ANALOG MODULATION by 2i158TX

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```									ANALOG MODULATION

PART II: ANGLE MODULATION
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
t=3

Phasor rotates with nonuniform speed
t=1

t=0

1999 BG Mobasseri                                         3
Angular Velocity
   Since phase changes nonuniformly vs.
time, we can define a rate of change
di (t)
i 
dt
   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 
2

   Where
– 2πfc=angle of unmodulated carrier

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

fi(t)=fc+kfm(t)

1999 BG Mobasseri                    9
FM Signal
   We saw that I.F. is the derivative of the
phase
1 di t 
fi t  
2 dt
   Therefore,
t
i t   2fc t  2k f  mt 
0

               t

st   Ac cos fc t  2k f  m(t)dt 
2
               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
1
FM              Inst.frequency
message
0.8
Moves with the
0.6
Message amplitude

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1
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 
where
f  frequency deviation k f Am
then
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
KHz?
150
f        75KHz
2
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
bandwidth

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

Baseband bandwidth
=W

1/2W

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
mmax
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

f

4W

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

f

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.

f
2W

1999 BG Mobasseri                        24
Range of frequenices

lowest   highest

f

   Above range lies
<fc-kfmp-2W,fc+kfmp+2W>

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

BFM=4W+2kfmp
 Using =∆f/W with ∆f=kfmp
BFM=2(+2)W

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
BFM=2(+1)W

1999 BG Mobasseri                        27
Commercial FM
   Commercial FM broadcasting uses the
following parameters
– Baseband:15KHz
– Deviation ratio:5
– Peak freq. Deviation=75KHz
BFM=2(+1)W=2x6x15=180KHz

1999 BG Mobasseri                28
Wideband vs. narrowband
FM
   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
carrier

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
+
mono

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                    +
transmitter
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
spectrum
Left+right
DSB-SC

19 KHz   38 KHz
15 KHz

1999 BG Mobasseri                     35
 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
Left+right
DSB-SC

19 KHz   38 KHz
15 KHz
1999 BG Mobasseri                       36
+
lowpass         Left+right                +             left
+
filter(15K)
coherent detector
15 KHz
bandpass                                   - +         right
19 KHz 38 KHz                              X       lowpass
at 38KHz
FM                                                                  +
PLL
X          lowepass

Divide 2                 VCO

1999 BG Mobasseri                                                      37
Subsidiary communication
authorization(SCA)
 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

Left+right
DSB-SC
SCA signal

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

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

RF

IF                   Discrimi-
mixer                        limiter               deemphasis
nator

AF power
LO
amp
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 
2
               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
amplifier
 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
Limiter
 A limiter is a circuit whose output is
constant for all input amplitudes above a
threshold
 Limiter’s function in an FM receiver is to
remove unwanted amplitude variations of
the FM signal

Limiter

1999 BG Mobasseri                      43
Limiting and sensitivity
 A limiter needs about 1V of signal, called
quieting or threshold voltage, to begin
limiting
 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,
normally

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
 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
Discriminator
   The heart of FM is this relationship
fi(t)=fc+kfm(t)
   What we need is a device that linearly
follows inst. frequency         f    is at the IF frequency
Of 10.7 MHz
carrier

Disc.output

-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
VCO

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
 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
Crossing
limiter                    vibrator    circuot
detector

FM input

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

multiV

Averaging circuit

1999 BG Mobasseri                                              52
NOISE IN ANALOG
MODULATION

AMPLITUDE MODULATION
    The objective here is to establish a
relationship between input and and output

Modulated signal s(t)l

BPF          detector        output

filter   BT=2W

Noise n(t)

-fc                  fc

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

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

1999 BG Mobasseri                  55
   Tuner plus coherent detection

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

n(t)                       Cos(2πfct)

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

1999 BG Mobasseri                                      56
   Also defined as channel SNR:

2
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
SNRo
1
SNRc

   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
performance
 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
threshold
 For DSB-AM with envelope detection, this

1999 BG Mobasseri                  61
NOISE IN ANALOG
MODULATION

FREQUENCY MODULATION
FM                                            FM               LPF
s(t)                BFP           Limiter
detector           (W)

n(t)
   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 
noise
where
 t    m(t)dt
1999 BG Mobasseri                                      63
Phasor model
   We can see the effect of noise graphically

(t)

(t)                 (t)

reference

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
=[r⁄Ac]Sin(
 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
ratio
SNRo 3 2
 
SNRc 2

   SNR rises as power of 2 of bandwidth; e.g.
SNR       Bandwidth-SNR exchange

1999 BG Mobasseri                  66
Comparison with AM
 In DSB-SC the ratio was 1 regardless.
 For commercial FM, =5. Therefore,
(SNR)o/(SNR)c=(1.5)x25=37.5
 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
bandwidth
 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:
Bn=BT/W=2W/W=2
   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

2
SNRo        SNRc
2 2

Bn  2

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

(SNR)o=(SNR)c
Bn=2
   SSB
(SNR)o=(SNR)c
Bn=1

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
deemphasis
 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

+3dB

-3dB
deemphasis

-17dB
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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