Chapter 3 Inductance and Capacitanceengineering.snu.ac.kr/lecture_pdf/EE/Chapter03_SNU.pdf ·...
Transcript of Chapter 3 Inductance and Capacitanceengineering.snu.ac.kr/lecture_pdf/EE/Chapter03_SNU.pdf ·...
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Chapter 3Inductance and Capacitance
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Goal1. Current (voltage) for a Capacitance or Inductance
given the voltage (current) as a function of time.
2. Capacitance of a Parallel-plate Capacitor.
3. Stored Energy in a Capacitance or Inductance.Passive Elements : Resistor, Capacitor, Inductor
Not Generate Energy, But Store Energy
4. Typical Physical Construction of Capacitors and Inductors
5. Voltages across mutually coupled inductances in terms of the currents.
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CAPACITANCE
Positive Charge is Balanced by Negative Charge of Equal Amount
Water Pressure : PotentialWater Amount : Charge
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dtdvCi =
)(Cvdtd
dtdqi ==
Cvq =q : stored charge
C : capacitance
Stored Charge
at fixed Voltage
Unit : Farad = Coulombs / Volt
∫ +=t
ttvdtti
Ctv
0
)()(1)( 0
Ctqtv )()( 0
0 =∫ +=t
t Ctqdtti
Ctv
0
)()(1)( 0
∫ +=t
ttqdttitq
0
)()()( 0
Voltage in Terms of Current
Cvq =
Initial voltage
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Example of Current in terms of Voltage
)(10)( 6 tvCvtq −==
dttdv
dttdvCti )(10)()( 6−== sV
dttdv /105)( 6×=
AdttdvCti 5)()( ==
sVdttdv /10)( 7−=
AdttdvCti 10)()( −=
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Example of Voltage in terms of Current
)10sin(5.0)( 4 tti =
∫ +=t
ttqdttitq
0
)()()( 0
∫ −×==t
ttdtttq
0
))10cos(1(105.0)10sin(5.0)( 444
))10cos(1(500)()( 4 tCtqtv −×==
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Ctq
2)(2
=
)()(21 tqtv=
)(21 2 tCv=
∫=)(
0
tvCvdv∫=
t
tdt
dtdvCv
0∫=t
tdttptw
0
)()(
dtdvCvtp =)()()()( titvtp =
Stored Energy
powerdtdvCi =
energy
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dtdvCi 11 =
CAPACITANCES IN SERIES AND PARALLEL
dtdvCi 22 = dt
dvCi 33 =
321 iiii ++=
dtdvC
dtdvC
dtdvC 321 ++=
dtdvCCC )( 321 ++=
321 CCCCeq ++=dtdvCeq=
Capacitances in Parallel
321 1111
CCCCeq ++
=
Capacitances in Series
∫=t
tdtti
Ctv
0
)(1)(
KCL
KVL 321 vvvv ++=
∫++=t
tdtti
CCC 0
)(]111[321
∫=t
teq
dttiC 0
)(1
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PHYSICAL CHARACTERISTICS OF CAPACITORS
0εεε r=
dAC ε
=
rε0ε = 8.85 ⅹ 10-12 F/m
: relative dielectric constant 78.54.33.47.05.51.0
WaterQuartzPolysterMicaDiamondAir
Materials rε
Real Capacitor
Parasitic Element Rs, Ls, Rp
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INDUCTANCE
dtdiLtv =)( dttv
Ldi )(1=
∫∫ =t
t
ti
tidttv
Ldi
00
)(1)(
)(
)()(1)( 00
tidttvL
tit
t+= ∫
L : Inductance Unit : HH : Volt sec/Ampere
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)(21)( 2 tLitw =∫=
)(
0
tiLidi∫=
t
tdt
dtdiLi
0∫=t
tdttptw
0
)()(
dtditLitp )()( =)()()( tvtitp =
Stored Energy
dtdiLtv =)(power
energy
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Inductor Current with Constant Voltage
t=0 : i=0 because Open Switch
)()(1)( 00
tidttvL
tit
t+= ∫
i(to)=0
051021)(
0
>== ∫ tAdttit
t
dtdiLtv =)(
If Open Switch at t=1s, di/dt=-Infinite Infinite Voltage : Impulse Occur (Surge)
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INDUCTANCES IN SERIES AND PARALLEL
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Practical Inductor
Examples of Series & Parallel
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Practical Application : Electronic Flash
Power Transfer From Battery to Flash is not Possible1) Battery Voltage : a few ten volts2) Maximum Power Transfer : 1W
Electronic Switch : 10,000 times / sec ON/OFFduring ON : Battery cause to Build up Current in Inductorduring OFF : Inductor force Currents to flow through diode to Charge Capacitor
Diode Prevent Charge from CapacitorMultiple On/OFF Build-up several Hundred Voltage at CapacitorFlash Switch On Flash Discharge
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Electronic Switch
Diode
Capacitor
Flash Tube
Battery
Voltage : Water PressureCurrent : Water Amount
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MUTUAL INDUCTANCE
LVDT (Linear Variable Differential Transformer)
)cos()( tKxtvo ω=