ECE201 Lect-19 1
Capacitors (5.1); Inductors (5.2); LC Combinations (5.3)
Dr. Holbert
November 6, 2001
ECE201 Lect-19 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-19 3
Power Generation and Distribution
• Energy storage elements model electrical loads:
– Capacitors model computers and other electronics (power supplies).
– Inductors model motors.
ECE201 Lect-19 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-19 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 RAM’s.
ECE201 Lect-19 6
Electromagnetics
• For high frequency signals, inductance and capacitance are more significant effects than resistance.
ECE201 Lect-19 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-19 8
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-19 9
Capacitor
i(t) +
–
v(t)
Therestofthe
circuit
dt
tdvCti
)()(
ECE201 Lect-19 10
Capacitor Voltage
t
dxxiC
tv )(1
)(
t
t
dxxiC
tvtv0
)(1
)()( 0
ECE201 Lect-19 11
Energy Stored
)(2
1)( 2 tCvtwC
ECE201 Lect-19 12
Class Examples
• Learning Extension E5.2
• Learning Extension E5.3
ECE201 Lect-19 13
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-19 14
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-19 15
Inductor
i(t)+
–
v(t)
Therestofthe
circuit
dt
tdiLtv
)()(
H
ECE201 Lect-19 16
Inductor Current
t
dxxvL
ti )(1
)(
t
t
dxxvL
titi0
)(1
)()( 0
ECE201 Lect-19 17
Energy Stored
)(2
1)( 2 tLitwL
ECE201 Lect-19 18
Class Examples
• Learning Extension E5.4
• Learning Extension E5.5
ECE201 Lect-19 19
Inductor Combinations
• Series inductors combine like series resistors
Lser = L1 + L2 + L3 + · · ·
• Parallel inductors combine like parallel resistors
1/Lpar = 1/L1 + 1/L2 + 1/L3 + · · ·
ECE201 Lect-19 20
Capacitor Combinations
• Series capacitors combine like parallel resistors (opposite)
1/Cser = 1/C1 + 1/C2 + 1/C3 + · · ·
• Parallel capacitors combine like series resistors (opposite)
Cpar = C1 + C2 + C3 + · · ·
ECE201 Lect-19 21
Class Examples
• Learning Extension E5.7
• Learning Extension E5.8