Modulation (AM/DSB/SSB)

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doc describing modulation of signals using AM, DSB/SC, SSB/SC, outlining their similarities and differences

Transcript of Modulation (AM/DSB/SSB)

  • AM Modulators: ReviewEE 179, Lecture 9, Handout #14

    Multiplier modulator (perhaps using variable gain amplifier)

    Nonlinear modulator, using square-law device

    Switching modulator effectively multiplies signal by square wave

    Multiplying a signal by a sinusoid shifts the frequency band.

    Super-heterodyning: mix = c + I .

    Sub-heterodyning: mix = c I .

    EE 179, April 18, 2014 Lecture 9, Page 1

  • Demodulation of DSB-SC Signals

    Both modulator and demodulator use a multiplier by carrier signal.

    Modulator uses bandpass filter

    Demodulator uses lowpass filter

    The carrier used by the demodulator must be in phase with the transmittercarrier (taking into account transmission delay).

    Such a receiver is called synchronous, coherent, homodyne.

    0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.5

    0

    0.5e2(t) = x(t) * sin(2*pi*fc*t)

    0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.1

    0.05

    0

    0.05

    0.1e2(t) lowpass filtered

    homo = same, dyne = power (irregular suffix)

    EE 179, April 18, 2014 Lecture 9, Page 2

  • Demodulation of DSB-SC Signals (cont.)

    The phase of the carrier in the received signal must be extracted.

    Suppose that the signal is not ideal (frequency is shifted):

    r(t) = Acm(t t0) cos(

    (c +)(t t0))

    = Acm(t t0) cos(

    (c +)t d)

    where d = (c +)t0.

    The receiver has a local oscillator that must be adjusted to stay in phasewith the received signal.

    A voltage-controlled oscillator (VCO) that is controlled by a phase-lockedloop (PLL) is commonly used.

    If the goal is cheap receivers, then we can eliminate the PLL bytransmitting the carrier signal along with the modulated message.

    AM(t) = A cosct+m(t) cos ct = (A+m(t)) cos ct

    The tone A cosct contains the desired carrier in correct phase.

    EE 179, April 18, 2014 Lecture 9, Page 3

  • AM Modulation

    AM modulation is a form of amplitude modulation. For ka > 0,

    s(t) = (Ac +m(t)) cos(ct) = Ac(1 + kam(t)) cos(2fct)

    We need bandwidth of m(t) fc and modulation index ka < 1.

    Spectrum of modulated signal:

    S(f) = 12Ac

    (

    (f + fc) + (f fc))

    +

    1

    2kaAc

    (

    M(f + fc) +M(f fc))

    EE 179, April 18, 2014 Lecture 9, Page 4

  • DSB-SC vs. AM

    DSB-SC modulated signals undergo phase reversal when m(t) changes sign.It is difficult to extract carrier from received signal.

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    1

    0.5

    0

    0.5

    1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    1

    0.5

    0

    0.5

    1

    EE 179, April 18, 2014 Lecture 9, Page 5

  • DSB-SC vs. AM (cont.)

    In AM, the carrier signal is modulated by Ac +m(t) = Ac(1 + kam(t)).Examples: ka = 1 and ka = 0.5.

    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22

    1

    0

    1

    2

    ka = 1

    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21.5

    1

    0.5

    0

    0.5

    1

    1.5

    ka = 0.5

    EE 179, April 18, 2014 Lecture 9, Page 6

  • AM Signal and Its Envelope

    EE 179, April 18, 2014 Lecture 9, Page 7

  • Envelope Detection of AM Signals

    The term detection means extracting signal from received data. In somecases it means demodulation.

    Suppose that a signal x(t) can be written as

    x(t) = E(t) cos ct ,

    where E(t) varies slowly compared to the carrier cosct.

    Then |E(t)| is called the envelope of x(t).

    For envelope detection to work, we need

    fc bandwidth of m(t)

    Otherwise positive and negative spectral components overlap.

    A+m(t) 0

    Otherwise phase reversals occur when A+m(t) < 0.

    EE 179, April 18, 2014 Lecture 9, Page 8

  • Message Signal Peak and Offset

    The requirement for envelope detection,

    A m(t)

    is equivalent toA mmin = minm(t)

    Typically m(t) has zero offset, i.e., minm(t) = maxm(t) = mp.

    The modulation index of the modulated signal is defined by

    =mpA

    Larger modulation index reduces power but makes demodulation harder.

    Broadcast AM stations use modulation index close to 1. Input signals arecontrolled using automatic gain control (AGC).

    Zero offset is not the same as zero DC value.

    EE 179, April 18, 2014 Lecture 9, Page 9

  • Modulation Index Example

    For tone modulation,m(t) = b cosmt

    the message peak is b and = b/A.

    AM(t) = (A+ b cosmt) cos ct = A(1 + cosmt) cosct

    EE 179, April 18, 2014 Lecture 9, Page 10

  • Modulation and Demodulation of AM Signals

    Modulation: use DSB-SC modulator with A cosct added to signal.

    Demodulation: we could use coherent DSB-SC demodulator.

    But this approach fails to use the carrier component.

    EE 179, April 18, 2014 Lecture 9, Page 11

  • Envelope Detector for AM

    EE 179, April 18, 2014 Lecture 9, Page 12

  • AM Demodulation: Rectifier + Lowpass Filter

    Diodes were the first semiconductor electronic devices. The discovery of crystals rectifying abilities was made by German physicist

    Ferdinand Braun in 1874. The first semiconductor diodes, called cats whisker diodes, developed around 1906, were made of

    mineral crystals such as galena. Today most diodes are made of silicon, but other semiconductors such as germanium are

    sometimes used.

    EE 179, April 18, 2014 Lecture 9, Page 13

  • AM Demodulation Experiment

    m(t) = cos 2t , fc = 10 , h(t) =1

    RCet/RCu(t)

    0 0.5 1 1.5 22

    1

    0

    1

    2

    0 0.5 1 1.5 20

    0.5

    1

    1.5

    2

    0 0.5 1 1.5 20

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0 0.5 1 1.5 20.4

    0.3

    0.2

    0.1

    0

    0.1

    0.2

    0.3

    EE 179, April 18, 2014 Lecture 9, Page 14

  • Cats Whiskers (Crystal) Radio

    This radio was powered only by received radio energy.

    The point-contact semiconductor detector was subsequently resurrected around WorldWar II because of the military requirement for microwave radar detectors.

    EE 179, April 18, 2014 Lecture 9, Page 15

  • Corncob Pipe Radio

    EE 179, April 18, 2014 Lecture 9, Page 16

  • Single Sideband (SSB)

    DSB-SC is spectrally inefficient. It uses twice the bandwidth of themessage.

    The signal can be reconstructed from either the upper sideband (USB) orlower sideband.

    SSB transmits a bandpass filtered version of the modulated signal.

    EE 179, April 18, 2014 Lecture 9, Page 17

  • Single Sideband (cont.)

    EE 179, April 18, 2014 Lecture 9, Page 18

  • Single Sideband (cont.)

    EE 179, April 18, 2014 Lecture 9, Page 19

  • Single Sideband Modulation and Demodulation

    SSB can be transmitted using a DSB-SC modulator with a narrowerbandpass filter. For USB, center frequency is

    fc = fc +1

    2B

    and cutoff frequency is B/2.

    The bandfilter must roll off quickly to eliminate unwanted contributionsfrom the other sideband.

    Message frequencies near 0 will be affected by the nonideal filter.

    SSB demodulation can use a DSB-SC demodulator with no change.

    The input to the lowpass filter is different from that of DSB-SC.

    EE 179, April 18, 2014 Lecture 9, Page 20