FM- Frequency Modulation PM - Phase PM and digital modulation [] [] s p where 2 is the pk-pk phase...

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Transcript of FM- Frequency Modulation PM - Phase PM and digital modulation [] [] s p where 2 is the pk-pk phase...

  • 1

    1

    FM- Frequency ModulationPM - Phase Modulation

    EELE445-14Lecture 30

    DSB-SC, AM, FM and PM

    ( )

    [ ]

    =

    =

    =

    +=

    =

    tf

    p

    dmjDc

    tmjDc

    c

    c

    c

    eAtg

    eAtg

    tmjtmAtg

    tmAtg

    tmAtg

    )(

    )(

    )(

    )(

    )()()(

    )(1)(

    )()(

    :EnvelopeComplex FM

    :EnvelopeComplex PM

    :EnvelopeComplex SC-SSB

    :EnvelopeComplex AM

    :EnvelopeComplex SC-DSB

  • 2

    FM and PM

    [ ] [ ])(cos)(Re)(

    )()(

    )()( )()(

    ttAetgts

    AtgtR

    eAetRtg

    cctj

    c

    tjc

    tj

    c

    +==

    ==

    ==

    :signal modulated-angle dTransmitte

    constantis power constant ais envelope real the

    EnvelopeComplex

    FM and PM

    [ ] [ ]

    voltHzD

    voltradD

    dmDt

    voltradD

    tmDtttAetgts

    f

    f

    t

    f

    p

    p

    cctj c

    2

    sec

    )()(

    )()()(cos)(Re)(

    =

    =

    =+==

    constant modulation or deviation frequency

    :FM for

    constant modulation or ysensitivit phase

    :PM for

    :signal modulated-angle dTransmitte

  • 3

    FM and PM

    Relationship between mf(t) and mp(t):

    dmDD

    tm

    dttdm

    DD

    tm

    t

    fp

    fp

    p

    f

    pf

    =

    =

    )()(

    )()(

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 58 Angle modulator circuits. RFC = radio-frequency choke.

  • 4

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 58 Angle modulator circuits. RFC = radio-frequency choke.

    Instantaneous Frequency

    2)()(

    21)(

    21)(

    ))(cos()(cos)(cos)()(

    tfdt

    tdttf

    ttAPMorFMtA

    ttRts

    cii

    cc

    c

    +=

    ==

    +===

    :is Hz in frequencyous instantane The

  • 5

    FM and PM differences

    radianstmDt p )()( =

    PM: instantaneous phase deviation of the carrier phase is proportional to the amplitude of m(t)

    voltradiansinDp

    Modulation Constant Modulation sensitivity Phase sensitivity

    2)(

    2)(

    2)()(

    )()()(

    tmDftf

    dttdtf

    tmDtttt

    pcci

    pcc

    +=+==

    +=+=

    : Hz in frequencyous Instantane

    :radians in phaseous Instantane

    FM and PM differencesFM: instantaneous frequency deviation from the carrier frequency is proportional to m(t)

    radiansdmDtt

    f = )()(

    2)(

    2)(

    2)()(

    )()()(

    tmDftf

    dttdtf

    dmDtttt

    fcci

    t

    fcc

    +=+==

    +=+=

    : Hz in frequencyous instantane The

    :radians in phaseous instantane The

    secvoltradiansinD f

  • 6

    FM and PM differencesFM: instantaneous frequency deviation from the carrier frequency is proportional to m(t)

    )(21)(

    21)()( tmDtftftf fcid

    ==

    voltHz

    voltradKD

    voltradiansKD

    ff

    pp

    2sec

    =

    =

    =Modulation Constants

    FM

    [ ]

    m(t) of bandwidth the is indexmodulationfrequency

    deviationfrequencypeak

    deviationfrequency

    BBF

    tmV

    VDdt

    tdF

    dttdftftf

    f

    p

    pf

    cid

    =

    =

    =

    =

    ==

    )(max21)(

    21max

    )(21)()(

  • 7

    PM and digital modulation

    [ ][ ]

    s

    p

    T duration, symbol one in change phase pk-pk the is 2 where

    :index modulation the signals Digital For

    then deviation, frequency peak same the have signals FM and PM the that such set signal sinusoidal a is m(t) when

    :note

    index modulation phase

    deviationphasepeak deviation phase

    =

    =

    =

    ==

    2

    )(max

    )(max)(

    h

    tmV

    VDtt

    fp

    p

    pp

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 59 FM with a sinusoidal baseband modulating signal.

  • 8

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 59 FM with a sinusoidal baseband modulating signal.

    FM from PM and PM from FM

  • 9

    FM/PM s(t) waveforms

    FM and PM with m(t)=cos(2fmLet

    For PM

    For FM

    Define the modulation indices:

  • 10

    FM and PM Signals

    Define the modulation indices:

    FM and PM SignalsThen

  • 11

    Spectrum Characteristics of FM

    FM/PM is exponential modulationLet

    ( )))2sin(2(Re))2sin(2cos()(

    tftfjc

    mcc

    mceA

    tftfAtu

    +=

    +=

    )2sin()( tft m =

    u(t) is periodic in fmwe may therefore use the Fourier series

    Spectrum Characteristics of FM

    FM/PM is exponential modulation

    ( )))2sin(2(Re))2sin(2cos()(

    tftfjc

    mcc

    mceA

    tftfAtu

    +=

    +=

    u(t) is periodic in fmwe may therefore use the Fourier series

  • 12

    Spectrum with Sinusoidal Modulation

    u(t) is periodic in fmwe may therefore use the Fourier series

    )2sin()( tfj metg =

    Jn Bessel Function

  • 13

    Jn Bessel Function

    TABLE 52 FOUR-PLACE VALUES OF THE BESSEL FUNCTIONS Jn ()

  • 14

    TABLE 53 ZEROS OF BESSEL FUNCTIONS: VALUES FOR WHEN Jn() = 0

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 511 Magnitude spectra for FM or PM with sinusoidal modulation for various modulation indexes.

    ))1(2cos()1()2cos()1(

    ))1(2cos()1(

    11

    0

    11

    tffJAtfJA

    tffJA

    cc

    cc

    cc

    ==

    +=

  • 15

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 511 Magnitude spectra for FM or PM with sinusoidal modulation forvarious modulation indexes.

    30

    NBFM- Narrowband Frequency ModulationWBFM - Wideband FrequencyModulation Carsons Bandwidth Rule

    EELE445-14Lecture 31

  • 16

    Narrowband FMOnly the Jo and J1 terms are significantSame Bandwidth as AMUsing Eulers identity, and (t)

  • 17

    Frequency Multiplication:Wideband FM from Narrowband FM

    (s(t))nsi(t)cFM

    so(t)n x cn x FM

    The Output Carrier frequency = n x fcThe output modulation index = n x fmThe output bandwidth increases according to Carsons Rule

    min

    2)(2)(

    )()(

    )Re()Re()(

    ffmout

    t

    f

    tnfjtjnntfjtjo

    n

    dmnDtn

    eeeets cc

    =

    =

    ==

    Effective Bandwidth- Carsons Rule for Sine Wave ModulationWhere is the modulation

    index fm is the sinusoidalmodulation frequency

    Notice for FM, if kfa>> fm, increasing fm does not increase Bc muchBc is linear with fm for PM

  • 18

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 511 Magnitude spectra for FM or PM with sinusoidal modulation forvarious modulation indexes.

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 511 Magnitude spectra for FM or PM with sinusoidal modulation forvarious modulation indexes.

  • 19

    Couch, Digital and Analog Communication Systems, Seventh Edition 2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

    Figure 511 Magnitude spectra for FM or PM with sinusoidal modulation for Various modulation indexes.

    When m(t) is a sum of sine waves

  • 20

    When m(t) is a sum of sine waves

    Sideband PowerSignal Amplitude: Ac 1V:=

    Modulating frequency: fm 1KHz:=

    Carrier peak deveation: f 2.4KHz:=

    Modulation index: ffm

    := 2.4=

    Reference equation: x t( )

    n

    Ac Jn n ,( ) cos c n m+( ) t =

    Power in the signal: PcAc

    2

    2 1 := Pc 0.5 W=

    Carsons rule bandwidth: BW 2 1+( ) fm:= BW 6.8 103 1s

    =

    Order of significant sidbands predicted by Carsons rule: n round 1+( ):= n 3=

    Power as a function of number of sidebands: Psum k( )

    k

    k

    n

    Ac Jn n ,( )( )22 1

    =

    :=

    Percent of power predicted by Carsons rule: Psum n( )

    Pc100 99.118=

  • 21

    Power vs Bandwidth

    0 0.5 1 1.5 2 2.5 30

    50

    100PERCENT OF TOTAL POWER

    Psum k( )

    Pc100

    k

    Sideband Power =2.4

    k 0 10..:=Jk Jn k ,( ):= 2.4=Pk Jk( )2:=

    n 3=

    P0 2

    1

    n

    j

    P j=

    + 0.991=

    J

    0012345678910

    -32.508100.52

    0.4310.1980.0640.016

    -33.36710-45.92710-59.07610-51.2310-61.49610

    = P

    0012345678910

    -66.288100.2710.1860.039

    -34.13510-42.63810-51.13410-73.51310-98.23710

    -101.51310-122.23810

    =