2-Dieu Che Tuong Tu

Download 2-Dieu Che Tuong Tu

Post on 20-Jan-2016

25 views

Category:

Documents

0 download

Embed Size (px)

TRANSCRIPT

  • Chapter 3Analog Modulation

    Contents3.1 Linear Modulation . . . . . . . . . . . . . . . . . . . . 3-3

    3.1.1 Double-Sideband Modulation (DSB) . . . . . . 3-3

    3.1.2 Amplitude Modulation . . . . . . . . . . . . . . 3-8

    3.1.3 Single-Sideband Modulation . . . . . . . . . . . 3-21

    3.1.4 Vestigial-Sideband Modulation . . . . . . . . . . 3-35

    3.1.5 Frequency Translation and Mixing . . . . . . . . 3-38

    3.2 Angle Modulation . . . . . . . . . . . . . . . . . . . . 3-463.2.1 Narrowband Angle Modulation . . . . . . . . . 3-48

    3.2.2 Spectrum of an Angle-Modulated Signal . . . . 3-50

    3.2.3 Power in an Angle-Modulated Signal . . . . . . 3-56

    3.2.4 Bandwidth of Angle-Modulated Signals . . . . . 3-56

    3.2.5 Narrowband-to-Wideband Conversion . . . . . . 3-63

    3.2.6 Demodulation of Angle-Modulated Signals . . . 3-63

    3.3 Interference . . . . . . . . . . . . . . . . . . . . . . . 3-733.3.1 Interference in Linear Modulation . . . . . . . . 3-74

    3.3.2 Interference in Angle Modulation . . . . . . . . 3-76

    3.4 Feedback Demodulators . . . . . . . . . . . . . . . . . 3-81

    3-1

  • CHAPTER 3. ANALOG MODULATION

    3.4.1 Phase-Locked Loops for FM Demodulation . . . 3-81

    3.4.2 PLL Frequency Synthesizers . . . . . . . . . . . 3-102

    3.4.3 Frequency-Compressive Feedback . . . . . . . . 3-106

    3.4.4 Coherent Carrier Recovery for DSB Demodulation 3-108

    3.5 Sampling Theory . . . . . . . . . . . . . . . . . . . . . 3-1123.6 Analog Pulse Modulation . . . . . . . . . . . . . . . . 3-117

    3.6.1 Pulse-Amplitude Modulation (PAM) . . . . . . . 3-117

    3.6.2 Pulse-Width Modulation (PWM) . . . . . . . . . 3-119

    3.6.3 Pulse-Position Modulation . . . . . . . . . . . . 3-119

    3.7 Delta Modulation and PCM . . . . . . . . . . . . . . . 3-1203.7.1 Delta Modulation (DM) . . . . . . . . . . . . . 3-120

    3.7.2 Pulse-Code Modulation (PCM) . . . . . . . . . 3-123

    3.8 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . 3-1263.8.1 Frequency-Division Multiplexing (FDM) . . . . 3-127

    3.8.2 Quadrature Multiplexing (QM) . . . . . . . . . . 3-130

    3.8.3 Time-Division Multiplexing (TDM) . . . . . . . 3-131

    3.9 General Performance of Modulation Systems in Noise 3-135

    3-2 ECE 5625 Communication Systems I

  • 3.1. LINEAR MODULATION

    We are typically interested in locating a message signal to somenew frequency location, where it can be efficiently transmitted

    The carrier of the message signal is usually sinusoidal A modulated carrier can be represented as

    xc.t/ D A.t/ cos2fct C .t/

    where A.t/ is linear modulation, fc the carrier frequency, and.t/ is phase modulation

    3.1 Linear Modulation

    For linear modulation schemes, we may set .t/ D 0 withoutloss of generality

    xc.t/ D A.t/ cos.2fct /with A.t/ placed in one-to-one correspondence with the mes-sage signal

    3.1.1 Double-Sideband Modulation (DSB)

    Let A.t/ / m.t/, the message signal, thusxc.t/ D Acm.t/ cos.2fct /

    From the modulation theorem it follows that

    Xc.f / D 12AcM.f fc/C 1

    2AcM.f C fc/

    ECE 5625 Communication Systems I 3-3

  • CHAPTER 3. ANALOG MODULATION

    t t

    m(t) xc(t) carrier filled envelope

    DSB time domain waveforms

    M(0)M(f)

    Xc(f)

    AcM(0)1

    2

    fc

    -fc

    f

    f

    LSB USB

    DSB spectra

    Coherent Demodulation

    The received signal is multiplied by the signal 2 cos.2fct /,which is synchronous with the transmitter carrier

    LPFm(t) x

    c(t) x

    r(t) d(t) yD(t)

    Accos[2f

    ct] 2cos[2f

    ct]

    DemodulatorModulator Channel

    3-4 ECE 5625 Communication Systems I

  • 3.1. LINEAR MODULATION

    For an ideal channel xr.t/ D xc.t/, sod.t/ D Acm.t/ cos.2fct / 2 cos.2fct /D Acm.t/C Acm.t/ cos.2.2fc/t/

    where we have used the trig identity 2 cos2 x D 1C cos 2x The waveform and spectra of d.t/ is shown below (assumingm.t/ has a triangular spectrum in D.f /)

    D(f)

    AcM(0)

    2fc

    -2fc

    f

    AcM(0)1

    2A

    cM(0)1

    2

    W-W

    Lowpass modulation recovery filter

    d(t)

    t

    Lowpass filtering will remove the double frequency carrier term

    Waveform and spectrum of d.t/

    Typically the carrier frequency is much greater than the mes-sage bandwidth W , so m.t/ can be recovered via lowpass fil-tering

    The scale factor Ac can be dealt with in downstream signalprocessing, e.g., an automatic gain control (AGC) amplifier

    ECE 5625 Communication Systems I 3-5

  • CHAPTER 3. ANALOG MODULATION

    Assuming an ideal lowpass filter, the only requirement is thatthe cutoff frequency be greater than W and less than 2fc W The difficulty with this demodulator is the need for a coherent

    carrier reference

    To see how critical this is to demodulation ofm.t/ suppose thatthe reference signal is of the form

    c.t/ D 2 cos2fct C .t/where .t/ is a time-varying phase error

    With the imperfect carrier reference signald.t/ D Acm.t/ cos .t/C Acm.t/ cos2fct C .t/yD.t/ D m.t/ cos .t/

    Suppose that .t/ is a constant or slowly varying, then thecos .t/ appears as a fixed or time varying attenuation factor

    Even a slowly varying attenuation can be very detrimental froma distortion standpoint

    If say .t/ D f t and m.t/ D cos.2fmt /, then

    yD.t/ D 12cos2.fm f /tC cos2.fm Cf /t

    which is the sum of two tones

    Being able to generate a coherent local reference is also a prac-tical manner

    3-6 ECE 5625 Communication Systems I

  • 3.1. LINEAR MODULATION

    One scheme is to simply square the received DSB signalx2r .t/ D A2cm2.t/ cos2.2fct /

    D 12A2cm

    2.t/C 12A2cm

    2.t/ cos2.2fc/t

    ( )2 BPF

    LPF

    divideby 2

    xr(t) yD(t)

    xr(t)2

    Acos2fct

    very narrow (tracking) band-pass filter

    Carrier recovery concept using signal squaring

    Assuming that m2.t/ has a nonzero DC value, then the doublefrequency term will have a spectral line at 2fc which can bedivided by two following filtering by a narrowband bandpassfilter, i.e., Ffm2.t/g D k.f /C

    k

    2fc

    fSpe

    ctru

    mof m

    2 (t) Filter this component

    for coherent demod

    Note that unless m.t/ has a DC component, Xc.f / will notcontain a carrier term (read .f fc), thus DSB is also calleda suppressed carrier scheme

    ECE 5625 Communication Systems I 3-7

  • CHAPTER 3. ANALOG MODULATION

    Consider transmitting a small amount of unmodulated carrier

    k

    m(t) xc(t)

    Accos2f

    ct

    ffc

    -fc

    AcM(0)/2

    use a narrowband filter (phase-locked loop) to extract the carrier in the demod.

    k

  • 3.1. LINEAR MODULATION

    t

    xc(t)

    a < 1

    m(t)

    A

    A + m(t)

    Accos[2f

    ct]

    xc(t)

    Bias term

    Note that the enve-lope does not cross zero in the case of AM having a < 1

    0A

    c(1 - a)

    A + max m(t) A + min m(t)

    Generation of AM and a sample wavefrom

    Note that ifm.t/ is symmetrical about zero and we define d1 asthe peak-to-peak value of xc.t/ and d2 as the valley-to-valleyvalue of xc.t/, it follows that

    a D d1 d2d1 C d2

    proof: maxm.t/ D minm.t/ D jminm.t/j, sod1 d2d1 C d2 D

    2.AC jminm.t/j/ .A jminm.t/j/2.AC jminm.t/j/C .A jminm.t/j/

    D jminm.t/jA

    D a

    ECE 5625 Communication Systems I 3-9

  • CHAPTER 3. ANALOG MODULATION

    The message signal can be recovered from xc.t/ using a tech-nique known as envelope detection

    A diode, resistor, and capacitor is all that is needed to constructand envelope detector

    eo(t)x

    r(t) C R

    t

    Recovered envelope with proper RC selection

    eo(t)

    0The carrier is removed if 1/f

    c

  • 3.1. LINEAR MODULATION

    The simple envelope detector fails if Ac1C amn.t/ < 0 In the circuit shown above, the diode is not ideal and

    hence there is a turn-on voltage which further limits themaximum value of a

    The RC time constant cutoff frequency must lie between bothW and fc, hence good operation also requires that fc W

    ECE 5625 Communication Systems I 3-11

  • CHAPTER 3. ANALOG MODULATION

    Digital signal processing based envelope detectors are also pos-sible

    Historically the envelope detector has provided a very low-costmeans to recover the message signal on AM carrier

    The spectrum of an AM signal is

    Xc.f / D Ac2

    .f fc/C .f C fc/

    pure carrier spectrum

    C aAc2

    Mn.f fc/CMn.f C fc/

    DSB spectrum

    AM Power Efficiency

    Low-cost and easy to implement demodulators is a plus forAM, but what is the downside?

    Adding the bias term to m.t/ means that a fraction of the totaltransmitted power is dedicated to a pure carrier

    The total power in xc.t/ is can be written in terms of the timeaverage operator introduced in Chapter 2

    hx2c .t/i D hA2c1C amn.t/2 cos2.2fct /iD A

    2c

    2h1C 2amn.t/C a2m2n.t/1C cos.2.2fc/t i

    If m.t/ is slowly varying with respect to cos.2fct /, i.e.,hm.t/ cos!cti ' 0;

    3-12 ECE 5625 Communication Systems I

  • 3.1. LINEAR MODULATION

    then

    hx2c .t/i DA2c2

    1C 2ahmn.t/i C a2hm2n.t/i

    D A

    2c

    2

    1C a2hm2.t/i D A2c

    2Pcarrier

    C a2A2c2hm2n.t/i

    Psidebands

    where the last line resulted from the assumption hm.t/i D 0(the DC or average value of m.t/ is zero)

    Definition: AM Efficiency

    EffD a

    2hm2n.t/i1C a2hm2n.t/i

    alsoD hm2.t/i

    A2 C hm2.t/i

    Example 3.1: Single Sinusoid AM

    An AM signal of the formxc.t/ D Ac1C a cos.2fmt C =3/ cos.2fct /

    contains