889

7.3 Electrical Meters and Sensors

P. M. GLATTSTEIN

(1972, 1982)

B. G. LIPTÁK

(1995)

P. M. B. SILVA GIRÃO

(2003)

Meter Types and Accessories:

A. Permanent magnet moving coil meterB. Permanent magnet moving coil with electronicsC. Moving iron vane meterD. Electrodynamic meterE. Electrostatic meterF. Digital meterG. Current transformerH. ShuntI. Potential transformerJ. Resistor for DC voltmeters(Note: See the Orientation Table 7.3a for a summary of volt, watt, and ammeter features.)

Ammeter Choices and

For AC current: B, C, or F

Accessories:

For high-range AC current: B, C, or F with GFor DC current: A or FFor high-range DC current: A or F with H

Voltmeter Choices and

For AC voltage: B, C, or F

Accessories:

For high-range AC voltage: E; or B, C, or F with IFor DC voltage: A or FFor high-range DC voltage: E; or A or F with J

Wattmeter Choices and

For one or three-phase AC power: D or F with G and H

Accessories:

For DC power: D or FFor high-range DC power: D or F with H

Inaccuracy:

A. 0.3 to 2% of full scaleB. 3% of full scaleC, D. 0.5 to 2% of full scaleE. 0.5 to 2% of full scaleF. From a few ppm to 2% of full scaleG. 0.6 to 1.2% of secondary ratingH. 0.25% of shunt ratingI. 0.3 to 0.6% of secondary ratingJ. 0.25% of resistor rating

Costs:

A, C, F, and G: about $50B and I. About $150D. About $500E. About $500F. From about $100 to up to a few thousand dollars for special purpose metersI. From 230 V AC to 120 V AC at 100 to 500 W, about $50; to 1000 W, about $100.

The cost range of handheld, battery-operated digital multimeters capable of detectingtemperature, AC and DC current and voltage, resistance, frequency, and capacitanceis about $125. Clamp-type AC current testers also cost about $125. A kW transducerfor single or three-phase and three- or four-wire systems costs about $500. A power

Generator EI

JI

Voltmeter

Wattmeter

IE

Current Transformer

Flow Sheet Symbol

© 2003 by Béla Lipták

890

Safety and Miscellaneous Sensors

analyzer that displays and detects 12 energy parameters (including true RMS voltageand current, instantaneous and average power factors, etc.), all at 1% of measurementinaccuracy, costs about $2500. A universal power analyzer with DC rectifier mea-surements costs about $10,000.

Partial List of Suppliers:

Agilent Technologies (www.agilent.com)Ametek Power Instruments (www.rochester.com)Amprobe Instruments (www.amprobe.com)Anritsu Corporation (www.anritsu.com)AVO International (www.avoint.com)Boonton Electronics (www.boonton.com)Campbell Scientific, Inc. (www.campbellscientific)Chauvin Arnoux Métrix SA (www.chauvin-arnoux.com)CROPICO Ltd. (www.cropico.com)Dranetz BMI (www.dranetz.com)Electronics Product Design, Inc. (www.epd.com)Farnell (www.farnell.com)Fluke Corp. (www.fluke.com)GE Industrial Systems (www.geindustrial.com)GMC Instruments Inc. (www.gmcinstruments.com)Hameg Instruments (www.hameg.com)Hioki USA Corporation (www.hiokiusa.com)Indotech Devices Pvt. Ltd. (www.indotechonline.com)Keithley Instruments Inc. (www.keithley.com)Kyoritsu Electrical Instr. Works, Ltd. (www.kew-ltd.co.jp)Langlois SARL (www.langlois-france.com)Leader Electronics Corp. (www.leader.co.jp)RS Electronics (www.rselectronics.com)Simpson Electric Corp. (www.simpsonelectric.com)Teradyne (www.teradyne.com)Triplett Corp. (www.triplett.com)Yokogawa Electric Corporation (www.yokogawa.com)Weschler Instruments (www.weschler.com)

INTRODUCTION

The direct measurement of electrical quantities is the topic ofthis section. Indicators, recorders, and other display devicesare discussed in the

Process Control

volume of this handbookand are not covered here. Also not covered are instrumentsand methods that allow access to electrical quantities valuesby indirect means such as those using measuring transducers.While this section concentrates on the measurement of cur-rent, voltage, and wattage, instruments such as handheld mul-timeters that are listed in the feature summary at the beginningof this section can also measure other quantities, namely, resis-tance, frequency, capacitance, and temperature.

Electrical quantities can be measured by either analog ordigital instruments. Analog instruments display the value ofthe quantity by the position of a pointer on a scale, whiledigital instruments display the same value numerically. Inboth cases the absolute value of the reading is a function ofthe selected range.

Digital measuring instruments have many advantages overanalog ones making them attractive and popular. They are easierto read, provide higher resolution (up to 1 part in 2

×

10

8

), andbetter accuracy (up to a few parts per million). They also arecapable of remote operation and can provide multifunction

capabilities when used with transducers. Analog instrumentsfind their use restricted to special applications, namely, whenthe advantage of a continuous display provided by the positionof a pointer on a scale is important. This is the case in thedetection of a critical value or limit and when the rate at whicha quantity is changing needs to be detected (e.g., null detection).

ANALOG MEASURING INSTRUMENTS

Analog electric meters have been in use for nearly two cen-turies thanks to the discoveries of Oersted (1819), Ampere(1821), Faraday (1821), Kelvin (1867), D’Arsonval (1881),and Weston (1889). There are four basic types of analogmeasuring instruments: permanent magnet moving coilinstruments (PMMCs), moving iron vane instruments, elec-trodynamic instruments, and electrostatic instruments. Thepermanent magnet moving coil instrument can be upgradedusing electronic components (rectifiers and amplifiers) andthermoelectric converters.

There is an element in all analog sensors and to that ele-ment a pointer is attached. This element, when subjected toa torque, is allowed to rotate around an axle. A spring mightbe used to apply a counter-clockwise restoring torque to theaxle, while the measured quantity generates an acting torque

© 2003 by Béla Lipták

7.3 Electrical Meters and Sensors

891

TABLE 7.3a

Orientation Table for Ammeters, Voltmeters, and Wattmeters

Meters Type of MeterAccessories

Required

Full-Scale Meter Range (A, Amperes; V,

Volts; W, Watts)

Permissible Overload in Multiple of Full

Scale and for Noted Time Duration

RecommendedApplications

AMMETERSAC Rectifier

Moving iron vaneMoving iron vane

Digital

Digital

None

NoneTransformer

None

Transformer/Hall effect probe

0.5–20

×

10

–3

A

1–50 A10–8000 A

200

×

10

–6

A–10 A

2–1000 A

For meters:

1.2

×

: 8 hr100

×

1 sec

For transformer:

50

×

: 2 secVaries, often protected

Low-range, high frequency

General use up to 750 voltsHigh-range, over 750 volts, long meter leads

General use, medium frequency

High range medium frequency

DC Permanent magnet moving coil

Permanent magnet moving coil

DigitalDigital

None

Shunt

NoneCurrent probe

0.02

×

10

−

3

50 A20–20,000 A

200

×

10

–6

A

–

10 A2–1000 A

1.2

×

: 8 hr

100

×

: 1 sec

Varies, often protected

General use

High-range

General useHigh range

VOLTMETERSAC Rectifier

Moving iron vaneMoving iron vane

ElectrostaticDigital

None

NoneTransformer

NoneNone

3–800 V

3–600 V150–18,000 V

10–1000 V100

×

10

–3

V–750 V

For meters:1.2

×

: continuous100

×

: 1 secFor transformer:1.1

×

: continuous1.25

×

: 1 min

Varies, often protected

Low-range, high-frequency

General useHigh-range, circuit isolation

High rangeGeneral use, medium frequency

DC Permanent magnet moving coil

Permanent magnet moving coil

Digital

None

Resistor

None

1–600 V

250–30,000 V

100

×

10

–3

V–750 V

1.2

×

: continuous100

×

: 1 sec

Varies, often protected

General use

High-range, high-sensitivity

General use

WATTMETERS

Single-phase AC

Three-phase AC

1-element electrodynamic

Digital

1-element electrodynamic

2-element electrodynamic

2

1

/

2

-element

electrodynamicDigital

None

None

Transformer

Transformer

Transformer

None

125–1000 W

2 mW – 15000 W

1000–100

×

10

6

W

1000–100

×

10

6

W

1

×

10

4

–1

×

10

8

W

2 mW–15000 W

For current:

1.2

×

: continuous100

×

: 1 sec

For current:

1.2

×

: continuous10

×

: 1 sec

Low power, single-phase 2-wirecircuits

General use, single-phase 2-wirecircuits

General use, single-phase circuits

General use, three-phase, three-wire

General use, three-phase, four-wire

General use, three-phase, three or four-wire

DC 1-element electrodynamic

Digital

None

None

100–2000 W

2 mW – 15000 W

General use, low-power

General use

© 2003 by Béla Lipták

892

Safety and Miscellaneous Sensors

(or motor torque). If this torque exceeds the restoring torquegenerated by the spring, a new angular position is established.The stability of the system is a function of the accelerationof the rotating system and of the amount of damping (damp-ing torque), which is mainly a function of the speed of thesystem. Because the inertial and damping torques exist onlywhen the rotating system is in motion, the final position ofthe pointer depends only on the motor and restoring torques.

For mechanical reasons, the rotating system has a low-pass characteristic with a typical cutoff frequency of 1 Hz,which means that it only reacts to motor torques of frequen-cies lower that 1 Hz. For normal applications, only the DCcomponent of the motor torque is inside the bandwidth ofthe system. Therefore, the final position of the pointer resultsfrom the balance between that component of the motor torqueand the restoring torque.

Permanent Magnet Moving Coil Instruments

More commonly known as the D’Arsonval type, these instru-ments consist of a pointer attached to a coil of fine wiresuspended between the poles of a permanent magnet(Figure 7.3b). Current through the coil creates a magnetic fieldthat reacts with the field of the permanent magnet, causing amotor torque proportional to the intensity of current.

1

The coil shaft is usually mounted on jeweled bearings,and hairsprings provide the force necessary to restore thepointer to zero (restoring torque). An alternative method isto support the coil by flat metal bands attached to a supportingframework. The bands carry current to the coil and furnishthe necessary restoring force. Permanent magnet moving coilmeters are accurate and sensitive, consume small amounts ofpower, possess linear display scales, and are widely used tomeasure DC current and voltage. Since the field of the per-manent magnet is static, the torque depends on the directionof the current in the coil.

The two terminals of the instrument are usually identifiedeither by color (red is positive) or by plus and minus symbols

to indicate the connecting mode that produces a correctdeflection: clockwise for 0 left meters and clockwise or anti-clockwise for 0 center meters. Even if some models areprovided with means of switching a current’s direction, careshould be taken when connecting this type of instrument.

Electronic Components

The addition of electronic compo-nents to a PMMC meter can provide:

1. Extended measuring bandwidth up to the hundreds ofmegahertz

2. Increased measuring range and sensitivity3. Improved input impedance

For AC measurements, a PMMC can be combined withsilicon rectifiers, which are arranged in a half or full wave bridge(Figure 7.3c). Rectifier current ratings limit these meters torelatively low ranges of AC current and voltage measurements.A wide band of frequencies can be accommodated becauseaccuracy is not affected by frequency. Scales are essentiallylinear with some crowding at the lower end, because of changesin rectifier values at very low currents. Meters must be cali-brated to read effective or root mean square (RMS) values sincethe instrument responds to average AC values.

The addition of amplifiers to PMMCs improves theirmeasuring range, sensitivity and input impedance. The simul-taneous inclusion of amplifiers and rectifiers allows theimplementation of instruments that are basically voltmeters,but that can be used to measure current, for instance, bymeasuring the voltage drop it produces on a calibrated resis-tor. These voltmeters are sometimes referred to as electronicvoltmeters. They have very high input impedance (very lowpower consumption), are sensitive, and possess both a largebandwidth and a wide measuring range.

The main limitation of these instruments (Figure 7.3d) isthat the indication depends on the input waveform. PMMCelectronic meters that do not have this limitation are usuallyidentified as true RMS meters. They make use of thermo-electric converters that replace the rectifier and produce a DCquantity whose value equals or is proportional to the rootmean square of the AC quantity to be measured. Able tooperate up to some 100 MHz, PMMCs with thermoelectricconverters and amplifiers are the wider bandwidth true RMSanalog electrical measuring instruments and have rangesfrom millivolts up to a few hundred volts.

FIG. 7.3b

Internal construction of a permanent magnet moving coil meter.

Pointer

Hairspring

Coil Leadto MeterTerminal

MagnetPolePiece

Moving Coil Coil Shaft

N S

FIG. 7.3c

Rectifier movement with full wave bridge circuit.

Permanent MagnetMoving CoilMovement

Silicon Rectifier

AC Input

++

−

−Meter

Terminal

© 2003 by Béla Lipták

7.3 Electrical Meters and Sensors

893

Moving Iron Vane Instruments

These instruments consist of two cylindrical soft iron vanesmounted within a fixed current-carrying coil (Figure 7.3e).One vane is held immobile and the other is free to rotate,carrying with it the pointer shaft. Current in the coil inducesboth vanes to become magnetized, and repulsion between thesimilarly magnetized vanes produces a proportional rotation(repulsion moving iron vane). The motor torque is propor-tional to the square of the current in the coil, making theinstrument a true RMS meter. A hairspring provides therestoring torque.

Only the fixed coil carries current, and the meter may beconstructed so as to withstand high current flows. Movingiron vanes instruments may be used for DC current and voltagemeasurement. However, small DC errors due to residual mag-netism cause them to be more widely utilized for AC currentand voltage detection even though sensitivity is low andpower consumption is moderately high. These instruments

indicate effective or root mean square values and are subjectto minor frequency errors only.

Even if their bandwidth can reach the few hundred hertz,their errors depend slightly on frequency. They should beused in a narrower band, usually 40 to 60 Hz. Their scalesare nonlinear and somewhat crowded in the lower third,because the deflection of the pointer is approximately pro-portional to the square of the coil current.

Electrodynamic Instruments

These instruments are similar to the PMMC-type elementsexcept that the magnet is replaced by two serially connectedfixed coils that produce the magnetic field when energized(Figure 7.3f). The motor torque is proportional to the productof currents in the moving and fixed coils. These instrumentscan measure AC or DC current, voltage, and power. In thefirst two cases, the moving and fixed coils are serially con-nected. For power measurement, one of the coils (usually thefixed) passes the load current and the other coil passes acurrent proportional to the load voltage.

Cost and performance compared with other types ofinstruments restrict the use of this design to AC and DCpower measurement. When used for power measurement, itsscale is linear (calibrated in average values for AC). Its accu-racy is high but its sensitivity is low. The bandwidth ofelectrodynamic instruments goes from DC to a few hundredhertz. Similarly to moving iron vane instruments, the elec-trodynamic instruments are true RMS responding meters.

Electrostatic Instruments

In contrast with the three meter types already mentioned, themotor torque of electrostatic instruments is due to electricinteraction of charge distributions. Figure 7.3g represents acommon implementation of the instrument (rotating-platetype). It is a capacitor with a fixed and a moving semicircularplate. The plates are mounted on a shaft that also supports thepointer. When a voltage is applied to the capacitor, the chargedistribution on the plates produces an attractive torque thattends to bring the plates closer. The motor torque is proportional

FIG. 7.3d

Block diagram of an AC PMMC based electronic meter.

FIG. 7.3e

Internal construction of a moving iron vane-type meter.

PMMC

+ Vcc

− Vcc

OACB

CA

+

−

+ −

Pointer

Hairspring

Coil Leadsto Meter

Terminals

MovingIron Vane

Fixed CylindricalCoil

Shaft(Attached to Moving Vane)

FixedIron Vane

FIG.7.3f

Internal construction of an electrodynamic meter.

Pointer

Hairspring

Coil Leadsto Meter

Terminals

MovingCoil

FixedCoil

© 2003 by Béla Lipták

894

Safety and Miscellaneous Sensors

to the square of the voltage between the two plates and therestoring torque is, as usual, generated by a spiral spring.

Because of their high input impedance, electrostaticinstruments are used only as voltmeters. The motor torquealso depends on the derivative of capacitor’s value. Formechanical reasons, this derivative is small so that a motortorque able to produce a significant angular displacement ofthe moving plate is only possible for voltages higher thansome tens of volts. For this reason, and in spite of its largebandwidth (from DC up to some tens of MHz) and high inputimpedance, electrostatic voltmeters are used mainly in highvoltage measurements. Today the name electrostatic voltme-ter is also used to designate electronic voltmeters that mea-sure voltage without charge transfer.

2

DIGITAL MEASURING INSTRUMENTS

In the last few decades, the development of sensors and instru-mentation have been influenced by the technologies of solidstate electronics and integrated circuitry. As cost effectiveanalog-to-digital converters (ADCs) became available, instru-mentation shifted from analog to digital. This trend was rein-forced by the convenience of automation of digital instruments.

Figure 7.3h represents a simplified block diagram of adigital instrument. The value displayed results from the out-put of an ADC. The input conditioner circuits serve to trans-form the measured quantity into a proportional DC voltageor current signal that is within the range of the ADC. Thenature of the signal conditioner depends on the quantity orquantities to be measured and on the characteristics of themeter. Finally, the controller circuitry supports the requiredcontrol functions.

For a true RMS digital multimeter, Figure 7.3i details theblock diagram in Figure 7.3h. Assuming that the ADC operateson voltage, the input voltage and current must both be con-verted into a DC voltage. If the input is a DC voltage, onlyattenuation may be needed. If the input is AC, the attenuatedvoltage must be sent to a circuit that is able to produce a DCvoltage whose value is equal to the RMS of its input voltage.

There are several possible solutions to implement such a circuit(named RMS converter). These include those that are basedon the definition of RMS value and on the thermal effectsassociated with an electric voltage.

A wide range of measurements can be covered by digitalvoltage and current sensing instruments. Typical ranges ofgeneral purpose 3

1

/

2

digittrue RMS multimeters are from 2mA to 2 A, or from 200 mV to 200 V. Their inaccuracy isaround 0.5% of full scale and bandwidth 0 to 50 kHz.

Wattmeters

Instantaneous power is the product of the instantaneous val-ues of the current and voltage, while active power is the time-averaged value of instantaneous power. Figure 7.3j shows apossible implementation of a single-phase digital wattmeter.The value presented in the display is calculated from thedigitized values of current and voltage. It is obtained byprocessing the current and voltage signals in conditioningcircuits prior to their being converted by the ADCs. Thesample and hold circuits are placed before the ADCs to assureDC inputs for the converters during their conversion times.

Since the instrument includes a processing unit, severalother electric and nonelectric quantities can be derived anddisplayed: RMS values of current and voltage, reactive power(sine wave input), phase angle, energy, period, etc. The designshown in Figure 7.3j allows measurement of both AC andDC power.

UTILIZATION OF ELECTRICAL METERS

Current Measurement

AC Current

Alternating current indicators are almost exclu-sively of the moving iron vane type because of their widerange and low sensitivity to frequency variations (less thanthe electrodynamic type) and waveform errors, and digital.

Moving iron vane meters in ranges from 1 to 50 A fullscale can be used for higher current ranges by the additionof external current transformers. Operating voltage is limitedto approximately 750 V. Above this level a current transformermust be used even if the current is within the meter rating.

FIG. 7.3g

Internal construction of an electrostatic meter.

Fixed Plate

Moving Plate Pointer

u

Pointer

Marked Scale

Spring

(a) (b)

FIG. 7.3h

Simplified block diagram of a digital meter.

Control

InputConditioner

Analog toDigital

Converter (ADC)

InputDisplay

© 2003 by Béla Lipták

7.3 Electrical Meters and Sensors

895

Meters calibrated for 60 Hz are usable from 25 to 400 Hz,with an additional error of only 1

/

2% full scale and may berecalibrated for use at levels as high as 1000 Hz. For mea-surement of small currents at frequencies above 400 Hz, orwhen variable frequencies must be measured, digital metersand electronic PMMC meters should be used.

This meter is available in ranges from 500

µ

A to 20 mAfull scale and may be used from 20 to 10,000 Hz without lossof accuracy on sine wave circuits. The upper limits of currentand frequency for digital meters are 10 A and 50 kHz with aninaccuracy of about 5%. For higher values of current, currentprobes (current transformers or Hall effect type) must be used.

FIG. 7.3i

Digital meter: detailed block diagram.

FIG. 7.3j

Block diagram of a digital wattmeter (sampling type).

RangeSelector

ResistanceConditioner

VoltageConditioner

CurrentConditioner

V/Ω

A

Common

DC

AC

RMSConverter

ADCand

Controller

Display

DecimalPoint

VoltageConditioner

CurrentConditioner

Sample&

Hold

Sample&

Hold

ADC

ADC

ProcessingUnit

and ControlDisplay

u

i

Control

Control

© 2003 by Béla Lipták

896

Safety and Miscellaneous Sensors

Current Transformers

For current measurement above the range of moving ironvane and digital meters, a current transformer is the easiestand cheapest solution. When inserted in the circuit, it providesthe proper ratio between the meter range and the measuredcurrent (Figure 7.3k). Most current transformers are designedto deliver 5 A at the secondary terminals when full primarycurrent is flowing. The primary winding can be the currentcarrying conductor, which is passed through the center of thesecondary winding in the form of a single-turn coil. This designrequires no mechanical connection or break in insulation.

Primary Turns

Selection of the current transformers ratioshould be based on the closest standard primary rating overthe maximum current to be measured. Because there are largeintervals between standard primary ratings for current trans-formers, it is often desirable to modify the transformer ratioby passing the primary conductor through the center of thesecondary winding two or more times. A typical currenttransformer with a rating of 100 to 5 A has a normal ratio of1 primary turn to 20 secondary turns or 1:20.

Passing the primary conductor through the center of thesecondary winding twice (Figure 7.3l) increases the primaryturns to two. Therefore, the ratio becomes 1:10, giving a newrating of 50:5 A. By taking additional primary turns, therating may be modified to correspond more closely to thedesired scale.

Secondary Turns

The new primary rating is determined bydividing the original primary rating by the number of turnstaken. Small adjustments to the transformer ratio may be madeby passing one of the secondary leads through the center of

the secondary winding so as to effectively add or subtractsecondary turns (Figure 7.3m). A current transformer with a100 to 5 A rating has 20 secondary turns. Therefore, the addi-tion of one secondary turn changes the turns ratio to 1:21, fora new rating of 105:5 A. By adding or subtracting the requirednumber of secondary turns, the rating may be adjusted toalmost any value. The new primary rating is determined bysecondary rating, which is 5 A in all cases. When both primaryand secondary turns are modified, the new primary rating maybe calculated by Equations 7.3(1) and 7.3(2):

7.3(1)

7.3(2)

FIG. 7.3k

Alternating current ammeter connections.

Meter Case

Meter Case

Coil

Meter Terminal

Coil

Meter Terminal

AC Source

AC Source

Load

Load

(1) Self-Contained Ammeter Connection

PrimaryWinding

SecondaryWinding

XI

(2) Transformer Rated Ammeter Connection

CurrentTransformer Terminal(Secondary Terminal)

FIG. 7.3l

Current transformer with two primary turns added.

FIG. 7.3m

Modifying the number of secondary turns on a current transformer.

ToLoad

SecondaryPolarity Mark

H1

X1PrimaryPolarity Mark

PrimaryConductor

FromSource

SecondaryTerminal

X1

To Meter

SecondaryPolarity Mark

PrimaryPolarity Mark

SecondaryTerminals

SecondaryLead

To Meter

SecondaryPolarity Mark

PrimaryPolarity Mark

SecondaryTerminals

SecondaryLead

(1) Adding Secondary Turns

(2) Subtracting Secondary Turns

H1

X1H1

original secondary turns =original primary turns

secondary rating

adjusted primary rating

(total secondary turns) (secondary rating)primary turns

=

© 2003 by Béla Lipták

7.3 Electrical Meters and Sensors

897

Polarity and Inaccuracy

Primary and secondary polaritymarkings are provided on current transformers with the pri-mary identified as H1 and the secondary terminal as X1. Toadd secondary turns, one should connect a lead to terminalX1 and pass it through the center of the secondary windingfrom the side opposite the H1 polarity mark, as indicated inFigure 7.3m. To subtract secondary turns, connect a lead toterminal X1 and pass it through the secondary winding fromthe same side as the H1 polarity mark.

Current transformer inaccuracy is expressed as the max-imum error for a particular load class as specified by theUnited States Standards Institute. Although load inaccuracydata are available from the meter manufacturers, it is seldomnecessary to check the meter. This is because if the meter islisted as transformer rated, it is also designed to maintain itsaccuracy when it is connected with #14 AWG leads at lengthsup to 150 ft (45 m) and #12 AWG leads at lengths up to 250ft (75 m).

Current transformers are generally insulated for use onsystems up to 600 V, but 600 V transformers may be used athigher voltages if the primary conductor is fully insulated.Current transformers designed for ammeters are availablewith 0.6 and 1.2% inaccuracy and in the following standardprimary ratings: 100, 150, 200, 250, 300, 400, 500, 600, and800 A.

Current transformers used to extend the measuring rangeof AC current meters must operate with a very low secondaryload, close to short-circuit, to assure that the magnetizationcurrent is small enough. Care must be taken when connectingthe transformer. Particularly, one should make sure that thesecondary is not left open; if that happens, the magnetizationcurrent will be approximately equal to the primary current.Under these conditions the electromechanical stress to whichthe magnetic material is subjected can destroy it. This canoccur in form of an explosion.

Hall Effect Probes

The current range of digital meters with voltage-sensingcapability can also be increased using probes designed onthe basis of the Hall effect. A Hall sensor detects and displaysthe magnetic field caused by the current and produces avoltage proportional to that current. Currents up to somehundred amperes can be measured at frequencies up to tensof kilohertz. The inaccuracy of measurement is about 3%.

DC Current

Direct current indicators are either analog or digital. Theanalog designs can be the PMMC type, which take advantageof the low power consumption and inherent linear scale factor,while avoiding the residual magnetic errors of the iron vanetypes or the slower response of electrodynamic movements.

Current carrying capacity of the internal connections tothe coil of PMMC meters limits the self-contained meters toa range of 20

µ

A to 1 A full scale. So-called self-contained

meters are available for up to 50 A; however, they are actuallylow-range instruments with an internal shunt. Above thisrange external shunts are employed. Meters are suitable foruse on up to 600 V circuits. Above this value other types ofmeters or transducer-rated meters are generally used.

Digital current meters are available with ranges frompicoamperes (useful in applications such as measurement ofconductivity or low conductivity or insulating materials) tosome tens of amperes. The use of shunts to extend the upperlimit of that range is possible; nonetheless, Hall effect probesare more often used for that purpose.

Ammeter Shunts

Direct current ammeter ranges can be greatly extended byconnecting a shunt of the proper resistance in parallel withthe meter so that a specific proportion of the current passesthrough the meter, the remainder being carried by the shunt(Figure 7.3n). Analog meters designed for shunts are ratedeither at 50 or 100 mV, depending on the voltage drop acrossthe meter terminals at full-scale deflection. When a shunt isused it must have a corresponding millivolt rating. The actualresistance value of the proper shunt does not have to beknown since shunts are rated on the basis of full-scale metercurrent and are available from 5 to 20,000 A, calibrated to

±

0.25% inaccuracy.Shunt-rated ammeters are calibrated for a particular shunt

lead resistance, factors that vary from one manufacturer toanother, and the correct calibrated shunt leads should be usedfor maximum accuracy or the meter should be recalibratedfor use with different leads. Noncalibrated shunt leads of #14AWG wire have an additional error of 1

/

2% for 50-mV metersat distances up to 25 ft (7.5 m) or for 100-mV meters atdistances up to 40 ft (12 m).

FIG. 7.3n

Direct current ammeters with internal and external shunts.

MeterCase

Meter Case

Coil

Meter Terminal

Coil

Meter Terminal

DC Source

DC Source Load

Load

(1) Self-Contained Ammeter with Internal Shunt

(2) Ammeter with External Shunt

InternalShunt

ExternalShunt

CalibratedShunt-Lead

ShuntTerminal

+

+

−

+

−

−

+ −

© 2003 by Béla Lipták

898 Safety and Miscellaneous Sensors

Voltage Measurement

AC Voltage Indicators for AC voltage measurement can bedigital or analog. Analog designs include the moving ironvane, electronic PMMC, or electrostatic types. As discussedbelow, each has its own advantages and each is preferred fora particular voltage range.

The performance of digital voltmeters is generally supe-rior. Their input impedance is usually higher than 1 MΩ andtheir ranges extend from microvolts to hundreds of volts.Their sensitivities are better than 1/2000 of full scale andtheir bandwidths are higher than some tens of kilohertz. Theirerrors are usually under 1% of full scale.

Moving iron vane voltmeters have the advantage of highaccuracy and wide range, although their sensitivity is poor.Voltmeter sensitivity is determined by the coil current, whichis required for full-scale detection and is expressed in ohmsper volt since the coil current is inversely proportional to thetotal resistance. A series resistor is generally installed withinthe meter case to provide the total resistance required by themovement so that full voltage equals full-scale meter current.

Self-contained moving iron vane voltmeters are availablein ranges from 3 to 600 V full scale. Their correspondingsensitivities range from 4 to 250 Ω/V. These meters are usu-ally calibrated for 50 or 60 Hz; however, they may be usedin circuits from 25 to 1000 Hz when calibrated for a specificfrequency.

Rectifier-type PMMC meters have an advantage in thattheir high-resistance coils permit greatly increased sensitiv-ity. However, due to a variety of rectifier losses, they are notas accurate as the moving iron vane type. They are availablein full scale ranges from 3 to 800 V and with standard sen-sitivity of 1000 Ω/V at all ranges. Calibrated for 60 Hz, thesemeters may be used from 20 to 10,000 Hz without loss ofaccuracy, although they become inaccurate if used in circuitswith wave shapes other than the sine wave (non true RMSmeters).

Electrostatic meters have the advantage of extremely highinput impedance and large bandwidth but have poor sensitivity.

Potential Transformers

For measurements on circuits above 600 V or on lower volt-age circuits in which isolation is desirable, a moving ironvane meter is used with a potential transformer to providethe proper ratio between circuit voltage and meter movement(Figure 7.3o). Meters used with transformers are usually pro-vided with a 150 V range having a sensitivity of 100 Ω/V.The corresponding potential transformers are always fur-nished with a ratio based on a 120-V secondary to permitindication of small over voltages. For this reason potentialtransformers must be selected on the basis of maximum cir-cuit voltage and not on full-scale meter reading.

Potential transformer errors are specified by the UnitedStates Standards Institute in a manner similar to that of cur-rent transformer inaccuracy. Checking is seldom required,

because the error is not exceeded until the lead lengths exceedseveral hundred feet. Potential transformers are availablewith primary ratings from 120 to 14,400 V and with 120-Vsecondary. Their inaccuracies at frequencies from 50 to400 Hz are 0.3 to 0.6%.

When connecting potential transformers to high voltagecircuits it is good practice to connect one of the secondaryterminals to ground to assure that the meter and the operatorwork at low potentials relative to the ground. Due to thecapacitance between the primary and secondary windings,allowing the secondary to float may lead to high potentialsin the secondary.

DC Voltage Almost all analog meters for DC voltage mea-surement are of the PMMC type because of their high sen-sitivity, linear scale, and wide range. Self-contained DC volt-meters are available in ranges from 1 to 600 V full scale witha standard sensitivity of 1000 Ω/V in all ranges. Above thisrange, self-contained meters are not available because theirinternal resistance would become very high and resistorlosses would result in excessive heating.

External resistors can be used on circuits above 600 Vto extend the measurement range of the PMMC. Circuit iso-lation is not possible in this arrangement, and the meter willbe damaged if the external resistor is accidentally shorted.Instruments with sensitivities of up to 20,000 Ω/V are avail-able, although not in all ranges.

Digital voltmeters for DC voltage measurement have thesame metrological characteristics as do the AC digital voltme-ters already discussed. To measure voltages that are higher thanthe upper range of the instrument, voltage dividers are used.

FIG. 7.3o Alternating current voltmeter installations.

Meter Case

Coil

Meter Terminal

Coil

Meter Case

AC Source

AC SourceLoad

Load

(1) Self-Contained Voltmeter Wiring Diagram

Meter Terminal

InternalResistor

PotentialTransformerTerminals

InternalResistor

Secondary Winding

+

−

+

−

Primary Winding

(2) Voltmeter Installation Utilizing a Potential Transformer

© 2003 by Béla Lipták

7.3 Electrical Meters and Sensors 899

These can be either of the resistive or preferably of thecapacitive type.

Voltmeter Resistors Inserting an external resistor of theproper value in series with a PMMC voltmeter (Figure 7.3p)permits measurement of higher voltages or increased sensi-tivity at low ranges. Meters with external resistors generallyhave 1 mA movements and 125Ω internal resistance. Stan-dard resistors designed to afford a sensitivity of 1000 Ω/Vmay be selected on the basis of full-scale meter readingwithout the necessity of calculating resistance. Standardresistors are available in voltage ratings from 250 to 30,000V, and resistors for nonstandard voltages may be calculatedusing Equations 7.3(3) and 7.3(4):

7.3(3)

7.3(4)

Instruments requiring less current for full-scale deflectionpermit greater sensitivity. Once the total resistance has beendetermined for a particular voltage range, the new sensitivitymay be calculated by using Equation 7.3(5) below:

7.3(5)

Measurement accuracy is not noticeably affected by leadlength because the value of the external resistor is usually

very high. The calibrated inaccuracies of these units are±0.25%.

Power Measurement

The unit of electric power is the watt, which equals 1 J ofwork or 1 J of energy per second (W = J/s). The watt is alsoequivalent to 3.4 Btu/hr or 0.001341 hp. The power in a DCelectric circuit is the product of the current flowing throughit and the voltage existing across it. In AC circuits, the instan-taneous power, p, is:

p = iu 7.3(6)

where i and u are the instantaneous values of current andvoltage, respectively. The active power P is the time averagevalue of the instantaneous power:

P = (iu)av 7.3(7)

If the circuit is under sine wave regime, 7.3(7) can bewritten under the form:

P = IUcos(φ) 7.3(8)

where I = RMS value of AC current, U = RMS value of ACvoltage, and φ = Phase angle between U and I.

The power factor, P.F. = cos(φ), can assume valuesbetween 1 and 0. It is 1.0 in a purely resistive circuit and is0 in an ideal (total reactive) capacitor or inductor. In actualcircuits it is always between 0 and 1.0. In other words, thepower factor is the ratio between the true power and theapparent power (Papp = IU).

A wide variety of devices are used to measure electricpower.3 The units most widely used in industry are describedbelow.

AC Power Analog indicators for AC power measurement areusually constructed with electrodynamic movements becausethe separate fixed and moving coils permit two different typesof input signals for the same movement. The fixed coils areusually connected to measure currents, and the moving onesare connected to monitor voltage (Figure 7.3q). Connection ofthe coils in this way causes a deflection of the moving coilproportional to the instantaneous product of the circuit currentand voltage. Inertia prevents the moving coil from respondingquickly to current and voltage variations in AC circuits above25 Hz, and pointer will indicate the average AC power regard-less of wave shape. The way wattmeters are wired introducesa certain amount of error; this can be minimized by alteringthe wire connections as a function of current and voltage valuesbeing measured.

Single Element Wattmeters In the wattmeter shown inFigure 7.3q, the current in the current-carrying coils is thetrue load current. However, the voltage across the potentialcoil is higher than the load voltage by an amount equal tothe voltage drop across the current coils. This arrangementwill result in a positive error in power measurement by an

FIG. 7.3p Direct current voltmeter installations.

MeterCase

Meter Case

Coil

Meter Terminal

Coil

Meter Terminal

DC Source

DC Source Load

Load

(1) Self-Contained Voltmeter Wiring Diagram

(2) Voltmeter Installation with External Resistor

InternalResistor

ExternalResistor

InternalResistor

+ −

−

+

+

+

−

−

total resistancefull-scale meter readingfull-scale meter current

=

external resistor value total resistance – meter resistance=

sensitivitytotal resistance

full-scale meter reading=

© 2003 by Béla Lipták

900 Safety and Miscellaneous Sensors

amount equal to the power consumed by the current coils.This error will be lowest when the wattmeter is used on high-voltage circuits with low-current loads.

If the external wiring is changed, as shown in Figure 7.3r,the voltage across the potential coil will be the true loadvoltage. In this case, the current drawn by the potential coilwill also pass through the current coil and the wattmeterreading will be high by an amount equal to the power con-sumed in the potential coil. The error will be lowest whenthe meter is used in low-voltage circuits with high-currentloads.

Meter scales are linear and their accuracy is high, but lowsensitivity is the result of the high power consumption. Theunits are usually calibrated for 50 or 60 Hz and recalibrationis necessary when used at frequencies up to 400 Hz.

Wattmeters are rated for maximum current and voltagein addition to maximum wattage. This is because circuitswith large phase angle differences between current and volt-age (circuits with low power factor) can overload the currentor voltage coils without causing large wattage readings.Power measurement in single-phase, two-wire circuits

requires a single element wattmeter consisting of two fixedcurrent coils and one moving potential coil.

The fixed current coils are wound with heavy wire asrequired by the meter current rating. The moving coil isusually wound with fine wire and is provided with a seriesresistor to ensure a high-resistance, low-inductance circuitfor potential measurement.

Self-contained meters have ranges from 125 to 1000 Wfull scale with current ratings from 1.25 to 10 A at 120 V.Transformer-rated meters are also available. Their rating is5 A at 120 V and their available scale ranges are from 1000W to above 100 MW, depending on current transformer andpotential transformer ratios.

Also available are wattmeters with a full scale that is apercentage (often 10%) of the product of current and voltageranges. These instruments (low power factor wattmeters) areparticularly suited for power measurement on circuits withlow power factors.

Multielement Wattmeters Power measurement in three-phase,1 three-wire circuits necessitates a two-element wattmeter(Aron method) consisting of two single-element movementswith the moving coils attached to a common shaft that is wiredas shown in Figure 7.3s. Each of the elements measures aportion of the power drawn by the load and adds to thecommon moving coil shaft a proportional torque so that thepointer will indicate total power. Using two independent single-phase wattmeters and in sine wave regime, this configurationallows the measurement of reactive power (differencebetween the readings of the wattmeters) and power factor.1

The transformers of multielement wattmeters are almostalways rated with 5-A current coils and 120 to 600 V potentialcoils. Meter ranges from 5000 W to more than 100 MWare common, although ranges as low 1000 W are also available.

Power measurements can be made in three-phase, four-wirecircuits by a three-element wattmeter. Such a design is seldomutilized because the two-element wattmeter movement can

FIG. 7.3q Single-element wattmeter, wired for accurate detection of low-currentand high-voltage loads.

FIG. 7.3r Single element wattmeter, wired for accurate detection of high-current and low-voltage loads.

AC Source Load

InternalResistor I P P I

MovingPotential Coil

FixedCurrent Coils

MeterCase

CurrentTerminal

PotentialTerminal

I P P I

AC Source Load

InternalResistor

MovingPotential Coil

FixedCurrent Coils

MeterCase

CurrentTerminal

PotentialTerminal

FIG. 7.3s Two-element wattmeter wired for three-phase, three-wire loads.

Load

InternalResistor

MovingPotential Coil

FixedCurrent Coil

MeterCase

CurrentTerminal

PotentialTerminal

Three-PhaseFourWireAC

Source

L2

L3

N

L1

I I I I IIP P P P

© 2003 by Béla Lipták

7.3 Electrical Meters and Sensors 901

be modified to permit measurement on three-phase, four-wiresystems by reconnecting one of the fixed coils for each ele-ment (Figure 7.3t). Meters of this type are known as 21/2-element wattmeters. They will correctly indicate power forthree-phase, four-wire loads as long as the lines to neutralvoltages are balanced for all three phases. Meter ranges from10,000 W to more than 100 MW are available in this design,with ratings of 5 A at 120 or 240 V.

Digital wattmeters are available for both AC and DCapplications for both single and multiphase measurements.Without using external components, the ranges can extendfrom a few milliwatts to some tens of thousands of watts.With the use of potential and current transformers or shuntsand voltage dividers, the range can be increased dependingon the characteristics of these external devices. The two watt-meter (Aron method), as shown in Figure 7.3s, is also com-monly used for AC power measurement.

DC Power Direct current wattmeters are the same as single-element AC wattmeters but it is advisable to calibrate them foruse on DC circuits. Ranges from 100 to 2000 W are availablewith ratings from 1 to 20 A at 120 V. Higher ranges may beaccommodated by adding an external resistor to the potentialcircuit for use on high voltages, although this introduces addi-tional errors. Because of these errors, other measuring solutionssuch as DC watt transducers are often used for higher ranges.

Meter Scales

In general, the best choice of meter-scale range is one inwhich the maximum anticipated value of current, voltage, orpower will fall at 80% of the full-scale reading. Scale selec-tion on this basis provides reasonable utilization of the meterscale, furnishing good visibility with the capability to indicatemoderate overloads.

When many analog meters are grouped in a small area,it may be desirable to have all normal readings at the midscale

region in order to permit easier identification of abnormalconditions. The midscale pointer position on nonlinear scalescorresponds to a value of approximately 65% of full scale,while on linear displays it corresponds to a value of 50% offull scale.

References

1. Berlin, H.M. and Getz, F.C., Principles of Electronic Instrumentationand Measurement, Columbus, OH: Merrill Publishing Company, 1988.

2. TREK, Inc., “Electrostatic Voltmeter System,” Medina, NY, January30, 2002, www.trekinc.com/Voltmeters.htm.

3. Pedro, M.B.S.G. et al., Volt-Ampere Meters, New York: John Wiley &Sons, 2000.

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FIG. 7.3t A 21/2-element wattmeter wired for three-phase, four-wire loads.

Load

InternalResistor

MovingPotential Coil

FixedCurrent Coil

MeterCase

CurrentTerminal

PotentialTerminal

ThreePhaseThreeWireAC

Source

L2

L3

L1

I I I IP P P P

© 2003 by Béla Lipták

902 Safety and Miscellaneous Sensors

“Power Measurement and Analysis,” Measurements and Control, December1993.

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© 2003 by Béla Lipták