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Juliusz B. GajewskiProfessor of Electrical Engineering
1
2222
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
33
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.
4
Electric Circuit Elements
Vacuum0 8.854×1012 F/m0 4×107 H/m
0 S/mc2 (0×0)1 c (0×0)0.5 2.997956×108 m/s
relative permittivity relative permeability conductivity
Physical Constants
5
Electric Circuit Elements
If the physical (electrical) constants: the relative permittivity ,the relative permeability , and the conductivity do not dependon the electric field strength and the magnetic field strength, thena given medium is l i n e a r.
Physical Constants
6
Electric Circuit Elements
Circuit and its ElementsE l e c t r i c c i r c u i t is a closed path in space along whichelectrons can flow or an electromagnetic wave can travel. A fragmentof space, where one can isolate phenomena related to conversion ofthe electric energy, is called an e l e m e n t of an electric circuit. Theelements can be active — the sources of electric energy for the circuit;they may be batteries, direct-current generators, or alternating-currentgenerators, and passive — resistors, inductors, and capacitors.
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Electric Circuit Elements
P a r a m e t e r s of elements of an electric circuit are thecoefficients, that combine a current flowing through a given elementwith a voltage at its terminals, or their derivatives. The essentialparameters are: resistance R, capacitance C and inductance L.The values of the parameters of electric circuit’s elements depend ontheir geometrical size (length, cross-sectional area) and the physicalproperties of a medium (relative permittivity, relative permeability andconductivity) in which an electric current flows or an electromagneticwave travels.The values can be determined experimentally by studying the voltage-current or current-voltage characteristics of an element.
Parameters of Circuit
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Electric Circuit Elements
Parameters of CircuitAn element has l u m p e d p a r a m e t e r s if its geometricallinear dimensions are m u c h smaller, e.g. ten times, than the lengthof an electromagnetic wave travelling over the element. Otherwise,the larger physical dimensions cause the model of an element to beconsidered as a d i s t r i b u t e d–p a r a m e t e r m o d e l (ordistributed-element model).
f
l
22 c speed of wave in any medium
wavelength in any medium
element’s length
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Electric Circuit Elements
S t a t i o n a r y e l e m e n t is such an element whose parametersdo not vary with time, otherwise the element is n o n-s t a t i o n a r y.
Stationary Elements
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Electric Circuit Elements
Multiport ElementsEach element of an electric circuit has terminals or ports that permitan electric current to flow into or leave them (energy can be suppliedor withdrawn). If the same current enters and leaves two terminals,then the terminals constitute a port. An element that has two terminals(one port) is called a t w o–t e r m i n a l element (resistors, capaci-tors, inductors, diodes, batteries, direct-current generators). Elementsthat have more terminals are called t h r e e–t e r m i n a l elements(transistors) or f o u r–t e r m i n a l (two-port) elements (transfor-mers, filters).
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Electric Circuit Elements
Multiport Elements
Two-
term
inal
ele
men
t
Four
-ter
min
al e
lem
ent
12
Electric Circuit Elements
Multiport Elements
resistortransistor
transformerwith iron core
amplifier
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Electric Circuit Elements
Symmetrical ElementsS y m m e t r i c a l (r e v e r s i b l e) e l e m e n t has the sameproperties regardless of the way an element is connected in a cir-cuit and of the polarity of the voltage applied — the direction of acurrent flow.
I
U
diode
resistor
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Electric Circuit Elements
AUI
~0)( uUtu
~0~0~0)( iIAuAUuUAti
current-voltage characteristic
linear element response
Linear Elements
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Electric Circuit Elements
Linear Elements
I
U
16
Electric Circuit Elements
I
U
i(t)
t
u(t)
t
t1 t2 t3 t4
t8 t7
t5 t6
t1 t2
t3 t4
t8 t7 t5
t6
Linear Elements
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Electric Circuit Elements
Non-Linear Elements
2AUI
~0)( uUtu
~0
2~
20
2~~0
20
2~0
22)(
uAUiIAuuAUAUuUAti
current-voltage characteristic
non-linear element response
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Electric Circuit Elements
Non-Linear Elements
I
U
19
Electric Circuit Elements
Non-Linear Elements
I
U
i(t)
t
u(t)
t
t1 t2 t3 t4
t8 t7
t5 t6
t1 t2
t3 t4
t8 t7 t5
t6
20
Electric Circuit Elements
Active Elements
ttte
d)(d)(
SB dd
cosBS SB
Generator. Faraday’s Law
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Electric Circuit Elements
Active ElementsGenerator. Faraday’s Law
B
l
d
cos2cos rBlBS SB tStS cos)(
22
Electric Circuit Elements
Active ElementsGenerator. Faraday’s Law
tBSt cos)(
tBStt sin
d)(d
tEtBSte sinsin)( m
BSUE mm
tUtu sin)( m
23
Electric Circuit Elements
Active ElementsVoltage sources
E E
E
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Electric Circuit Elements
Active ElementsVoltage sources
Ri
E
U EIRU i
EUUIREIIU
0
is
00
real voltage source
short circuit state
no load state
25
Electric Circuit Elements
Active ElementsVoltage sources
U
E
I
ideal
real
0 Is E/Ri
Voltage-current characteristics
26
Electric Circuit Elements
Active ElementsCurrent sources
I I Is Ri
si IUGI ii 1 RG
s
si0
00
IIUIRUUI
no-load state
short-circuit state
real current source
27
Electric Circuit Elements
Active ElementsCurrent sources
I
Is
U
ideal
real
0 U0 I/Gi
Current-voltage characteristics
28
Electric Circuit Elements
Passive ElementsrErF ddd qW
tptuiquW dddd
t
tpW 0d
)()()( titutp
t t
ttituttituWtW0 0
0d)()(d)()(0)(
condition for element’s passiveness
29
Electric Circuit Elements
photoresistor otorezystor
varistor
resistor resistor
resistor
variable resistor nastawny
variable resistor—potentiometer potencjometryczny
Passive ElementsResistor
30
Electric Circuit Elements
)()(or)(1)( tRitutuR
ti
I
U
I
U
0d)(d)()()( 2R
ttRittitutWtt
Passive ElementsResistor
31
Electric Circuit Elements
S
l
lS
lSG
Sl
SlR
1or1
[] = ·m or ·m2/m (·mm2/m)[] = S/m or S/(m2/m) S·m/m2
Passive ElementsResistor
32
Electric Circuit Elements
S
l
TRTTRTRR TT 11)( 00 0
Passive ElementsResistor
33
Electric Circuit Elements
Passive ElementsResistor
Types of windings in wire resistors:1. common,2. bifilar,3. common on a thin former,4. Ayrton-Perry.
34
Electric Circuit Elements
Passive ElementsResistor
35
Electric Circuit Elements
Resistivity of some materialsMaterial [10-6·W·m]
SilverCuprumGoldAluminumTungstenBronze MS 63IronPlatinumTinManganin WM 43Constantan WM 50MercuryCoal (graphite)Cable paper — impregnatedRubberTransformer oilPolyethylene
0.0156 (162)0.017250.0220.0283 (290)0.05480.0740.09780.1110.1140.430.490.95820–10010131013–10141011–10121020–1022
Passive Elements
Resistor
36
Electric Circuit Elements
capacitor capacitorpolarized
capacitor
trimmer capacitor
variable capacitor
electrolytic capacitor
Passive ElementsCapacitor
37
Electric Circuit Elements
uqC
Q
U
Q
U
tqti
dd)(
tuCtid(t)d)(
ttiC
utut
d)(1)0()(0
Passive ElementsCapacitor
38
Electric Circuit Elements
0)(21
d)(ddd)(d)()()(
2
C
tCu
utuCttuCtuttitutW
ttt
)(21d)(d)(d)()( 2
00
0
C tCuutuCutuutuCtWtt
Passive ElementsCapacitor
39
Electric Circuit Elements
S
d
dSC 0
[] = – (dimensionless number)0 = 8.854×1012 F/m
Passive ElementsCapacitor
40
Electric Circuit Elements
Passive ElementsCapacitor
41
Electric Circuit Elements
Pemittivity of some materialsMaterial [–]
VacuumAirKerosene, teflonIcePolyethyleneTransformer oilRubberWoodPaper – impregnatedBakeliteGlassPetrolPVCSiliconeMethanolWater – distilledCeramics X7RCeramics Z5U
1.00001.00062.02.0–3.02.22.2–2.52.5–2.83.3–3.53.5–84.4–5.45.0–165.76.112338015005000
Passive Elements
Capacitor
42
Electric Circuit Elements
air core inductor iron-core inductor (ferromagnetic core)
nonlinear inductor
variable inductor
slug-tuned inductorwith ferrite core
Passive ElementsInductor
43
Electric Circuit Elements
I I
iL
tz
ttetu
dd
dd)()(
tiLtud(t)d)(
ttuL
itit
d)(1)0()(0
Passive ElementsInductor
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Electric Circuit Elements
0)(21
d)(d)(ddd)()()(
2
L
tLi
itiLttitiLttitutW
ttt
)(21d)(d)(d)()( 2
00
0
L tLiitiLitiitiLtWtt
Passive ElementsInductor
45
Electric Circuit Elements
S
l
z
lSzL 20
[] = – (dimensionless number)0 = 4×107 H/m
Passive ElementsInductor
46
Electric Circuit Elements
Passive ElementsInductor
47
Electric Circuit Elements
Permeability of some materialsMaterial [–]
BismuthCuprumWaterVacuumAirAluminumNickelMild steelSpecialty (special-purpose) steel
0.999840.999990.9999911.000001.0000041.000004< 300< 5000< 10 000
Passive ElementsInductor
48
Electric Circuit Elements
BlF dd I
lrBrBlrF
dddd=ddd
IIW
SB dd IW
d 2r
F
F I I d
B
N
S
work equivalent to torque
Electric Motor. Ampere’s ForcePassive Elements
49
Electric Circuit ElementsThank you for your attention!
© 2010 Juliusz B. Gajewski