review: lecture 3 - trinity college dublin · 2015. 12. 16. · review: lecture 3 •linear circuit...
TRANSCRIPT
Review: Lecture 3
• Linear circuit
• Superposition
• Equivalent Circuits
—Simple Circuits
—Y- Transforms
—Source transformation
—Thevenin's theorem
—Norton's theorem
• Maximum power transfer
Lecture 4 DC Circuits Capacitors and Inductors
Objectives
• Review the basics of capacitors and inductors
• Series and parallel capacitors/inductors
• Applications
—Integrator
—Differentiator
—Analog Computer
Capacitors
Capacitors: fundamental passive components.
— Basic form: two conductive plates separated by an insulating dielectric
— Capacitance: the ability to store charge (electric potential energy)
The charging process…
BA
VS
+
+
+++++++++
A capacitor with stored charge can act as a temporary battery.
Vs
Conductive plate
dielectric
E
The physical dimensions of the capacitor determine the
charge ‘storage ability’
The external source cannot move charge any more: fully charged
Cvq
Parallel-plate Capacitors
d
A
v
qC
The permittivity of the dielectric
The spacing between plates
The surface area of the plates
• Current and voltage relation — — Linear element
•
—Passive sign convention: • Being charged:
• A capacitor is an open circuit to dc —
• The voltage on a capacitor cannot change abruptly —
• Power and energy stored: — Power: — Energy stored:
Circuit behaviour of capacitors
Cvq dt
dvC
dt
dqi
0
000 ki
dt
dvkC
dt
kvdCikvv
0,0;0 ,0 iviv
0 ,0 const, idt
dvv
Circuit theorems valid Superposition, Thevenin…
)(1
0
0
tvidtC
v
t
t
dt
dvCi
dt
dvCvvip
)(
)(
2
t
-2
1
tv
v
t
Cvdtdt
dvCvdtpw
Capacitor voltage depends on the past history of the current
Passive elements p=vi >0, ‘consume’ energy:
charging
Current is undefined.
Ideal capacitors do not dissipate energy
Series and Parallel Capacitors • Parallel-plate capacitors
— — Series: — Parallel:
• Behaviour consideration — Series: KVL
— Parallel: KCL
d
AC
21
21
T21
21
11
C
1 , ,
CCA
d
A
d
dd
ACddd TT
CC)(
, 2121
21
d
AACAAA TT
Nvvvv ...21)(
10
0
tvidtC
v
t
t
)(1
...11
)(...)()(1
...11
)(1
...)(1
)(1
0
1
00201
1
00201
1
0
000
000
tvidtCCC
tvtvtvidtC
idtC
idtC
tvidtC
tvidtC
tvidtC
v
t
tN
N
t
tN
t
t
t
t
N
t
tN
t
t
t
t
Niiii ...21
NT CCCC
1...
111
1
dt
dvCi
dt
dvCCC
dt
dvC
dt
dvC
dt
dvCi
N
N
...
...
21
21
NT CCCC ...21
Inductors
Inductors: fundamental passive components.
— Basic form: a length of wire is formed into a coil
— Store energy in its magnetic field
Current change
Magnetic field change
Induce voltage
opposite
Inductance is greatly magnified by adding turns and winding them on a magnetic core material.
Air core Iron core Ferrite core Variable
2N AL
l
inductance in henries
number of turns of wire
permeability in H/m (same as Wb/At-m)
• Current and voltage relation — — Linear element
•
—Passive sign convention: • Energy stored:
• An inductor is an short circuit to dc —
• The current on an inductor cannot change abruptly —
• Power and energy stored: — Power: — Energy stored:
Circuit behaviour of inductors
dt
diLv
212121
21
)(vv
dt
diL
dt
diL
dt
iidLviii
0,0;0 ,0 iviv
0 ,0 const, vdt
dii
)()(1
0
0
tidttvL
i
t
t
dt
diLv
dt
diLivip
)(
)(
2
t
-2
1
ti
i
t
Lidtdt
diLidtpw
Ideal inductors do not dissipate energy
Series and Parallel Inductors
• Series: KVL
• Parallel: KCL
Nvvvv ...21
dt
diLLL
dt
diL
dt
diL
dt
diLv
N
N
...
...
21
21
Neq LLLL ...21
Niiii ...21
)(1
...11
)(...)()(1
...11
)(1
...)(1
)(1
0
21
00201
21
002
2
01
1
0
000
000
tivdtLLL
tititivdtL
vdtL
vdtL
tivdtL
tivdtL
tivdtL
i
t
tN
N
t
tN
t
t
t
t
N
t
tN
t
t
t
t
N
n neq LL 1
11
Typical passive elements
As long as all the elements are of the same type, the delta-wye transformation can be extended to C and L
Integrator
CR ii
R
vi iR
dt
dvCi o
C
dt
dvC
R
v oi dtRC
vdv i
o
t
o
ioo dtvRC
vtv1
)0()(
t
o
io dtvRC
tv1
)(Assume vo(0)=0
Differentiator
CR ii
R
vi oR
dt
dvCi i
C
dt
dvRCv i
o
Analog Computer
Analog Computer
t
o
io dtvRC
tv1
)(
0.5
Analog Computer
t
o
io dtvRC
tv1
)(
Analog Computer – after class practice
Evaluate the circuit:
Appendix
Practical issues of capacitors
• Leakage resistance
• Dielectric breakdown — insulating materials forced to conduct
— sudden surge of current
—Burn, melt, vaporize: permanent damage
• Capacitor types — paper, air, polycarbonate, polyester, polypropylene,
polystyrene, mixed, silvered mica, electrolytic(aluminium, tantalum), ceramic…
• Capacitor labelling —Small capacitor: 0.01.. Microfarads
—103: 10x103 pF: Third digit is the multiplier
Practical issues of inductors
• Winding resistance and capacitance
• Inductor types
• Applications: —Power supplies, transformers,
radios, TVs, radars, and electric motors.
LRW
CW
The winding resistance is in series with the coil; the winding capacitance is in parallel with both.
Encapsulated Torroid coil Variable
Applications
• Capacitors
— temporary voltage source
—frequency discrimination
• Inductors
— temporary current source
— spark/arc suppression
—Converting pulsating dc voltage into relatively smooth dc
— frequency discrimination
Lecture 5 DC Circuits Transient Circuits