A.3 Additional Instrument Theory by dfsdf224s


									A.3 Additional Instrument Theory
The three most common types of meters used in the power laboratory are DC Voltmeters and
Ammeters, 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 addition
of aeries resistance allows the measurement of voltage. The addition of a battery allows the
measurement 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 making
use of the well-known fact that when a current-carrying conductor is placed in a magnetic field, a
force is exerted on the conductor. Furthermore, the force is directly proportional to the current. The
way direct-current ammeters and voltmeters make use of this interaction between the magnetic field
and the current is best described with the aid of the diagrams in Figure A.7. The current to be
measured is passed through the movable coil, where it reacts with the magnetic field of the permanent
magnet, thus creating a torque on the coil. The coil rotates until the torque on it is balanced by the
restoring spring. This spring is designed so that its torque is directly proportional to the angle
through which the coil rotates, and the uniform magnetic field is oriented so that the force on the coil
is always perpendicular to its axis. Thus, the deflection of the pointer is directly proportional to the
current in the movable coil. The numerical value of the current is read from a calibrated scale placed
at the end of the pointer.

      Figure A.7: Basic parts of a permanent-magnet, moving-coil (d'Arsonval) meter.
             a) Schematic diagram,                     (b) Pictorial diagram
One of the most important characteristics of the permanent-magnet moving-coil instrument is that
a given coil, or meter movement, can be used to measure a wide range of currents and voltages. The
range of the meter is controlled by the choice of resistors, which are electrically connected to the
moveable coil. In the next section we will show how a given meter movement can be used to build
either an ammeter or a voltmeter.

A.3.1.2 The DC Ammeter Circuit

The basic direct-current ammeter circuit consists of a pmmc meter movement in parallel with a
resistor, as shown in Figure A.8. The purpose of the shunting resistor Rs is to control the amount of
current passing through the meter movement. Thus the shunting resistor Rs and the meter movement
can be thought of as forming a current-dividing circuit.

                                                The design of the ammeter circuit is based on the
                                                maximum current that is to be read by the meter and
                                                the electrical characteristics of the meter movement.
                                                Meter manufacturers specify the electrical
                                                characteristics of a meter movement by giving the
                                                movable coil a voltage and current rating. For
                                                example, one commercially available meter movement
                                                is rated at 50 mV and 1 mA. The significance of these
                                                ratings is as follows: when the coil is carrying its
                                                rated current, the pointer is deflected to its full-scale
  Figure A.8: Basic DC Ammeter Circuit position 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 $.

We will demonstrate the function of the ammeter circuit by showing how we can use a 50 mV, 1 mA
meter 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 9
mA must pass through the shunting resistor Rs.

                                                Our problem is depicted schematically in Figure A9
                                                where Kirchhoff's voltage law requires:

                                                        9 x 10-3 x Rs = 1 x 10-3 x 50

                                                        or RS = 50/9 = 5.555 $

                                              Thus with a shunting resistance of 5.555 $, the 50
                                              mV, 1 mA meter movement becomes a 10 mA (full-
                                              scale) ammeter. Note also that the current through the
                                              meter movement will always be directly proportional
       Figure A.9: 10 mA Example
                                              to 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 external
resistor to form a voltmeter.

A.3.1.3 The DC Voltmeter Circuit

When the pmmc meter movement is used to measure direct-current voltages, the movement is
connected in series with a resistor as shown in Figure A.10. The purpose of the series resistor Rv is
to limit the voltage applied to the meter movement. Thus, the series resistor Rv and the meter
movement can be thought of as forming a voltage-divider circuit, which divides the voltage at the
terminals of the voltmeter to a value within the voltage rating of the meter movement.

                                                To illustrate the design of a voltmeter, let us calculate
                                                the numerical value of Rv that is necessary to make a
                                                50 mV, 1 mA movement read 150 V at full-scale.
                                                Since full-scale deflection requires 50 mV to be
                                                applied to the meter movement and the meter
                                                movement has a resistance of 50 $, the voltage-divider
                                                equation is:

                                                         50 ×10	3    
 50 × 50
                                                                       RV  50

Figure A.10: Basic DC Voltmeter Circuit From which we obtain:

        RV = 150,000 - 50 = 149,950 $

It is important to note that once Rv has been selected on the basis of the full-scale voltage reading,
the meter will correctly read voltages between zero and full-scale. For example, if the voltage drops
to 50 V at the terminals of the voltmeter, it will drop to (50/150) x 50 mV at the terminals of the
meter 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 circuit
disturbs the circuit in which the measurement is being made. An ammeter adds resistance in the
branch in which the current is being measured, while a voltmeter adds resistance across the terminals
where the voltage is being measured. How much the meters disturb the circuit in which the
measurements are being made depends on the resistance of the meters in comparison to the
resistances of the circuit. For example the 10 mA ammeter circuit discussed in the previous section
will add a resistance of (50 x 10-3)/(10 x 10-3) or 5 $ in any branch where it is inserted. If the
resistance of the branch without the ammeter is in the k$ range, the insertion of the ammeter will
have a negligible effect. If, however, the resistance of the branch is of the same order of magnitude
as the ammeter resistance, the insertion of the meter could have a significant effect on the current in
the branch. In this latter case the current measured by the ammeter would not be the same as the
current in the branch without the ammeter.

The loading effect of a voltmeter depends on the resistance of the voltmeter in comparison with the
resistance 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 so
that the user can quickly determine the total resistance that the voltmeter adds to the circuit. For

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

In concluding this introductory discussion of meter loading effects it is important to point out that
this loading effect is not peculiar to pmmc meter movements. In any system where we are making
physical measurements, we must extract energy from the system in the process of making the desired
measurements. 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 measurement
system we must always be conscious of the burden the measuring system imposes on the system being

A.3.1.5 The Ohmmeter Circuit

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

                                      The operation of the ohmmeter is as follows. The
                                      ohmmeter terminals are short circuited, and the
                                      regulating resistor R is adjusted to give full-scale
                                      deflection of the meter. This corresponds to zero
                                      resistance on the scale. When the unknown resistance
                                      R x is connected to the ohmmeter terminals, the
                                      deflection is less than full-scale, and hence a calibrated
                                      scale can be constructed reading from right to left.
                                      One of the disadvantages of the ohmmeter is the
                                      inherently nonuniform resistance scale. With a little
                                      thought, it should be apparent that the resistance scale
  Figure A.11: Basic Ohmmeter Circuit
                                      will 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 is
used to compensate for changes in the internal resistance of the battery. That is, the regulating
resistor enables R + Rb to be held constant, so that as long as v is constant the ohmmeter scale stays
in calibration.

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

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 sinusoidal
measurements. It differs from the permanent-magnet, moving-coil meter previously described in that
the 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.

                       Figure A.12: The Electrodynamometer Instrument
 The torque exerted on the moving-coil of the electrodynamometer is proportional to the meter
current squared. This follows directly from the fact that the current in the moving-coil is reacting
with a magnetic field established by the same current in the fixed coil. Since the torque is
proportional to the current squared, it is unidirectional. It should also be evident that if the meter
current 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 the
moving-coil from responding to the instantaneous torque, and consequently the deflection is
proportional to the average torque exerted on the coil. It follows, therefore, that the deflection of
the meter is proportional to the average of the current squared. Since the rms value is simply the
square root of the average of the current squared, the meter scale is easily calibrated to read the rms
value of the metered current.

The electrodynamometer can be used as either an ammeter or a voltmeter. The technique is the same
as described for the pmmc movement. That is, a resistance is added in series with the coils to form
a voltmeter and in parallel with the moving-coil to form an ammeter. The amplitude range of currents
and voltages that can be measured with the electrodynamometer can be extended by means of
instrument transformers. The transformer is discussed in Chapter 3 of Alden’s notes. For the
present, the instrument transformer can be thought of as a device that reduces sinusoidal currents and
voltages 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 advantage
in this application because the relatively strong field attainable with the permanent magnet in the
pmmc meter cannot be duplicated by the magnetic field produced by the fixed coils in the
electrodynamometer.         Hence the pmmc dc meter is much more sensitive than a dc

electrodynamometer. For example, electrodynamometer voltmeters have sensitivities from 10 to 30
$/V compared to a range of 100 to 20,000 $/V for pmmc voltmeters. Electrodynamometer
ammeters can be designed to measure currents in the milliampere range, whereas pmmc ammeters
can be designed to measure currents in the micro-ampere range.

As mentioned at the outset of this section, the electrodynamometer is primarily a low-frequency
meter. Most of its applications are in the power frequency spectrum of from 25 to 60 Hz. There are
some applications of the instrument in the lower audio range of frequencies (up to 2500 Hz), but, in
general, at the higher frequencies encountered in communication circuits, it is not well suited for
measurements because of its high loading effect on the circuit. Thermocouple instruments can be
used 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 the
movable coil. The amount of current that can be carried by the movable coil is determined by the
restraining 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 100
mA. Thus, electrodynamometer ammeters, which measure more than 100 mA, require carefully
calibrated shunts. These characteristics of the electrodynamometer movement make it desirable to
use another basic meter movement, which eliminates the need for conducting current to the moving
part of the movement. In the moving-iron meter movement, the moving element consists of a piece
of easily magnetized metal. The movable piece of iron is located in the magnetic field of a fixed
electrical coil. When the coil is energized, the iron moves toward a position that will maximize the
magnetic 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 the
coil is energized. In the rotating-vane arrangement, the vane twists so that its plane is perpendicular
to the plane of the energized coil. The coil and vane are tilted at approximately 100o. In the
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 vane
rotates toward the tapered end of the fixed vane to maximize the magnetic flux linking the coil. These
three moving-iron configurations are converted into meter movements by providing mechanical
support for the moving piece of iron and restraining springs that measure the amount of force or
torque exerted on the moving iron.

   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 to
be conducted to the moving parts of the meter, the fixed coils can be designed to carry relatively large
currents. Small panel ammeters can be designed to carry 100 A and large panel meters will handle
up to 500 A. Beyond 500 A current transformers are needed to scale the currents to within the range
of the meter movement. The impedance of the fixed coil limits the use of the moving-iron movement
to ammeters designed to measure currents in the milliampere range. For example, in a 15 mA
moving-iron movement the fixed coil can have an impedance as high as 3000 $ at 60 Hz.

Moving-iron voltmeters can be designed to measure rms voltages up to 750 V. The sensitivity of the
moving-iron voltmeter is quite low (85 to 200 $/V), and hence loading effects must be carefully
evaluated. 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 now
discussed three basic meter movements that can be generally classified as electro-mechanical
movements. The pmmc, electrodynamometer, and moving-iron movements are all designed to move
a mechanically supported and restrained pointer across a calibrated scale. They have two
characteristics 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-mechanical
movements. In the cathode-ray oscilloscope the measured signals deflect an electron beam instead
of a mechanical pointer. This means the instrument can respond to signal frequencies in MHz. The
power drawn from the system being measured is reduced a thousandfold or more when compared to

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/s
involve electronic devices we will limit our discussion in this section to the power measurement in
low-frequency circuits. However, it is important to bear in mind that power measurements can be
made throughout the frequency spectrum. In fact, they can even be made at the high end of the
frequency spectrum where the lumped-parameter circuit is no longer a valid model of the electrical
system. Thus, power can be measured in electrical systems even when current and voltage cannot
be measured.

                                                     In low-frequency circuits, power is measured by means
                                                     of the electrodynamometer wattmeter.                 The
                                                     electrodynamometer movement in the wattmeter is
                                                     very similar to the electrodynamometer movement
                                                     discussed in Section A.3.2 in conjunction with AC
                                                     ammeters and voltmeters. The basic difference
                                                     between the movements is that in the wattmeter the
                                                     fixed 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 current
                                                     that is directly proportional to the load voltage. Figure
  Figure A.14: Wattmeter Connection                  A.14 shows how a wattmeter is connected to a load to
measure the power.

                                                     In Figure A.15, the wattmeter is represented
                                                     schematically with the current in the moving coil
                                                     denoted by im. To show why the wattmeter responds
                                                     to the power delivered to the load, we must first note
                                                     that the instantaneous torque on the moving coil is
                                                     proportional to the product of the coil currents, i.e.:

                                                            T  im × i

                                                     This follows directly from our discussion of the
                                                     electrodynamometer movement in Section A.3.2.
   Figure A.15: Internal Arrangement
Now if the resistance in series with the moving coil (Rm in Figure A.15) is large compared to the
impedance of the moving coil, then the current in the coil will be directly proportional to the load
voltage, i.e.:
                       Rm      Zmoving coil    Rm

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

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


If the inertia and damping of the meter movement is large enough, the moving coil will not be able
to respond to the instantaneous variations in load power, and hence the deflection of the moving coil
will depend on the average power. If v and i are sinusoidal functions of time, the wattmeter will read
V 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. The
purpose of this winding is to eliminate the error in the wattmeter reading that arises because the
wattmeter cannot simultaneously measure the exact load voltage and load current. For example, in
the 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 across
                                                 the fixed coils of the meter. Therefore, the wattmeter
                                                 reading is, in fact, equal to the average power
                                                 delivered to the load plus the average power delivered
                                                 to the fixed coils of the meter. If the wattmeter is
                                                 reconnected as shown in Figure A.16, the meter
                                                 reading is still in error, because now the current is not
                                                 the exact load current. In the connection shown in
                                                 Figure A.16, the wattmeter reading corresponds to the
                                                 average power delivered to the load plus the average
 Figure A.16: Alternate Wattmeter Conn. power delivered to the moving coil.

The compensating winding in a wattmeter is designed to compensate for the potential coil (i.e., the
moving 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 Im exists in both
the current coil and the compensating coil, the effect of im on the deflection of the wattmeter is
                                                 canceled. Figure A.17 illustrates the physical
                                                 relationship between the current coil and the
                                                 compensating coil.

                                     If an electrodynamometer wattmeter does not have a
                                     compensating winding, the user should determine
                                     from the meter constants whether or not the power
                                     consumed by the meter is negligible compared to the
                                     power being measured. If the meter power is not
                                     negligible, the wattmeter reading must be reduced by
  Figure A.17: Compensated Wattmeter the meter consumption.

Note in conclusion that instead of thinking of the electrodynamometer movement as just a power
meter we should rather view it as a multiplying and averaging device. Thus, it can be thought of as
a 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 signify
                                          power. For example, a wattmeter can be used to measure
                                          the reactive power |V| |I| sin 0 by simply shifting the load
                                          voltage 90 before applying the voltage to the potential
                                          coil of the meter. The application of the wattmeter to
                                          measure reactive power is shown schematically in Figure

     Figure A.18: Reactive Power


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