What is Angle Modulation?
 In angle modulation, information is
  embedded in the angle of the carrier.
 We define the angle of a modulated carrier
  by the argument of...

                            st   Ac cos t 

        1999 BG Mobasseri                            2
Phasor Form
   In the complex plane we have

                                   Phasor rotates with nonuniform speed


         1999 BG Mobasseri                                         3
Angular Velocity
   Since phase changes nonuniformly vs.
    time, we can define a rate of change
                                  di (t)
                             i 
   This is what we know as frequency

                                  
                                         d i
         st   Ac cos2fct  c         2fc
                         i t       dt

         1999 BG Mobasseri                             4
Instantaneous Frequency
 We are used to signals with constant
  carrier frequency. There are cases where
  carrier frequency itself changes with time.
 We can therefor talk about instantaneous
  frequency defined as

                                       1 di t 
                            fi t  
                                      2 dt

        1999 BG Mobasseri                           5
Examples of Inst. Freq.
   Consider an AM signal

                                         
                                                d i
       st   1  km(t)cos2fc t  c         2fc
                              i t         dt
   Here, the instantaneous frequency is the
    frequency itself, which is constant

           1999 BG Mobasseri                                  6
Impressing a message on
the angle of carrier
   There are two ways to form a an angle
    modulated signal.
    – Embed it in the phase of the carrier
    Phase Modulation(PM)
    – Embed it in the frequency of the carrier
    Frequency Modulation(FM)

           1999 BG Mobasseri                     7
Phase Modulation(PM)
   In PM, carrier angle changes linearly with
    the message

         st   Ac cos i t   Ac cos fct  k pmt 

   Where
    – 2πfc=angle of unmodulated carrier
    – kp=phase sensitivity in radians/volt

           1999 BG Mobasseri                                   8
Frequency Modulation
   In FM, it is the instantaneous frequency
    that varies linearly with message
    amplitude, i.e.


          1999 BG Mobasseri                    9
FM Signal
   We saw that I.F. is the derivative of the
                                    1 di t 
                         fi t  
                                   2 dt
   Therefore,
                    i t   2fc t  2k f  mt 

                                          t
             st   Ac cos fc t  2k f  m(t)dt 
                                          0        

          1999 BG Mobasseri                               10
FM for Tone Signals
 Consider a sinusoidal message m(t)  Am cos2fmt 
 The instantaneous frequency
  corresponding to its FM version is

            fi t   fc  k f m(t)
                      fc            k f Am cos2 fmt 
                resting frequency

        1999 BG Mobasseri                                   11
Illustrating FM
                                                                 FM              Inst.frequency
                                                                                 Moves with the
                                                                                 Message amplitude








     0   0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08    0.09     0.1

                1999 BG Mobasseri                                                              12
Frequency Deviation
   Inst. frequency has upper and lower
    bounds given by
             fi t   fc  f cos2fmt 
             f  frequency deviation k f Am
             fi max  fc  f
             fi min  fc  f

          1999 BG Mobasseri                     13
FM Modulation index
   The equivalent of AM modulation index is
     which is also called deviation ratio. It
    quantifies how much carrier frequency
    swings relative to message bandwidth

                                 f          f
                                        or
                                 W           fm
                               baseband     tone

          1999 BG Mobasseri                        14
Example:carrier swing
   A 100 MHz FM carrier is modulated by an
    audio tone causing 20 KHz frequency
    deviation. Determine the carrier swing
    and highest and lowest carrier frequencies
         f  20KHz
         frequency swing  2f  40KHz
         frequency range :
         fhigh  100MHz  20KHz  100.02MHz
         flow  100MHz  20KHz  99.98MHz

          1999 BG Mobasseri                   15
Example: deviation ratio
   What is the modulation index (or deviation
    ratio) of an FM signal with carrier swing of
    150 KHz when the modulating signal is 15
                       f        75KHz
                           f 75
                                 5
                            fm 15

          1999 BG Mobasseri                    16
Myth of FM
 FM was initially thought to be a bandwidth
  efficient communication because it was
  thought that FM bandwidth is simply 2f
 By keeping frequency deviation low, we
  can use arbitrary small bandwidth
 Not so!

        1999 BG Mobasseri                  17
FM bandwidth
 Deriving FM bandwidth is a lot more
  involved than AM and it can barely be
  derived for sinusoidal message
 There is a graphical way to illustrate FM

        1999 BG Mobasseri                     18
Piece-wise approximation of
   Look at the following representation

                                       Baseband bandwidth


              1999 BG Mobasseri                   19
Corresponding FM signal

 FM version of the above is an RF pulse for
  each square pulse.
 The frequency of the kth RF pulse at t=tk is
  given by the height of the pulse. i.e.

                            fi  fc  k f mtk 

        1999 BG Mobasseri                          20
Range of frequencies?
 We have a bunch of RF pulses each at a
  different frequency.
 Inst.freq corresponding to square pulses
  lie in the following range
    fi max  fc  k f mmax
    fi min  fc  k f mmin

              1999 BG Mobasseri                 21
A look at the spectrum
   We will have a series of RF pulses each at
    a different frequency. The collective
    spectrum is a bunch of sincs
                              lowest   highest



          1999 BG Mobasseri                      22
So what is the bandwidth?
   Measure the width from the first upper
    zero crossing of the highest term to the
    first lower zero crossing of the lowest
    term                     lowest      highest


          1999 BG Mobasseri                        23
Closer look
 The highest sinc is located at fc+kfmp
 Each sinc is 1/2W wide. Therefore, their
  zero crossing point is always 2W above
  the center of the sinc.


        1999 BG Mobasseri                        24
Range of frequenices

                             lowest   highest


   Above range lies

         1999 BG Mobasseri                          25
FM bandwidth
   The range just defined is one expression
    for FM bandwidth. There are many more!

 Using =∆f/W with ∆f=kfmp

          1999 BG Mobasseri                    26
Carson’s Rule
   A popular expression for FM bandwidth is
    Carson’s rule. It is a bit smaller than what
    we just saw

          1999 BG Mobasseri                        27
Commercial FM
   Commercial FM broadcasting uses the
    following parameters
    – Baseband:15KHz
    – Deviation ratio:5
    – Peak freq. Deviation=75KHz

         1999 BG Mobasseri                28
Wideband vs. narrowband
   NBFM is defined by the condition
    – ∆f<<W             BFM=2W
    – This is just like AM. No advantage here
   WBFM is defined by the condition
    – ∆f>>W            BFM=2 ∆f
    – This is what we have for a true FM signal

          1999 BG Mobasseri                       29
Boundary between narrowband and
wideband FM

   This distinction is controlled by 
    – If >1 --> WBFM
    – If <1-->NBFM
   Needless to say there is no point for going
    with NBFM because the signal looks and
    sounds more like AM

          1999 BG Mobasseri                   30
Commercial FM spectrum
   The FM landscape looks like this
                                                 25KHz guardband

     FM station A                 FM station B            FM station C

                                  150 KHz

                                     200 KHz

              1999 BG Mobasseri                                          31
FM stereo:multiplexing
 First, two channels are created; (left+right)
  and (left-right)
 Left+right is useable by monaural
                     Left channel

                     Right channel           +


        1999 BG Mobasseri                               32
Subcarrier modulation
   The mono signal is left alone but the
    difference channel is amplitude modulated
    with a 38 KHz carrier

    Left channel
                            +                                 Composite baseband
                                         mono             +
    Right channel           +
                     +                   DSB-SC
                                        fsc=38 kHz

                                 fsc=            freq
                                38KHz           divider
               1999 BG Mobasseri                                           33
Stereo signal
   Composite baseband signal is then
    frequency modulated

                                                   Composite baseband
    Left channel
                         +                                                  FM
                                    mono                    +
    Right channel        +
                    +               DSB-SC
                                   fsc=38 kHz

                         fsc=                    freq
                        38KHz                   divider

               1999 BG Mobasseri                                                      34
Stereo spectrum
   Baseband spectrum holds all the
    information. It consists of composite
    baseband, pilot tone and DSB-SC

                              19 KHz   38 KHz
           15 KHz

          1999 BG Mobasseri                     35
Stereo receiver
 First, FM is stripped, i.e. demodulated
 Second, composite baseband is lowpass
  filtered to recover the left+right and in
  parallel amplitude demodulated to recover
  the left-right signal

                              19 KHz   38 KHz
                15 KHz
        1999 BG Mobasseri                       36
 Receiver diagram
                             lowpass         Left+right                +             left
                                                   coherent detector
15 KHz
                            bandpass                                   - +         right
         19 KHz 38 KHz                              X       lowpass
                            at 38KHz
           FM                                                                  +
                             X          lowepass

                                 Divide 2                 VCO

                    1999 BG Mobasseri                                                      37
Subsidiary communication
 It is possible to transmit “special
  programming” ,e.g. commercial-free
  music for banks, department stores etc.
  embedded in the regular FM programming
 Such programming is frequency
  multiplexed on the FM signal with a 67
  KHz carrier and 7.5 KHz deviation

       1999 BG Mobasseri                38
SCA spectrum

                                               SCA signal

                    19 KHz     38 KHz   59.5     67     74.5   f(KHz)
  15 KHz

           1999 BG Mobasseri                                     39
FM receiver
   FM receiver is similar to the superhet


                       IF                   Discrimi-
     mixer                        limiter               deemphasis

                                 AF power
             1999 BG Mobasseri                                   40
Frequency demodulation
   Remember that message in an FM signal
    is in the instantaneous frequency or
    equivalently derivative of carrier angle
                                           t
              st   Ac cos fc t  2k f  m(t)dt 
                                           0        

                                                          t
                                        
      s t   Ac 2fc  2k f mt  sin 2fc t  2k f  m(t)dt
                                                                 
                      Do envelope detection on s’(t)

            1999 BG Mobasseri                                           41
Receiver components:RF
 AM may skip RF amp but FM requires it
 FM receivers are called upon to work with
  weak signals (~1V or less as compared to
  30 V for AM)
 An RF section is needed to bring up the
  signal to at least 10 to 20 V before mixing

        1999 BG Mobasseri                    42
 A limiter is a circuit whose output is
  constant for all input amplitudes above a
 Limiter’s function in an FM receiver is to
  remove unwanted amplitude variations of
  the FM signal


        1999 BG Mobasseri                      43
Limiting and sensitivity
 A limiter needs about 1V of signal, called
  quieting or threshold voltage, to begin
 When enough signal arrives at the
  receiver to start limiting action, the set
  quiets, i.e. background noise disappears
 Sensitivity is the min. RF signal to
  produce a specified level of quieting,

        1999 BG Mobasseri                      44
Sensitivity example
 An FM receiver provides a voltage gain of
  200,000(106dB) prior to its limiter. The
  limiter’s quieting voltage is 200 mV. What
  is the receiver’s sensitivity?
 What we are really asking is the required
  signal at RF’s input to produce 200 mV at
  the output
       200 mV/200,000= 1V->sensitivity

        1999 BG Mobasseri                      45
   The heart of FM is this relationship
   What we need is a device that linearly
    follows inst. frequency         f    is at the IF frequency
                                    Of 10.7 MHz


                      -75 KHz
                                                      +75 KHz
                                         fcarrier                         f

                                   Deviation limits
              1999 BG Mobasseri                                               46
Examples of discriminators
   Slope detector - simple LC tank circuit
    operated at its most linear response curve
                                          This setup turns an FM signal
       output                             into an AM

                                fc   fo            f

            1999 BG Mobasseri                                        47
Phase-Locked Loop
   PLL’s are increasingly used as FM
    demodulators and appear at IF output
                                                                 Output proportional to
                                                                 Difference between fin and fvco
       fin       Phase           Error signal   Lowpass
               comparator                         filter

                                                                 Control signal:constant
                                                                 When fin=fvco

                            fvco                     VCO input

             1999 BG Mobasseri                                                             48
PLL states
   Free-running
    – If the input and VCO frequency are too far apart,
      PLL free-runs
   Capture
    – Once VCO closes in on the input frequency, PLL
      is said to be in the tracking or capture mode
   Locked or tracking
    – Can stay locked over a wider range than was
      necessary for capture

           1999 BG Mobasseri                              49
PLL example
 VCO free-runs at 10 MHZ. VCO does not
  change frequency until the input is within
  50 KHZ.
 In the tracking mode, VCO follows the
  input to ±200 KHz of 10 MHz before losing
  lock. What is the lock and capture range?
    – Capture range= 2x50KHz=100 KHz
    – Lock range=2x200 KHz=400 KHz

         1999 BG Mobasseri                     50
Advantages of PLL
 If there is a carrier center frequency or LO
  frequency drift, conventional detectors
  will be untuned
 PLL, on the other hand, can correct itself.
  PLL’s need no tuned circuits

                            output             If fc drifts detector has no way of
           Slope detector                      correcting itself

                                     fc   fo               f

        1999 BG Mobasseri                                                            51
Zero crossing detector
      FM                        Zero                             Output
               Hard                        Multi-    Averaging
               limiter                    vibrator    circuot

        FM input

   Hard limiter                                                           more frequent
                                                                          ZC’s means
                                                                          higher inst freq
                                                                          in turn means
                                                                          Larger message
     ZC detector                                                          amplitudes


Averaging circuit

                  1999 BG Mobasseri                                              52

Receiver Model
    The objective here is to establish a
     relationship between input and and output
     SNR of an AM receiver

    Modulated signal s(t)l

                                BPF          detector        output

                                                  filter   BT=2W

                Noise n(t)

                                       -fc                  fc

                   1999 BG Mobasseri                                  54
Establishing a reference
   Define “channel” SNR measured at
    receiver input

(SNR)c=avg. power of modulated signal/
avg. noise power in the message bandwidth

         1999 BG Mobasseri                  55
Noise in DSB-SC Receiver
   Tuner plus coherent detection

    DSB-SC                          x(t)                      v(t)
                           BPF                          LPF

                n(t)                       Cos(2πfct)

             st   Ac m(t)cos2fc t 
              s2 t   avg.power  Ac 2  m2 (t)  / 2  Ac P / 2
             P  avg. message power

                1999 BG Mobasseri                                      56
Receiver input SNR
   Also defined as channel SNR:

                                          Ac 2 P / 2                  Ac P
             (SNR)c                                               
                                           WN o                      2WN o
                            noise power in the message bandwidth

Flat noise spectrum:white noise                   No/2

Noise power=hatched area

                                     -W                   W

                 1999 BG Mobasseri                                           57
Output SNR
   Carrying signal and noise through the rest
    of the receiver, it can be shown that
    output SNR comes out to be equal to the
    input. Hence

   Therefore, any reduction in input SNR is
    linearly reflected in the output

          1999 BG Mobasseri                    58
(SNR)o for DSB-AM
   Following a similar approach,
                    SNRo   k2P
                               2 1
                    SNRc 1  k P
                    k : AM modulation index
                    P : avg. message power
   Best case is achieved for 100%
    modulation index which, for tone
    modulation, is only 1/3

          1999 BG Mobasseri                   59
DSB-AM and DSB-SC noise
 An AM system using envelope detection
  needs 3 times as much power to achieve
  the same output SNR as a suppressed
  carrier AM with coherent detection
 This is a result similar to power efficiency
  of the two schemes

        1999 BG Mobasseri                        60
Threshold effect-AM
 In DSB-AM (not DSB-SC) there is a
  phenomenon called threshold effect
 This means that there is a massive drop in
  output SNR if input SNR drops below a
 For DSB-AM with envelope detection, this
  threshold is about 6.6 dB

        1999 BG Mobasseri                  61

Receiver model
FM                                            FM               LPF
s(t)                BFP           Limiter
                                            detector           (W)

   Noisy FM signal at BPF’s output is
                x t   st   n(t) 
                Ac cos2fct   t   r(t)cos2fc t   t 
                 t    m(t)dt
              1999 BG Mobasseri                                      63
Phasor model
   We can see the effect of noise graphically


                         (t)                 (t)


         The angle FM detector will extract

           1999 BG Mobasseri                                     64
Small noise
 For small noise, it can be approximated
  that the noise inflicted phase error is
 So the angle available to the FM detector
  is +
 FM Detector computes the derivative of
  this angle. It will then follow that...

        1999 BG Mobasseri                     65
FM SNR for tone modulation
   Skipping further detail, we can show that
    for tone modulation, we have the following
                              SNRo 3 2
                                     
                              SNRc 2

   SNR rises as power of 2 of bandwidth; e.g.
    doubling deviation ratio quadruples the
    SNR       Bandwidth-SNR exchange

          1999 BG Mobasseri                  66
Comparison with AM
 In DSB-SC the ratio was 1 regardless.
 For commercial FM, =5. Therefore,
 Compare this with just 1 for AM

        1999 BG Mobasseri                 67
Capture effect in FM
 An FM receiver locks on to the stronger of
  two received signals of the same
  frequency and suppresses the weaker one
 Capture ratio is the necessary
  difference(in dB) between the two signals
  for capture effect to go into action
 Typical number for capture ratio is 1 dB

        1999 BG Mobasseri                  68
Normalized transmission
 With all these bandwidths numbers, it is
  good to have a normalized quantity.
 Define
       normalized bandwidth=Bn=BT/W
Where W is the baseband bandwidth

        1999 BG Mobasseri                    69
Examples of Bn
   For AM:
   For FM
              Bn=BT/W~2 to 3
 For =5 in commercial FM, this is a very
  large expenditure in bandwidth which is
  rewarded in increased SNR

         1999 BG Mobasseri                   70
Noise/bandwidth summary
   AM-envelope detection

                    SNRo        SNRc
                             2 2

                    Bn  2

         1999 BG Mobasseri                  71
Noise/bandwidth summary
   DSB-SC/coherent detection

   SSB

          1999 BG Mobasseri            72
Noise/bandwidth summary
   FM-tone modulation and =5
        (SNR)o=1.5 2(SNR)c=37.5 (SNR)c
                 Bn~16 for =5

         1999 BG Mobasseri                73
Preemphasis and
 High pitched sounds are generally of
  lower amplitude than bass. In FM lower
  amplitudes means lower frequency
  deviation hence lower SNR.
 Preemphasis is a technique where high
  frequency components are amplified
  before modulation
 Deemphasis network returns the
  baseband to its original form

       1999 BG Mobasseri                   74
 Pre/deemphasis response
      Flat up to ~500Hz, rises from 500-15000 Hz
  17dB                                                            Deemphasis circuit
                                                                  Is between the detector
                                                    preemphasis   And the audio amplifier



                                 500 Hz   2120 Hz     15KHz

             1999 BG Mobasseri                                                75
Suggested homework
 3.41
 5.3
 5.7

         1999 BG Mobasseri   76

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