving system runs on hardened steel pivot. A pinion engages the shaft with the counting mechanism. There are no springs and no

controlling torque. 3. Braking system:

A permanent magnet is placed near the aluminums disc for braking mechanism. This magnet reproduced its own field.

The disc moves in the field of this magnet and a braking torque is obtained. The position of this magnet is adjustable and hence braking torque is adjusted by shifting this magnet to different radial positions. This magnet is called Braking magnet.

4. Registering mechanism:

It records continuously a number which is proportional to the revolutions made by the aluminums disc. By a suitable system, a train of reduction gears. The pinion on the shaft drives a series of pointers. These pointers rotate on round dials which are equally marked with equal divisions.

Fig.19. Single Phase Energy Meter

Working

Since the pressure coil is carried by shunt magnet M2 which connected across the supply, it carries current proportional to the voltage.

Series magnet M1 carries current coil which carries the load current. Both these coils produce alternating fluxes φ 1 and φ 2 respectively.

These fluxes are proportional to currents in their coils. Parts of each currents are induced in the disc and induces e.m.f. in it.

Due to these e.m.f.s eddy currents are induced by the electromagnet M2 react with magnetic field produced by M1.

Also eddy currents induced by electromagnet M1 react with magnetic field produced by M2. Thus each portion of the disc experiences a mechanical force and due to motor action, disc

rotates. The speed of disc is controlled by the C shaped magnet called braking magnet. When disc rotates in the air gap, eddy currents are induced in disc which oppose the cause

producing them i.e. relative motion of disc with respect to magnet. Hence braking torque Tb is generated. This is proportional to speed N of disc. By adjusting

position of this magnet, desired speed of disc is obtained. Spindle is connected to recording mechanism through gears which record the energy supplied.

Let us study theory behind the working. Let V = Supply voltage

I2 = current through pressure coil proportional to V φ 2 = flux produced by I2

I1 = current through current coil i.e. load

φ 1 = flux produced by I1

The phasor diagram is shown in the Fig 20.

Now I2 lags V by 90

0 as pressure coil is highly inductive and copper shading band. And φ 2

and φ 1 are in phase. While φ 1 lags V by φ . whereφ is decided by the load connected. The

flux φ 1 and I1 are in phase.

E1 = induced e.m.f. in disc due to φ 1

E2 = induced e.m.f. in disc due to φ 2

Ish = eddy current due to E1 Ist = eddy current due to E2

The induced e.m.f. lags the respective flux producing it by 900. The eddy currents are in phase with the induced e.m.f. producing them.

Now there is Interaction between φ 1 and Ish which produce torque T1 and the interaction

between φ 2 and Ise which produces torque.T2.

T2 is in opposite direction to T1. Hence net deflecting torque is, Td α T2-T1 α φ 2 Ise cos (φ 2

^Ise) - φ 1 Ish cos (φ 1^Ish)

Now φ 2^ Ise = φ and φ 1

^Ish = φ from Fig 20

∴ Td ∞ φ 2Ise cos φ - φ 1 Ish cos (180-φ )

∴ Td ∞ φ 2Ise cos φ+φ 1Ish cosφ

as cos (180-φ 1) = - cosφ

But φ 2 ∞ I2∞V, Ise ∞E1 ∞ I1, φ 1∞ I1, Ish ∞E2 ∞ I2 ∞V

∴ Td ∞ K1 V I1 cosφ+K2 I1, Vcosφ

∴ Td ∞ (K1+K2)V I1cosφ

∴ TdαV I1cosφ i.e. power consumed by load.

Now braking torque is proportional speed N with which disc rotates. ∴ Td ∞ N For constant speed Tb = Td ∴ N ∞ V I1 cosφ

Multiplying both side by t, N t ∞ V I1 t cos φ ∞ P t

Number of revolutions in time t ∞ energy supplied:

The power P x t is energy supplied in time t while Nt are the number of revolutions in time t Thus by counting number of revolutions, electrical energy consumed can be measured. Some adjustments are normally provided for such energy meter like power factor

adjustment, friction adjustment, main speed adjustment, creep adjustment so as to minimize the errors and to go accurate reading.

Calibration of an Energymeter

Calibrating the energy meter means to find out the error in the measurement of energy by

energy meter. Every energy meter has its own characteristic constant specified by the manufacturer which

relates the energy measured in joules and the number of revolutions of the disc. For example say ‘x’ revolutions corresponds to the measurement of ‘y’ joules. But practically

the value of ‘x’ is very large and can not be measured in the laboratory. Hence using this constant, energy recorded for certain less number of revolutions say 5, is calculated in the laboratory for the calibration purpose. This energy is denoted as Er. Thus Er can be caculated from ‘x’ as,

Er = joulesy

x5

Calibration of single phase Energy meter

To have zero error, the actual energy consumed by the load for the time corresponding to the

5 revolutions must be same as Er. This energy is called actual energy denoted or the true energy denoted as Er

Experimental set up used in the laboratory to obtain the value of Et is shown in the Fig 21

For various loads, the time required to complete the 5 revolutions of disc is measured with the help of stop watch. The voltage and current readings are observed on the ammeter and voltmeter connected in the circuit. The readings can be tabulated as :

Sr.No. Voltage

9V) Current (A)

Time for 5 revolutions

True enrgy Et = VI t J

1. 2. 3.

Now, Er is fixed for the 5 revolutions, while Et is obtained practically. Hence erroe for each

load condition can be obtained as,

% error = 100xE

EE

t

tr −

The graph of % error against the load current I can be obtained, which is called calibration

curve for the energy meter. When there is no load, I = 0 and hence true energy Et is also zero. Thus calibration curve passes is also zero. While Et is also zero. Hence the error is also zero. Thus calibration curve passes through origin. The errors can be positive or negative. Such a curve is shown in the Fig.22..

Fig.22.

Once the calibration curve is obtained, by observation of the curve, in which range of the load

current error is severe, can be easily predicted. And if error is not within the permissible limits then by using the various adjustments

discussed earlier, the error can be minimized.

Advantages

The various advantages of induction type energy meters are, 1. Its construction is simple and strong. 2. It is cheap in cost. 3. It has high torque to weight ratio, so frictional error are less and we can get

accurate reading. 4. It has more accuracy. 5. It requires less maintenance. 6. Its range can be extended with the help of instrument transformers.

Disadvantages

1. The main disadvantage is that is can be used only for ac. circuits. 2. The creeping can cause errors. 3. Lack of symmetry in magnetic circuit may cause errors.

Three Phase Energy meter

In a three phase, four wire systems, the measurement of energy is to be carried out by a three phase energy meter.

For three phases, three wire system, the energy measurement can be carried out by two element energy meter, the connections of which are similar to the connections of two wattmeters for power measurement in a three phase, three wire system.

So these meters are classified as i) three element energy meter and ii) two element energy meter.

Three Element Energy meter:

This meter consists of three elements. The construction of an individual element is similar to that of a single phase energy meter.

The pressure coils are denoted as P1, P2 and P3. The current coils are denoted as C1, C2 and C3. All the elements are mounted in a vertical line in common case and have a common spindle,

gearing and registering mechanism. The coils are connected in such a manner that the net torque produced is sum of the torques due to all the three elements. These are employed for three phase, four wire system where fourth wire is a neutral wire.

The current coils are connected in series with the lines while pressure coils are connected across a line and a neutral Fig. 23. shows a three phase energymeter.

Three phase energy meter:

One unit of three elements, three phase element is always cheaper than three units of single phase energy meter.

But due to interaction between eddy currents produced by one element with the flux produced by another element, there may be errors in the measurement by three phase energy meter. Such errors may be reduced by suitable adjustments.

Two Element Energy meter :

The Fig. 24. Shows a two element energy meter and a simplified connection diagram. This energy meter is used for three phase, three wire systems.

The meter is provided with two discs each for an element. The shunt magnet is carrying pressure coil while a series magnet carries a current coil.

The pressure coils are connected in parallel and the current coils in series. The connection are similar to the connections of two wattmeter’s for power measurement in three phase, three wire system.

Torque is produced in same manner as in a single phase energy meter, in each element. The total torque on the registering mechanism connected to moving system, is sum of the torques of the individual elements.

Fig.24. Two element energy meter

Review:

The power consumed by the instruments for their operation should be as small as possible

The PMMC is the most accurate type for measurements

In the MI instruments deflection is proportional to the square of the current through the

coil.

The greater accuracy is obtained than the linear ramp technique.

Questions for Practice

Choose the Best Answer 1. Electro – dynamometer type moving coil instruments are mainly used as a) Indicator type instruments b) standard instruments for calibration of other instruments c) transfer instruments only d) both as standard instruments and transfer instruments 2. An electro-dynamic instrument can be employed for measurement of a) DC voltage b) AC voltage c) Dc as well as AC voltage rectification is necessary 3. The scale of a dynamometer type instrument marked in terms of rms value would be a) Uniform throughout b) non- uniform crowded near full scale c) non- uniform crowded at the beginning d) Non- uniform crowded around mid-scale 4.In a dynamometer type moving coil instrument a swamping resistance is provided in order to a) control the deflecting torque b)reduce the bulk of the moving system c) reduce the current flowing through the moving coil d) provide equal time constant for moving coil and fixed coil, when used for ac measurement 5. The hot wire ammeter a) Is used only for dc measurements b)is used only for dc measurements c) give same deflection for ascending and descending values d) Reads equally well on dc and / or ac circuits 6. A wattmeter is reading backward upscale reading can had by reversing a) Connections of CC only b) connections of PC only c) either A and B d)both A and B

Answer: 1. (d) 2. (c) 3. (c) 4.(d) 5. (d) 6. (c)

Fill in the Blanks: 7. ------------wattmeter cannot be used on dc circuit .

8. A dc ampere – hour meter register ----------- is connected to voltage lower

than rated.

9. The meter constant of an energy meter is expressed in --------------------

10. The energy meter used on ac is in variably ---------------------type energy meter

11. The induction type single phase energy meter is a/an --------------meter

Answer: 7. Induction type 8. High 9. rev./Kwh 10. Induction 11. watt-hour

True or False: 12. Swamping resistance is connected in series with a voltmeter coil order to

reduce the full – scale current

13. Voltmeter should be of very high resistance so that loading effect is reduced

14. Moving iron instruments are suitable for measurement of ac up to 1MHz

15. Moving iron instruments are free from ageing errors

16. Permanant magnet moving coil instrument is the most accurate

and useful for dc measurement

Answer:

12. False 13. True 14. False 15.False 16. True

Magnetic Measurements Objectives:

• Magnetic measurements

• Determination of B-H curve and measurements of iron loss

• Instrument transformers

• Instruments for measurement of frequency and phase.

Introduction

The measurements of various properties of a magnetic material are called magnetic measurements.

The magnetic materials play a very important role in the operation of electrical machines hence measurement of various characteristics of a magnetic materials is important from the point of view of designing and manufacturing of electrical machines.

The magnetic measurements include, 1. Measurement of flux density B in a specimen of Ferro-magnetic material. 2. Measurement of magnetizing force H, producing the flux density B, in air. 3. Determination of B-H curve and the hysteresis loop. 4. Determination of eddy current and the hysteresis losses. 5. Testing of permanent magnets.

For such magnetic measurements following tests are performed: 1. D.C. Tests:

These are used to determine B-H curve and hysteresis loop of ferro-magnetic materials. The direct current is used to have variable m.m.f. and flux meter is used to measure the flux density. A ballistic galvanometer can be used to measure flux density. Such tests are also called ballistic tests. 2. A.C. Tests: When a ferromagnetic material is subjected to a cycle of magnetization and demagnetization then the eddy current and hysteresis losses occur. Hence alternating current is used to determine iron losses, having provision of a variable frequency and form factor. Such tests are carried out at power, audio or radio frequencies. 3. Steady State Tests: The flux in the air gap plays an important role in the operation of various electrical equipments. Such a flux is measured using steady state tests. Such tests give steady state value of the flux in the air gap of a magnetic material.

The results of magnetic measurements are not very accurate because of following reasons : 1. The magnetic materials are non homogeneous. 2. The condition at the time of calculations are different than the conditions existing at the time

of testing of magnetic material. 3. Various groups of test specimens have no uniformity.

Fluxmeter:

A special ballistic galvanometer with very small controlling torque and high electro-magnetic damping is used as a flux meter.

It consists of a small cross-section carrying a coil C. The cross-section is suspended in the narrow air gap of permanent magnet.

The cross-section is suspended with the help of spring support and a single thread of silk. The current is injected to the coil through very thin, annealed silver springs as shown in the Fig. 43.

Fig.43. Fluxmeter

The pointer is fitted to the moving system of the flux meter and the scale is calibrated in terms

of flux turns. Such a flux meter is designed by Grassot and hence it is called Grassot flux meter. The spirals of silver springs keep the controlling torque to minimum.

As controlling torque is minimum, pointer takes time to come back to the zero position. But readings may be taken by observing the difference in deflections at the beginning and end of the change in flux, without waiting for pointer to restore its zero position.

The resistance RS of the search coil connected to the flux meter must be small. The inductance of search coil may be large.

Letφ 1 and φ 2 are the interlinking fluxes at the beginning and the end of the change in flux to

be measured respectively. The corresponding deflections are φ 1 and φ 2 respectively. Then,

dφ = Change in deflection = θ2- θ1 dφ = Change in flux = φ 2-φ 1 .

and it can be proved that, Gdφ = Ndφ

where G= Constant of flux meter called displacement constant N = Number of turns on search coil

dθ = G

Ndφ

In modern flux meters, the coil is supported with pivots and mounted in jewelled bearings. The current is passed to the coil through fine ligaments.

Measurement of Flux Density (B)

Let us study the measurement of flux density in a ring specimen. A coil with sufficient

number of turns is wound on a ring specimen. This coil is called search coil or a B coil. This coil is then connected to a flux meter or a ballistic galvanometer, as shown in the Fig. 44.

The magnetizing winding carries a current 1 which produces the flux to be measured. The current 1 in the magnetizing coil is reversed using a reversing switch. Thus flux linkages associated with the search coil also change inducing e.m.f in it. This e.m.f. drives a current through a ballistic galvanometer, causing the corresponding deflection.

Theory of Flux Density Measurement : Let φ= Flux linking with search coil

N = Number of turns of search coil R = Resistance of ballistic galvanometer circuit. t = Time require to reverse current I i.e time require to reverse flux φ .

The average e.m.f induced in the search coil is given by,

e = N dt

dφvolts

Initial flux = φ , After reversal = -φ .

∴ dφ=φ - (-φ ) = 2φ .

dt =t

∴ e =t

2N φV

Thus the average current through ballistic galvanometer is,

i = R

e=

Rt

N2 φA

Hence the charge Q discharged through the galvanometer during t sec is,

i = t

Q

∴ Q = it =Rt

N2 φ.

T= R

N2 φCoulombs

The deflection of the galvanometer is proportional to the charge discharged through it, ∴ Q =Kθ ’ where K = Galvanometer constant.

∴ R

N2 φ=Kθ ’

∴ φ= N2

'RK

N2

R'K θ=

θWb

Thus if A is the area of cross- section of the specimen then flux density can be obtained as,

∴ B = A

φ=

NA2

'RKθ Wb/m2

Thus flux and flux density can be measured from the deflection of the ballistic galvanometer. Correction of Air Flux

In the above discussion, it is assumed that the flux is uniform throughout the specimen and area or cross – section coil and specimen is equal. But practically cross- section of search coil is higher than that of specimen. Hence total flux linking with the search coil is sum of the flux in the specimen and the flux existing in the air gap between search coil and the specimen.

∴ Total flux observed = Flux in specimen + Flux in air gap between coil and specimen. Let B’ = Observed value of flux density

Bt = True value of flux density Ac = Area of cross –section of search coil.

B’A= Bt A+ 0µ H (Ac-A)

Bt =B’ - 0µ H

−1

A

A c

This is called correction of air flux.

Measurement of Magnetising Force H

The magnetizing force H is also measured by using a search coil and a ballistic galvanometer. The arrangement is shown in the Fig. 45.

Fig.45. Measurement of H In such method H can not be obtained directly but is to be calculated by measuring flux

density by the method of current reversal, as described earlier. The position of search coil shown in the Fig. 2.88 is for the measurement of flux density Ba in

air, by reversing current I which the help of reversing switch. The search coil used for such measurement is called H coil. Once B0 is measured then H can be obtained as,

H = 0

0B

µA/m

Where 0µ = 4πx 10-7 H/m

Thus search coil is placed in the air gap itself if H in the air gap is to be determined. While if magnetizing force N within the ferromagnetic material specimen is to be obtained then H is measured on the surface of the specimen as the tangential components of field are of equal in magnitude for both side of the interface. While the value of H inside a specimen can be calculated as,

H = l

NIAT/m

Where l= Mean circumference of the ring inm N = Number of turns of specimen

I = Current flowing through specimen . ∴

. Determination of B-H Curve

There are two methods by which B-H curve can be obtained for the magnetic material specimen.

1. Method of reversals 2. step by step method

Method of Reversals:

A ring specimen with known dimensions is taken for the test. A thin tape is wound on the ring. The search coil insulated by the paraffined wax is wound over the tape. Another layer of tap is wound on the search coil. Then the magnetizing winding is wound uniformly on the specimen. The overall circuit used is as shown in the Fig. 46..

The complete specimen is demagnetized before the test. Using the variable resistance, the magnetizing current is adjusted to its lower value, at the beginning of the test.

The ballistic galvanometer switch K is closed and reversing switch S is thrown backward and forward for about twenty times. This brings the iron specimen into ‘reproducible cyclic magnetic state’.

The galvanometer key K is now opened and the flux in the specimen corresponding to this value of H is measured from the deflection of the ballistic galvanometer, by reversing the switch S.

The change in flux, measured by the galvanometer, when the reversing switch S is quickly reversed, will be twice the flux in the specimen, corresponding to the value of H applied. This value of H can be obtained as

H = l

NI1

Where N= Number of turns on the magnetising winding I1 = Corresponding mangetising current l= Mean circumference length of specimen in m

While the flux density B is obtained by dividing the flux measured by the area of cross-section of the specimen.

The procedure is repeated for the different values of H by increasing H upto the maximum testing point value. The graph of B against H gives the required B - H curve for the specimen.

Step by Step Method

In this method reversal of magnetizing current is not used. The magnetizing current in the winding is supplied through a potential divider as shown in the Fig. 47.

Fig.47. Step by Step Method

The potential divider has number of tapping. The tapping are arranged in such a way that the magnetizing force H increases in suitable number of steps, up to the required maximum value.

The specimen is completely demagnetized before starting Vie test. The switch S1 is closed with switch S, at tapping 1. Due to this there will be some change in the flux hence there will be increase in the flux density from 0 to B,. This value can be obtained by observing the deflection of the ballistic galvanometer.

Recording the value of corresponding magnetizing current the corresponding value of the magnetizing force H1 can be obtained.

The switch S2 is instantaneously changed to tapping 2 which increases the magnetizing force to H2. Due to this there is increase in flux and hence flux density by the amount ∆B. This can be determined from the galvanometer throw.

Hence B2 at H2 can be obtained as B1 + ∆B. The procedure is repeated for various tappings till maximum value of H is achieved. The graph of B against H is then plotted which is nothing but the B - H curve for the specimen under test. This is shown in the Fig.48.

Fig.48. B - H curve Instrument Transformers: In heavy currents and high voltage a.c. circuits, the measurement can not be done by using

the method of extension of ranges of low range meters by providing suitable shunts. In such conditions, specially constructed accurate ratio transformers called instrument

transformers. These can be used, irrespective of the voltage and current ratings of the a.c. circuits.

These transformers not only extend the range of the low range instruments but also isolate them from high current and high voltage a.c. circuits. This makes their handling very safe. These are generally classified as (i) current transformers and (ii) potential transformers.

Current Transformer (C.T.): The large alternating currents which can not be sensed or passed through normal ammeters

and current coils of wattmeter’s, energy meters can easily be measured by use of current transformers along with normal low range instruments.

A transformer is a device which consists of two windings called primary and secondary. It transfers energy from one side to another with suitable change in the level of current or voltage

. A Current transformer basically has a primary coil of one or more turns of heavy cross-sectional area. In some, the bar carrying high current may act as-a primary. This is connected in series with the line carrying high current. This is shown in the Fig. 49 (a). The bar type primary is shown in the Fig.49 (b). The secondary of the transformer is made up of a large number of turns of fine wire i.e. having small cross-sectional area. This is usually rated for 5A Current. This is connected to the coil of normal low range meter.

These transformers are basically step up transformers i.e. stepping up a voltage from primary to secondary.

Hence obviously current considerably gets stepped down from primary to secondary. For example CT. is of 500: 5 range i.e., if primary current is 500A it will reduced it to 5A on secondary. But it steps up the primary voltage 100 times.

2

1

2

1

N

N

I

I=

This is the current and number of turns, relationship for the current transformers. Hence if current ratio of CT. is known and meter reading is known, the actual high line current value can be determined.

It is very important that the secondary of C.T. should not be kept open. Either it should be shorted or must be connected in series with a low resistance coil such as current coils of wattmeter, coil of ammeter etc. If it is left open, then current through secondary becomes zero hence the ampere turns produced by secondary which generally oppose primary ampere turns becomes zero.

As there is no counter m.m.f.; unopposed primary m.m.f. (ampere turns) produce high flux in the core. This produce excessive core losses, heating the core beyond limits. Similarly heavy .e.m.fs will be induced on the primary and secondary side. This may damage the insulation of the C.T.

This is danger from the operator point of view as well. It is usual to ground the CT. on the secondary side to avoid a danger of shock to the operator.

Fig.49

Potential Transformer (P.T.)

The basic principle of these transformers is same as current transformers. The high alternating voltage are reduced in a fixed proportion for the measurement purpose with the help of potential transformers.

The construction of these transformers is similar to the normal transformer. These are extremely accurate ratio step down transformers. The windings are low power rating windings.

Primary winding consists of large number of turns while secondary has less number of turns and usually rated for 110 V, irrespective of the primary voltage rating.

The primary is connected across the high voltage line while secondary is connected to the low range voltmeter coil. One end of the secondary is always grounded for safety purpose. The connections are shown in the Fig. 50 As a normal transformer, its ratio can be specified as,

2

1

2

1

N

N

V

V=

So if voltage ratio of P.T. is known and the voltmeter reading is known then the high voltage to be measured can be determined.

Fig.50. Advantages and Disadvantages: The advantages of instrument transformers can be listed as,

1. The normal range voltmeter and ammeter can be used along with these transformers to measure high voltage and currents.

2. The rating of low range meter can be fixed irrespective of the value of high voltage or current to be measured.

3. These transformers isolate the measurement from high voltage and current circuits. This ensures safety of the operator and makes the handling of the equipments very easy and safe.

4. These can be used for operating many types of protecting devices such as relays or pilot lights.

5. Several instruments can be fed economically by single transformer.

Disadvantages: The only disadvantage of these instrument transformers is that they can be used only for a.c. circuits and not for d.c. circuits. Errors in the Instrument Transformer:

For an instrument transformers, it is necessary that the transformation ratio must be exactly equal to turns ratio and phase of the secondary terms (voltage and current) must be displaced by exactly 1800 from that of the primary terms (voltage and current). Two types of errors affect these characteristics of an instrument transformer which are,

1. Ratio error 2. Phase angle error

Ratio Error

In practice it is said that current transformation ratio I2/ I1 is equal to the turns ratio N1 / N2. But actually it is not so.

The current ratio is not equal to turns ratio because of magnetizing and core loss components of the exciting current.

It also gets affected due to the secondary current and its power factor. The load current is not a constant fraction of the primary current.

Similarly in case of potential transformers, the voltage ratio V2 /V1 is also not exactly equal to N2 / N1 due to the factors mentioned above. thus the transformation ratio is not constant but depends on the load current, power factor of load and exciting current of the transformer.

Due to this fact, large error is introduced in the measurements done by the instrument transformers. Such an error is called ratio error. The ratio error is defined as,

% Ratio error = ratioactual

ratioacturalrationormal −x100

= R

RK n −x100

Where Kn = currentondarysecrated

currentprimaryrated … for C.T.

= rated primary voltage …for P.T.

and R = currentondarysecingcorrespond

currentparimaryactual … for C.T.

= voltageondarysecingcorrespond

voltageparimaryactual .. for. P.T.

The approximate formula to calculate R is given by,

R ≈n+ 2

C

I

I

Where n = turns ratio IC= loss component of exciting current. I2= secondary current.

Now I2 = n

I1

∴ R≈n +1I

nIc≈

+

1

C

I

I1n

Where I1 = Primary current. While precisely the formula to calculate R is,

R = n+ 2

Cm

I

cosIsinI δ+δ

∴ Where Im = magnetizing component of exciting current δ = angle between secondary winding induced voltage and secondary winding current.

δ is positive for lagging p.f. and negative for leading p.f.

Phase Angle Error.

In the power measurements, it is must that the phase of secondary current is to be displaced by exactly 1800 from that of primary current for C.T.

While the phase of secondary voltage is to be displaced by exactly 1800 from that of primary voltage, for P.T. But actually it is not so.

The error introduced due to this fact is called phase angle error. It denoted by angleθ by which the phase difference between primary and secondary is different from 1800. The precise expression to calculate the angle θ is,

θ=

δ−δ

π 2

Cm

nI

sinIcosI180degree

While the approximate formula to calculate θ is,

θ=

π 2In

Im180=

π

n

Inx

I180

1

m

=

π In

I180 m degree

Similar to ratio error, this error, this error also depends on the components of exciting current (I0), load current i.e. secondary current and power factor. This error does not affect the measurements of only current or voltage but do affect at the time of power and energy measurements. Ex. 1 The no load current components of a current transformer are,

Magnetizing component = 102A. Core loss component =38A The current transformation ratio is 1000 / 5A. calculate the approximate ratio error at full load. Sol: Im = 102A, IC= 38A.

Kn = nominal ratio = 5

1000=200

At full load, I2 = 5A

∴ R= n+ 2

C

I

I= 200 +

5

38

= 207.6

∴% ratio error = R

RK n −x100 =

6.207

6.207200 −x100

Frequency Meters:

The meters which are used in the circuit to indicate the frequency of the supply are called frequency meters The frequency meters are classified based on the principle of operation as,

1. Mechanical resonance type frequency meter 2. Electrical resonance type frequency meter 3. Weston type frequency meter

The mechanical resonance type frequency meter is called vibrating reed type frequency meter. The electrical resonance type frequency meter is called ferro dynamic frequency meter.

Vibrating Reed Type Frequency Meter:

This meter works on the principle of mechanical resonance. The meter consists of number of thin steel strips called reeds. The bottom of the reed is rigidly fixed to an electromagnet. The upper part of the reed is free and bent at right angles.

This upper part is called a flag. An electromagnet has a laminated iron core, which carries an excitation coil having large number of turns. This coil is connected across the voltage whose frequency is to be measured.

The flags are painted white to have good visibility on the black background. The basic construction of this type of meter and the construction of reed is shown in the Fig.51

Fig.51. The reeds are manufactured such that their weights and dimensions are different. Hence their

natural frequencies of vibration are different.

The reeds are arranged in the ascending order of their natural frequencies and the natural frequencies are generally differ by half cycle.

So natural frequency of first reed may be 48 Hz, next may be 48.5 Hz, next may be 49 Hz and so on.

When meter is connected in the system, the coil carries current i which alternates at the supply frequency. This produces an alternating flux. This produces a force of attraction on the reeds which is proportional to square of the current i2 .

And hence all the reeds vibrate with a force which varies at twice the supply frequency. But the reed whose natural frequency is twice the frequency of supply voltage will be in resonance and will vibrate most.

The tuning in such meters is so precise that for a 1 to 2% change in the frequency away from resonating frequency, the amplitude of vibration decreases drastically and becomes negligible.

Thus when a reed corresponding to 50 Hz is vibrating with maximum amplitude, other reeds vibrate but with negligible amplitudes which can not be notice . This is s shown in the Fig.

The advantages of this frequency meter are that the reading is not affected by the changes in the waveform of the supply voltage and simple mechanism. But if supply voltage is low, the vibrations may not be noticed.

So supply voltage should not be low for the effective operation. One more limitation of the meter is that the difference in the frequencies of the adjacent reeds is 0.5 only.

So reading corresponding to less than half the frequency difference can not be obtained. So precise frequency measurement is not possible. The accuracy of the meter depends on the proper tuning of the reeds.

Electrical Resonance Type Frequency Meter:

The Fig. 52 shows the construction of the electrical resonance type frequency meter.It consists of a laminated iron core. On one end of the core a fixed coil is wound which is called magnetizing coil.

This coil is connected across the supply whose frequency is to be measured. This coil carries current which has same frequency as that of supply. On the same core, a moving coil is pivoted which carries a pointer. A capacitor C is connected across the terminals of the fixed coil.

Let I = Current through magnetizing coil φ= Flux in the iron core

The flux φ is assumed to be in phase with the current I.

This flux induces the voltage in the moving coil which always lags flux φ by 900.

Let i = Current through moving coil.

Fig.52.

The phase of the current I depends on the inductance of the moving coil and the capacitorC. Consider the different cases and the corresponding phasor diagrams to understand the working of the meter, as shown in the Fig.53 (a), (b) and (c).

Fig.53 In Fig.53 (a) the circuit of moving coil A is assumed to be inductive, hence current I lags the

induced voltage e by angle α . Hence the torque acting on the moving coil is given by, Td α I I cos (90+α ) ….(1)

In Fig. 53 (b) the circuit of moving coil A is assumed to be largely capacitive, hence current i leads the induced voltage e by angle β . Hence the torque acting on the moving coil is given

by, Td α i cos (90-β ) …(2)

This torque is in opposite direction to the torque, produced in case of inductive nature of the moving coil circtuit.

The Fig.53 (c) shows the resonance condition where the inductive reactance is equal to the capacitive reactance. So current i is in phase with e a1d, the torque acting on the moving coil is given by,

Td α I i cos (900) = 0 Hence under resonance condition, torque acting on the moving coil is zero.

Now the capacitive reactance XC=C

1

ω=

fC2

1

π is constant for a given frequency.

But the inductive reactance XL = ωL not only depends on the frequency but also depends on the position of the moving coil on the core. Nearer the moving coil to the magnetizing coil, higher is its inductance.

Thus for a given frequency, moving coil moves in such a way to achieve a position where XL =XC and electrical resonance is achieved. At this position, torque on the moving coil is zero anal the pointer indicates the corresponding frequency.

The design of the instrument is such that for a normal frequency, the coil takes a mean position. The capacitor C is chosen is chosen such that electrical resonance takes place at this mean position and pointer indicates the normal frequency.

If frequency is higher than the normal value, then XC =fC2

1

π decreases. Hence XL= 2π fL must

decrease in order to achieve resonance. So moving coil moves away from the magnetizing coil on the core and pointer moves to the right of the mean position, indicating higher frequency.

If frequency is lower than normal value, XC =fC2

1

π increases. So to achieve XL = XC, the

moving coil moves towards the magnetizing coil where inductance increases. Thus pointer moves to the left of the mean position, indicating the lower frequency.

An important advantage of the instrument is that the great sensitivity is achieved as the inductance of the moving coil changes slowly with variation of its position on the core. This meter is also called Ferro-dynamic frequency meter.

Weston Frequency Meter:

This is moving iron type instrument. It works on the changes in current distribution between two parallel circuits, one of which is inductive and other non inductive, when the frequency changes.

This is due to the fact that the impedance of the inductive circuit changes with the change in the frequency. (XL =27π fL) The Fig. 54 shows the constructional details of the Weston frequency meter. It consists of two fixed coils, each divided in two parts A1-A2 and B1-B2.

The axes of the two coils are mutually perpendicular to each other. At the centre of the axes, a soft iron needle is pivoted which is thin and long. The needle carries a pointer and damping vanes. There is no controlling device to produce controlling torque.

Fig.54. The coil A is connected in series with an inductor LA across a noninductive resistance RA. The

coil B is connected in series with a noninductive resistance RB across an inductance LB. The resistance RA and LB are in series with another inductor L and the combination is across

the supply voltage. The main purpose inductor L is for damping out the harmonics in the waveform of the current. This eliminates the errors caused due to the harmonics.

When the meter is connected across the supply, both the coils carry currents. The two magnetic fields produced by the two currents are at right angles to each other.

These fields act upon the soft iron needle, causing its deflection. So position of needle and hence the pointer depends on the currents through the coils A and B.

In practice, the values of RA, RB, LA and LB are so chosen that the equal currents flow through the coils and needle takes the mean position, which indicates the normal frequency.

If the frequency increases above the normal value, then reactance’s LA and LB increase while noninductive resistances RA and RB remain same. So impedance of the coil A increases. Hence the current through coil A is reduced. While voltage drop across RA remains same.

While the current through coil B increases due to its parallel combination with coil A. This makes the magnetic field produced by coil B more stronger. So the needle moves in such a way that it lies more nearly parallel to the axis of the coil B. So needle tries to become vertical and pointer deflects to the right indicating higher frequency.

When the frequency decreases than the normal value, the opposite action takes place and pointer deflects to the left.

Digital Frequency Meter:

The signal waveform whose frequency is to be measured is converted to trigger pulses and applied continuously to one terminal of an AND gate. To other terminal of the gate a pulse of 1 sec is applied as shown in the Fig.55. The number of pulses counted at the output terminal during period of I sec indicates the frequency.

Fig.55. The signal whose frequency is to be measured is converted to trigger pulses which is nothing

but train of pulses with one pulse for each cycle of the signal. At the output terminal of AND gate, the number of pulses in a particular interval of time are

counted using an electronic counter. Since each pulse represents the cycle of the unknown signal, the number of counts is a direct

indication 'of the frequency of the signal which is unknown. Since electronic counter has a high speed of operation, high frequency signals can be measured.

The basic block diagram of digital frequency meter is as shown in Fig. 56.

Fig.56 The signal waveform whose frequency is to be measured is first amplified. Then the

amplified signal is applied to the schmitt trigger which converts input signal into a square wave with fast rise and fall times.

This square wave is then differentiated and clipped. As a result, the output from the schmitt trigger is the train of pulses for each cycle of the signal. The output pulses from the schmitt trigger are fed to a START/STOP gate.

When this gate is enabled, the input pulses pass through this gate and are fed directly to the electronic counter, which counts the number of pulses. When this gate is disabled, the counter stops counting the incoming pulses.

The counter displays the number of pulses that have passed through it in the time interval between start and stop. If this interval is known, the unknown frequency can be measured.

Frequency Measurement: The basic block diagram of an electronic counter with its function switch set to measure the

frequency of input signal is as shown in Fig. 56. The input signal is first applied to the signal shaper circuit. This converts the input signal to

the uniform pulses. The input signal is in the form of continuous wave or pulses. The number of pulses summed in decade counting assemblies for selected period of time represents the frequency of input signal.

The numeric readout gives the counted frequency. The readout is with decimal point and it is maintained till next sample is taken. The rate of sampling determines the time for displaying measured frequency, initiates the counter reset in next measurement cycle.

The gating interval depends on the time base selector switch. The decimal point and appropriate unit is also depends on selector switch.

Fig.56

Phase Meter:

The phase meter is a device which measures the phase difference between the two signals. In

the simplest method of phase measurement, one of the two signals is used as a reference

signal.

A zero center galvanometer is used for deflection. When the signal is applied, the indicating

galvanometer deflects depending on the phase relationship of that signal with the reference

signal.

The Fig. 57 shows the phase sensitive detector i.e. phase meter.

Let VS = signal voltage

Vr = reference signal voltage

For the first half cycle, the instantaneous polarity of Vr causes the rectified current to flow

through the rectifier diode DI. This produces positive voltage drop across RI as shown in the

Fig. 57 (a). Due to this meter deflects to the right.

Fig.57.

In the second half cycle, the polarity of Vr changes. Thus the current flows through diode D2. This causes a positive voltage drop across R2 as shown in the Fig.57 (b). The meter deflects to the left.

Infact as these two deflections are equal and opposite, the average deflection of a meter over a full cycle is zero, when the input VS =0.The two diodes D1 and D2 are providing the rectifier action.

Now consider that the input signal voltage VS is applied. This voltage helps or opposes the voltage Vr, depending upon whether it is in phase or out of phase with it.

If it is in phase with Vr, the signal voltage will help the instantaneous a.c. voltage in the upper half of the transformer secondary. This will produce the large current through diode D1 and hence large d.c. output voltage across R1.

As long as VS is less than Vr, the diode D2 will not conduct. Thus voltage in upper half is VS + Vr while in lower half it is VS - Vr .

In the next half cycle, VS polarity is reversed. D1 now stops conducting. VS will oppose the instantaneous a.c. voltage to produce small d.c. voltage across R2. The galvanometer deflects to the right indicating that the VS is in phase with Vr.

If VS is 1800 out of phase, then the two voltages aids each other in the lower half on the

transformer secondary. Thus the galvanometer deflects to the left proportional to the magnitude of the input signal. As the method uses voltage addition principle, it is called as voltage addition method of phase

measurement. The advantages of this method are : i. The method is very simple. ii. The value of the input signal voltage VS can be calculated.

The disadvantages of this method are:

i. The phase difference of 1800 or in phase condition only can be detected. Other phase angles cannot be measured.

ii. The accuracy is poor. To overcome these disadvantages the digital phase meter is used.

Digital Phase Meter: This meter uses two flip-flops. The two signals of the same frequency are applied to the

meter. In this meter, both the signals are shaped to a square waveform, without any change in

their phase relationship, which is required to be measured.

The function of two flip-flops is that the one enables the output control gate while the other

disables the output control gate.

The number of pulses allowed to pass during enabling and disabling the gate are counted

which are proportional to the phase difference between the two signals.

The schematic block diagram of the digital phase meter is shown in the Fig. 58.

Fig.58. It consists of two pre-amplifiers, zero crossing detectors, J-K flip-flops and an output control

gate. The phases of the two input signals are 0φ and xφ . The frequency of the inputs is same.

As 0φ signal increases in the positive half cycle, when it crosses zero, the zero crossing

detector senses the zero crossing and changes its state. This causes first J-K flip flop to be set (1), and its output Q becomes high.

This enables the AND gate and thus output gate is enabled which allows the clock pulses to fed directly to the counter. Now 0φ is having a certain phase difference with respect to 0φ .

This means, it will cross zero, after the 0φ crosses the zero. This zero crossing of 0φ is

detected by second zero crossing detector which causes its state to change. Thus the output of second J-K flip-flop goes high. This is connected to the clear input of first J-K flip-flop. This resets the first J-K flip-flop and output Q of J-K flip-flip one goes low (0). Due to this AND gate is disabled and counter stops counting.

The number of pulses counted while enabling and disabling of AND gate is directly proportional to the phase difference.

The display unit displays accurately the phase difference between the two signals. For accurate measurements, if input signal frequency is f, then the clock frequency must be 360 times the input frequency.

The advantages of the method are : i) High accuracy. ii) Any phase angle difference can be detected and measured. iii) The speed of operation is fast. iv) The circuit is simple to design.

The disadvantages of the method are : i) Both inputs must have same frequency. ii) It is difficult to measure small phase differences. iii)For very accurate results, the clock frequency should be 360

times the input frequency.

No Analog type Digital type 1 This is called balanced modulator

method This is called filp-flop method.

2 Accuracy is very less Accuracy is high as 0.10 can be achieved.

3 Less stable and sensitive Highly stable, sensitive and reliable.

4 D.C. meter is used at output Display unit is used at output. 5 The output meter swings proportional

to phase difference The number of pulse counted are proportional to phase difference.

6 The input signal can be directly applied

Input signal must be converted to square wave.

7 Clipper circuit is absent. The slew rate of clipper circuit may cause some error.

8 The clock is not required as deflection of output meter indicates phase difference.

The clock is required to gate direct indication of phase angle in degrees.

Ex. 2.29: In a phase meter circuit as shown in Fig.2.110, the voltages E1 and E2 are 10 volt (RMS) and 15 volt (RMS). Find the output voltage neglecting the voltage drop in the diodes, when the phase difference between E1 and E2 is 60

0. The frequency of E1 and E2 is 1000Hz. FIGURE Sol: The given values are E1 = E1m sin ωt E2 = E2m sin (ωt-60)

E1m = E1rms x 2

= 10 2

E2m = E2 rms x 2

= 15 2 In the positive half cycle, the voltage across AB is proportional to E1+E2. Hence its average value is,

E+ = ∫π

π0

m1E2

1sin ωt+ ∫

π

π0

m2E2

1sin (ωt-60)

= π2

1 [ ] [ ][ ]ππ −ω−+ω− 0m20m1 )60tcos(EtcosE

= π2

1 [ ] [ ][ ])60cos()120cos(E11E m2m1 −+−++

=π2

1[2E1m+E2m]

In the negative half cycle the output is proportional to E1= E2 .

∴ E- =π2

1[2E1m- E2m]

∴EAB= E+ - E_ =π2

1[2E1m +E2m-2E1m+E2m]

= π

=π

215

2

E2 m2

= 6.752V. Adjustments in Energy meter: The adjustments are require in the energy meters so that they read accurately with minimum possible errors.

i) Main Speed adjustment: The measurement of energy is dependent on the speed of the rotating disc. For accurate measurements, speed of the disc must be also proportionate. The speed of the meter can be adjusted by means of changing the effective radius of the braking magnet shown in Fig 2.31. moving the braking magnet in the direction of the spindle, decreases the value of the effective radius, decreasing the banking torque. The increases the speed of the meter. While the movement of the braking magnet in the outward direction i.e. away from the centre of the disc, increases the radius, decreasing the speed of the disc. The fine adjustments of the speed can be achieved by providing and additional flux diverter.

ii) Power factor adjustment It is absolutely necessary that meter should measure correctly

for all power factor conditions of the loads. This is possible when the flux produced due to current in the pressure coil lags the applied voltage by 900. But the iron loss and resistance of winding do not allow flux to lag by exact 900 with respect to the voltage.

To have this adjustment, the shading ring called quadrature loop is provided on the centre limb of shunt magnet carrying pressure coil. The find adjustments can be achieved by the movement of this loop upwards or downwards and meter can be made to read accurately at all the power factors.

iii) Friction adjustment Inspite of proper design of the bearings and registering mechanism, there is bound to exist some friction. Due to this speed of the meter gets affected which cause the error in the measurement of the energy.

To complete for this, a metallic loop or strip is provided between central limb of shunt magnet and the disc. Due to this strip an additional troque independent of load in produced which acts on the disc in the direction of rotation. This compensates for the friction and meter can be made to read accurately. This is shown as L2 in the Fig. 2.31.

iv) Creep adjustment It is seen that, without any current through current coil, disc rotates due to the supply voltage exciting its pressure coil. This is called creeping. This creeping may be because of over friction compensation.

To eliminate this, two holes are drilled in the disc 1800 opposite to each other. When this hole comes under the shunt magnet pole, it gets acted upon by a torque opposite to its rotation. This restricts its rotation, on no load condition. These adjustments are almost similar though meter is single phase, two element three phase or three element three phase energy meter.

Servo Potentiometric Type DVM : In the potentiometric type voltmeters internal reference voltage is provided. The reference voltage is denoted as Vref. The voltage to be measured is the input voltage and is denoted asVin. A voltage comparison technique is used to measure the input voltage. The unknown voltage is compared with the reference voltage with the help of the setting of the calibrated potentiometer ie. Potential divider. The arm of the potentiometer is varied to obtain the null condition i.e. balancing condition . The internal reference voltage is present at the two terminals of the potentiometer. When the null condition is obtained, the value of the unknown voltage is indicated by the dial setting of the potentiometer. The basic principle of potentiometer voltmeter Magnetic Potentiometer: The device used to measure the magnetic potential between any two points in a magnetic field is called magnetic potentiometer. It consists of uniform helix of a thin wire wound on a thin strip of some flexible insulating and non-magnetic material. This is used along with the ballistic galvanometer for the measurement of magnetic potential. The arrangement of magnetic potentiometer is shown in the Fig. 2.89. FIGURE The coil of thin wire is wound on a flexible non-magnetic material. The two ends 1-1’ of the coil are to be connected to a ballistic galvanometer. The two ends of the non-magnetic material strip are placed at the two points between which the magnetic potential is to be measured. The corresponding deflection of the ballistic galvanometer is to be observed, when the flux through the specimen is reversed. According to Ampere’s circuit law, the line integral of the magnetizing force H produced by a coil of N turns carrying current 1 is,

∫ dlH = NI around any closed path linking coil

This principle is used in magnetic potential measurement. Let A = Area of the flexible strip in m2 n = Number of turns per unit length of the strip H = Field strength at any point in tangential direction at that point in A/m. R = Resistance of ballistic galvanometer circuit. Then the flux linkages of a small infinitesimal part of the strip of length d/are, ψ= flux x turns = ( 0µ HA) ndl

φ=BA = 0µ HA and turns = ndl

Hence total flux linkages of the strip can be obtained as,

ψ T= ∫ 0µ HA ndl = 0µ A n ∫ Hdl

The integral is to be taken between the ends of the strip.when the flux is reversed the total change in the flux linkages is given by,

= 2 0µ An ∫ Hdl

But ∫ Hdl= in ς time t

Now Q = charge = it= R

et

∴ Q = CR

An2t.

R

1.

t

An2 00 ςµ

ςµ

But the galvanometer deflectionθ ’ is proportional to charge.

∴ Q = Kθ ’

∴ R

An2 0 ςµ= Kθ ’

∴ An2

'RK

0µ

θ=ς where K is galvanometer constant.

K can be determined by the calibrating coil. Such a potentiometer is used for the measurement of the magnetic potential drop across a given part of a magnetic circuit such as a joint, the measurement or magnetic leakage or measurement of m.m.f. around a closed path. The important advantage of the device is that the results are same whether the strip on which the helix is wound is straight or of other shape.

As the method does not give uniform values of H over the entire length AB and hence method is rarely used in practice for direct measurement of H. the potentiometer is also called Chattock magnetic potentiometer. Measurement of Leakage Factor:

In the electrical machines and other devices, the flux crossing the air gap is called useful flux while the flux in the actual pole is called total flux. The useful flux is less than the total flux due to leakage flux. The leakage is specified by -i facto: called leakage factor which is the ratio of the total flux to the useful flux denoted as λ .

λ= fluxUseful

fluxTotal

So to measure leakage factor, the flux crossing the air gap and reaching the armature from pole must be measured along with the measurement of flux in the pole bodies. This is possible by the flux meter. The ballistic galvanometer is not suitable for such measurements due to high inductance of the field winding. The arrangement for such measurement is shown in the Fig. 2.90.

The yoke of the machine carries the total flux produced by the field winding would on the

poles. Two search coils are wound on the yoke of the machine, one each on the either side of the pole as shown in the Fig. 2.90. Though the yoke carries total flux, there exists half of the total flux on

either side of the poles. Hence to measure the total flux the two search coils are connected in series. The coils are connected to the fluxmeter which gives the total flux of the machine.

The flux which reaches to the armature through air gap is called useful flux. A search coil is placed on the stationary armature such that it is in contact with the entire useful. It is then connected to the fluxmeter which gives the reading of the useful flux.

The ratio of the two readings thus obtained, is the leakage factor of the machine. The search coils with only one turn are preferred in such measurements so that flux meter directly gives the reading of the required flux. Ex. 2.21: A moving coil ballistic galvanometer of 200Ω resistance gives a throw of 70 divisions when the flux through a search coil to which it is connected is reversed. Find the flux density given that the galvanometer constant is 100µ C per division and the search coil has 1200 turns, a mean area

of 60 cm2 and a resistance of 15Ω . Sol : K = 100µ C/division, θ ’ = 70, N = 1200, A = 60cm2

R = Total resistance = 200 +15 = 215Ω .

B = NA2

'RKθ=

4

6

10x60x1200x2

70x10x100x215−

−

= 0.1045 Wb /m2 Ex. 2.22: A ring specimen has a mean length of 1m, with a cross- sectional area of 300 mm2. It is wound with the magnetizing winding having 120 turns. The search coil has 180 turns and is connected to a ballistic galvanometer having constant of 1.5 µ C per scale division. The total

resistance of the galvanometer circuit is 1500Ω . On reversing a current of 10A in the magnetizing winding the galvanometer shows a deflection of 75 scale divisions. Calculate the flux in the specimen and value of relative permeability at this flux density. Sol: Total m.m.f. of coil = N1 I1 =120 x 10=1200 AT.

H = l

1200

l

NI= = 1200 AT/m.

Charge through galvanometer is, Q = Kθ ’= 1.5x 10-6 x75= 1.125x 10-4 C. Now φ is the flux through the ring

Flux linkages of search coil, ψ= N2φ= 180φ .

Change in flux linkages due to reversal of current is, ∆ ψ=2(180φ ) = 360φ .

e= t∆

ψ∆=

t

360

∆

φwhere ∆ t = time of reversal

i = R

e=

t1500

360

∆

φ=

t

24.0

∆

φA

charge through search coil is, Q = i∆ t = 0.24φ C

Equating the charges, 0.24φ = 1.125x 10-4

∴ φ =4.6875x 10-4 Wb

∴ B = A

φ=

6

4

10X300

10X6875.4−

−

= 1.5625 Wb/m2

and B= µ H.

∴ µ = r0 µµ

∴ rµ = 0µ

µ=

7

3

10x4

10x3021.1−

−

π=1036.165 ≈ 1037.

Ex.2.23 :A ballistic galvanometer has a circuit resistance of 4000Ω and a constant of 0.1µ C per scale

division is connected one after the other in two parts of d.c machine. 1. With a coil of 2 turns wound round the field coil of a d.c. machine, producing 110 divisions

reading on galvanometer. 2. with armature surface with 3 turns, measuring flux entering the armature, producing 140

divisions reading on galvanometer. The reading are obtained by breaking the normal field current. Calculate the flux per pole and leakage coefficient. Soil : Let φ be flux linking with a search coil of N turns.

∴flux linkagesψ=Nφ .

The field current is broken to flux becomes zero in time∆ t. ∆ ψ=Nφ in time ∆ t

e = t∆

ψ∆=

t

N

∆

φ

i = R

e=

tR

N

∆

φ

Q= I x ∆ t= R

Nφ

But for a galvanometer charge is given by, Q = Kθ ’

Kθ ’=R

Nφ

φ=N

R'Kθ

i) For field coil i.e. pole flux, N =2, θ ’= 110.

∴ φ t= 2

4000x110x10x1.0 6−

=0.022 Wb.

ii) For armature flux, N =3, θ ’= 140.

∴ φ a=3

4000x140x10x1.0 6−

x 0.0186 Wb.

Thus flux per pole is 0.022 Wb i.e. total flux and useful flux is 0.0186 Wb.

∴ λ= Leakage factor = a

t

φ

φ=

0186.0

022.0= 1.1828.

Measurement of Power Using C.T. and P.T. The wattmeter to measure power in high voltage and current circuit is connected using

instrument transformers as shown in the Fig. 2.96.

The primary winding of C.T. is connected in series with the load and secondary is

Connected in series with an ammeter and the current coil of a wattmeter. The primary winding of P.T. is connected across the supply and secondary is connected across voltmeter and the pressure coil of the wattmeter. One secondary terminal of each transformer and the casing's are grounded.

Use of C.T and P.T in Energy Measurement: The single phase energy meter connections are similar to the connections of a wattmeter along with C.T and P.T for power measurement as shown in Fig. 2.54. The pressure coil of wattmeter is replaced by pressure coil of energy meter and current coil of wattmeter is replaced by current coil of energy meter.

But three phase energy meter connections along with C.T. and P.T. are little bit different than single phase but the basic principle of extending the ranges by using CT. and P.T. remains the same. Reduction of Ratio and Phase Angle Errors: The ratio and phase angle errors can be minimized by using following methods.

1. As the errors depend on components of exciting current, reduce the magnetizing and loss components of exciting current. This requires to provide smaller magnetic path, good core material and low flux density in core.

2. Reduction of resistance and leakage reactance. The values decide the secondary circuit power factor which affects the errors. This can be achieved by providing thick conductors and smaller length of mean turn.

3. Providing turns compensation at no load the actual ratio exceeds the turns ratio thus the solution to this is to reduce primary turns or increasing secondary turns and to make actual ratio equal to nominal ratio for one particular value of load.

Ex. 2 A current transformer has a single turn primary and 400 secondary turns. The magnetizing current is 90A while core loss current is 40A. secondary circuit phase angle is 280. Calculate the actual primary current and ratio error when secondary carries 5A current. Sol Im = 90A, IC = 40A, δ = 28

0, I2= 5A

n = 1

400= 400

∴Kn = n = 400

Now actual ratio R = n+ 2

Cm

I

cosIsinI δ+δ

= 400+ 5

28cosx4028sinx90 +

= 415514. actual primary current = actual ratio x I2 = 415.514x 5 = 2077.5703

∴ration error = R

RK n −x100 =

415514

415514400 −x100

Ex. 2.28 A current transformer has turns ratio 1 :399 and is rated as 2000/5A. The core loass component is 3A and magnetizing component is 8A, under full load conditions. Find the phase angle and ratio errors under full load condition if secondary circuit power factor is 0.8 loading. Sol: IC = 3A, Im = 8A, cosδ = 0.8 leading

n = 1

399= 399

nominal ratio = Kn = 5

2000=400

actual ratio = R =n+ 2

Cm

I

cosIsinI δ+δ

rated I2 = 5A. δ = cos-1 0.8 = -36.860 … negative as leading ∴ sin δ = sin (-36.860) = -0.6

∴ R = 399 + 5

8.0x3)6.0(x8 +−

= 398.52

∴% ratio error = R

RK n −x100 =

52.398

52.398400 −x100

= 0.3713%

And θ =

δ−δ

π 2

Cm

nI

sinIcosI180

=

−−

π 5x399

)6.0(x38.0x8180

= 0.23550 Digital Frequency Meter

The signal waveform whose frequency is to be measured is converted to trigger pulses and applied continuously to one terminal of an AND gate. To other terminal of the gate a pulse of 1 sec is

applied as shown in the Fig.2.104. The number of pulses counted at the output terminal during period of I sec indicates the frequency.

FIGURE

The signal whose frequency is to be measured is converted to trigger pulses which is nothing

but train of pulses with one pulse for each cycle of the signal. At the output terminal of AND gate, the number of pulses in a particular interval of time are counted using an electronic counter. Since each pulse represents the cycle of the unknown signal, the number of counts is a direct indication 'of the frequency of the signal which is unknown. Since electronic counter has a high speed of operation, high frequency signals can be measured.

The basic block diagram of digital frequency meter is as shown in Fig. 2.105. FIGURE

The signal waveform whose frequency is to be measured is first amplified. Then the amplified signal is applied to the Schmitt trigger which converts input signal into a square wave with fast rise and fall times. This square wave is then differentiated and clipped. As a result, the output from the schmitt trigger is the train of pulses for each cycle of the signal. The output pulses from the schmitt trigger are fed to a START/STOP gate. When this gate is enabled, the input pulses pass through this gate and are fed directly to the electronic counter, which counts the number of pulses. When this gate is disabled, the counter stops counting the incoming pulses. The counter displays the number of pulses that have passed through it in the time interval between start and stop. If this interval is known, the unknown frequency can be measured.

Review:

The Schmitt trigger which converts input signal into a square wave with fast rise and fall

times.

The primary winding of C.T. is connected in series with the load

The useful flux is less than the total flux due to leakage flux

A special ballistic galvanometer with very small controlling torque and high electro-magnetic

damping is used as a flux meter.

Questions for Discussion:

Choose The Best Answer 1. The hot wire ammeter a) Is used only for dc measurements b)is used only for dc measurements c) give same deflection for ascending and descending values d) Reads equally well on dc and / or ac circuits 2. A wattmeter is reading backward upscale reading can had by reversing a) Connections of CC only b) connections of PC only c) either A and B d)both A and B 3. In an inductance type energy meter a) There is no brake magnet b) there is a control spring c) disc revolves continuously d) There is no temperature error 4. Creeping is the phenomenon which occurs in a) Voltmeter b) wattmeter c) energy meter d) ammeter 5. Most commonly used ac bridge circuit for the measurement of capacitance is a) Maxwell Wien bridge b) Kelvin’s bridge c) De Sauty bridge d)Schering bridge

Answers: 11. (d) 12. (c) 13. (c) 14.(c) 15.(d)

Fill in the Blanks 6. Induction type energy meters are free from ------------------------- errors.

7. Maximum demand indicated operates on the principle of ---------- -----.

8. Reed frequency meter is, essentially a ----------------- measuring system.

9. Power factor meter has ------------------control spring(s) .

10. For accurate measurement of low resistances ------------.

is used

Answers: 6. Frequency 7. Thermal lag 8. Vibrating 9. No 10. Kelvin’s double bridge

True or False: 11. Moving iron instruments are free from ageing errors

12. Permanant magnet moving coil instrument is the most accurate

and useful for dc measurement

13. In three phase power measurement by two what meter method, if one of

the wattmeter indicates negative reading, the load should be capacitive

14. A dynamometer type wattmeter can be used for dc only

Answers:

11. False 12. True 13. False 14.False

Question Bank: TWO MARKS:

1. State the principle of digital voltmeter. (2)

2. Give the importance of iron loss measurement. (2)

3. List two instruments for measurement of frequency. (2)

4. Write the function of instrument transformer. (2)

5. Brief the principle of digital phase meter. (2)

6. Write any two advantages and disadvantages of digital voltmeter. (2)

7. Explain the purpose of Schmitt trigger in digital frequency meter. (2)

8. Which torque is absent in energy meter? Why? (2)

9. What are the errors that take place in moving iron instrument? (2)

10. Explain the principle of analog type electrical instruments. (2)

11. How a PMMC meter can be used as voltmeter and ammeter? (2)

12. What is loading effect? (2)

13. State the basic principle of moving iron instrument. (2)

14. Why an ammeter should have a low resistance? (2)

15. Define the sensitivity of a moving coil meter. (2)

16. Why PMMC instruments are not used for ac measurements?(2)

17. What is a transfer instrument?(2)

18. What is meant by true RMS meter?(2)

19. List the types of DC and AC bridges?(2)

20. What is meant by Measurement? (2)

21. How are instruments classified?(2)

22. What is an absolute instrument? Give examples.(2)

23. What is a secondary instrument? Give examples.(2)

24. How are the errors classified?(2)

25. What is Permanent Magnet Moving coil(PMMC)meter?(2)

26. List the advantages and disadvantages of PMMC meter.(2)

27. Why MI instruments can be used on both AC and DC?(2)

28. What are the errors that occurs in MI instruments?(2)

29. What is true RMS meter?(2)

30. Define leakage factor. (2)

31. What are the precautions taken while using a DC voltmeter and DC

32. Ammeter? (2)

33. What is the use of Multimeter? Write its advantages and disadvantages. (2)

34. Voltmeter has high resistance, why it is connected in series? (2)

35. What is an energy meter? Mention some advantages and disadvantages

36. of energy meter. (2)

37. What is meant by creep adjustment in three phase energy meter? (2)

38. List some advantages and disadvantages of electrodynamic instrument. (2)

39. List the advantages of electronic voltmeter. (2)

40. What is a magnetic measurements and what are the tests performed for

41. Magnetic measurements? (2)

42. Mention the advantages and disadvantages of flux meter. (2)

43. What are the methods used to determine B-H Curve? (2)

44. What are the errors in instrument transformers? (2)

45. What is frequency meter and classify it? (2)

46. What is phase meter and what are its type? (2)

47. Differentiate ammeter an voltmeter. (2)

PART – B (12 Marks)

1. (i) Describe the construction and working of a permanent magnetic moving

coil instruments. (8)

(ii) Explain the design of three phase wattmeter and give the reactive

power measurement in 3 phase circuits. (4)

2. (i) How B-H curve is determined for a ring specimen. (12)

3. Discuss why it is necessary to carry out frequency domain analysis of

measurement systems? What are the two plots obtained when the

frequency response of a system is carried out? (12)

4.Explain the function of three phase wattmeter and energy meter. (12)

5.Sketch the circuit and waveforms for ac voltmeter using a PMMC

instrument and half wave rectifier. Explain the circuit operation. (8)

(ii) Develop the torque equation for a PMMC instrument and show its scale

is linear. (4)

6. (i) Discuss in detail the working of the successive approximation DVM.(6)

(ii) With a neat diagram, explain the various methods of magnetic

Measurements. (6)

7. (i) Explain with a neat sketch the construction and working principle of

Single-phase induction type energy meter. 8)

(ii) How the range of d.c ammeter and d.c voltmeter can be extended?

Derive the expressions to calculate shunt resistance and multiplier

Resistance. (4)

8. (i) With a neat diagram explain the construction and working of

Electrodynamometer type instruments. Also derive its torque equation.(8)

(ii) Explain with neat diagram the working of Linear ramp type DVM. (4)

9. (i) Explain the different methods of determination of B –H curve (6)

(ii) With a neat block diagram explain the working principle of digital

frequency meter. (6)

10. (i) Explain the working principle of moving iron instrument. (6)

(ii) Give a detailed notes on Instrument transformers. (6)