EET1035C Chapter 8 No Quiz

5/21/2018 EET1035C Chapter 8 No Quiz

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Introduction to Alternating Current and Voltage

Chapter 8

Thomas L. Floyd

David M. Buchla

DC/AC Fundamentals: A Systems

Approach


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DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

2013 by Pearson Higher Education, Inc

Upper Saddle River, New Jersey 07458 All Rights Reserved

Homework

Page 372: Problems 2 & 4

Page 373: Problems 6, 8, 10, & 16

Page 374: Problems 24 & 26

Page 375: Problems 34, 36, 40 & 42

Due Thursday


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AC in Conductors

AC


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The sinusoidal waveform, or sine wave, is thefundamental alternating current (ac) and voltagewaveform.

Electrical sine wavesare named from themathematicalfunction with thesame shape.

Ch.8 Summary

Sine Waves


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A wave is a disturbance that is somewhat analogous to

the wave that is created when a rock is dropped into a

pond. Despite their similarities, however, electrical wavescannot be seen directly.

Ch.8 Summary

Waves

All periodic waves can be constructed from sine

waves, which is why sine waves are fundamental.


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Sine waves are characterized by the amplitude and

period. Theamplitudeis the maximum value of a

voltage or current; the periodis the time interval for

one complete cycle.The amplitude

(A) of this sine

wave is20 V

The period is50.0 us

Ch.8 Summary

Sine Waves

0 V

10 V

-10 V

15 V

-15 V

-2 0 V

0 25 37.5 50.0

20 V

5 V

5 V

12.5t (ms)

Amplitude

Period (time)


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The period of a sine wave can be measured between

any two corresponding points on the waveform.

T T T

T T

By contrast, the amplitude of a sine wave is only

measured from the center to the maximum point.

Ch.8 Summary

Sine Waves

A


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Frequency ( f ) is the number of cycles that a sine

wave completes in one second.

Frequency is measured in hertz(Hz).

If 3 cycles of a wave

occur in one second

(as shown), thefrequency is 3 Hz.

Ch.8 Summary

Frequency

1 second (s)


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The period and frequency are reciprocals of each other.

Thus, if you know one, you can easily find the other.

Example: If the period is of a sine waveis 50 ms, the frequency is 20 Hz

Ch.8 Summary

Period and Frequency

andTf

1

fT

1


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Sinusoidal voltages are produced by ac generators and

electronic oscillators.

N S

Motion of conductor Conductor

B

C

D

A

AB

C

D

A

BB

C

D

A

CB

C

D

A

D

When a conductor rotates in a constant

magnetic field, a sinusoidal wave is generated.

When the conductor is moving parallel

with the lines of flux, no voltage is

induced.

When the loop is moving perpendicular to the lines

of flux, the maximum voltage is induced.

B

C

D

A

Ch.8 Summary

Generation of a Sine Wave


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Generators convert rotational energy to electrical energy. A

stationary field alternator with a rotating armature is shown. The

armature has an induced voltage, which is connected through slip

rings and brushes to a load. The armature loops are wound on a

magnetic core (not shown for simplicity).

N S

slip rings

armaturebrushes

Small alternators may

use a permanent

magnet as shown here;other use field coils to

produce the magnetic

flux.

Ch.8 Summary

AC Generator (Alternator)


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2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 All Rights Reserved

By increasing the number of poles, the number of cycles per

revolution is increased. A four-pole generator produces two

complete cycles in each revolution.

Ch.8 Summary

AC Generator (Alternator)


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Function selection

Frequency

Output level (amplitude)

DC offsetCMOS output

Range

Adjust

Duty cycle

Typical controls:

Outputs

Readout

Ch.8 Summary

Function Generators

Sine Square TriangleSine Square Triangle

Courtesy of B+K Precision


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There are several ways to specify the voltage of a

sinusoidal voltage waveform. The amplitude of a sine

wave is also called the peak value, abbreviated as VP

for a voltage waveform.

The peak voltage of

this waveform is 20 V

Ch.8 Summary

Sine Wave Voltage and Current Values

0 V

10 V

-10 V

15 V

-15 V

-20 V

t (ms)

0 25 37.5 50.0

20 V

VP


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The voltage of a sine wave can also be specified as

either the peak-to-peakor the rmsvalue. The peak-to-

peak is twice the peak value. The rms value is 0.707

times the peak value.

The peak-to-peak

voltage is 40 V

The rms

voltage is 14.1 V

Ch.8 Summary


0 V

10 V

-10 V

15 V

-15 V

-20 V

t (ms)0 25 37.5 50.0

20 V

Vrms

VPP


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For some purposes, the average value (actually the

half-wave average) is used to specify the voltage or

current. By definition, the average value is as 0.637

times the peak value.

The average value

for the sinusoidal

voltage is12.7 V

Ch.8 Summary


0 V

10 V

-10 V

15 V

-15 V

-20 V

t (ms)0 25 37.5 50.0

20 V

Vave


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Angular measurements can be made in degrees (o) or

radians. The radian(rad) is the angle that is formed when the

arc is equal to the radius of a circle.There are 360oor 2p

radians in one complete revolution.

Ch.8 Summary

Angular Measurement

R

R

1 rad

1.0

-1.0

0.8

-0.8

0.6

-0.6

0.4

-0.4

0.2

-0.20 0 2ppp

2

p4

p4

3 p2

3p4

5 p4

7


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There are 2pradians in one complete revolution and 360oin

one revolution. To find the number of radians, given the

number of degrees:

To find the number of degrees,

given the number of radians:

This can be simplified to:

Ch.8 Summary

Angular Measurement

degrees360

rad2

rad

p

degrees180

radrad

p

radrad

180deg

p


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How Many Degrees in a Radian

deg = 180/x 1 rad = 57.29 degrees

radrad

180deg

p


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How many radians are in 45o?

How many degrees are in 1.2 radians?

Ch.8 Summary

Angular Measurement

rad0.78545180

rad

degrees

180

radrad

p

p

p

p

69rad1.2rad

180

radrad

180deg


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Instantaneous values of a wave are shown as vor i.

The equation for the instantaneous voltage (v) of a

sine wave is

where

If the peak voltage of a sine wave is 25 V, the

instantaneous voltage at 50 degrees is

VP=

q

Peak voltage

Angle in rad or degrees

19.2 V

Ch.8 Summary

Sine Wave Equation

q sinP

Vv


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A plot of the example in the previous slide (peak at 25 V) is

shown below. The instantaneous voltage at 50ois 19.2 V as

previously calculated. v = 25 Sin 50 = 19.2 V

Ch.8 Summary

Sine Wave Equation

v = =19.2 VVp sinVp

90

500

= 50

Vp

Vp

= 25 V


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0

0

90

90

180

180

360

The sine wave can be represented as the projection

of a vector rotating at a constant rate. This rotating

vector is called a phasor. Phasors are useful for

showing the phase relationships in ac circuits.

Ch.8 Summary

Phasors


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wheref Phase shift

The phaseof a sine wave is an angular measurement that

specifies the position of a sine wave relative to a reference.

To show that a sine wave is shifted to the left or right of this

reference, a term is added to the instantaneous voltage

equation:

Ch.8 Summary

Phase Shift

)sin( f P

Vv


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Voltage

(V)

270 3600 90 180

40

45 135 225 3150

Angle ()

3020

10

-20-30

- 40

405

Peak voltag e

Reference

Example of a wave that lags a reference wave:

v= 30 V sin (q-45o)

and the equation

has a negative phase

shift

Ch.8 Summary

Phase Shift

Notice that a lagging sine wave

is below the axis at 0o


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Voltage

(V)

270 3600 90 180

40

45 135 225 3150

Angle ()

3020

10

-20-30

-40

Peak voltage

Reference

-45

-10

Notice that a leading sine

wave is above the axis at 0o

Example of a wave that leads the reference wave

v= 30 V sin(q+ 45o)

and the equationhas a positive phase

shift

Ch.8 Summary

Phase Shift


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An important application of phase-shifted sine waves is in

electrical power systems. Electrical utilities generate AC

with three phases that are separated by 120 as illustrated.

120o

Normally, 3-phase

power is delivered to

the user with three hot

lines plus neutral. The

voltage of each phase,with respect to neutral is

120 V.

120o 120o

Ch.8 Summary

Phase Shift


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Bulbac or dcsource

0 V

170 VP@120 Vrms

0 V

120 Vdc+

-

The power relationships developed for DC circuits apply to AC

circuits except you must use rms values in AC circuits when

calculating power.

For example, the DC and the AC sources deliver the sameamount of power to the bulb:

Ch.8 Summary

Power in Resistive AC Circuits

RIP

R

VP

IVP

rms

rms

rmsrms

2

2


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Assume a sine wave with a peak value of 40 V is applied

to a 100 Wresistive load. What power is dissipated?

40

0

30

20

10

-20

-30

- 40

Voltage

(V)

V28.3V400.707707.0 Prms VV

Ch.8 Summary

Power in Resistive AC Circuits

W8100

V)(28.3 2

R

VP

2

rms


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Waveforms frequently contain both dc and ac voltages. They

can be added algebraically, to produce a composite waveform

of an ac voltage riding on a dc level.

Ch.8 Summary

Superimposed DC and AC Voltages


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Alternatorsare AC generators. Utility companies use 3-phase

alternators and deliver all three phases to industrial customers. A

simplified 3-phase alternator is represented here.

Ch.8 Summary

Alternators

N

S

Phase 1

Neutral

Phase 2

Phase 3


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In vehicles, alternators generate AC, which is converted to

DC for operating electrical devices and charging the battery.

AC is more efficient to produce and can be easily regulated,

hence it is generated and converted to DC by diodes.

The output is taken

from the rotor throughthe slip rings.

Ch.8 Summary

Alternators

Diode plate

Rotor

Stator coils

Housing

Slip ringsDiodes


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There are two major classifications of AC motors.

These are the induction motorand the synchronous

motor. Both types use a rotating field in the stator

windings.

Rotor current in an induction motor is induced by the

changing current in the stator. This current creates a

magnetic field that reacts with the moving field of the

stator, which develops a torque and causes the rotorto turn.

Ch.8 Summary

Induction AC Motors


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There are two major classifications of AC motors.

These are the induction motorand the synchronous

motor. Both types use a rotating field in the stator

windings.

Synchronous motors have a magnet for a rotor. In small

motors, this can be a permanent magnet, which keeps up

with the rotating field of the stator. Large motors use an

electromagnet in the rotor, with external DC supplied to

generate the magnetic field.

Ch.8 Summary

Synchronous AC Motors


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Ideal pulses

Ch.8 Summary

Pulse Definitions

Amplitude

Baseline

Amplitude

Baseline

(a) Positive-going pulse (b) Negative-going pulse

Leading (rising) edge

Trailing (falling) edge

Leading (falling) edge

Trailing (rising) edge

Pulse

widthPulse

width


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Non-ideal pulses

Notice that rise and fall times are measured between the

0.1A (10%) and 0.9 A (90%) levels; whereas pulse width

is measured at the 0.5A (50%) level.

Ch.8 Summary

Pulse Definitions

A

0.9 A

0.1A

t r tt

fW

t t

0.5 A

A

(a) (b)Rise and fall times Pulse width


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Triangular and sawtooth waveforms are formed by

voltage or current ramps (linear

increase/decrease)

Triangular waveforms have

positive-going and negative-

going ramps of equal

duration.

The sawtooth waveform

consists of two ramps, one of

much longer duration than the

other.

Ch.8 Summary

Triangular and Sawtooth Waves


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All repetitive non-sinusoidal waveforms are composed

of a fundamental frequency(repetition rate of the

waveform) and harmonic frequencies.

Odd-order harmonicsare frequencies that are

odd multiples of the fundamental frequency.

Even-order harmonicsare frequencies that are

even multiples of the fundamental frequency.

Ch.8 Summary

Harmonics


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A square wave is composed only of the fundamental frequency

and odd harmonics (of the proper amplitude).

Ch.8 Summary

Harmonics


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The oscilloscope is divided intofour main sections.

Ch.8 Summary

Oscilloscopes

Ch 1

Signal coupling

ACDC GND

Amp

Ch 2

AC

DC GNDAmp

Volts/Div

Verticalposition

ACDC

Ext

Triggersource

External triggercoupling

Ch 1Ch 2

Line

T

Time base

Sec/Div

Intensity

AC

DC to all sectionsPower supply

Vertical section

Display section

Trigger section

Digitalonly

Conversion/storage(Digital scopes only)


Analogonly


Horizontalposition

riggerlevel and

slope

Triggercircuits

Externaltrigger

Horizontal section

Ch 1 Conversion/storage(Digital scopes only)

Signal coupling

AC

DC GND

Amp

Ch 2 Conversion/storage

(Digital scopes only)

AC

DC GND

Amp

Volts/Div

Verticalposition

Vertical section

Externaltrigger

ACDC

Ext

Triggercoupling

Ch 1Ch 2

Line

circuits

AC

Trigger section

Trigger

sourceExternal trigger

vslope

Triggerle el and

From horizontal section

Intensity

Display section

Analogonly

From

vertical

section

Time base

Sec/Div

Horizontalposition

To display sectionDigitalonly

Horizontalsection

Control and process(Digital scopes only)


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Current that reverses direction in response to

a change in source voltage polarity.

The time interval for one complete cycle of a

periodic waveform.

A waveform that follows a cyclic sinusoidal

pattern defined by the formula y=Asin q.

A measure of the rate of change of a periodicfunction; the number of cycles completed in 1 s.

The unit of measure for frequency. One hertz

equals one cycle per second.

Ch.8 Summary

Key Terms

Sine wave

Alternat ing

cu rrent (AC)

Period (T)

Frequenc y (f)

Hertz


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Ch.8 Summary

Key Terms

The voltage or current value of a waveform at

its maximum positive or negative points.

The voltage or current value of a waveform

measured from its minimum to its maximum

points.

The voltage or current value of a waveform at

a given instant in time.

The value of a sinusoidal voltage thatindicates its heating effect, equal to 0.707

times the peak value. RMSstands for root-

mean-square.

Instantaneous

value

Peak value

Peak-to-peak

value

RMS value


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The maximum value of a voltage or current.

A type of waveform that consists of two equal and

opposite steps in voltage or current separated by a timeinterval.

The angle that is formed when the arc is equal to the

radius of a circle.2pradians equals 360.

The frequencies contained in a composite waveform,

which are integer multiples of the pulse repetition

frequency.

The relative angular displacement of a time-varying

waveform in terms of its occurrence with respect to areference.

Ch.8 Summary

Key Terms

Radian

Phase

Ampl i tude

Pulse

Harmonics

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EET1035C Chapter 8 No Quiz

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