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

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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