ECE201 Lect-28 1
Capacitors (5.1); Inductors (5.2);
Dr. S. M. Goodnick
November 7, 2003
ECE201 Lect-28 2
Energy Storage Elements
• Capacitors store energy in an electric field.• Inductors store energy in a magnetic field.• Capacitors and inductors are passive
elements:– Can store energy supplied by circuit– Can return stored energy to circuit– Cannot supply more energy to circuit than is
stored.
ECE201 Lect-28 3
Power Generation and Distribution
• Energy storage elements model electrical loads:
– Capacitors model computers and other electronics (power supplies).
– Inductors model motors.
ECE201 Lect-28 4
Signal ProcessingCommunicationInstrumentation
• Capacitors and inductors are used to build filters and amplifiers with desired frequency responses:– Instrumentation amplifiers.
• Capacitors are used in analog-to-digital (A/D) converters to hold a sampled signal until it can be converted into bits.
ECE201 Lect-28 5
Solid StateDigital Design
• Integrated circuits (ICs) have layers of conductors (metal, silicon with impurities) with insulators (glass) between. This is a capacitor!
• This capacitance is one of the limiting factors in processor speeds.
• This capacitance is used to create RAMs.
ECE201 Lect-28 6
Electromagnetics
• For high frequency signals, inductance and capacitance are more significant effects than resistance.
ECE201 Lect-28 7
Capacitance
• Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator).
• Charge on the two conductors creates an electric field that stores energy.
+- - - - - - - - - - - -
+ + + + + + + +
ECE201 Lect-28 8
CAPACITORSFirst of the energy storage devices to be discussed Typical Capacitors
Basic parallel-plates capacitor
CIRCUIT REPRESENTATION
NOTICE USE OF PASSIVE SIGN CONVENTION
ECE201 Lect-28 9
Capacitance
• The voltage difference between the two conductors is proportional to the charge:
q = C v
• The proportionality constant C is called capacitance.
• Units of Farads (F) – Coulomb/Volt
ECE201 Lect-28 10
Capacitor
i(t) +
–
v(t)
Therestofthe
circuit
dt
tdvCti
dt
tdq )()(
)(
ECE201 Lect-28 11
Capacitor Voltage
t
diC
tv )(1
)(
t
t
diC
tvtv0
)(1
)()( 0
ECE201 Lect-28 12
Energy Stored
)(2
1)( 2 tCvtwC
)(
)()(
tdvtvCtptw
dt
tdvtCvtitvtp
c
ECE201 Lect-28 13
Class Examples
• Learning Extension E5.2
• Learning Extension E5.3
ECE201 Lect-28 14
VOLTAGETHE FIND .4 FC
0 ) 0( v
20 t
mst 42 ][1082)( 3 Vttv
0;)(1
)0()(0
tdxxiC
vtvt
2;)(1
)2()(2
tdxxiC
vtvt
ECE201 Lect-28 15
Inductance
• Inductance occurs when current flows through a (real) conductor.
• The current flowing through the conductor sets up a magnetic field that is proportional to the current.
• The voltage difference across the conductor is proportional to the rate of change of the magnetic field.
ECE201 Lect-28 16
Inductance
• The voltage difference across the inductor is proportional to the rate of change of the current.
• The proportionality constant is called the inductance, denoted L
• Units of Henrys (H) - V·s/A
ECE201 Lect-28 17
Flux lines may extendbeyond inductor creatingstray inductance effects
Circuit representation for an inductor
A TIME VARYING FLUXCREATES A COUNTER EMFAND CAUSES A VOLTAGE TO APPEAR AT THETERMINALS OF THEDEVICE
INDUCTORS NOTICE USE OF PASSIVE SIGN CONVENTION
ECE201 Lect-28 18
Cell Phone: Much of Area Consumed by
discrete Inductors and Capacitors of
Filters
ECE201 Lect-28 19
Inductor
i(t)+
–
v(t)
Therestofthe
circuit
dt
tdiLtv
)()(
H
ECE201 Lect-28 20
Inductor Current
t
dxxvL
ti )(1
)(
t
t
dxxvL
titi0
)(1
)()( 0
ECE201 Lect-28 21
Energy Stored
)(2
1)( 2 tLitwL
)(
)()(
tditiLtw
dt
tditLitvtitp
L
ECE201 Lect-28 22
Class Examples
• Learning Extension E5.4
• Learning Extension E5.5