Transcript ANALOG MODULATION

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 
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Phasor Form

In the complex plane we have
t=3
Phasor rotates with nonuniform speed
t=1
t=0
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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
dt
  i t  
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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
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Examples of Inst. Freq.

Consider an AM signal


d i
st   1  km(t)cos2fc t  c  
 2fc
dt
 i t  

Here, the instantaneous frequency is the
frequency itself, which is constant
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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)
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Phase Modulation(PM)

In PM, carrier angle changes linearly with
the message
st   Ac cos i t   Ac cos2fct  k pmt 

Where
– 2πfc=angle of unmodulated carrier
– kp=phase sensitivity in radians/volt
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Frequency Modulation

In FM, it is the instantaneous frequency
that varies linearly with message
amplitude, i.e.
fi(t)=fc+kfm(t)
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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fct  2k f  mt 
0
t


st   Ac cos2fc t  2k f  m(t)dt 


0
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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
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Illustrating FM
1
Inst.frequency
Moves with the
Message amplitude
FM
message
0.8
0.6
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
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0.06
0.07
0.08
0.09
0.1
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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
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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
W
baseband
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f
or
fm
tone
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Example:carrier swing

A 100 MHz FM carrier is modulated by an
audio tone causing 20 KHz frequency
deviation. Determine the carrier siwng
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
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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
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Myth of FM

Deriving FM bandwidth is a lot more
involved than AM
 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
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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
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Piece-wise approximation of
baseband

Look at the following representation
Baseband bandwidth
=W
1/2W
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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 
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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
mmin
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mmax
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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
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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
highest
lowest
f
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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.
2W
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f
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Range of frequenices
lowest
highest
f

Above range lies
<fc-kfmp-2W,fc+kfmp+2W>
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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
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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
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Commercial FM

Commercial FM broadcasting uses the
following parameters
– Baseband;15KHz
– Deviation ratio:5
– Peak freq. Deviation=75KHz
BFM=2(+1)W=2x6x15=180KHz
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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
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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
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Commercial FM spectrum

The FM landscape looks like this
carrier
FM station A
FM station B
25KHz guardband
FM station C
150 KHz
200 KHz
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FM stereo:multiplexing

First, two channels are created; (left+right)
and (left-right)
 Left+right is useable by monaural
receivers
Left channel
+
mono
+
Right channel
+
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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=
38KHz
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freq
divider
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Stereo signal

Composite baseband signal is then
frequency modulated
Composite baseband
Left channel
+
mono
+
FM
transmitter
+
Right channel
+
DSB-SC
fsc=38 kHz
fsc=
38KHz
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freq
divider
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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
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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
Left+right
DSB-SC
19 KHz
38 KHz
15 KHz
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Receiver diagram
+
lowpass
filter(15K)
Left+right
+
left
+
coherent detector
15 KHz
19 KHz 38 KHz
bandpass
at 38KHz
X
lowpass
right
- +
+
FM
receiver
PLL
X
lowepass
Divide 2
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VCO
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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

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SCA spectrum
Left+right
DSB-SC
SCA signal
19 KHz
15 KHz
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38 KHz
59.5
67
74.5
f(KHz)
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FM receiver

FM receiver is similar to the superhet
layout
RF
mixer
IF
limiter
Discriminator
deemphasis
AF power
amp
LO
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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2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)
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Receiver components:RF
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
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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
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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
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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
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Discriminator

The heart of FM is this relationship
fi(t)=fc+kfm(t)

What we need is a device that linearly
f
is at the IF frequency
follows inst. frequency
Of 10.7 MHz
carrier
Disc.output
-75 KHz
+75 KHz
fcarrier
f
Deviation limits
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Examples of discriminators

Slope detector - simple LC tank circuit
operated at its most linear response curve
This setup turns an FM signal
into an AM
output
fc
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fo
f
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Phase-Locked Loop

PLL’s are increasingly used as FM
demodulators and appear at IF output
fin
Phase
comparator
Error signal
Lowpass
filter
Output proportional to
Difference between fin and fvco
Control signal:constant
When fin=fvco
fvco
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VCO
VCO input
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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
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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
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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
correcting itself
Slope detector
fc
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fo
f
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Zero crossing detector
FM
Hard
limiter
Zero
Crossing
detector
Multivibrator
Averaging
circuot
Output
FM input
Hard limiter
ZC detector
more frequent
ZC’s means
higher inst freq
in turn means
Larger message
amplitudes
multiV
Averaging circuit
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NOISE IN ANALOG
MODULATION
AMPLITUDE MODULATION
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
filter
output
BT=2W
Noise n(t)
-fc
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fc
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Establishing a reference
SNR

Define “channel” SNR measured at
receiver input
(SNR)c=avg. power of modulated signal/
avg. noise power in the message bandwidth
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Noise in DSB-SC Receiver

Tuner plus coherent detection
DSB-SC
BPF
x(t)
LPF
v(t)
s(t)
n(t)
Cos(2πfct)
st   Ac m(t)cos2fc t 
 s2 t   avg.power  Ac 2  m2 (t)  / 2  Ac2 P / 2
P  avg. message power
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Receiver input SNR

Also defined as channel SNR:
Ac2 P

2WN o
Ac 2 P / 2
WN o
(SNR)c 
noise power in the message bandwidth
Flat noise spectrum:white noise
No/2
Noise power=hatched area
-W
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W
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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
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(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
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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
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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
threshold is about 6.6 dB
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NOISE IN ANALOG
MODULATION
FREQUENCY MODULATION
Receiver model
FM
s(t)
BFP
Limiter
FM
detector
LPF
(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
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Phasor model

We can see the effect of noise graphically
(t)
(t)
(t)
reference
The angle FM detector will extract
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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...
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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.
doubling deviation ratio quadruples the
SNR
Bandwidth-SNR exchange
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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
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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
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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
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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
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Noise/bandwidth summary

AM-envelope detection
2
SNRo 
2  SNRc
2
Bn  2
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Noise/bandwidth summary

DSB-SC/coherent detection
(SNR)o=(SNR)c
Bn=2

SSB
(SNR)o=(SNR)c
Bn=1
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Noise/bandwidth summary

FM-tone modulation and =5
(SNR)o=1.5 2(SNR)c=37.5 (SNR)c
Bn~16 for =5
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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
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Pre/deemphasis response

Flat up to ~500Hz, rises from 500-15000 Hz
17dB
preemphasis
Deemphasis circuit
Is between the detector
And the audio amplifier
+3dB
-3dB
deemphasis
-17dB
500 Hz
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2120 Hz
15KHz
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Suggested homework

3.41
 5.3
 5.7
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