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    Purdue University ECET 207 AC Electronic Circuit Analysis

    ECET 207 AC Electric Circuit Analysis

    Class 3, lab. 3, cr. 4.Prereq: ECET 157, MA 151 or 154

    AC circuits including the j operator, phasors, reactanceand impedance are studied. Circuit laws, networktheorems, and the fundamental concepts of Fourieranalysis are applied and used in the study of topics suchas passive filters, IC filters, amplifiers, resonant circuits,single phase and three phase circuits, and elementarymagnetic circuits.

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Texts

    u J. Michael Jacob, Advance AC Electronics ,Delmar/Thomson

    u J. Michael Jacob, ECET 207 AC ElectronicsCircuit Analysis Study Guide & Lab Manual ,

    Learning Systems

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Syllabusu It is a contract.

    Read it! Use it!u General Information #8: Professional conduct

    u General Information #9: Cheating

    u Attendance

    u HW, Quizzes, Labs

    u Grading Policy

    u Standards: HW and Lab Reports

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Calendar

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    u Homework due BEGINNING of class WWW

    See course web site

    u Lab syllabus in lab

    u No ECET 207 parts kit, ECET 107 &157 needed.

    uFlash drive, or diskette, or career account accessneeded for lab this week.

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Role

    Nick name

    Initial beside your name, under todays date

    Attendance policy!

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Web Sitehttp://www2.tech.purdue.edu/eet/courses/eet207/

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Other handouts

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Waves

    u Alternating Currentu sinewave terms

    u average valueu effective value (RMS)

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Alternating Current

    u many waveforms ( waveshapes )u sineu

    squareu triangleu pulseu exponential

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    AC means

    volts

    time

    Sinusoidal

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Why Sine Waves?

    u Most easily and commonly generated

    u RLC do not alter the shape

    uAll other shapes can be made bycombining sine waves

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Period of a Sine Wave

    volts

    time

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Period of a Sine Wave

    time

    period

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Period of a Sine Wave

    time

    period = T

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Period of a Sine Wave

    time

    period

    Unit of measure = _________

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Period of a Sine Wave

    time

    period

    Unit of measure = seconds

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Wave Terms

    u periodu frequency

    u angular velocityu general equationu phase relationship

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Frequency of a Sine Wave

    u cycles per second

    u unit of measure: Hertz = Hz

    u f = 1/T

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Wave Terms

    u periodu frequency

    u angular velocityu general equationu phase relationship

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angle ( instead of time for x axis)

    u degreesu 360 o/cycle

    u radianangle whose arc distance = 1 radius2 rad/cycle

    ? o/rad360 o/cycle x 1 cycle /2 rad = 57.3 o/rad

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angle (instead of time on the x axis)

    volts

    angle

    360 o

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angle (instead of time on the x axis)

    volts

    angle

    180 o

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angle (instead of time on the x axis)

    volts

    angle

    90 o

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angle (instead of time on the x axis)

    volts

    angle

    270 o

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angle (instead of time on the x axis)

    volts

    angle

    ____rad ____rad ____rad ____rad

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angle (instead of time on the x axis)

    volts

    angle

    2 rad3/2 rad rad/2 rad

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angular Velocity (instead of frequency)

    units ?

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angular Velocity (instead of frequency)

    units

    rad /sec

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angular Velocity (instead of frequency)

    units

    rad /sec

    =t

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angular Velocity (instead of frequency)

    units

    rad /sec

    = =t T

    2

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Angular Velocity (instead of frequency)

    units

    rad /sec

    = = =t T

    f 2

    2

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Wave Terms

    u periodu frequency

    u angular velocityu general equationu phase relationship

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    General Equation of a Sine Wave

    A peak sin

    A imum A peak m=max = angle

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    General Equation of a Sine Wave

    A peak sin

    A imum A peak m=max = angle

    = t = t

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    General Equation of a Sine Wave

    A peak sin

    A imum A peak m=max = angle

    = t = t A t peak sin( )

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Solution a.

    v V = 152

    At t =3msec, calculate v(3msec).

    v(t) 168Vsin(377t)=

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Example b.

    At what time does v(t) = 100V ?

    v t V t ( ) sin( )= 168 377

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Solution b. continued

    t milli= 1 69. sec

    At what time does v(t) = 100V ?

    v t V t ( ) sin( )= 168 377

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Wave Terms

    u periodu frequency

    u angular velocityu general equationu phase relationship

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Phase Relationship : positive = leading

    time

    volts

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Phase Relationship : positive = leading

    time

    volts

    t

    360 o

    T

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Phase Relationship : positive = leading

    time

    volts

    t

    360 o

    T

    t T f =

    =

    360360

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Phase Relationship : negative = lagging

    360T

    t

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Complete General Equation

    v t A t pk ( ) sin( )=

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Complete General Equation

    v t A t pk ( ) sin( )=

    radians

    degrees

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Example c.

    At t = 3msec, calculate v(3msec).

    v t V t ( ) sin( )= + 168 377 50

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Example c.

    At t = 3msec, calculate v(3msec).

    v t V t ( ) sin( )= + 168 377 50

    v m V ( sec) .3 152 5=

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Waves

    u Alternating Currentu sinewave termsu

    average valueu effective value (rms)

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Average ValueVave = Vdc

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Average ValueVave = Vdc

    Vave = area under the curve / length

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Average ValueVave = Vdc

    Vave = area under the curve / length

    ( ) ( )V h l L L

    h l ave

    L

    = = 10

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Average ValueVave = Vdc

    Vave = area under the curve / length

    ( )( )V

    h l L L h l ave

    L

    =

    = 1

    0

    V A d Aave half wave peak peak _

    sin( ) = = 1 2

    0

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Average ValueVave = Vdc

    Vave = area under the curve / length

    ( )( )V

    h l L L h l ave

    L

    =

    = 1

    0

    V A d Aave half wave peak peak _ sin( ) = = 1 20

    V ave full wave _ = 0

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Waves

    u Alternating Currentu sinewave termsu

    average valueu effective value (rms)

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Effective Value

    u Indicated on a meter

    uAlso called rms (root mean squared)

    u The amplitude of a signal which will deliver

    the same power as a numerically equal dc .

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    DerivationLook it up !

    v T A d rms pk T

    = 1

    20 ( sin )

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    DerivationLook it up !

    v T A d rms pk T

    = 1

    20 ( sin )

    = V

    pk

    2

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    Sine Waves

    u Alternating Currentu sinewave termsu

    average valueu effective value (rms)

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    MATLAB demo

    Plot two cycles of a sine wave with:

    V p = 170 V p f = 60 Hz T = 16.7 ms 2 T = 33.4 ms

    v = V p sin(2 f t )

    66

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    Purdue University ECET 207 AC Electronic Circuit Analysis

    MATLAB demo