Signals 315 - Lecture 22 Modulators and Amplitude Modulation by olliegoblue23


									         Systems & Signals 315
Lecture 22: Modulators and Amplitude Modulation

          Dr. Herman A. Engelbrecht

               Stellenbosch University
               Dept. E & E Engineering

                23 March 2009

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  1   Modulators
        Multiplier Modulators
        Nonlinear Modulators
        Switching Modulators

  2   Double-sideband Modulation (DSB)
        DSB Modulation Recap
        DSB Demodulation Recap
        Comments on DSB modulation

  3   Amplitude Modulation (AM)
        AM Modulation
        Modulation Index
        AM Modulation

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Multiplier Modulators

            m(t)                  xDSB (t)

                             Ac cos(ωct)

      Multiply m(t) and cos(ωc t) using a analog
      Could use two logarithmic amplifiers, a summing
      amplifier and an antilogarithmic amplifier.
      Balanced modulator (ex. 1496 IC) can be used
      as a general multiplier but issues arise with
      linearity, especially at high frequencies.
      True multipliers are expensive and complex.
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Nonlinear Modulators
          Use nonlinear devices (diode, transistor) to
          achieve modulation.

                         y (t) ≈ ax(t) + bx 2 (t)

                         x1(t)        y1 (t)
   m(t)                          NL

                                       +       z(t)
                                        −                   4bm(t) cos(ωc t)

  cos(ωc t)                      NL
                         x2(t)        y2 (t)

                                     2                   2
  z(t) = y1 (t)−y2 (t) = ax1 (t) + bx1 (t) − ax2 (t) + bx2 (t)

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Nonlinear Modulators
  Let x1 (t) = cos(ωc (t) + m(t) and
  x2 (t) = cos(ωc (t) − m(t) then

       y1 (t) = a cos(ωc t) + am(t) + b cos2 (ωc t)
                  +2bm(t) cos(ωc t) + bm2 (t)
       y2 (t) = a cos(ωc t) − am(t) + b cos2 (ωc t)
                  −2bm(t) cos(ωc t) + bm2 (t)
        z(t) = 2am(t) + 4bm(t) cos(ωc t)

      Bandpass filter (BPF) can be used to remove

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Balanced Modulators
     z(t) only contains one of the inputs (i.e. m(t)).
     Circuit acts as a balanced bridge to the carrier
     Example of a class of balanced modulators.
     BPF must reject one of the inputs, thus the
     circuit is a single balanced modulator.
     Circuits which are balanced w.r.t. both inputs are
     called double balanced modulators.
     A ring modulator is an example of a double
     balanced modulator.

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Switching (Chopper) Modulators
      Multiply m(t) with a function other than the
      Periodic functions have impulses in the
      Use a rectangular pulse train - an on/off switch.
  Chopper modulator:
                                   m(t)                   c(t)
   c(t) = m(t) × pulse train
        = m(t) Π τ ∗ ∆Tc (t)
   τ = Tc 50% duty cycle
        2                                       control signal
   Tc = f1c

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Low-Cost Mixer

  m(t)               c(t)            xc (t)       m(t)       xc (t)
                              BPF             ≡
                            center = fc                  Ac cos(ωc t)
  control signal            bandwidth = 2W

         The switch is non-linear, but the total system is
         Can be used instead of a mixer (for messages
         that needs to be mixed up to fc ).

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DSB Modulation Recap
     xc (t) = Ac m(t) cos(ωc t)

  m(t)                  xDSB (t)

                  Ac cos(ωct)
     Mixer (“menger”) - Mix m(t) up to fc frequency.

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DSB Demodulation Recap
  xr (t)                                         Ac m(t)

                       2 cos(ωct)
       Need a cos-function at the receiver, with the
       same frequency and phase as the original
       carrier. Requires coherent or sinchronous
       Is there a way to demodulate DSB without
       Remove the phase-reversal of xc (t) by keeping
       m(t) from becoming negative i.e. add a DC
       component to m(t).

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Comments on DSB modulation
     The DSB spectrum does not contain a
     component at the carrier frequency fc , unless the
     message m(t) has a DC component.
     DSB systems with no spectral component at the
     carrier frequency is referred to as suppresed
     carrier systems (DSB-SC).
     By adding a DC component to the message m(t)
     we can ensure that xc (t) has a spectral
     component at the carrier frequency fc .
     Demodulation then becomes extracting the
     envelope of xr (t), which leads to Amplitude
     Modulation (AM).

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AM Modulation

    xc (t) = Ac [A + m(t)] cos(ωc t), A + m(t) ≥ 0
          = Ac [1 + µmp (t)] cos(ωc t) where
      Ac = Ac A
   mp (t) =
            |min m(t)|
            |min m(t)|
       µ =

     µ - the modulation index (or the percentage
     0 ≤ µ ≤ 1 - required condition for AM to be
     demodulated using an envelope detector

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Modulation Index
     The modulation index is a measure of the
     percentage modulation in the AM signal.
     µ = 0: no modulation - only the carrier is
     µ = 1: 100% modulation
     µ > 1: overmodulation - causes distortion in
     received message.
     µ < 1: undermodulation - causes some
     transmitted power to be wasted.

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AM Modulation
  Types of DSB modulation:
      Large carrier component: DSB-LC ≡ AM
      Suppressed carrier: DSB-SC ≡ DSB
  m(t)                            xc (t)

         A                    ′
                             Ac cos(ωc t)

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