LECTURE NOTES 3 CHAPTER 3 AMPLITUDE MODULATION by olliegoblue23

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									DTC5038                           ANALOG COMMUNICATION SYSTEM                 Trimester 3 2008-2009


                                 LECTURE NOTES 3

             CHAPTER 3: AMPLITUDE MODULATION

Subtopic:
3-1   Introduction to Modulation
3-2 Types of Modulation
3-3 Modulation Index

3-1       INTRODUCTION

A large number of information sources are analog sources such as speech, images, and videos.
Today, they are transmitted as analog signal transmission, especially in audio and video
broadcast. The transmission of an analog signal is either by modulation of the amplitude, the
phase, or the frequency of a sinusoidal carrier.


Modulation is the process of putting information onto a high frequency carrier for
transmission (frequency translation). Modulation occurs at the transmitting end of the system.

                                       Carrier signal




      Modulating signal                  Modulator                 Modulated signal



                        Figure 3-1: Block diagram of modulation process


At the transmitter, modulation process occurs when the transmission takes place at the high
frequency carrier, which has been modified to carry the lower frequency information. At the
receiver, demodulation takes place. Once this information is received, the lower frequency
information must be removed from the high-frequency carrier.



  Message         Modulator              Channel           Demodulator         Message
   signal                                                                       signal

             Figure 3-2: Block diagram of modulation and demodulation processes



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DTC5038                           ANALOG COMMUNICATION SYSTEM                   Trimester 3 2008-2009


There are several strong reasons why the modulation is important in analog communication
system:
(a) The frequency of the human voice range from about 20 to 30 kHz. If every one transmitted
      those frequencies directly as radio waves, interference would cause them to be inefficient.
      (so, we need a higher frequency to carry the baseband frequency)
(b) To overcome hardware limitation because transmitting such lower frequencies require
      antennas with miles in wavelength
(c) Modulation is to reduce noise which result in the optimization of signal to noise ratio, SNR
(d) To minimize the effects of interference



3-2       TYPES OF MODULATION

In analog communication systems, we use the sinusoidal signal as the frequency carrier. And as
the sinusoidal wave can be represented in three parameters; amplitude, frequency and phase,
these parameters may be varied for the purpose of transmitting information giving respectively
the modulation methods:
(a) Amplitude Modulation (AM) - the amplitude of the carrier waveform varies with                the
      information signal
(b) Frequency Modulation (FM) - the frequency of the carrier waveform varies with                the
      information signal
(c) Phase Modulation (PM) - the phase of the carrier waveform varies with the information
      signal




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DTC5038     ANALOG COMMUNICATION SYSTEM          Trimester 3 2008-2009




                Figure 3-3: Carrier wave




              Figure 3-3: Modulating wave




          Figure 3-4: Amplitude modulated wave




          Figure 3-5: Frequency modulated wave




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DTC5038                                 ANALOG COMMUNICATION SYSTEM              Trimester 3 2008-2009




                                            Amplitude Modulator




                               Figure 3-6: Amplitude modulation block diagram


3-2-1 Double Sideband – Large Carrier (DSB-LC)
Also known as full AM. In Amplitude Modulation, the baseband or the information signal is
modulated to the carrier signal to produce the modulated sine wave.


Consider the carrier signal,
s c (t ) = Ac cos(ω c t ) where ω c = 2πf c


The modulating signal (information signal),
s m (t ) = Am cos(ω m t )


Then, the amplitude-modulated can be expressed as
s (t ) = [ Ac + s m (t )]cos(ω c t )

      = [ Ac + Am cos(ω m t )]cos(ω c t )


The amplitude term of the AM signal s(t ) is

A = ( Ac + Am cos(ω m t ) )

  = ( Ac + mAc cos(ω m t ) )

  = Ac (1 + m cos(ω m t ))
where notation m in expression above is termed the modulation index. Simply a measurement
for the degree of modulation and bears the relationship of the ratio of Am to Ac ,




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DTC5038                                   ANALOG COMMUNICATION SYSTEM                                    Trimester 3 2008-2009


        Am
 m =
        Ac


Therefore the full AM signal may be written as
s (t ) = Ac (1 + m cos(ω m t )) cos(ω c t )
or
                          mAc                    mAc
s (t ) = Ac cos ω c t +       cos(ω c + ω m )t +     cos(ω c − ω m )t
                           2                      2


using: cos A cos B = 1 / 2[cos( A + B ) + cos( A − B )]



                                       s c (t ) = Ac cos ω c t


                                                                                                    mAc
                                                                          s (t ) = Ac cos ω c t +       cos(ω c + ω m )t
     s m (t ) = Am cos ω m t                  Modulator                                              2
                                                                              mAc
                                                                          +       cos(ω c − ω m )t
                                                                               2




The frequency description of the AM signal (i.e. frequency spectrum of AM) – DSB-LC:

         Sm ( f )                             S( f )
                               AM
                                          Ac
       Am                              mAc
                                        2                                                            f
                           f
                  fm                               fc − fm           fc         fc + fm

              B                                                     2B

From the above analysis, we found that the frequency spectrum of AM waveform DSB-LC:
•     A component of carrier frequency, f c

•     An upper sideband (USB), whose highest frequency component is at f c + f m

•     A lower sideband (LSB), whose highest frequency component is at f c − f m

•     The bandwidth of the modulated waveform is twice the information signal bandwidth




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DTC5038                                   ANALOG COMMUNICATION SYSTEM                           Trimester 3 2008-2009


•      Because of the two sidebands in the frequency spectrum with carrier frequency, thus it is
       often called Double Sideband with Large Carrier (DSB-LC)


3-2-2 Double Sideband – Suppressed Carrier (DSB-SC)
As noted earlier, where there are two sidebands in the frequency spectrum, USB and LSB, and it
is called as Double-sided band (DSB).

But the carrier component in full AM or DSB-LC does not convey any information, it may be
removed or suppressed during the modulation process to attain a higher power efficiency, hence
Double Side Band Suppressed Carrier (DSB-SC) Modulation.


Consider the carrier,
s c (t ) = Ac cos( wc t ) where ω c = 2πf c


The modulating signal (information signal),
s m (t ) = Am cos(ω m t ) where ω m = 2πf m
Then, the amplitude-modulated can be expressed as
s m (t ) = Ac cos(ω c t )Am cos(ω m t )

               Am Ac                   A A
           =         cos(ω c + ω m )t + m c cos(ω c − ω m )t
                 2                       2


                                    s c (t ) = Ac cos(ω c t )




                                          Modulator                        Am Ac                   A A
    s m (t ) = Am cos(ω m t )                                          =         cos(ω c + ω m )t + m c cos(ω c − ω m )t
                                                                             2                       2




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DTC5038                            ANALOG COMMUNICATION SYSTEM                    Trimester 3 2008-2009


The frequency description of the AM signal (i.e. frequency spectrum of AM) – DSB-SC:



     Sm ( f )                       S( f )
                       DSB-SC

    Am                           Am Ac
                                  2
                  f                                                          f
             fm                          fc − fm                 fc + fm

         B                                                2B

Note: Notice that there is no carrier frequency (band).


From the above analysis, we found that the frequency spectrum of AM waveform – DSB-SC:
•     No component of carrier frequency, f c

•     An upper sideband (USB), whose highest frequency component is at f c + f m

•     A lower sideband (LSB), whose highest frequency component is at f c − f m

•     The bandwidth is twice the modulating signal bandwidth
•     Because of the two sidebands in the frequency spectrum without carrier frequency, thus it is
      often called Double Sideband with Suppressed Carrier (DSB-SC)


3-2-3 Single Sideband (SSB)
Third type of amplitude modulation namely the SSB will be introduced here. Note that
conventional amplitude modulation (Full AM) and DSB-SC modulation require a transmission
bandwidth equal to twice the information signal bandwidth. One half the transmission
bandwidths is occupied by the upper sideband of the modulated signal. Whereas the other half
is occupied by the lower sideband. The basic information is transmitted twice, once in each
sideband. Since the sidebands are the sum and difference of the carrier and modulating signals,
the information must be contained in both of them. There is absolutely no reason to transmit
both sidebands in order to convey the information. One sideband may be suppressed. The
remaining sideband is called a single-sideband suppressed carrier (SSSC or SSB) signal. In
practical systems the carrier is also suppressed in SSB and should be described as SSB-SC.




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DTC5038                                  ANALOG COMMUNICATION SYSTEM                            Trimester 3 2008-2009


Therefore, from DSB-SC waveform equation:
                  Am Ac
USB : sUSB (t) =        cos (ω c t + ω m t )
                   2
                 A A
LSB : s LSB (t) = m c cos (ω c t − ω m t )
                   2


Either the USB or LSB is used to carry information.


                                   s c (t ) = Ac cos(ω c t )


                                                                                        Am Ac
                                                                      USB : sUSB (t) =        cos (ω c t + ω m t )
    s m (t ) = Am cos(ω m t )            Modulator                                       2
                                                                                       A A
                                                                      LSB : s LSB (t) = m c cos (ω c t − ω m t )
                                                                                         2

The frequency description of the AM signal (i.e. frequency spectrum of AM) – DSB-SC:

                                          S( f )


                                     Am Ac
                                      2
                                                                                            f
      Sm ( f )                                  fc − fm

                                SSB-SC
    Am

                       f
                                          S( f )
               fm

           B                         Am Ac
                                      2
                                                                                            f
                                                                             fc + fm

Note: Notice that it is either USB or LSB being transmitted.


From the above analysis, we found that the frequency spectrum of AM waveform – SSB-SC:
•      No component of carrier frequency, f c




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DTC5038                                               ANALOG COMMUNICATION SYSTEM               Trimester 3 2008-2009


•     It is either upper sideband (USB), whose highest frequency component is at f c + f m or

      lower sideband (LSB), whose highest frequency component is at f c − f m being transmitted

•     The bandwidth is equal to the modulating signal bandwidth
•     Because of the only one sideband in the frequency spectrum without carrier frequency, thus
      it is often called Single Sideband with Suppressed Carrier (SSB-SC)


3-3                   MODULATION INDEX


The degree of modulation is an important parameter and is known as the modulation index. It is
the ratio of the peak amplitude of the modulation signal, Am to the peak amplitude of the carrier

signal, Ac .

       Am
m=
       Ac


The modulation index, m is also referred as percent modulation, modulation factor and depth of
modulation. It is a number lying between 0 and 1 and is typically expressed as a percentage. The
modulation index can be determined by measuring the actual values of the modulation voltage
and the carrier voltage and computing the ratio.


In practice, the modulation index of an AM signal can be computed from Amax and Amin. as
below:


        1.5



              1
                                                           Amax ( p −t − p )
        0.5



              0
                                  Amin ( p −t − p )
       -0.5



          -1



       -1.5
                  0     5   10   15        20         25          30           35     40   45




Amax = half the peak-to-peak value of the AM signal

Amin = half the peak-to-peak value of the AM signal



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DTC5038                          ANALOG COMMUNICATION SYSTEM                   Trimester 3 2008-2009


Am = half the difference of Amax and Amin .

Ac = half the sum of Amax and Amin .


The values for Amax and Amin can be obtained directly from the oscilloscope.


The evaluation of the modulation index m can be achieved by invoking the following expression:
       1 ( Amax − Amin )
m=         2
       1 (A + A )
        2 max      min


       Am
   =
       Ac


Modulation index can determine the behavior of modulation index:
(a) under modulation
(b) ideal modulation
(c) over modulation


3-3-1 Under Modulation
When m < 1 , we call this as under modulation By ensuring the amplitude of sm (t ) to be less

than the carrier amplitude, message signal can comfortably be retrieved from the envelope
waveform of s (t ) .




3-3-2 Ideal Modulation
When m = 1 , this is the best modulation where to ensure successful retrieval of the original
transmitted information at the receiver end. The ideal condition for amplitude modulation (AM)
is when m = 1 also means Am = Ac ; this will give rise to the generation of the maximum

message signal outputs at the receiver without distortion.




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DTC5038                          ANALOG COMMUNICATION SYSTEM                     Trimester 3 2008-2009




3-3-3 Over Modulation
When m > 1 , we call this as over modulation. If the amplitude of the modulating signal is
higher than the carrier amplitude, this will cause severe distortion to the modulated signal.




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