ANALOG MODULATION

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ANALOG MODULATION

• PART II ANGLE MODULATION

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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...

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Phasor Form

• In the complex plane we have

t3
Phasor rotates with nonuniform speed
t1
t0
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Angular Velocity

• Since phase changes nonuniformly vs. time, we can
  define a rate of change
• This is what we know as frequency

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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

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Examples of Inst. Freq.

• Consider an AM signal
• 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
• Where
• 2pfcangle of unmodulated carrier
• kpphase 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)fckfm(t)

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FM Signal

• We saw that I.F. is the derivative of the phase
• Therefore,

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FM for Tone Signals

• Consider a sinusoidal message
• The instantaneous frequency corresponding to its
  FM version is

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Illustrating FM
Inst.frequency Moves with the Message amplitude
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Frequency Deviation

• Inst. frequency has upper and lower bounds given
  by

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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

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Examplecarrier 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

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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?

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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 ttk is
  given by the height of the pulse. i.e.

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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

mmax
mmin
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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

highest
lowest
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

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Closer look

• The highest sinc is located at fckfmp
• Each sinc is 1/2W wide. Therefore, their zero
  crossing point is always 2W above the center of
  the sinc.

f
2W
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Range of frequenices

• Above range lies
• ltfc-kfmp-2W,fckfmp2Wgt

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FM bandwidth

• The range just defined is one expression for FM
  bandwidth. There are many more!
• BFM4W2kfmp
• Using ??f/W with ?fkfmp
• BFM2(?2)W

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Carsons Rule

• A popular expression for FM bandwidth is Carsons
  rule. It is a bit smaller than what we just saw
• BFM2(?1)W

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Commercial FM

• Commercial FM broadcasting uses the following
  parameters
• Baseband15KHz
• Deviation ratio5
• Peak freq. Deviation75KHz
• BFM2(?1)W2x6x15180KHz

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Wideband vs. narrowband FM

• NBFM is defined by the condition
• ?fltltW BFM2W
• This is just like AM. No advantage here
• WBFM is defined by the condition
• ?fgtgtW BFM2 ?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 ?gt1 --gt WBFM
• If ?lt1--gtNBFM
• 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

25KHz guardband
carrier
FM station B
FM station A
FM station C
150 KHz
200 KHz
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FM stereomultiplexing

• First, two channels are created (leftright) and
  (left-right)
• Leftright is useable by monaural receivers

-
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Subcarrier modulation

• The mono signal is left alone but the difference
  channel is amplitude modulated with a 38 KHz
  carrier

-
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Stereo signal

• Composite baseband signal is then frequency
  modulated

Composite baseband
Left channel

FM transmitter
mono

Right channel


DSB-SC fsc38 kHz
-
freq divider
fsc 38KHz
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Stereo spectrum

• Baseband spectrum holds all the information. It
  consists of composite baseband, pilot tone and
  DSB-SC spectrum

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Stereo receiver

• First, FM is stripped, i.e. demodulated
• Second, composite baseband is lowpass filtered to
  recover the leftright and in parallel amplitude
  demodulated to recover the left-right signal

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Receiver diagram


Leftright
left
lowpass filter(15K)

coherent detector
15 KHz
right
-
bandpass at 38KHz
X
lowpass

38 KHz
19 KHz

FM receiver
PLL
X
lowepass
VCO
Divide 2
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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
Leftright
DSB-SC
SCA signal
38 KHz
19 KHz
59.5 67 74.5
f(KHz)
15 KHz
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FM receiver

• FM receiver is similar to the superhet layout

RF
mixer
limiter
Discrimi- nator
deemphasis
IF
LO
AF power amp
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Frequency demodulation

• Remember that message in an FM signal is in the
  instantaneous frequency or equivalently
  derivative of carrier angle

Do envelope detection on s(t)
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Receiver componentsRF 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
• Limiters 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
  limiters quieting voltage is 200 mV. What is the
  receivers sensitivity?
• What we are really asking is the required signal
  at RFs input to produce 200 mV at the output
• 200 mV/200,000 1?V-gtsensitivity

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Discriminator

• The heart of FM is this relationship
• What we need is a device that linearly follows
  inst. frequency

fi(t)fckfm(t)
fcarrier is at the IF frequency Of 10.7 MHz
Disc.output
-75 KHz
75 KHz
f
fcarrier
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
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Phase-Locked Loop

• PLLs are increasingly used as FM demodulators
  and appear at IF output

Output proportional to Difference between fin and
fvco
Phase comparator
Lowpass filter
fin
Error signal
Control signalconstant When finfvco
VCO
VCO input
fvco
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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 2x50KHz100 KHz
• Lock range2x200 KHz400 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. PLLs
  need no tuned circuits

If fc drifts detector has no way of correcting
itself
Slope detector
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Zero crossing detector
FM input
more frequent ZCs means higher inst freq in turn
means Larger message amplitudes
Hard limiter
ZC detector
multiV
Averaging circuit
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NOISE IN ANALOG MODULATION

• AMPLITUDE MODULATION

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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
BT2W
filter
Noise n(t)
fc
-fc
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Establishing a reference SNR

• Define channel SNR measured at receiver input
• (SNR)cavg. power of modulated signal/
• avg. noise power in the message bandwidth

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Noise in DSB-SC Receiver

• Tuner plus coherent detection

BPF
LPF
DSB-SC
x(t)
v(t)
s(t)
n(t)
Cos(2pfct)
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Receiver input SNR

• Also defined as channel SNR

No/2
Flat noise spectrumwhite noise
Noise powerhatched area
W
-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
• 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,
• 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

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Receiver model

• Noisy FM signal at BPFs output is

FM s(t)
BFP
Limiter
FM detector
LPF (W)
n(t)
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Phasor model

• We can see the effect of noise graphically

?(t)-?(t)
noise
??(t)
Received signal
FM signal
?(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/AcSin(????
• 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 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)x2537.5
• 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 bandwidthBnBT/W
• Where W is the baseband bandwidth

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Examples of Bn

• For AM
• BnBT/W2W/W2
• For FM
• BnBT/W2? 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

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Noise/bandwidth summary

• DSB-SC/coherent detection
• (SNR)o(SNR)c
• Bn2
• SSB
• (SNR)o(SNR)c
• Bn1

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Noise/bandwidth summary

• FM-tone modulation and ?5
• (SNR)o1.5 ?2(SNR)c37.5 (SNR)c
• Bn16 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
Deemphasis circuit Is between the detector And
the audio amplifier
preemphasis
3dB
-3dB
deemphasis
-17dB
500 Hz 2120 Hz 15KHz
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Suggested homework

• 3.41
• 5.3
• 5.7