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ECD4 Freq Response

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    FrequencyRespons

    e

    Chapter4

    BJT & FET Frequency

    Response

    Spring 2012

    4

    th

    Semest

    er

    Mechatr

    onicsSZABIST, Karachi

    1229

    CH 4

    Frequency2

    Response

    CourseSupport

    humera.rafique@szabist.edu.pk

    Office:100 Campus

    (404) Official:

    1

    mailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pkmailto:humera.rafique@szabist.edu.pk
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    ZABdesk

    Subsidiary:

    https://sites.google.com/site/zabistmechatronics/home/spring-2012/ecd

    ebooks:

    https://sites.google.com/site/zabistmechatronics/home/ebooks

    1229

    CH 4

    2

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    FrequencyResp

    onse

    ChapterContents3

    BJT & JFET FrequencyResponse Introduction

    Logarithms and Decibels

    GeneralFrequencyConsiderations

    Bode plot Low Frequency Analysis

    Low FrequencyResponse BJT Amplifier

    Low FrequencyResponse FET Amplifier

    High FrequencyResponse BJT Amplifier

    High FrequencyResponse FET Amplifier

    MultistageFrequencyEffects*

    12

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    CH 4

    Frequency4

    Response

    Introduction

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    12

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    CH 4

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    FrequencyResp

    onse

    Introduction5

    Frequency Response:

    Phase and amplitude plots and equations of an amplifier

    Frequency Response Prerequisites:

    1. Logarithms

    2. Semi-log plots

    3. Decibels

    4. Normalization

    12

    29

    CH 4

    Frequency6

    Response

    Logarithms

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    FrequencyResp

    onse

    Logarithms7

    Logarithms:

    The logarithm of a number is the exponent by which another

    fixed value, the base, has to be raised to produce that number.a ::: : ::: og

    10

    a

    Commonlogarithms:

    Natural

    logarithms:

    ::: og10

    a

    y ::: oge

    a

    Relationship of CL

    and NL:

    Benefits:

    ogea ::: 2 . og

    10a

    Plotting of a variable between wide limits

    Compression of large data

    12

    29

    CH 4

    Frequ

    encyResponse

    Logarithms8

    Logarithms:

    Broccoli,

    which grows

    in a

    logarithmic

    spiral

    A low pressure

    area over

    Iceland shows

    an

    approximately

    logarithmic

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    s piralpattern

    The

    whirlpool

    Galaxy

    A nautilusdisplaying a

    logarithmic

    spiral

    12

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    FrequencyResp

    onse

    Logarithms9

    Example 9-1:

    Using the calculator, determine the logarithm of the following

    numbers to the base indicated:

    a. log10

    106

    b. logee3

    c. log10

    102

    d. logee1

    Example 9-2:

    Using the calculator, determine the logarithm of the following numbers:

    a. log10

    64 b.

    loge64

    c. log10

    1600

    d. log10

    8000

    12

    29

    CH 4

    FrequencyResponse

    1Logarithms0

    og101 ::: 0

    10 10 10

    oga

    ::: og a og

    1og10

    ::: og10

    Example 9-3:

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    og10a ::: og

    10a og

    10

    Using calculator, determine the antilogarithm of the following expressions:

    a. 1.6 = log10

    a b. 0.04

    = logea

    Example 9-4:

    Using calculator, determine the logarithm of the following numbers:

    a. log10

    0.5

    b. log10

    (4000/250)

    c. log10

    (0.6 x 30)

    12

    29

    CH 4

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    Frequency11

    Response

    Semilog

    Plots

    12

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    FrequencyResponse

    SemiloggraphpaperSemilog Plots

    12

    2

    Linear

    1

    30% lo g102=0.3010

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    48%l

    o

    g1

    0

    9

    =

    0.9543

    log108 =

    0.9031

    log10

    7 =0.8451

    12

    29

    Log103 = 0.4771

    log104 =

    0.6021

    (60%)

    log106

    =

    0.7781

    log105 =

    0.6999

    CH 4

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    FrequencyResp

    onse

    Semilog Plots13

    Identifying the numerical values ofthe tic marks on a log scale

    12

    29

    CH 4

    FrequencyResponse

    Semilog Plots14

    Va ue ::: 10 x 10d1jd2

    d1

    d2

    1010 +1

    Example 9-5:

    Determine the value of the point appearing on the logarithmic

    plot in Fig. 9-4 using the measures made by a ruler (linear).

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    12

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    Frequency15

    Response

    Decibels

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    FrequencyResponse

    Decibels16

    ::: og

    P2

    10 P1

    e )

    :::10 og

    P2dB10

    P1

    dB )

    :::10 ogP2

    dB 10 P1R Oh s)

    dBrr)

    vdB 10

    ::: 20 ogV2

    V1

    dB )

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    AvT

    =Av1

    Av2

    Av3

    Avn

    dBT=

    dB1+

    dB2+ . . . . . +

    dBn

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    FrequencyResp

    onse

    Decibels17

    Example 9-6:

    Find the magnitude gain corresponding to a voltage gain of 100 dB.

    Example 9-7:

    The input power to a device is 10,000 W at a voltage of 1000 V. The output power is500 W and the output impedance is 20 .

    Example 9-8:

    An amplifier rated at 40 W output is connected to a 10 speaker. Calculate:

    a) The input power required for full power output if the power gain is 25 dB

    b) The input voltage for rated output if the amplifier voltage gain is 40 dB

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    Frequency18

    Response

    General FrequencyConsiderations

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    FrequencyResp

    onse

    Freq. Considerations19

    General Frequency Considerations:

    'r The frequency response of an amplifier refers to the

    frequency range in which the amplifier will operate with

    negligible effects from capacitors and device internal

    capacitance.

    'rThis range of frequencies can be called the mid-range.

    At frequencies above and below the midrange, capacitanceand any inductance will affect the gain of the amplifier.

    At low frequencies the coupling and bypass capacitors lower the gain.

    At high frequencies stray capacitances associated with the

    active device lower the gain.

    Also, cascading amplifiers limits the gain at high and low frequencies.

    12

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    CH 4

    FrequencyResponse

    Freq. Considerations20

    General Frequency Considerations:

    A Bode plotindicates the

    frequency response

    of an Amplifier:

    The horizontal

    scale indicates the

    frequency (in Hz)

    and the vertical

    19

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    scale indicates the

    gain (in dB)

    The mid-range

    frequency range

    of an amplifier

    is called the

    bandwidth of theamplifier

    The bandwidth is

    defined by the

    lower and upper

    cutoff frequencies

    Cutoff anyfrequency at which

    the gain has

    dropped by dB

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    CH 4

    20

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    FrequencyResp

    onse

    Freq. Considerations21

    General Frequency Considerations:

    12

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    Frequency22

    Response

    Normalization

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    FrequencyResp

    onse

    Normalization23

    Normalization Process:

    'rIn communication, a decibel plot vs frequency is normally

    provided rather than gain vs frequency

    'rAprocess in which the vertical parameter is divided by a

    specific level orquantity sensitive to a combination or

    variables ofthe system

    'rThe band frequencies define a level where the gain or

    quantity of interest will be 70.7% or its maximum value

    12

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    CH 4

    FrequencyResponse

    Normalization24

    NormalizationProcess:

    Normalizedgainversus frequency plot

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    Decibelsplots of the normalizedgainversus frequency plot

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    FrequencyResp

    onse

    Normalization25

    Example 9-9:

    Given the frequency response:a) Find the cutoff frequency f

    1and f

    2using the

    measurements provided b) Find the bandwidth ofthe responsec) Sketch the normalized response

    12

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    CH 4

    FrequencyResponse

    Normalization26

    Example 9-9:

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    FrequencyResp

    onse

    Normalization27

    Av

    /Avmid

    Av

    /Avmid

    |dB

    1 0

    0.7 -

    0 -

    0. -

    0. -

    dB Plot:

    Decibelplot of the normalizedgainversus frequency plot

    12

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    CH 4

    Frequency28

    Response

    Low Frequency

    Analysis

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    12

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    FrequencyResp

    onse

    LF AnalysisBode Plot29

    Low frequency response for the R-C circuit

    LowFrequency RCCircuitAnalysis:

    12

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    FrequencyResponse

    LF AnalysisBode Plot30

    Low Frequency RC Circuit Analysis:

    Av

    ::: 0 707Xc=R

    1f1 :::

    2rrRC1Av :::

    f1

    1f

    Av dB)

    ::: 20

    og10

    1

    2

    1

    f1

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    f

    Av dB)

    ::: 20

    og10

    f1

    ff

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    FrequencyResp

    onse

    LF AnalysisBode Plot31

    Low Frequency RC Circuit Analysis:

    f f1

    /f Av(dB)

    f 1 0 f 2 -6

    f 4 -12

    1/10f 10 -20

    12 29 CH 4

    FrequencyResponse LF AnalysisBode Plot 32

    Low Frequency RC Circuit Analysis:

    fA

    v(dB)

    f 1 0

    f1

    2 -

    f1

    4 -

    1/10f1

    1 -

    12 29 CH 4

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    FrequencyResponse LF AnalysisBode Plot 33

    Low Frequency RC Circuit Analysis: The piecewise linear plot of the asymptotes and associated breakpoints is called a

    Bode plot of the magnitude versus frequency

    A change in frequency by a factor of 2, equivalent to 1 octave, results in a6-dB change in the ratio as noted by the change in gain from f

    1/2 to f

    1.

    29 For a 10:1 change in frequency, equivalent to one decade,

    there is a 20-dB change in the ratio as noted by the change in

    gain from f1/10 to f

    1.

    A :::

    V+o::: 10

    Av

    v Vi

    dB)/20() ::: tan-1

    f1

    f

    12 CH 4

    FrequencyResponse

    LF AnalysisBode Plot 34

    Low Frequency RC Circuit Analysis:

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    Phase response for the RC circuit Example 9-9

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    FrequencyResp

    onse

    LF AnalysisBode Plot35

    Example 9-10:For the network of fig. 9-20: (R = 5 k, C = 0.1 F)

    a) Determine the break frequencyb) Sketch the asymptotes and locate the 3dB point c) Sketch the frequencyresponse curved) Find the gain at A

    v(dB)

    = 6 dB

    12

    29

    CH 4

    FrequencyResponse

    LF AnalysisBode Plot36

    Example 9-10:

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    FrequencyResponse

    Example 9-10:

    % bode plot of

    Example 9-10 f =

    10:10^4;

    fo = 318.5;

    A = 20*log(1./(1+(fo./f).^2).^(1/2));

    semilogx(f,A), xlabel('f

    (log scale)'),

    ylabel('Av(dB)')grid

    LF AnalysisBode Plot37

    ComputerAnalysis

    0

    -10

    -20

    -30

    Av(dB)

    -

    4

    0

    -

    5

    0

    -

    60

    -70 1 2 3 410 10 10 10f (log scale)

    12

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    CH 4

    Frequency38

    Response

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    Low FrequencyResponse

    BJT amplifiers

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    FrequencyResp

    onse

    LF Response BJT Amplifiers39

    BJT Amplifiers:

    .

    12

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    CH 4

    FrequencyResponse

    LF Response BJT Amplifiers40

    Effects of Cs on the LF response:

    38

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    39

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    FrequencyResp

    onse

    LF Response BJT Amplifiers41

    Effects of CC

    on the LF response:

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    CH 4

    FrequencyResponse

    LF Response BJT Amplifiers42

    Effects of CE

    on the LF response:

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    FrequencyResp

    onse

    LF Response BJT Amplifiers43

    Effects of Cs and CE

    on the LF response:

    The cutoff frequency due toC

    Scan be calculated by

    where

    fL s

    =

    1

    2 (Rs+ R

    i)C

    s

    Ri= R

    1||R

    2

    ||re

    The cutoff frequency dueto C

    Ccan be calculated

    withfLC=

    12 (R

    o

    + RL

    )Cc

    whereR

    o= R

    C||r

    o

    12

    29

    CH 4

    FrequencyResponse

    LF Response BJT Amplifiers44

    Example 9-11:

    a) Determine the lower cutoff frequency for the network ofFig. 9.23 using the following parameters:

    CS= 10 F, C

    E= 20 F, C

    C= 1 F,

    RS

    = 1 k, R1

    = 40 k, R2

    = 10 k, RE

    = 2 k, RC

    = 4 k, RL

    = 2.2 k,

    = 100, ro

    = , VCC

    = 20 V

    a) Sketch the frequency response using

    a Bode plot b) Verify the result using a

    Simulator.

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    12

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    FrequencyResp

    onse

    LF Response BJT Amplifiers45

    Example 9-11:

    12

    29

    CH 4

    Frequency46

    Response

    Low Frequency

    Response

    FET amplifiers

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    12

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    CH 4

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    FrequencyResp

    onse

    LF Response FET Amplifiers47

    FET Amplifiers:

    12

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    CH 4

    FrequencyResponse

    LF Response FET Amplifiers48

    FET Amplifiers:

    The cutoff frequency due to

    CGcan be calculated with

    1

    where

    f

    L G =2 (R

    sig

    + Ri

    )CG

    Ri

    = RG

    The cutoff frequency due to

    CCcan be calculated with

    1

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    where

    f

    L C = 2 (Ro

    + RL

    )CG

    RO

    = RD

    || rG

    12

    29

    CH 4

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    FrequencyResp

    onse

    LF Response FET Amplifiers49

    FET Amplifiers:

    The cutoff frequency due to

    CScan be calculated with

    fLS=

    1

    2 Req

    CS

    Req

    where

    R

    1e q= R

    S||g

    m rd

    12

    29

    CH 4

    FrequencyResponse

    LF Response FET Amplifiers50

    Example 9-12:

    a) Determine the lower cutoff frequency for the network of Fig.

    11.32 using the following parameters:

    CG

    = 0.01 F, CC= 0.5 F, C

    S= 2 F

    Rsig

    = 10 k, RG

    = 1 M, RD

    = 4.7 k, RS

    = 1 k, RL

    = 2.2 k

    IDSS

    = 8mA, VP

    = 4 V rd

    = , VDD

    = 20 V

    b) Sketch the frequency response using a Bode plot.

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    FrequencyResp

    onse

    LF Response FET Amplifiers51

    Example 9-12:

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    CH 4

    Frequency52

    Response

    HighFrequency

    Response

    FET amplifiers

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    12

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    FrequencyResp

    onse

    HF Response FET Amplifiers55

    FET Amplifiers:

    Capacitances that affect the high-frequency response are

    Junction capacitancesC

    gs, C

    gd, C

    ds

    Wiring capacitancesC

    wi, C

    wo

    Coupling capacitors

    CG, C

    C

    Bypass capacitor

    CS

    12

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    CH 4

    FrequencyResponse

    HF Response FET Amplifiers56

    FET Amplifiers:

    fHi=

    12R

    Thi

    Ci

    Ci=C

    Wi+ C

    gs

    + CMi

    CMi= (1 A

    v)

    Cgd

    R

    T

    hi

    Figure 9-64 (a) & (b)

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    fHo

    =

    1

    2RTho

    Co

    Co= C

    Wo+C

    ds+C

    Mo

    ? 1 ?C = 1 C

    Mo ?? gd?A

    v ?

    RTho

    = RD

    ||RL

    ||rd

    12

    29

    CH 4

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    FrequencyResp

    onse

    HF Response FET Amplifiers57

    Example 9-14:

    12

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    Frequency58

    Response

    Square Wave

    Testing

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    FrequencyResp

    onse

    Square Wave Testing59

    Square Wave Testing:

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    FrequencyResponse

    Square Wave Testing60

    Square Wave Testing:

    58

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    59

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    FrequencyResp

    onse

    Square Wave Testing61

    Example 9-15:

    The application of a 1-mV, 5-kHz square wave to an amplifier

    resulted in the output waveform of Fig. 9-72.

    (a) Write the Fourier series expansion for the square wave

    through the ninth harmonic.

    (b) Determine the bandwidth of the amplifier

    (c) Calculate the low cutoff frequency.

    12

    29

    CH 4

    FrequencyResponse

    Home Task62

    Reading:

    1. Summary

    2. Equations3. Computer analysis

    Problems:

    1. Sec 8.2: (odd)

    2. Sec 8.3: 17,18

    3. Sec 8.4: 19,21

    4. Sec 8.5:23,25

    5. Sec 8.6: 27,29

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    6. Sec 8.7: 31

    7. Sec 8.8: 33,35,37

    8. Sec 8.10: 39,41

    9. Sec 8.11: 43

    10. Sec 8.12: 45

    11. Sec 8.14: 47

    12. Sec 8.15: 49

    12

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    CH 4

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    Frequency

    Response

    References63

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    FET

    1. Bolestad

    2. Paynter

    CH 1

    12 29

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