ECE201 Lect-17 1

Capacitors (6.1); Inductors (6.2); LC Combinations (6.3)

Dr. Holbert

April 5, 2006

ECE201 Lect-17 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-17 3

Power Generation and Distribution

• Energy storage elements model electrical loads:

– Capacitors model computers and other electronics (power supplies).

– Inductors model motors.

ECE201 Lect-17 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-17 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-17 6

Electromagnetics

• For high frequency signals, inductance and capacitance are more significant effects than resistance.

ECE201 Lect-17 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-17 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-17 9

Capacitor

i(t) +

–

v(t)

Therestofthe

circuit

dt

tdvCti

)()(

ECE201 Lect-17 10

Capacitor Voltage

t

dxxiC

tv )(1

)(

t

t

dxxiC

tvtv0

)(1

)()( 0

ECE201 Lect-17 11

Energy Stored

)(2

1)( 2 tCvtwC

ECE201 Lect-17 12

Class Examples

• Learning Extension E6.2

• Learning Extension E6.3

ECE201 Lect-17 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-17 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-17 15

Inductor

i(t)+

–

v(t)

Therestofthe

circuit

dt

tdiLtv

)()(

H

ECE201 Lect-17 16

Inductor Current

t

dxxvL

ti )(1

)(

t

t

dxxvL

titi0

)(1

)()( 0

ECE201 Lect-17 17

Energy Stored

)(2

1)( 2 tLitwL

ECE201 Lect-17 18

Class Examples

• Learning Extension E6.4

• Learning Extension E6.5

ECE201 Lect-17 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-17 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-17 21

Class Examples

• Learning Extension E6.7

• Learning Extension E6.8