201:Voltage Measurement
Halit Eren
Curtin University 01Technology,Perth, WesternAustralia, Australia
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1 INTRODUCTION
The output signal fonTI to be measuredin the majority of
sensorswill require the measurementof either a voltage
(this article), a current (Artide 202, CorreDi Measuremeni, Volume 3), or a resistancelimpedance
(Artide 203,
ResistanceMeasurement, Volume 3). Thus, their explanation is fundamentalto most measurements.
So far as voltage measuringdevicesare concerned,voltage measurementcan be classified as
1. low-voltage measurements,such as those generatedby
sensors;
2. medium-voltage measurements,such as those that
exist in the power mains, laboratories, and industriaI
operations;
3. bigh-voltage measurements,sueh as a rise in power
generators,transmissionlines. and with plasma effects.
-
Consequently,thereis a wide rangeof voltage measuring
techniquesand devicesin use. This article concentrateson
medium-voltageand high-voltagemeasurements.
Low-voltage measurementsfor sensorsrequire sophisticated signal processingschemes- see Artide 121, Signals
in the Presenceor Noise, Volume 2; Artide 176, Signals
and Signal-to-noise Ratio, Volume 3; Artide 178, Noise
Matching and Preamplifier Selection, Volume 3; Artide 179, Input Connections; Grounding and Shielding,
Volume 3; and Artide 181, Amplitude Modulated Signals: The Lock-in Amplifier, Volume 3.
Common to alI techniquesare three major aspectsthat
characterizethe measurements:
1. Amplitude: li the voltage is smaller than a few millivolts. we may'òeed to use suitable electronic components to amplify the'signals. li the voltage is large. in
the kilovolts and megavolts region. we may need to
attenuatethe magnitudein order to bring it to manageable levels.
2. Frequency: The frequencyof a voltage signal plays an
important role in configuring the appropriate components of a voltage measuring device. The frequency
of interest can range from DC to a few gigahertz.
If digital techniquesof measuring afe used. sampling
of the voltage signals must conCorroto the Nyquist
sampling criteria. The signal frequencywaveform also
needscareful considerationtest errors be generated.
3. Duration: The duration of a signal is significant in
deterrnining the appropriate technique to use for the
measurement.Duration may vary from continuous signals; as in the case of power supplies. to impulses
appearing for a few microseconds;as in the casesof
surges. and corona effects in power transmission and
distribution.
Handbook01Measuring SystemDesign. edited by Peter H. Sydenhamand Ricbard 'l'borA,
e 2005 Jobo Wiley & Soo8.Ltd. ISBN: 0-470-02143-8.
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1354 CommonMeasurands
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5.
instruments:
signal.
signal
(LCDs).
Cathode
acteristic
truments
4.
Since most common signals afe in voltage fonTI, there afe
many different techniquesfor processingthe signals generatedby a particular variable. However, some instruments
called voltmeters afe deliberatelydesignedto measurevoltages.There are five common types of voltmeters; theseare
1. Electromechanicalinstruments:These instruments afe
based on the mechanical interaction between various
currents. between currents and magnetic fieJds. or
.
digital eIectronic instruments afe obtained.
Oscilloscopes or vacuum tube instruments: These
3 MEASURING NETWORKS
electromechanicalinstruments,
thennal type instruments,
electronic instruments,
Cathode Ray Oscilloscopes (CRO) or vacuum tube
instruments(VTI),
5. virtual instruments.
a
instruments:
effects
bui
others
These
reading
The
thermal
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on
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to
to
pointer
springs.
usually
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voltage
the
measurement.
instruments
analog
employed
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Electronic
3.
that
Although the concepì of electric potential is useful in
understandingelectrical phenomena,it is worth I\Oting that
only the differences in potential energy are measurable.
Therefore, it is commonly understoodthat the term voltage
refers to potential differences. The measurementunit far
the voltage is, in the InternationalSystemof Units (SI), the
volt (symbol: V).
Measurementof voltage is of utmost importance and
extensivelyusedin the electrical and electronicengineering,
especia1lyin the power industry. Moreover, when electronic
devices far signal processingare involved, such as those
used in telecommunicationsysterns,control systems,and
informatics, the majority of signals are in the voltage and
current formo Therefore, voltage measurementconstitutes
an important areain industriai and scientific measurements,
and in a diverse range of sensorsof chemical, biological,
and physical variables.
the
voltage.
(1)
input
= cou1omb
ljou1e
as
lvolt
of
mechamcal
square
the
to
generated
The
torque,
mechanical
instrument
proportional
the
voltage
dispiacement
on
Thermal
2.
ductor.
Voltage measurementis essentialin electrical engineering
as well as in many other disciplines of engineering and
science. Voltage measurementinvolves determination of
the electric potential difference between two points. The
potential difference is the amount of work neededto move
a unit charge located in an electric field from a reference
point to another point. Hence, the potential difference is
always relative to some referencepoint such as the Earth.
The potential difference is taken as the work per unit
charge and the volt is related to the unit of work (joule J) and the unit of charge(coulomb - C) by
or
generate
between
2 BASIC THEORY
eIectri~ed
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can be made by a single instrumenttermed as multimet~
Voltage Measurement
or volt-ohm-multimeters(VOMs). The VOM is a combination of the necessarycircuits of a DC ammeter, DC
voltmeter, AC ammeter, AC voltmeter, and a multirange
ohmD1eter.The typical DC voltage range of a common
VOM is O to lOOOV,although with extemaI resistor networks and voltage transformers,the range can be increased
further, to say 5000V. The DC current range is usua11y
lO A but with the use of externa1resistive shunt networks,
or current transformersthe range can be extendedto much
higher levels.
Particularly in power generation and transmission networks, precise, and adequatesystem measurementsat the
contrai centers are criticai far high quality of operationaI
decisionmaking. The measurementstalcingpiace in remote
locationsare made available to the controllers by networks
suchasthe Rea!TIme SupervisoryControl and Data Acquisition systemsSCADA. The digital devicesthat collect the
voltage measurementsfrom the substationinstruments and
transducersafe called remote terminaI units (RTUs). The
RTIJs communicatewith the SCADA aver dedicated telephone lines, sometimesthe transmissionline itself and/or
microwavechannels.
The collection of anaIogmeasurementsand the status of
the circuit breakersfrom remotely monitored and controlled
substationsare telemeteredby meansof the cyclic scansof
SCADA system.TypicaIly, eachscanlasts from 1 sto tOso
This information has to be sufficient in number and evenly
distributed acrossthe network so that the observability of
the systemcan be ensured.
4 VOLTAGE TRANSFORMERS
Transformersafe extensivelyusedin high-voltage measurementsprimarily to step the voltage down to a lower level
that can be less expensivelymeasured.
Transfonners are devices tbat change tbc voltage level
in tbe process of energy transfer from ODe AC system
to another. The transfonner has two coils, primary and
secondary,botb of which are wound on an iron core as
shown in Figure l.
Tbe magneticftux generatedby tbe primary current links
tbe secondarywindings to generatea secondary voltage.
Assuming 100%magneticcoupling, tbe ratio of tbe primary
voltage (VI) and secondaryvoltage (V2) can be expressed
by tbe turns ratio NI and N2 as
VI
V2 --
N)
N2
(2)
This meansthe secondaryvoltage can be steppedup or
down dependingon the turos carlo. For example, if N l is
1355
Figure 1. TransformerconStructioD.
lO times greatertban N2' tbe secondaryvoltage is lO times
smaller tban primary voltage.
Voltage measurementinstruments afe used throughout
tbe electric power system for monitoring and control purposes.Instrurnentationcomponentsrequired to accomplish
tbe measurementsare tbe transducers,signal conditioners, and tbe analysis and monitoring equipment. Voltage
transducersconvert tbe system voltage to an acceptable
level neededas tbe input to tbe signal conditioning equipmento The transducersare required to produce a scaled
down replica of tbe input voltage to the accuracyexpected
for a particular measurement.Commonly used transducers afe electromagn~ticvoltage transformer (VT), capacitive voltage transfonner (CVf), and tbe cascade voltage transfonner.
Voltage measurementtransfonners need to be specially
designedto ensuretbe ratio is constant.Voltage transformers are much like small power transformersbut tbey nero
to operatewitb secondarywinding operating close to open
circuitoThe winding voltage drops are made small, and tbe
rated ftux density in tbe core is designedto be well below
saturationdensity. Theseconditions maintain tbe calibrated
voltage ratio.
Measuring very high frequency componentsin tbe voltage requires eitber a capacitive divider, or pure resistive
divider. Special-purposecapacitordividers can be obtained
for accuratecharacterizationof transientsand hannonicsup
to at least l MHz. A disadvantageof such dividers is tbat
tbey do not provide electrical isolation between tbe high
voltage and tbe measuringsystemsand so impose special
conditions for tbeir use.
The cost of tbc electromagneticVT tends to increase
at an exponential rate witb tbe rated voltage increase.An
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1356 CommonMeasurands;~
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alternative, more economie solution has been found in the
CVT. This combines a capacitivepotential divider with an
auxiliary electromagnetic voltage transformer. This combination enablesthe insulation requirementsof the electromagneticunit to be reducedwith associatedsavingsin costo
The CVT was developed to reduce the high così of
conventional VT by compromising on the frequency and
transientresponse.Another possiblesolution to the problem
is to use the cascadeVT that is formed by connecting
tWo or more electromagnetictransformerunits in cascade.
The primary windings of thesetransformersare connected
in series and in this way the primary voltage is broken
down in several distinct and separatestages.This solves
the insulation problem and reducescosts. The secondary
winding consistsof a single winding on the last stageonly.
Optical voltage sensorsafe also under development as
replacementsfor VTs. They lower the costs compared to
conventional CTs and VTs when massproduced.jIowever,
questions remain about their stability, sensitivity, and linearity. The sensitivity of the optical sensorsto vibration and
.
temperatureehanges must be ID1D1ID1Z
.. . edby el' th er deslgn
or.
AD important device that is capableof measuringvoltages without drawing currents is the potentiometei.This
device is not actually an instrument. but a set of electrical networks that afe suitably arranged for the purpose.
This arrangementalso inciudes a galvanometeror indicatoro The main purpose of the potentiometeris to perforro
an accuratecomparisonof an unknown emf againsta standard oDe.There afe many different types of potentiometers
that can suit the requirementsof a particular measurement,
such as the slide-wire De, slide-wire AC, Gall- Tinsley
AC, and Drysdale- Tmsley AC Potentiometers.Owing to
limited space.as an example.only the slide-wire DC potentiometer will be explainedbere.
1. The slide-wire DC potentiometer: The principle of
operation of a slide-wire potentiometer can best
be described by the slide-wire variety illustrated
in Figure 2. The description of the various tenns
employed in this figure is as follows: E is the supply
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signal processing. The long-term stability of these sensors
battery emf, R IS the regulatrng reslstance; I IS the slide~
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.
.
.
Wlre c~nt
at bal~ce c~ndiUon~; r ~s the reslstance
is under study in field trials, but techniquesfor calibrat-
per urnt length of.slide-wlre; E) IS the battery ernf to ,::
ing them in the field and in the test laboratory
be measored;
bave yet to
~2 IS ~e emf of standar~. batte~;
:;
the len.gth of slide-wlre
An important branchof voltagemeasurementis the determination of harmonicsof suchpararnetersasthe fundamen-
E! ; 12IS the length of slide-wlre at balanceCOndltiO~ ..
Wlth standardernf E2.
Wl~ ~~.:.
A battery of unknown emf E1 is inserted in the circui~
at a point shown in Figure 2. The galvanometerswitch S is,"
elosed and the contact B moved along the slide-wire unti1%
the balance condition (zero reading on the galvanomete'i'c,
is achieved.In this condition, no current ftows through th~,
galvanometercircuito The current j supplied by battery E'\
ftows tbrough the slide-wire. By Ohm's Law:
,"
the problem.
Instrumentsand systemsfor power quality measurements
can help identify the sourcesof power quality degradation
and protect customerequipment.Many power quality monitoring instruments are designedfor input voltages up to
600 V rms and current inputs up to 5 A rms. In measurements, appropriatevoltage transducersmust be selectedto
provide thesesignal levels.
EI
= irll
,
5 POTENTIOMETERS
There afe many applications in which voltage measurements must be performedwithout drawing any current from
the circuit to which the measurementdevice is connected.
A typical case is the measurementof the electromotive
rocce(emf), or no-load voltage,of a sourcewith high internaI resistance.
conditions
l) is
be developed,
tal power-frequency voltage, voltage dips, spikes, sorgesti.,
and sags,and other transientbehaviors.
Specific reasonsfor taking harmonic measurementsinelude confirming the presenceof harmonics,evaluating the
severity of the problem relative to acceptablelimits, establishing compliancewith standardsand guidelines,harmonic
filter design, providing input data for harmonic software
analysis program, and designing an analytical model of
~t bal~e
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Figure 2. Slide-wirepotentiometer.
-
Single-phase voItage controllar
1.0
With purely resistive load, from (6), the rms value output
voltage can be determinedto be
V.
o,. =v.
111
/---+1
Ot
sin2a
2
21Z'
41Z'
(7)
Equation (7) indicates that the output voltage is a function
of the firing angleof the thyristors.The nonnalizednns load
voltage versus firing angle far a single-phasecontroller is
illustrated in Figure 4.
The DC averagevalue is then
Vi)= -l
1"+. Vmsin(wt)d(wt) = -2!.
2V
cosa
K a
7 RECTIFIERS
K
The amplitude of the AC terms can be calculatedfrom
v" = J a: + b2.
For AC measurements,most instruments contain AC-toDC conversion (or rectificatiòn), which afe made from
germanium or silicon diodes so that the voltages can be
expressedin rms values. Depending on the signals, the
rectification can be performed by transistor or operational
amplifier circuits or by the SCRs.
AC/DC converters (rectifiers) operate on similar principles as the voltage controllers. These rectifiers can be
configured in uncontrolled, semicontrolled, or fully controlled forms. Some of the configurationsafe
. single-phasehalf-wave rectifiers,
. single-phasefull-wave rectifiers,
. polyphasehalf-wave rectifiers,
.
where
a
Il
=-
b =
2Vm
11:
2V",
Il
11:
[ cos<n+
-
1)(1- cos(n 1)(1
n+l
[ Sin(n + l)a
n+l
n-l
-
sin(n -l)a
]
] for n = 2,4,6...
n-l
The Fourier series for the current is determinedby superposition
where
polyphasefull-wave rectifiers.
Rectifiers can be configuredby using center-tappedtransformer arrangementsor by bridge forms. Since there afe a
variety of techniquesavailable,bere,as an example,we will
The outputs of the controlled rectifiers can be improvedby
suitable arrangementsof capacitive-inductive (L-C) filterS..;
VoltageMeasuremem1359
The spring has a large number of turns greatly reducing the deformation per unit length and giving an angle
of deftection (9) directly proportional to the deftecting
torque. Occasionally. a long helical SPrÌng replaces the
spiraI spring. In some instrurnents.a single strip of phosphor-bronze provides tbe necessaryspfing control. Often
two springs. wound in opposite directions are employed.
This method is employed in order to reduce the reading errors.
Although tbe electromechanicalinstruments represent
0100 tecbnologyin comparisonto tbe electronic techniques.
and the digital ones.in particular. they are stilI extensively
used in many areas such as Panel displays in industry.
dashboarddisplays in motor vehicles. general-purposelow
cost measurementsand laboratories.
tbe moving-coil electromagneticvolbneters (D'ArsonvaI GaIvanometer);
the moving-iron electromagneticvoltmeters;
the electrodynamicvoltmeters;
the electrostaticvoltmeters;
electromechanicaImultimeters or VOMs.
99 DIGITAL
DIGITAL VOLTMETERS
VOLTMETERS
The basic structure of a digital voltmeter (DVM) consists
of the following three main stages:
I. analog signal processing,
2. analog-to-digital (AID) converter,
3. digital signal processor(DSP).
I
Figure 6. Schernaticof a spring control1edvoltage indicator.
The first stageof the device conditions the input signal,
adapting it to the dynamicsof the AID. The AID converter
is responsiblefor samplingof the input signal and converting each sampledvalue into a digital formo The sequence
of digital values obtained~afterthe sampling and conversion operationsis stored into the memory of the DSP and
processedin order to attain the desired measuredvalues.
The detailed structure of a digital multimeter is given in
Figure 7.
1360 CommonMeasurands
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Figure 7. Block diagramof a typicaldigital multimeter.
DVMs may differ from eachother in the following ways:
. number of measurementranges,
. number of digits,
.
.
.
accuracy,
speedof readings,
operating principles.
In a modero DVM, the basic measurementranges to
obtain fun-scale vaIues are as low as 0.111V. If an appropriate voltage divider is used, it is aIso possible to obtain
fun-scale vaIuesas high as lOOOV.The DVM, with a suitable input stage, can be used as an ammette having very
broad measurementrangesfrom I nA to lO A.
When the measurementresult is displayedon the instrument front panel, it is usualIypresentedin decimaInumbers,
with a number of digits that typica11yrange from 3 to 6.
When the measurementresult is sent to a DSP system,
its representationtakes the form of a binary-coded output
signaI. The number of bits of this representationtypicaIly
rangesfrom 8 to 16, though 18-bit and 24-bit AID converters are available.
The accuracyof a DVM is usuaIly coITelatedto its resolution. This is quite obvious, since assigningan uncertainty
lower than 0.1% of the range to a three-digit DVM makes
no sense,since this is the displayedresolution of the instrumentoSimilarly, a poorer accuracy makes the three-digit
resolution quite useless.Presently, a six-digit DVM can
feature an uncertainty, for short periods of time in controned environment, as low as the 0.0015% of reading or
0.0002% of the full range.
The spero of reading of a DVM can be as high as
1000 readings per secondoWhen the AID conversion is
considered,the conversionrate is takeninto accountinstead
of the speedof reading. Presently,the conversion rate for
12-bit, successiveapproximation AID can be as high as
nominalIy lO MHz. The conversion rate can be on the
order of 1GHz for lower resolutions when flash AID
converters afe used - see Artide 139, Analog-to-Digital
(AID) Converters, Volume 3.
lO VOLTAGE AND VOLTAGE
MEASUREMENT STANDARDS
Voltage is an important property in electrica! engineering
and measurementtechnology. Hence. strict standardsafé
developedin two major areas:
l.
2.
by its own standardssuch
standard- see Artide 43,
techniquesafe standardized.
t~:
suit specific areasof application, such as the IEEE S~
1122 for digital recorders,IEC 60060 for high-voltagl:
impulse calibrations.
The primary voltage standardis, today, the Josephso~
junction standard.Other voltage standardsare nevertheles~'
employed in the metrologicallaboratoriesas they afe mo~
convenient and, far example,afe the lime honoredstandar~:
cells, although their accuracy is lower than that of th~
Josephsonjunction.
.
The Josephsonjunction standard describesthe quantum
standardof voltage. A Josephsonjunction consistsof tW°o
super conductors separatedby a thin insulation barrier:
The junction is supercooledin belium cryostat and whelf'
it is irradiated by microwave energy (in the frequency
range 10-100 GHz), the voltage-current characteristicsget~
broken to the steppedformoThe height of eachvoltagestep
can be found from
...
(12):
.
where h is the Plank constant,f is the frequencyat wbicb
the junction is irradiated, and e is the electron charge. ..<
.
uncertainty
.
The standardcells are madefrom saturatedelectrochemical Weston cells, which consist of electrodesof mercury
(positive)andmercurycadmiumamalgam(negative)placed
in an electrolyte of saturatedcadmium sulfate solution containedin an H-shapedglasscontainer.There afe two types
of Weston cells
-
the saturated celI and the unsaturated celI.
The saturated celI has a voltage variation of approximately -40 ~ V per 1 K, whereas the unsaturated celI
has a negligible temperaturecoefficient at normal room
temperatures.
.
By using precisionpotentiometers,the standard-cellvoltagecanbe comparedwith better than 1 part in 107accuracy.
However, the saturatedcells afe very sensitive to environmenta! conditions and the current they supply introduces
further uncertaintyin calibrations.
The various national standard IAboratoriesrefer to the
Josephsonjunction standardas their primary standardfor
voltage.However, since the standardcells are much easier
to employ, they also maintain a number of saturatedcells,
referred to by the Josephsonjunction standard, as the
primary standardsfor voltage. Cells afe kept in an oH bath
to control their temperaturewithin :i:0.01 K. The voltage
of the WestonsaturatedcelI at 293.5K is 1.01858V. They
remain satisfactoryas voltage standardsfor a period of 15
to 20years with a drift voltage of about 1 ~V per year.
Electronic voltage standards, also known as the transfer standards,afe basedon electronic componentssuch as
diodes.When the voltage acrossa diode rises above a certain level, a current starts ftowing (e.g. Zener breakdown)
through it and the diode acts as a constant voltage device.
When thesediodes afe fed by well-stabilized sources,they
can provide a reference voltage that is stable by l part
in l rI'. Ofren, they are used together with other electronic
componentssuch as transistors,operationalamplifiers, and
integrated circuits for stability and compensation of the
environrnentalfactors like temperature.They afe widely
used sioce they afe oot affected by environmental cooditioos, as is the casewith standardcenso
Numerous standardsdefine the proceduresand methods
for voltage determinatioos,particularly in power circuits.
Some of these standardsafe -
.
.
.
.
.
.
.
IEC Std 60060-2 standard for high-voltage impulse
calibrations;
IEEE Std 519-1992 standard for harmonic control in
electrical power systems;
IEEE Std 4-1995 standardfor high-voltage testing;
IEEE Std 181-2003standardfor transition. pulses, and
related waveforms;
IEEE Std 1122 standardfor digital reeordersused with
measurementsin high-voltage impulse tests;
IEEE Std 1451-1999standardfor smart sensors;
IEEE Std 1459-2000standardfor the Measurementof
Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced,or UnbalancedConditions.
FURTHER READING
Dyer. S.A. (ed) (2001) Instruments.Surveyoflnstrumentation and
Measurement.Wiley. New York.
Eren, H. (2002) Analogue and Discrete InputlOutput, Costs, and
Signal Processing,Chapter 1.9, in lnstrumentation Engineers
Handbook, 4th edn (ed. B. Liptak), CRC Press, Boca Raton,
FL (pp. 123-141).
&eo, H. (2003) Electronic Portable Instrument s- Design and
Applications, CRC Press,LLC, Boca Ratoo, FL.
&en, H. and Fernro, A. (2003) Galvanometersand Electromechanical Voltmeters entIAmmetersin EncyclopediaoJLiJe SuppOrI Systems.EOLSSIID{ESCO, URL: http://www.eolss.netl
E6-39A-toc.aspx.
"I
Eren, H. and Ferraro, A. (2003) Electronic Voltmetersand Ammeters in Encyclopedia 01 Lile Support Systems,EDLSSIUNESeD, URL: http://www.eolss.netlE6-39A-toc.aspx.
Hoeschelle,D.F. (1994) Analog-to-Digital and Digital-to-Analog
Conversion Techniques,ISBN: 0-4715-7147-4 Wiley, New
York.
SchIabbach,J. (2001) Voltage Quality in Electrical Power Systems, ISBN: 0-8529-6975-9,IEE, Stevenage.
Webster,J.G. (ed) (1999) TheMeasurements,/nstnunentationand
SensorsHandboo/c,ISBN: 0-8493-8347-1,CRC, IEEE Press,
New York.
202: Curreot
Measuremeot
Halit Eren
Curtin University oJ Technology,Perth, WesternAustralia, Australia
J .
1 Introduction
2 Basic Theory
3 Measuring Networks
4 Current Transducers
5 Current Shunts
6 Converters
7 Rectifiers
8 Indicators
9 Digital Instruments
IO Standards
Furtber Reading
". I.~:, ..~. .
1362
1362
1363
using carefully selectedtransducersto meet the particul~,
characteristicsand specificationsof the processo
In this arti",l
de, the operationof ammetersandmultimetersis explained,
current transducersafe discussed,and examplesafe give,!:"
1365
1366
2 BASIC THEORY
1367
1367
1368
1368
1369
1369
1 INTRODUCTION
A charged body in an electric field is subject to a force.'!f'
the body is not restrained, it will start moving in the electlC-'
field. The result of the movement of charged bodies fròhl;
ODepoint to another point in the space is the electric curreqiC
In the metallic conductors used in the electric circuits,ffi~,;,
charged bodies that can llow through the conductors' a1~.,
the electrons. A basic property of an electron is its chargei
(1.603 x 10-19 C).
1\".
Electric eurrent is the rate of eharge llowing in a ero
seetion
of the
eondueting
'"
and the unit
of rime
(secondelement
s) by~1~:in a secondancbi.'~
measurement unit is, in the SI, the ampere (symbol: A).<) l''
.
KnowIedge of the voltage Iocated at the terminaI of each
circuit element as well as the current ftowing in each
elementgives full knowIedgeof the circuit behavior. Moreover, when eIectronic devices for signal processing are
involved, suchas thoseusedin measuringsystems,telecommunication systems,control systems,and informatics, the
majority of involved signalsafe in the voltage and current
forms. Therefore, the voltage and CUITentmeasurements
constitute an important area in industriaI and Iaboratory
measurements,sensors,and systems.
Electrical CUITentscan be measuredin many different
ways. Once the current is convertedto voltage form, the
oscilloscope (strictly a voltage measuringdevice) is a typ-
ical devicethat canbe usedto measure
currents.Thereafe
many analog and digital ammetersand multimeters that are
offered by many vendors.In someapplications,specialcurrenI measurementtechniquesmay bave to be designedby
.
.
'
Sinee the current is taken as the eharge llow per UDÌtL
lime. ils measurement unit is related to Ibe uoil of C"" ,
.
..
1 ampere= 1 coulombjsecond
I
(1)1
",~,
A current will flow in any medium in which there aree
fr~'\
chargesto move. These conduction chargesmay be el~;-:',
,,"trons, positively charged 'holes', or positive or negativ~~
ions, depen~ing on the ~ate~al.
random mobon and collide wlth
They afe in cont~uoN~;i'
each other and Wlth m~,
atomic structure of the material. When a conductingma~
riaI is placed in an electric field, the conducting chargèf
are acceleratedin the direction of the field. The velocity:
acquiredis small comparedwith the averagevalueof~
random velocity (typically in the arder of 106m çl).
HandbookoJMeosuringSystem
Design,editedby PeterH. Sydenhamand Richard Thorn.
e 2005JohnWiley & Sons,Ltd. ISBN:0-470-02143-8.
.
. . ..
.
..
..
.
.;ì~
~
~
"",."c,.. "'..CU.uucrncnl .I.:JO.)
1363
:
The correDIftowing through a circuit element is related
to tbe propertiesof tbe circuit element and to tbe vol.
ss its terminals by tbe well-known Ohm's law:
V=Rl
(2)
(2)
. where R is a quantity representingtbe electric bebavior of
me circuit elementoUnder DC cooditions this quantity ia
calledresistanceand its measurernentuniI is, in tbc SI, tbe
I,
'obm (O).
" In mogI of tbc usually met applications of electrical
ìmd electronic engineering,voltages and currents exist in
,
I
,
continuousforms. This meanstbat a generic voltage v and
a genericcorrent ; can be representedasfunctions of Urne ,:
v
= ve,)
and ;
= jet)
(3)
(3)
,In tbc DC systems,voltagesand correDI! are constant,tbat
is
v
,
.
= v(t) = Voc, const.
and ;
= jet) = IOCt const.
.
~)
The voltmeters and ammetersfor DC systernsafe realizcd
in order to measureVoc and loc respectively.
In AC systems,the voltage and current are defined witb
respectto time as
T1 lo(T ;(1)2dt =
-]
./2JDaX
(8)
whereT is tbeperiodo In tbe caseof a circuit containingonly a resistive load, tbe
single frequencycurrent wave is entirely symmetrical witb
tbe voltage wave. Tbe current wave lags behind tbe voltage
wave in tbe caseof inductive loads. In a purely capacitive
load. tbe current wave leads tbe voltage wave. In generaI,
circuits contain elements of resistance, inductance, and
capacitancein varying amounts and tbey must, tberefore,
assumesomeintermediatecondition of phaseansie between
voltage and current.
Ammeters far AC systems afe realized primarily by
using AC-to-OC conversion techniquesor by using suitable transducers,botb of which will be explained in tbe
following sections.
Different kinds of signals, such as pulse, random, and
discrete signals can also be found in nature, especially at
tbe atomic scale. Such signals, however, require measurement witb different kinds of instruments, which are not
covered bere.
33 MEASURING NETWORKS
~
t,
v(t) = Vmax
sin(CL!t
+ a)
(5)
(5)
l where Vmaxis tbe maximal value of tbc sinusoidal voltage
.anda is tbe phaseangle of tbe voltage:
"
Tbere exists a diverse range of metbods and instruments
available far current measurements,and some of tbeseafe
.
; (t)
= lmaxsin(CL!t+ fJ)
(6)
(6)
where lmaxis tbe maximal value of tbe sinusoidal current
,
and fJ is the phase angle of the current. CL!
represents angular
. frequencyand t is tirne in (5) and (6). Quantities tbat afe
~
usedto characterize
sinusoidalvoltageandcorrentafe
I..,= I
,~
v=
(1)
.
I. tbermal type ammeter,
-. multimeters
. oscilloscopes
. virtual instruments.
-"
'...' electromechanìcalammeters
"
..
Electromechanicalammetersprovide readingsin analog
form by moving a pointer tbat indicates tbe measured
value on a scale. The scale is a linear scale if tbe pointer
displacementis proportional to tbe measuredquantity. Tbe
energy required to dispiace the pointer is taken direcdy
from tbe circuit to which the instrumentis connected.This
energy is tbe so-called instrument self-consumption and,
in electromechanical instruments, can be nonnegligible.
Electromechanicalammeterscan be c1assifiedaccording to
tbeir deftecting movementsas
I. moving-iron electromagneticammeters,
2. electrodynamicammeters,
3. moving-coil electromagnetic ammeters (D'Arsonval
(D'Arsonval
galvanometers),
4. electromechanicalmultimetersor VOM.
Although electromechanicalammetersstili find extensive
applications, they are not used as much as their electronic counterparts,so they will not be explained further.
However, becauseof its special features, the D'Arsonval
galvanometerswill be visited in Section 8 of this artic1e.
Thermal type ammetersare based on the thermal effect
producedby a corrent ftowing in a conductor.Theseammeters are also known as the thermo-instrumentsor true rms
devices.Irrespectiveof the shapeof the input signal waveCorro,the active power dissipatedin the heated conductor
is equal to the heat generatedand is proportional to the true
rms value of the input current.
A simplified constructionof this kind of ammeters,also
called the 'hot-wire instrument' is shown in Figure 1. The
heated element has a negligible temperaturecoefficient of
resistance(that is, its resistancewill remain essentiallyconstant over its operating range) and a constant temperature
coefficient of expansion. Since the heating effect is proportional to the square of the current, àccurate effective
(rrns) values of AC currents afe measurableirrespective
of frequency and waveform. Also, since no magnetism is
involved in providing scaledeftection,stray magneticfields
bave no effect on the operation.
The hot-wire elementis madeof platinum-iridium, which
has a constant resistanceand temperature coefficient of
expansion over its operating range. The element is about
0.1 mm in diameter. Platinum-iridium has the added benefit of being able to withstand high temperatureswithout
oxidation. Attached to the hot wire is a phosphor-bronze
'magnifying' wire. A silk thread, connectedto the magnifying wire, passesaround a pulley before being tìxed to a
spring, which keeps the system under tension. When the
Figure 1. A hot-wirevoltmeter.
hot-wire element expands,its slack and that in the magi
fying wire is taken up by the tension in the spring and t
silk thread causing the pulley to rotate and the pointer
deftect on the scale.
Multimeters are instrumentsthat can measurevoltagl
currents,and resistances.Theseinstrumentsafe alsoknO\
as volt-ohm-multimeters(VOMs). The VOM is a combÙ
tion of a DC ammeter,a DC voltmeter, an AC anuneter,
AC voltmeter, and a multirange ohmmeterwith a switcb
select the ODeto use. The DC voltage range of a COtnm
VOM is O to lOOOV,althoughwith an externalresistort
range can be increasedto 5000V. The DC current range
usua11yup to lO A, although with an external sbunt it c
be extendedto 20 A or more.
For AC measurements,the instrumentcontainsa rectif
ing circuit madefrom germaniumor silicon diodes.Becau
of the inertia of the moving coil, the meterindicatesa steal
deftection proportional to the averagevalue of the Curre
Since AC currentsand voltagesafe expressedin rms valU(
the meter is scaledto readthe nns valuesof sinusoidalvo
agesthrough the form factor 1r/2./2. The indicatedreadil
of a nonsinusoidalvoltage may be erroneous,sinceits av(
age value may differ considerablyfrom the averageValI
of a pure sinusoidal voltage.
Owing to the fact that tbe internai structure of ti
VOM cannot be optimized for a single measurement,ti
temperatureand frequency rangescan be limiting factol
For example, a deterioration of 0.5% in the readingsm.
be expectedfor every l-kHz rise in frequency.
Further information on multimeters is provided
Section 8.
Qscilloscopes are probably the most versatile instr
ments for ali forms of pbysical investigation,since a1mc
any physical phenomenoncan be convertedinto a corr
sponding electric voltage and the oscilloscopemakestJ
wavefonn versustime visible for bumanobservation.Me
surementsafe performedon the borizontal axis and vertic
axis since the screenfeaturesa graduatedgridoNowaday
digital storage oscilloscopesDSO are commonly used
voltage and current measurements.They samplethe inp
signal and convert it into a sequenceof data. whicb a
stored in the DSO memory and displayed on cathode-n
tubesCRT or liquid-crystal displays(LCD). A typical stnJ
tUTeof a digital oscilloscopeis shown in Figure 2.
Virtual instruments use computers,interfaceelectronic
and software to emulate the operational featuresof mo
traditional instruments. In this technology, plug-in da
acquisition (DAQ) boards,PCMIA cards,and parallel po
UO devices are used to interface sensorsand transduce
of the system under investigation with computers.OD
the signal is interfaced, the computer can be programm
to act just lite a stand-aloneinstrument; but it can al!
~
I
Current Measurement 1365
Data
out
,,:
in
~ ;~.'
: ~'J"
.~,?f.
::l
;~
CURRENTTRANSDUCERS
.
.
.
Currenttransformers(CT),
HalI-effect transducers,and
Rogowski Coils,
optical current transducers(0CTs), and
current shunts(explainedin detail in Section 4).
Current transformers bave two windings, designatedas
primary and secondary, which afe insulated from each
other. The pJimary winding is connectedin serieswith the
circuit carrying th~ line current to be measured,and the secondary winding is"i;connectedto instruments or protective
devices. The secondarywinding supplies a secondarycurrent in direct proportion to the primary current aImostwithout any differencein phaseangle.Hence,the CT transforms
line current into valuessuitable for measuringinstruments,
meters, protective relays, and other similar apparatus.CT
also isolates the instrumentsand the relays from line voltages.The four common types of CT design are
.
.
,
~
.
.
.
wound type
bar type
window type
bushing type.
The current in any system changesmore often and with
greatermagnitudethan the voltage. Hence,selectingproper
transducer for currents could be difficult. The right CT
current rating and tums ratio to be used dependson the
measurementobjective.
In the caseof disturbancerecordersor protective devices,
where fault or inrush currents afe of concem, the CT
.
must be sized in the range of 20 to 30 times of normal
load current. This will result in low resolution of the
load currents and inability to accuratelycharacterizeload
current harmonics.
Conventional current transformersafe designedto operate within a frequency range from 15 to 100Hz. With the
need to measureharmonic content of the primary current,
the frequency responseof current transformers is essential to the measurementprocessoThe frequencyresponseof
current transformersis e"ffectivelydeterminedby the capacitance present in the transformer and its relationship with
the transformerinductance.The standardmeteringclass CT
is generally adequatefor frequenciesup to 2 kHz. Phase
angle shift between primary and secondarycurrents may
start to become significant when the frequency is close to
2 kHz. For higher frequenciesthan 2 kHz, a window-type
Cf with a high ratio should be used. Desirable attributes
for a CT, when harmonicsare measured,include large ratio,
small remanent flux, large core area (the mor~ steel used
in the core, the better the frequency responseof the Cf),
secondary winding resistanceand leakage impedance (as
small as possible).
Rogowski Coi/s afe more specializedtransducersusually
used for the measurementsof very large currents, which
last for a very short duration (hundredsof kiloamperes in
less than a microsecond).The Rogowski Colli is a solenoid
air core winding of a small cross-sectionlooped around a
conductor carrying the large primary current. The voltage
induced on the terrninals of the coil is proportional to the
derivative of the primary transient current and number of
turns. The coil is connected to an integrator. Integrated
induced voltage gives a measure of the current in the
primary conductor. The Rogowski Coils bave the advantage of being free from saturationproblems and bave fast
responsetinte.
Hall-effect sensorsoperateon voltage difference across
a thin conductor carrying current. The current dependson
the intensity of the magnetic field applied perpendicular
to the direction of current flow, as shown in Figure 3.
AD electron moving through a magnetic field experiences
Lorentz rocceperpendicularto the direction of motion and
to the direction of the field. The responseof electronsto the
Magnetic field
eml t
Lorentz force createsa voltage known as tbe Hall Voltage.
If a current l ftows through tbe sensor.tbe Hall voltagecan
matbematically be found by
v = RH! H/t
(9),
where RH is the Hall coefficient (cubic metersper degreeof
Celsius), B is the flux density (Tesla),and t is the thickness,
of the sensor(meters).
The value of RH depends on the material used, tem::.
perature, and field magnitude. Its characteristicscan 00.
control1ed to a certain extent by doping the base mate-~
riai with some impurities. For example,doping gennaniW:
with arsenic can reduce the temperaturedependenceat the:
expenseof magnitude.
Semiconductor materials, such as gallium arsenide
(GaAs), indium antimonide (InSb), and indium arsenid~.
(InAs), produce the highest and most stable Hall.
coefficients. Because of its combined low temperature',
coefficient of sensitivity «0.1 %/ °C), low resistanceand,
relatively good sensitivity, InAs is the material favoredb~,
commerciai manufacturersof Hall-effect devices.
,~
Optical transducersrepresentODepossiblesolutionto th~
need for reliable and economical sensorsin high-voltagc;:
measurementsystems.Conventional transducersfor volt;4
age and current afe expensive and require large volum~i
of electrical insulation when used on high-voltage lines;'~
Optical current transducersafe designedwith all solid ins~~
lating materialsand afe thereforeintrinsically gare.Becau~i
OCT is an electronic device, it differs fundamentallyfro~
Cf with respect to the signal power involved. In a ~
the secondary signal has a power level of severa!watts~
while p()wer in theOCT secondarysignal is typically ~
few microwatts.
.:
A numberof quite different OCTsare available.Diversiti
is present in alI elementsof the system. The sensorma~
be optical or electronic. The insulator may be ceramici
polymer and it may be used to support OCT or it may ~"
suspendedfrom it. All types of ocr use optics to isola~
a high-voltage part of the system from a secondarysid~
that carries information. The current being measuredby ari.
OCT is representedas modulatedlight. Typically, the link
between sensorand user device (measuringinstrument)is
an optical fiber.
.'.'
,'o
5 CURRENT SHUNTS
Apart from CUlTenttransformers,cfs, and Hall-effect seni
. "
sors, cUITentshuntsare a most common and cost-effecUV~
J
folTO of transducers that are used for CUlTentsensing.
A Hall-effect sensor.
'
It consistsof a low-value resistorconnectedto the currenf
path of the circuit, as shown in Figure 4. The wavefortn
Current Measurement 1367
.
In applicationswhere curreot shuntsare selectedfor current measurements,attention must be paid to the inductive
effects on shunts, terminaI resistancesof connections,and
the types of leads used. This is especially so as the frequency content of the sigttal rises.
FuI!current
6 CONVERTERS
across
the
of
In many applications, signals afe deliberately convertedto
currents for transmissionof information (e.g. the 4-20 mA
transmission method) to be connectedback to voltage at
the receiving end. Voltage-to-current(V-I) and currentto-voltage (I-V) converters afe used extensively in the
processindustry to transmit information from ODelocation
to another. Current transmission is convenient because
of its good immunity to electromagneticinterference and
noise.
Figures 5(a) and (b) showhow suchconvertersareimplemented using op-amp circuits. In the case of a V - I converter, the output is a current lo proportional to the input
voltage ~. Note that the portion of circuit betweenpoints
A and B acts as a current source controlled by the input
voltage
Sleeveshunts can be used for measuringimpulse currents up to 500 A. The ohmic value of shunts can be
changedby replacementof the active parts.
Cageshuntscan be used for currents up to lO kA. The
housing is usually filled with special sand to enhance
operationsand thermal characteristics.
Tubularcoaxial shuntscan handlecurrentsup to 100kA
for short durations.
Specialhigh current shuntsare usedfor high currentsin
high-voltageapplications,such as the arrestor testing.
~.
In the case of the I-V
converter, the output
is a voltage Vo proportional to the input current li' Also,
note that whateverthe load resistorplaced at the output, the
entire input current li will flow through resistor R). Thus,
the portion of the circuit betweenpoint S and ground acts
as a voltage sourcecontrolled by the input current li'
In some applications, it is important to note that the
current-to-voltage converter can simply be a suitable terminating resistor thatp1akesuse of Ohm' s Law to generate
a voltage.
'-Cf
7 RECTIFIERS
In many applications, AC voltages and currents are measured by means of DC voltmeters and ammeterswith an
additioo of a rectifyiog circuit in the input stage.Rectifiers
VI
10=R
Vo'" -~/I
(b)
Figure 5. (a) Voltage and (b) current convertersbasedon operational amplifiers.
.
.
1368
CommonMeasurands
-
~sphor~'
sIIfp
suspen8lan
.
N . i
!
/
:
Perm8nent
PoIe ~
'
i
Figure 6. Rectifier-based
AC ammeter.
can be classifiedas controlled or uncontrolled rectifiers, tbe
majority of which Me controlled types, which are obtained
using tbyristors and triacs.
Controlled rectifiers can vary tbe average value of tbe
voltage applied to tbe load. They are suitable for use
in rectification of single-phase or tbree-phase voltages
and currents from constant AC supplies. A typical basic
structure for a rectifier used in ammeters is shown in
Figure 6.
1be rea1izedmeter becomesan averagevoltage detector
that can be used as an rms ammeter by labeling tbe
scale to measurecurrents, provided tbat tbe input signal
is a sinewave.
8 INDICATORS
Indicators are base<!ODelectromagneticammeter principles; ODetypical exampie is the O' Arsonval galvanometer. This galvanometeris an iDstrumentspecially designed
for the measuremeDtof very Iow currents (in the order
of 10-8 A) and is therefore employed as null indicator
in a majority of balance measurementmethods (like the
bridge and potentiometermethods). Becauseof the internaI resistance of its coil, it can be alSOused to measure very Iow voltages, in the order of 10-7 V or even
lesso
The galvanometerstructurecomprisesa rectangularcoil
of fine copper wire suspendedbetween the pole faces of
a permanentmagnet.The magnetpole faces are curved to
provide a radiaI flux. A fixed cylindrical iron core provides
continuity of the magneticcircuitoThe amplitude of the air
gap between the fixed CyliDdrical iron core and the permanent magnetis about 3 rom. Each coil side lies.halfway
Figure 7. O' Arsonval galvanometerstructure.
betweentbc core and correspondingpole tace. 1be suspension is a single fine strip of pbosphorbronzeand servesasa
lead to tbc upper eod of the coil. 1be lower end is connected
to a lead consisting of a spirai spring. In the most accurate
executions, tbe restraining torque is given by tbe torsion
of the suspensionstrip. In this way, the friction torque is
also practically removed.A small minor, fixed to the suspension, reftects a narrow beam of light through a glass
window in tbe outer case surrounding tbe galvanometer
00 to a scale placed a meter away, on wbich tbe deftection is measured.Simply winding tbc coil on aluminium
frame provides eddy curreot damping. Resistive damping
may also be obtained by connectinga variable resistor in
parallel witb tbe deftection coil. Proper adjustmentof this
resistancegives criticai damping, tbereby reducing measurement time. A typical galvanometerstructureis shown
in Figure 7.
9 DIGITAL INSTRUMENTS
Digital ammeters (multimeters) obtain tbe required measurements by converting tbe analog input signal into a
sequenceof digital samplesuniformly spacedin time in
tbe early stages of tbc signal processing.The input signals are tberefore processedin tbc discrete-time domain
and tbe measurement results afe displayed in a digital formo It is worthwhile to note tbat tbe distinction
between analog and digital meters is not becauseof tbc
way tbc measurementresults are displayed.but becauseof
Current Measurement 1369
Current
i(t) -
DSP ~
S&H
Digital
output
Figure8. Structure
of a modero digital meter.
the domain (continuous-time or discrete-time domain) in
which the input signals are processedin the main body of
the devices.
A more modero approach to this type of measuremeni exploits the capability of a fully digital structure
as shown in Figure 8 that represents a voltmeter. The
same structure can be adapted to an ammeter operation,
provided that a current-to-voltageconversion input stage
is inserted.
This structure samplesthe input signal Vj(t) at constant
sampling rate fs and converts each sampled value into a
digital code. The whole sequenceof converted codes is
stored in the memory of the DSP and then processedfor
the evaluation of information.
Assume that the input signal is periodic, with period T,
and that the frequency spectrum is upper-limited by the
harmoniccomponentof order N. Digital signal processing
theory, and in particular tbe sampling theorem,ensurestbat
the inforrnation associatedwitb tbe input signal can be
tota1lyretrieved from tbe sequenceof tbe sampled data if
at least (2N + l) samplesare taken over a period T in such
a way tbat (2N + I)Ts = T, where the sampling period Ts
being Ts= li/s'
If vi (kTs) is the kth sample, tbe rms value of tbe input
signal is given by
V
=
1
2N
+
L
vf(kTs)
1=0
lO STANDARDS
The unit of current is defined as, 'the ampere is that
constantcurrentwhich, if maintainedin two straightparallel
conductorsof infinite length, of negligible circular crosssection,and placed l meter apartin vacuUID,would produce
betweentheseconductorsa rocceequal to 2 x 10-7 Newton
per meter of length'.
There is no definedstandardfor electrical current as such
as it is mainly derived from existing electrical standardsof
resistanceand voltage, which are based on the quantum
Hall effect and the Josephsoneffect respectively.
However, there exist numerousdocument standardsfor
the current generation,harmonic contents,durationsof currents in high-voltage applications,electrical and electronic
circuits, batteries, grounding and safety aspects, circuit
breakersana fuses,and so OD.Some examplesare
.
.
2N
1
full resolution of the instrument without clipping or distorting the measuredsignal. To obtain the most accurate
representationof the signal being monitored, it is important to use as much of the fun range of the ADe as
possible.
(10)
.
As an example,
a true rrns AC ammeterbasedon tbis
approachcan feature an uncertainty as low as the 0.1% of
the CulI-scalevalue with a 12-bit resolution analog-to-digital
converter (ADe). According to the sampling theorem, the
instrument bandwidth is limited to half the sampling frequency. This means that a 500-kHz bandwidth can be
attainedwith modero devices.Although wider bandwidths
can be obtained, this is paid for in terrns of a lower resolution of the ADC devices.
In many cases,such as current measurementsin highvoltage and power quality applications, special arrangements can be made by using appropriate current transducers and supporting equipment. In these cases, carefuI consideration is needed when sizing the transducers
(e.g. cfs) required so that they take advantage of the
.
."
IEEE C37.09-1979 for eircuit breakers;
ASTM 0495-99 for test method for high-voltage. loweurrent, dry are resistaneeof solid electrieal insulation;
mc 60255-8 for high-voltage eurrent-limiting fuses;
AS 2024-1991for high-voltage AC switehgear.
FURTHER READING
Dyer, S.A. (ed.) (2001) Survey of lnstrumentation and Measurement, Wiley, New York.
Eren,H. (2003) Electronic Portable Instrumems-Design
and
Applications.
CRC PressLLC, Boca Raton, FL.
Eren, H. and Ferraro,A. (2003) Electronic Voltmetersand Ammeters, EncyclopediaoJ liJe Support Systems,EOLSSIUNESCO,
http://www .eolss.netlE6-39
A-toc.aspx.
Eren, H. and Ferraro, A. (2003) Galvanometersand Electromechanical Voltmetersand Ammeters, EncyclopediaoJ LiJe SuppOrI Systems,EOLSS/UNESCO,http://www.eolss.netlE6-39Atoc.aspx.