A-10

Figure A.7: Basic parts of a permanent-magnet, moving-coil (d'Arsonval) meter.a) Schematic diagram, (b) Pictorial diagram

A.3 Additional Instrument Theory

The three most common types of meters used in the power laboratory are DC Voltmeters andAmmeters, AC Voltmeters and Ammeters, and Wattmeters.

A.3.1 Basic DC Meters

Many dc meters use the d’Arsonval (pmmc) meter movement which measures current. The additionof aeries resistance allows the measurement of voltage. The addition of a battery allows themeasurement of resistance.

A.3.1.1 The Permanent-Magnet, Moving-Coil Meter Movement (pmmc)

Many direct-current ammeters and voltmeters are designed to measure current and voltage by makinguse of the well-known fact that when a current-carrying conductor is placed in a magnetic field, aforce is exerted on the conductor. Furthermore, the force is directly proportional to the current. Theway direct-current ammeters and voltmeters make use of this interaction between the magnetic fieldand the current is best described with the aid of the diagrams in Figure A.7. The current to bemeasured is passed through the movable coil, where it reacts with the magnetic field of the permanentmagnet, thus creating a torque on the coil. The coil rotates until the torque on it is balanced by therestoring spring. This spring is designed so that its torque is directly proportional to the anglethrough which the coil rotates, and the uniform magnetic field is oriented so that the force on the coilis always perpendicular to its axis. Thus, the deflection of the pointer is directly proportional to thecurrent in the movable coil. The numerical value of the current is read from a calibrated scale placedat the end of the pointer.

One of the most important characteristics of the permanent-magnet moving-coil instrument is thata given coil, or meter movement, can be used to measure a wide range of currents and voltages. Therange of the meter is controlled by the choice of resistors, which are electrically connected to themoveable coil. In the next section we will show how a given meter movement can be used to buildeither an ammeter or a voltmeter.

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Figure A.8: Basic DC Ammeter Circuit

Figure A.9: 10 mA Example

A.3.1.2 The DC Ammeter Circuit

The basic direct-current ammeter circuit consists of a pmmc meter movement in parallel with aresistor, as shown in Figure A.8. The purpose of the shunting resistor R is to control the amount ofs

current passing through the meter movement. Thus the shunting resistor R and the meter movements

can be thought of as forming a current-dividing circuit.

The design of the ammeter circuit is based on themaximum current that is to be read by the meter andthe electrical characteristics of the meter movement.Meter manufacturers specify the electricalcharacteristics of a meter movement by giving themovable coil a voltage and current rating. Forexample, one commercially available meter movementis rated at 50 mV and 1 mA. The significance of theseratings is as follows: when the coil is carrying itsrated current, the pointer is deflected to its full-scaleposition and the voltage drop across the coil is the

rated coil voltage. The current and voltage rating of the coil also specifies the resistance of the coil.For example, a 50 mV, 1 mA coil has a resistance of 50 6.

We will demonstrate the function of the ammeter circuit by showing how we can use a 50 mV, 1 mAmeter movement to measure a current of 10 mA. Since the meter movement can handle only 1 mA,we must divide the 10 mA total current into two components of 1 mA and 9 mA. Obviously, the 9mA must pass through the shunting resistor R . s

Our problem is depicted schematically in Figure A9where Kirchhoff's voltage law requires:

9 x 10 x R = 1 x 10 x 50-3 -3s

or R = 50/9 = 5.555 6S

Thus with a shunting resistance of 5.555 6, the 50mV, 1 mA meter movement becomes a 10 mA (full-scale) ammeter. Note also that the current through themeter movement will always be directly proportionalto the current being measured, so that the ammeter

will correctly read currents less than 10 mA. For example, if the measured current drops to 5 mA,the current in the meter movement drops to 0.5 mA.

In the next section, we will show how the pmmc meter movement can be combined with an externalresistor to form a voltmeter.

50 ×103

50 × 50RV � 50

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Figure A.10: Basic DC Voltmeter Circuit

A.3.1.3 The DC Voltmeter Circuit

When the pmmc meter movement is used to measure direct-current voltages, the movement isconnected in series with a resistor as shown in Figure A.10. The purpose of the series resistor R isv

to limit the voltage applied to the meter movement. Thus, the series resistor R and the meterv

movement can be thought of as forming a voltage-divider circuit, which divides the voltage at theterminals of the voltmeter to a value within the voltage rating of the meter movement.

To illustrate the design of a voltmeter, let us calculatethe numerical value of R that is necessary to make av

50 mV, 1 mA movement read 150 V at full-scale.Since full-scale deflection requires 50 mV to beapplied to the meter movement and the metermovement has a resistance of 50 6, the voltage-dividerequation is:

From which we obtain:

R = 150,000 - 50 = 149,950 6V

It is important to note that once R has been selected on the basis of the full-scale voltage reading,v

the meter will correctly read voltages between zero and full-scale. For example, if the voltage dropsto 50 V at the terminals of the voltmeter, it will drop to (50/150) x 50 mV at the terminals of themeter movement. Thus, the meter will deflect to 1/3 of full-scale and correctly indicate 50 V.

A.3.1.4 Meter Insertion Disturbance

It is important to keep in mind that the insertion of either an ammeter or a voltmeter into a circuitdisturbs the circuit in which the measurement is being made. An ammeter adds resistance in thebranch in which the current is being measured, while a voltmeter adds resistance across the terminalswhere the voltage is being measured. How much the meters disturb the circuit in which themeasurements are being made depends on the resistance of the meters in comparison to theresistances of the circuit. For example the 10 mA ammeter circuit discussed in the previous sectionwill add a resistance of (50 x 10 )/(10 x 10 ) or 5 6 in any branch where it is inserted. If the-3 -3

resistance of the branch without the ammeter is in the k6 range, the insertion of the ammeter willhave a negligible effect. If, however, the resistance of the branch is of the same order of magnitudeas the ammeter resistance, the insertion of the meter could have a significant effect on the current inthe branch. In this latter case the current measured by the ammeter would not be the same as thecurrent in the branch without the ammeter.

The loading effect of a voltmeter depends on the resistance of the voltmeter in comparison with theresistance the voltmeter shunts in the circuit. The higher the total resistance of the voltmeter circuit,the smaller the loading effect. Commercial voltmeters are given a sensitivity rating in ohms/volt sothat the user can quickly determine the total resistance that the voltmeter adds to the circuit. For

A-13

Figure A.11: Basic Ohmmeter Circuit

example, the 150 V voltmeter circuit discussed earlier in this section would be given a sensitivityrating of 1000 6/V, since the total resistance of the voltmeter is 150,000 6 and the full-scale ratingof the meter is 150 V. Direct-current voltmeters that use the pmmc meter movement can havesensitivity ratings ranging from 100 6/V to 20,000 6/V.

In concluding this introductory discussion of meter loading effects it is important to point out thatthis loading effect is not peculiar to pmmc meter movements. In any system where we are makingphysical measurements, we must extract energy from the system in the process of making the desiredmeasurements. The more energy we extract relative to the amount of energy available in the system,the more severely we disturb the very thing we are trying to measure. Therefore, in any measurementsystem we must always be conscious of the burden the measuring system imposes on the system beingmeasured.

A.3.1.5 The Ohmmeter Circuit

The ohmmeter is a simple, convenient-to-use, direct-reading resistance meter. It consists of a pmmcmovement in series with a battery and a regulating resistance. The basic ohmmeter circuit is shownin Figure A.11.

The operation of the ohmmeter is as follows. Theohmmeter terminals are short circuited, and theregulating resistor R is adjusted to give full-scaledeflection of the meter. This corresponds to zeroresistance on the scale. When the unknown resistanceR is connected to the ohmmeter terminals, thex

deflection is less than full-scale, and hence a calibratedscale can be constructed reading from right to left.One of the disadvantages of the ohmmeter is theinherently nonuniform resistance scale. With a littlethought, it should be apparent that the resistance scalewill be cramped at the high-resistance end of the scale.

The successful operation of the ohmmeter depends on a stable dc supply. The regulating resistor isused to compensate for changes in the internal resistance of the battery. That is, the regulatingresistor enables R + R to be held constant, so that as long as v is constant the ohmmeter scale staysb

in calibration.

Although the ohmmeter is not a precision instrument (accuracy is normally about 10%), it is anextremely useful tool in the laboratory, because it is so simple to use. Frequently, the ohmmeter isused for checking the continuity of a circuit, or for getting an approximate value of an unknownresistance prior to measuring the resistance on a precision instrument that requires time-consumingbalancing.

A-14

Figure A.12: The Electrodynamometer Instrument

A.3.2 Basic AC Meters

We look at two kinds of ac meter design - the moving-coil (electrodynamometer) and moving-iron.

A.3.2.1 The Electrodynamometer

The electrodynamometer is often considered the basic indicating meter for low-frequency sinusoidalmeasurements. It differs from the permanent-magnet, moving-coil meter previously described in thatthe permanent-magnet is replaced by a fixed coil, that carries the same current as the moving coil.The basic configuration of the electrodynamometer is illustrated in Figure A.12.

The torque exerted on the moving-coil of the electrodynamometer is proportional to the metercurrent squared. This follows directly from the fact that the current in the moving-coil is reactingwith a magnetic field established by the same current in the fixed coil. Since the torque isproportional to the current squared, it is unidirectional. It should also be evident that if the metercurrent is varying with time, the torque exerted on the moving-coil must also vary with time.However, the inertia of the moving parts, along with the damping of the meter movement, keeps themoving-coil from responding to the instantaneous torque, and consequently the deflection isproportional to the average torque exerted on the coil. It follows, therefore, that the deflection ofthe meter is proportional to the average of the current squared. Since the rms value is simply thesquare root of the average of the current squared, the meter scale is easily calibrated to read the rmsvalue of the metered current.

The electrodynamometer can be used as either an ammeter or a voltmeter. The technique is the sameas described for the pmmc movement. That is, a resistance is added in series with the coils to forma voltmeter and in parallel with the moving-coil to form an ammeter. The amplitude range of currentsand voltages that can be measured with the electrodynamometer can be extended by means ofinstrument transformers. The transformer is discussed in Chapter 3 of Alden’s notes. For thepresent, the instrument transformer can be thought of as a device that reduces sinusoidal currents andvoltages to levels that can be safely handled by the electrodynamometer.

It is also possible to use the electrodynamometer as a dc meter. However, there is little advantagein this application because the relatively strong field attainable with the permanent magnet in thepmmc meter cannot be duplicated by the magnetic field produced by the fixed coils in theelectrodynamometer. Hence the pmmc dc meter is much more sensitive than a dc

A-15

electrodynamometer. For example, electrodynamometer voltmeters have sensitivities from 10 to 306/V compared to a range of 100 to 20,000 6/V for pmmc voltmeters. Electrodynamometerammeters can be designed to measure currents in the milliampere range, whereas pmmc ammeterscan be designed to measure currents in the micro-ampere range.

As mentioned at the outset of this section, the electrodynamometer is primarily a low-frequencymeter. Most of its applications are in the power frequency spectrum of from 25 to 60 Hz. There aresome applications of the instrument in the lower audio range of frequencies (up to 2500 Hz), but, ingeneral, at the higher frequencies encountered in communication circuits, it is not well suited formeasurements because of its high loading effect on the circuit. Thermocouple instruments can beused to measure rms currents and voltages from dc to frequencies as high as 100 MHz.

A.3.2.2 Moving-iron Meters

In the electrodynamometer movement, the metered current has to be conducted to the movable coil.In commercial meters, this is done by using the restraining springs as electrical connections to themovable coil. The amount of current that can be carried by the movable coil is determined by therestraining spring as well as by the size of the wire used to form the movable coil.Electrodynamometer movements can be designed to carry a maximum current of approximately 100mA. Thus, electrodynamometer ammeters, which measure more than 100 mA, require carefullycalibrated shunts. These characteristics of the electrodynamometer movement make it desirable touse another basic meter movement, which eliminates the need for conducting current to the movingpart of the movement. In the moving-iron meter movement, the moving element consists of a pieceof easily magnetized metal. The movable piece of iron is located in the magnetic field of a fixedelectrical coil. When the coil is energized, the iron moves toward a position that will maximize themagnetic flux linking the electrical coil.

Three moving-iron configurations that are used in commercial meters are shown in Figure A.13 a,b, and c. In the plunger arrangement, the plunger attempts to center itself in the coil whenever thecoil is energized. In the rotating-vane arrangement, the vane twists so that its plane is perpendicularto the plane of the energized coil. The coil and vane are tilted at approximately 100 . In theo

concentric-vane arrangement, the outside vane is stationary and tapered as shown in Figure A13c.As the coil establishes a magnetic field upward through the concentric vanes, the movable vanerotates toward the tapered end of the fixed vane to maximize the magnetic flux linking the coil. Thesethree moving-iron configurations are converted into meter movements by providing mechanicalsupport for the moving piece of iron and restraining springs that measure the amount of force ortorque exerted on the moving iron.

A-16

Figure A.13: Three moving-iron meter movements. (a) Magnetic plunger movement.b) Inclined rotation-vane movement. (c) Concentric-vane movement.

The moving-iron meter movement is used in both ammeters and voltmeters. Since no current has tobe conducted to the moving parts of the meter, the fixed coils can be designed to carry relatively largecurrents. Small panel ammeters can be designed to carry 100 A and large panel meters will handleup to 500 A. Beyond 500 A current transformers are needed to scale the currents to within the rangeof the meter movement. The impedance of the fixed coil limits the use of the moving-iron movementto ammeters designed to measure currents in the milliampere range. For example, in a 15 mAmoving-iron movement the fixed coil can have an impedance as high as 3000 6 at 60 Hz.

Moving-iron voltmeters can be designed to measure rms voltages up to 750 V. The sensitivity of themoving-iron voltmeter is quite low (85 to 200 6/V), and hence loading effects must be carefullyevaluated. Moving-iron movements are designed for use in a frequency range of from 25 to 150 Hz.There are some moving-iron movements that can be used at frequencies up to 2400 Hz. have nowdiscussed three basic meter movements that can be generally classified as electro-mechanicalmovements. The pmmc, electrodynamometer, and moving-iron movements are all designed to movea mechanically supported and restrained pointer across a calibrated scale. They have twocharacteristics that prohibit their use in some areas of electrical measurements.

1. The meter movements require relatively large amounts of power to operate. 2. The frequency range the movements will respond to is normally several hundred Hz. and

even with special designs it is limited to audio frequencies and below.

The cathode-ray oscilloscope overcomes these two limiting features of the electro-mechanicalmovements. In the cathode-ray oscilloscope the measured signals deflect an electron beam insteadof a mechanical pointer. This means the instrument can respond to signal frequencies in MHz. Thepower drawn from the system being measured is reduced a thousandfold or more when compared to

im

vRm � Zmoving coil

�

vRm

A-17

Figure A.14: Wattmeter Connection

Figure A.15: Internal Arrangement

the power drawn by the electro-mechanical movement. The same can be said for digital instruments.

A.3.3 The Wattmeter

Because power measurements in lumped-parameter circuits operating at frequencies above 800 c/sinvolve electronic devices we will limit our discussion in this section to the power measurement inlow-frequency circuits. However, it is important to bear in mind that power measurements can bemade throughout the frequency spectrum. In fact, they can even be made at the high end of thefrequency spectrum where the lumped-parameter circuit is no longer a valid model of the electricalsystem. Thus, power can be measured in electrical systems even when current and voltage cannotbe measured.

In low-frequency circuits, power is measured by meansof the electrodynamometer wattmeter. Theelectrodynamometer movement in the wattmeter isvery similar to the electrodynamometer movementdiscussed in Section A.3.2 in conjunction with ACammeters and voltmeters. The basic differencebetween the movements is that in the wattmeter thefixed and moving coils are not connected in series.The fixed coils are designed to carry the load current,and the moving coil is designed to carry a small currentthat is directly proportional to the load voltage. FigureA.14 shows how a wattmeter is connected to a load to

measure the power.

In Figure A.15, the wattmeter is representedschematically with the current in the moving coildenoted by i . To show why the wattmeter respondsm

to the power delivered to the load, we must first notethat the instantaneous torque on the moving coil isproportional to the product of the coil currents, i.e.:

T � i × im

This follows directly from our discussion of theelectrodynamometer movement in Section A.3.2.

Now if the resistance in series with the moving coil (R in Figure A.15) is large compared to them

impedance of the moving coil, then the current in the coil will be directly proportional to the loadvoltage, i.e.:

Combining the two previous equations we see that the instantaneous torque on the moving coil of

A-18

Figure A.16: Alternate Wattmeter Conn.

Figure A.17: Compensated Wattmeter

the wattmeter is proportional to the instantaneous power delivered to the load; thus:

T � v × i

If the inertia and damping of the meter movement is large enough, the moving coil will not be ableto respond to the instantaneous variations in load power, and hence the deflection of the moving coilwill depend on the average power. If v and i are sinusoidal functions of time, the wattmeter will readV I cos � as can be seen by referring to equation 2.9 in Alden’s notes.

Commercial wattmeters are sometimes equipped with a so-called compensating winding. Thepurpose of this winding is to eliminate the error in the wattmeter reading that arises because thewattmeter cannot simultaneously measure the exact load voltage and load current. For example, inthe circuit of Figure A.14, the voltage across the moving coil of the wattmeter is not identical to the

load voltage because of the small voltage drop acrossthe fixed coils of the meter. Therefore, the wattmeterreading is, in fact, equal to the average powerdelivered to the load plus the average power deliveredto the fixed coils of the meter. If the wattmeter isreconnected as shown in Figure A.16, the meterreading is still in error, because now the current is notthe exact load current. In the connection shown inFigure A.16, the wattmeter reading corresponds to theaverage power delivered to the load plus the averagepower delivered to the moving coil.

The compensating winding in a wattmeter is designed to compensate for the potential coil (i.e., themoving coil) current. A schematic diagram of the compensated wattmeter is shown in Figure A.17.Physically, the compensating coil is wound with the current coil and has the same number of turns,but the sense of its turns are exactly opposite to the current coil turns. Now, since I exists in bothm

the current coil and the compensating coil, the effect of i on the deflection of the wattmeter ism

canceled. Figure A.17 illustrates the physicalrelationship between the current coil and thecompensating coil.

If an electrodynamometer wattmeter does not have acompensating winding, the user should determinefrom the meter constants whether or not the powerconsumed by the meter is negligible compared to thepower being measured. If the meter power is notnegligible, the wattmeter reading must be reduced bythe meter consumption.

A-19

Figure A.18: Reactive PowerMeasurement

Note in conclusion that instead of thinking of the electrodynamometer movement as just a powermeter we should rather view it as a multiplying and averaging device. Thus, it can be thought of asa device that will multiply and average the two electrical signals applied to its two windings.

The signals do not have to come from the same circuit,nor does the product of the two signals have to signifypower. For example, a wattmeter can be used to measurethe reactive power |V| |I| sin -0 by simply shifting the loadvoltage 90 before applying the voltage to the potentialo

coil of the meter. The application of the wattmeter tomeasure reactive power is shown schematically in FigureA.18.