# Analog Modulation

Document Sample

```					Analog Modulation

AM(Amplitude Modulation)
Demodulation of AM Signals
Angle Modulation
Why modulate ?
   Ease of radiation
   The size of antenna  /4 = c/4f
   If we wish to throw a piece of paper(baseband signal), it
cannot go too far by itself. But by wrapping it around a
stone(carrier), it can be thrown over a longer distance
   Simultaneous transmission of several signals
   FDM(Frequency Division Modulation)
   Reduce the influence of interference
   Frequency Hopping
   Effecting the exchange of SNR with B
   Shannon’s equation :          C  B log 2 (1  SNR)
   C is rate of information change per second (bit/s)
Properties of analog modulation
   Time domain representation of the modulated signal
   Frequency domain representation of the modulated
signal
   Bandwidth of the modulated signal
   Power component of the modulated signal
   SNR after demodulation

Message                 Modulated
Modulator   Signal

Signal
(or modulating
Signal)
AM (Amplitude modulation)
   Also known as “Linear modulation)
   Small bandwidth, Power inefficient
   Applications
   AM radio, TV video broadcasting(VSB), Point-to-point
communications(SSB), Transmission of many telephone channels
over microwave links
   Class of AM
   DSB-AM(Double Side Band – AM)
   BW = 2W = 2 * BW of the message signal
   SSB-AM(Single Side Band – AM)
   BW = W
   VSB-AM(Vestigial Side Band – AM)
   BW = W ~ 2W
DSB – AM
   Amplitude of modulated signal is
proportional to the message signal
m(t )                         u(t )  Ac m(t ) cos(2 f ct )

c(t )  Ac cos(2 fc t )
DSB-AM at frequency domain
   Take FT
Ac               A
 U ( f )  F [ Ac m(t ) cos(2 f c t )]       M ( f  fc )  c M ( f  fc )
2                 2
   Transmission Bandwidth: BT
   BT = 2W

DSB-AM                                U(f)
M(f)                                                              2W
A
AAc2/2
f                                                           f
-W 0 W                                       -fc                          fc
Power of modulated signal
   If m(t) is lowpass signal with frequency
contents much less than 2fc
1 T /2 2               1 T /2 2 2
 P  T  T / 2 u (t ) dt  T  T / 2 Ac m (t ) cos (2 f c t ) dt
2
u   lim                      lim
T                      T
1 T / 2 2 2 1  cos(4 f c t )
 lim          Ac m (t )                dt
T  T T / 2                  2                    0
2
Ac       1 T /2 2                 1 T /2 2
2 T  T T / 2
      {lim          m (t )dt  lim  m (t ) cos(4 f c t )dt}
T  T T / 2

Ac2
      Pm
M(f)            2                                           U(f)
Ac/2
Pm       Ac   2P
m/2                                             f
-fc                         fc
SNR for DSB-AM
   Equal to baseband SNR
S     P
 ( )0  R
N    N0W

U(f)                               R(f)
Ac2Pm/2
PR
Transmit
fc             -Distortion
fc
-Loss
N(f)
N0/2         WN0
White Gaussian Noise

2W
Homework
   Illustrative Problem
   3.1, 3.2
   What happens if the duration of message
signal t0 changes? What is the effect on the
BW and SNR ?
   Repeat illustrative problem 3.1 with t0 = 0.015,
0.15, 1.5 with fixed Pn=0.0833
Demodulation of AM signals
   Demodulation
   The process of extracting the message signal from
modulated signal
   Type of demodulation
   Coherent demodulation
   Local oscillator with same frequency and phase of the carrier at the
receiver
   DSB – AM , SSB – AM
   Noncoherent demodulaion
   Envelope detector which does not require same frequency and phase
of carrier
   Easy to implement with low cost : Conventional AM
DSB – AM demodulation
   Coherent demodulation
u(t )  Ac m(t ) cos(2 f ct )                   Lowpass                      Ac
m(t )
Filter                     2

cos(2 fc t )
y(t )  Ac m(t ) cos(2 f c t ) cos(2 f c t )
Ac        Ac
    m(t )  m(t ) cos(4 f c t )
2         2
   Local oscillator
   How do we generate cos(2 fc t ) ?
   Frequency and phase should be synchronized to incoming signal
   PLL or FLL
DSB – AM demodulation
   Frequency domain
Ac        Ac                  Ac
   Y( f )     M(f )    M ( f  2 fc )     M ( f  2 fc )
2         4                   4

M(f)             DSB-AM                                  U(f)
Modulation                       Ac/2
f
0 W                                     -fc                        fc
Lowpass Filter
With BW=W                 Y(f)

f
Demodulation
-2fc                  0                  2fc
Effect of phase error on DSB – AM
   In practice, it is hard to synchronize phase
u(t )  Ac m(t ) cos(2 f ct )                     Lowpass                    Ac
m(t ) cos( )
Filter                   2

cos(2 fc t   )
y(t )  Ac m(t ) cos(2 f c t ) cos(2 f c t   )
Ac                A
      m(t ) cos( )  c m(t ) cos(4 f c t   )
2                  2
   Power in 2lowpass
Ac
   Pdem       Pm cos2 ( )
4
3 dB power loss when    4  cos ( )  1 2
2


   Nothing can be recovered when    2  cos2 ( )  0
Homework
   Illustrative Problem 3.5
   Problem
   3.1, 3.2, 3.8, 3.11
More on Demodulation
   Coherent demodulation requires carrier
replica generated at LO(Local Oscillator)
   Frequency and phase should be synchronized to
carrier
   Generally, 2 types of carrier recovery loop
   Costas loop
   Squaring loop
   Noise performance of 2 types are equivalent
   Implementation is depends on cost and accuracy
Squaring loop
    Recover frequency using squaring
u(t )  Ac m(t ) cos(2 f ct )                        Lowpass                 Ac A0
m (t )
Filter                  2

A0 cos(2 fc t )

Squaring                                             Frequency
Device                                                Divider
1 2 2
Ac m (t )[1  cos(4 f c t )]                   A0 cos(4 fc t )
2
Bandpass                                                Limiter
Filter               1 2 2
Ac m (t ) cos(4 f c t )      (or PLL)
2
Costas loop(or Costas PLL)
    Goal of Costas loop: e0
Ac A0
m(t ) cos( e )
Baseband      2
LPF

u (t )                       A0 cos(2 fc t   e )
Ac m(t ) cos(2 f c t )
VCO                  LPF
1 Ac A0
[     m(t )]2 sin(2 e )
2 2
-90              K sin(2 e )
, for small  e
Phase shift
A0 sin(2 fc t  e )
Baseband
Ac A0
LPF             m(t ) sin( e )
2
What if ?
   What happens if –m(t) instead of m(t) is used
   Both Costas loop and Squaring loop have a 180
phase ambiguity
   They don’t distinguish m(t) and –m(t)
   A known test signal can be sent after the loop is turned
on so that the sense of polarity can be determined
   Differential coding and decoding may be used
More on PLL
   PLL(Phase Locked Loop)
   Tracks the phase (and frequency) of incoming
signal

PD(Phase Detector)           x(t )  sin(i  0 )  sin(4 fc t  i  0 )

u(t )  Ac cos(2 fc t  i )                     Loop filter                e0 (t )
H(f)
A0 sin(2 fc t   o )               v0  A0 cos(2 fc t  o )

-90
VCO
output                        Phase shift
VCO(Voltage Controlled Oscillator)
   An oscillator whose frequency can be
controlled by external voltage

eo (t )
VCO           cos(2 fc t  ceo (t ))

Free running frequency
(frequency when eo(t)= 0)

Constant of VCO
PLL tracks Phase or Frequency ?
   All that is needed is to set the VCO free
running frequency as close as possible to the
incoming frequency
   If the VCO output is v (t )  A cos(2 f t   )
o        0        c   o

   We can express it as
vo (t )  A0 cos(2 f c t   0 )
 A0 cos(2 f c t  2 ( f c  f c )t   0 )
 A0 cos(2 f c t   0 )

d
   Note that        dt
 (t )  2 f
How the PLL works ?
   Output of PD
   x(t )  Ac A0 sin(2 f c t   o ) cos(2 f c t   i )
1
     Ac A0 [sin( i   o )  sin(4 f c t   i   o )]
2
   Output of LPF
   Loop Filter is lowpass narrow band filter
1                        1
   eo (t )   Ac A0 sin( i   o )  Ac A0 sin( e )
2                        2
1
 Ac A0 e , for small  e
2
How the PLL works ?
   At steady state: e  i o  eo (t )  0
   If input changes to:
Ac cos(2 ( f c  k )t   i )  Ac cos(2 f c t  (kt   i ))  Ac cos(2 f c t   i )

   It causes increasing of phase error
    Or increasing of eo(t):             eo (t ) 
1
Ac A0 sin( e )
2

   It causes increasing of VCO output
    The PLL tracks the phase(or frequency) of incoming
signal
More on PLL
   Hold-in(or Lock) range
   A PLL can track the incoming frequency over a finite
range of frequency shift
   If initially input and output frequency is not close enough,
PLL may not acquire lock
   If Doppler shift exists, Acquisition is needed
   Pull-in(or Capture) range
   The frequency range over which the input will cause the
loop to lock
   If input frequency changes too rapidly, PLL may lose
lock
PLL used in frequency synthesizer
   Generate a periodic signal of frequency
Oscillator                               Vin     Ve
Frequency                          LPF
Frequency Standard
Divider, M
f=fx                                         Vo

In steady state                         Frequency
VCO
Ve = 0, Vin = Vo                        Divider, N
N
fx   f            f out      fx
 out                    M
M     N
By choosing M,N
We can generate desired frequency
Oscillator
   What happens if frequency standard is
incorrect ?
   Errors of Crystal Oscillator
   More than 50ppm
   Drift : Sensitive to temperature
   TCXO
   Temperature Compensated Crystal(X-tal) Oscillator
   Less than 5ppm

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 9 posted: 11/26/2011 language: English pages: 26
How are you planning on using Docstoc?