juliusz b. gajewskifluid.itcmp.pwr.wroc.pl/elektra/l 09.pdfmeter’s scale is calibrated in average...

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Juliusz B. GajewskiProfessor of Electrical Engineering

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FACULTY OF MECHANICAL AND ELECTRIC POWER ENGINEERING

Process Engineering and Equipment, Electrostaticsand Tribology Research Group

Wybrzeże S. Wyspiańskiego 2750-370 Wrocław, POLAND

Building A4 „Stara kotłownia”, Room 359Tel.: +48 71 320 3201; Fax: +48 71 328 3218

E-mail: [email protected]: www.itcmp.pwr.wroc.pl/elektra

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Contents

1. Terms. Fundamental Definitions and Units.2. Electrostatics. Electrostatic and Electric Fields.3. Electrodynamics. DC Current.4. Electromagnetism. Magnetic Field of DC Current.5. Electric Circuit Elements.6. Sinusoidal AC Voltage.7. Complex Frequency Concept.8. Electric Filters.9. Electrical Measurements.

10. Three-Phase Circuits.11. Electrical Signals.12. Electric Switches.

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Electrical Measurements

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„Regardless of its character, information is usually encoded as a magnitude of a physicalquantity, and measurement is necessary in order to determine it. In the measurementprocess the magnitude of the respective parameter is expressed by a number which iscompared with an appropriate scale for that same parameter. Only two techniques forcomparison are known. The first is an analog technique using a classical measuringinstrument with a pointer. The position of the pointer is compared with a scale. Theactual comparison is made by an observer. The second technique is based on ananalog/digital (A/D) converter. The electric voltage, current or signal frequency is com-pared to a reference voltage, current or frequency by means of electronic digital tech-niques. The result of the comparison is a numerical value which is presented in a digitalcode. The great variety of physical parameters requires a great number of alternativetechniques of comparison. If one is to measure such quantities, their magnitudes must beconverted into magnitudes of a reference voltage, current or frequency, or into a magni-tude of the displacement of the pointer of an instrument. All these cases of conversioninvolve energy exchange. Therefore the magnitude of the respective physical quantity,the magnetic field, for instance, is converted into a certain kind of energy, a definiterelationship existing between it and the basic parameter”.*)

Philosophy of Measurements

*) Citation from „Solid State Magnetic Sensors” by Roumenin, C.S., Elsevier 1994

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Measurements of electrical quantities: voltage, current, powerand work of current, etc. are performed with instruments in whichthe phenomena that follow or are a result of a current flow areused: t h e r m a l, c h e m i c a l and m a g n e t i c. The mostsignificant phenomena from the practical point of view are themagnetic ones and forces that act in the magnetic field of current.

In the steady-state conditions measurements are carried out withthe use of p o i n t e r m e a s u r i n g i n s t r u m e n t s(meters). In these meters a d r i v i n g t o r q u e acts on amoving organ (part) and causes a pointer to moves over the scaleof a meter to show the value of the quantity measured. In the caseof measurements of periodically varying currents and voltages themeter’s scale is calibrated in average or effective values.

Analog, Pointer Measuring Instruments

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The moving organ produces a restoring torque that balances thedriving torque and to do so spiral springs are used. To set up apointer in the zero position an eccentric cam is used. A counter-balance balances the moving organ in order that its centre of gravi-ty be on the axis of rotation.

Under the driving torque the pointer deflects by an angle , atwhich the balance of the driving torque by the restoring torque. Asa result of the moving part’s inertia the state of equilibrium can beachieved after some number of sways (oscillations) and not atonce. To shorten the time of sways one uses a damper that pro-duces a damping torque within the movement of the movingorgan. The air and eddy-current dampers are most frequently used.


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In the air damper the movement is attenuated with the drag of airin a chamber in which a wing of the damper moves. The eddy-current dampers work is based on eddy currents induced in a platemoving in the field of a magnet.

The fundamental part of each meter is its measuring structure, thatis that part of a meter in which any electrical quantity is measuredand is converted into the deflection of a pointer. With regard to theconstruction and principle of operation, the magnetic field-basedinstruments are as follows: m a g n e t o e l e c t r i c, e l e c t r o m a g n e t i c, e l e c t r o d y n a m i c, i n d u c t i o n.


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Analog, Pointer Measuring InstrumentsPointer,

counterbalanceand

restoring spring

Air damper and eddy-current damper

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1. Permanent magnet.2. Coil at the aluminum frame.3. Soft-iron armature core —

core of the soft magnetic material.

4. Two spiral restoring springs.5. Pole pieces.

Types: permanent-magnet moving-coil

instrument — moving coil and stationary permanent magnet

moving-magnet instrument

Magnetoelectric Meters

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Analog, Pointer Measuring InstrumentsMagnetoelectric Meters

M o v i n g-c o i l i n s t r u m e n t — A measuring instrument inwhich current or voltage is determined by the couple on a smallcoil pivoted between the poles of a magnet with curved poles,giving a radial magnetic field. When a current flows through thecoil it turns against a return spring. If the angle through which itturns is , the current I is given by I k/BAN, where B is themagnetic flux density, A is the area of the coil, and N is its numberof turns; k is a constant depending on the strength of the returnspring. The instrument is suitable for measuring DC but can beconverted for AC by means of a rectifier network. It is usuallymade as a galvanometer and converted to an ammeter or voltmeterby means of a shunt or a multiplier.

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IkBANIrBIlNrFNMM 1dn 22

2rz kMM

kIIkk

2

1

Driving torque

Restoring torque

Pointer’s deflection angle

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The direction of the torque generated in a moving-coil instrument isdependent on the instantaneous direction of the current through the coil,that is the direction of the deflection depends on the polarity, so thatunmodified indicators are usable only on DC and unidirectional pulsat-ing currents, and may have a centre zero if required. Thus an alternatingcurrent produces no steady-state deflection and the pointer indicateszero. Moving-coil instruments are provided with an AC response by theuse of a full-wave bridge rectifier. The bridge rectifier converts the ACsignal into a unidirectional signal through the moving-coil instrumentwhich then responds to the average DC current through it. Such instru-ments measure the mean absolute value of the waveform and are cali-brated to indicate the RMS value of the wave on the assumption that it isa sinusoid.

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Magnetoelectric moving-coil instruments can be used as: g a l v a n o m e t e r s, v o l t m e t e r s, a m m e t e r s.Coils are made of thin wires and in general are to be used for the lowcurrents (up to several dozen miliampers), and because of its lowresistance the range of the volatges measured is also narrow. To extendthe measuring range of the instruments special resistors are connected inparallel with ammeters — s h u n t s — or in series with voltmeters —m u l t i p l i e r s.

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A

I

Ra Ia

I Ia

Rs saaa RIIIR 1

a

a

aas

nR

IIIRR

ShuntMagnetoelectric Meters

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V I

U

Uv U Uv

Rv Rm

IRUUIRU mvvv and vvvm 1 RnUUURR

MultiplierMagnetoelectric Meters

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Magnetoelectric Meters



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Analog, Pointer Measuring InstrumentsElectromagnetic Meters

Types: one-core (solenoid- or

attraction-type) meter two-core (repulsion-type)

meter1. Core (vane, disc) of the soft

magnetic material.2. Fixed foil.3. Movable vane.4. Unmovable fixed coil.5. Fixed (unmovable) vane.

2020



2

21 LIW

dd

2dd 2

dnLIWMM

dd2 LkI

constdd

L

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In the one-core, attraction-type instruments current passes through a coilof wire (solenoid) wound on a hollow tube of some non-magneticmaterial. Therefore the coil becomes a magnet and its lines of force tendto pull the soft-iron plunger into the coil. The stronger the current, thegreater is the magnetic field and the greater is the pull on the plungerwhich pulls the pointer attached to it over the face of the scale. Theamount of deflection of the pointer over the scale is an indication of thestrength of the current flowing through the coil and being measured.

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In the more often used two-core, repulsion-type instruments in theinterior of the cylinder-shaped coil are two soft-iron vanes (pieces): oneof them is fixed and the other is free to move. A current passes throughthe coil and the vanes become magnetized in the magnetic field so pro-duced. Since they are magnetized in the same way, the two vanes repeleach other both for DC and AC currents. As a result, the movable vane isdeflected around the centre shaft, turning the shaft and carrying thepointer with it. The greater the current flowing through the coil, thegreater is the deflection of the pointer. The scale is not even, uniform; itis of the square-law type and cramped at the lower end. The pointer’sdeflection is proportional to the RMS value of the current measured andthus the instrument provides a steady-state deflection from an AC cur-rent. The scale is calibrated in terms of RMS values. If the scale is alsovalid for DC currents, the adequate information (a sign) is given usuallybelow the scale.

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The electromagnetic meters are used to measure DC and AC current as: v o l t m e t e r s, a m m e t e r s.The voltmeter has the coil made of thin wire with many turns to increaseits resistance which results in a weak current flowing through it. Theammeter’s coil in turn is made of thick wire with the small number ofturns to have low resistance.

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Such instruments can measure the voltages from single volts even up to600 V, while the currents measured can range from 50 mA to ca. 300 A.To measure high voltages or very strong currents special measuringtransformers are used which are called the c u r r e n t transformers andthe v o l t a g e transformers.

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A

I1 K L

k l

k l

K L

A

z1

z2 I2

Current transformer

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Voltage transformer

V

M N

m n

z1

z2

U2

U1

2

1

2

1

1

2

2

1

zz

UU

zz

II

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Analog, Pointer Measuring InstrumentsElectrodynamic Meters

1. Unmovable fixed coil.2. Movable coil.3. Spring.

cos21IkI

2kI

vv R

UI

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The electrodynamic meters are used to measure DC and AC current as: a m m e t e r s, v o l t m e t e r s, w a t t m e t e r s.Both unmovable and movable coils are connected in series (an ammeter)or in parallel (a voltmeter) and put into a measuring circuit. Te deflectionof the pointer is proportional to the square of current that flows throughthe measuring structure. Electrodynamic ammeters and voltmeters havemore complex structure and are more expensive than magnetoelectricand electromagnetic meters and therefore are not too often used; they aremainly the standard laboratory instruments of high accuracy.

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The electrodynamic instruments are mainly used to measure the electricpower of AC current as e l e c t r o d y n a m i c w a t t m e t e r s. Thewattmeter consists of a pair of fixed coils, known as current coils, and amovable coil known as the potential coil. The fixed coils are made up ofa few turns of a comparatively large conductor. The potential coilconsists of many turns of thin wire. It is mounted on a shaft, carried injeweled bearings, so that it may turn inside the stationary coils. Themovable coil carries the pointer which moves over a suitably markedscale. Spiral coil springs hold the needle to a zero position.

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vv R

UI

The fixed unmovable current coil is connected in series with the circuit(load), and the movable potential coil is connected across the line. Whenline current flows through the current coil, the magnetic field is set uparound the coil. The strength of this field is proportional to the linecurrent and in phase with it. The potential coil generally has a high-resistance resistor connected in series with it. This is for the purpose ofmaking the potential-coil circuit of the meter as purely resistive aspossible. As a result, current in the potential-coil circuit is practically inphase with line voltage. Therefore, when voltage is applied to the circuit,current Iv is proportional to and in phase with the line voltage U:

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PcUIcRUkIkII ww

vv coscoscos

max

nnnw

cos

IUc

Wattmeter constant

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Analog, Pointer Measuring InstrumentsInduction Watt-Hour Meters

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In induction watt-hour meters an effect of a magnetic filed flux on theeddy currents induced in a metal (aluminium) disc by the currentflowing in the coil of an electromagnet. To increase a driving torquetwo-flux meters.The induction meter operates by counting the revolutions of thealuminium disc which is made to rotate at a speed proportional to thepower. The number of revolutions is thus proportional to the energyusage. It consumes a small amount of power, typically around 2 watts.

Induction Watt-Hour Meters

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The metallic disc is acted upon by two coils. One coil is connected insuch a way that it produces a magnetic flux in proportion to the voltageand the other produces a magnetic flux in proportion to the current. Thefield of the voltage coil is delayed by 90 degrees using a lag coil. Thisproduces eddy currents in the disc and therefore a force is exerted on thedisc in proportion to the product of the instantaneous current andvoltage. A permanent magnet exerts an opposing force proportional tothe speed of rotation of the disc. The equilibrium between these twoopposing forces results in the disc rotating at a speed proportional to thepower being used. The disc drives a register mechanism which integratesthe speed of the disc over time by counting revolutions in order to rendera measurement of the total energy used over a period of time.


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cos21d fIcIM

PcUIckM 11d cos

ncM 2r

Pccn

2

1

tt

cAtPcctnN

02

1

0

dd

Angular velocity

Revolutions


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Analog, Pointer Measuring InstrumentsInduction Watt-Hour Meters

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4040


U

A

V

IE

Rx Rv

Iv I Iv v

v RUI

vv

x

RUI

UII

UR

IUR *x

v

*x

x

x*x

RR

RRR

vx RR Rx 1.0

vR

Technical Method of Resistance MeasurementAccurate DC Measurement of Voltage

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IUR *x

a*x

a

x

x*x

RRR

RRR

ax RR Rx 1.0

U

A

V

I

Rx

Ra ax RI

UR

0a R

Technical Method of Resistance MeasurementAccurate DC Measurement of Current


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Pomiar oporu czynnego (rezystancji)

0.1 (1.0) Rx 106

D

V

A B

C

E

Rx Rn

R1 R2

W2

W1

DBCBADAC i UUUU

12x1 RIRI

22n1 RIRI

2

1x R

RRR n

Rx 0.1 (1.0) — Thomson (Kelvin) bridge

Resistance MeasurementWheatstone Bridge


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R U

I W

UIP

Measurement of Active and Apparent Powersand Power Factor

Active Power and Resistance


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Active Power and Impedance

Z U

I W

PcUIcUIP ww cossince,cos


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Z U

I A

V

W

SPUISUIP cos,cos


Apparent Power, Power Factor and Impedance


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Oscilloscope


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Oscilloscope

cathode-ray tube

Y input amplifier

power supply230 V~

time-base generator

amplifier

internal synchronization

system

X input


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Oscilloscope


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Oscilloscope

Lissajous figures

Frequency Measurement

1:1 2:1 1:5


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OscilloscopePhase Measurement

x

y

ymax

0°

y0 0

max

0sinyy

x

y

ymax 1.0y0 0.5

30°


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OscilloscopePhase Measurement

max

0sinyy

x

y

ymax 1.0y0 0.707

45°

x

yy ymax

90°


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Measurement of Non-Electric Quantities with Electrical Methods

To measure a non-electric quantity a special device must be used whichis a first input unit of a given measuring instrument and which convertsthe quantity X measured into a proportional electric signal Y: Y f(X).Such an element is called a t r a n s d u c e r or often a s e n s o r.The transducer is any device or element which converts an input signalinto an output signal of a different form. For example: the microphone,phonograph pickup, loudspeaker, barometer, photoelectric cell, automo-bile horn, doorbell, and underwater sound transducer. The sensor in turnis a device that senses either the absolute value or a change in a physicalquantity such as temperature, pressure, flow rate, or pH, or the intensityof light, sound, or radio waves and converts that change into a usefulinput signal for an information-gathering system; a television camera istherefore a sensor, and a transducer is a special type of sensor.


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transducer or sensor or probe

processing electronics

display or meter

electric energysource

X Y = f(X)


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Sometimes the sensor can be an input unit of the transducer. Where thiselement is not brought into contact with the object measured or does notdisturb (or disturbs to a small extent) a given process occurring in thisobject, such a transducer is called a p r o b e. Once it was permitted thatthe probe could be in contact with the object or process measured.The electric transducer converts the non-electric quantity measured intovoltage, current or charge and then it does not require any auxiliarysource of electric energy. It is called the a c t i v e t r a n s d u c e r. Thetransducer that changes one or more parameters of a measuring circuitunder the effect of the quantity measured, e.g. R, L, C, etc., is called thep a s s i v e t r a n s d u c e r since it must be powered from an externalsource of energy.


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Active transducers: i n d u c t i o n (electrodynamic, electrostatic, electromagnetic, etc.), p i e z o e l e c t r i c, t h e r m o e l e c t r i c, h a l l o t r o n (Hall effect), p h o t o e l e c t r i c, otherPassive transducers: r e s i s t a n c e (potentiometer, tensometric, etc.), i n d u c t a n c e (differential transformer, eddy-current, etc.), c a p a c i t a n c e, c o n d u c t a n c e, t h e r m i s t o r, e l e c t r o l y t i c, other.


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juliusz b. gajewskifluid.itcmp.pwr.wroc.pl/elektra/l 09.pdfmeter’s scale is calibrated in average...

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