F9-CS-CH4-FM- part 1-3
description
Transcript of F9-CS-CH4-FM- part 1-3
12/4/2009
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EEN 303 Communication SystemsEEN 303 Communication SystemsBETM (Fall 2009)BETM (Fall 2009)
Frequency Frequency
ModulationModulation
Engr. Engr. HumeraHumera RafiqueRafique
Assistant Professor (CS & Engineering)Assistant Professor (CS & Engineering)
BahriaBahria University, Karachi CampusUniversity, Karachi Campus
[email protected]@bimcs.edu.pk
Course web: Course web: http://dcs.telecom.googlepages.com/communicatiohttp://dcs.telecom.googlepages.com/communicationnsystemssystems
4-Dec-09CH:4 FM EEN303 Communication
Systems
Text and ReferenceText and Reference
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TextText
1.1. CommunicationCommunication ElectronicsElectronics:: ((22/e)/e) LouisLouis EE.. FrenzelFrenzel
2.2. ModernModern ElectronicElectronic CommunicationCommunication:: ((88/e)/e) Beasley/MillerBeasley/Miller
ReferenceReference
1.1. PrinciplesPrinciples ofof ElectronicElectronic CommunicationCommunication SystemsSystems ((33/e)/e) LouisLouis EE..
FrenzelFrenzel
2.2. ElectronicElectronic CommunicationCommunication SystemsSystems ((44/e)/e) CanedyCanedy
CH:4 FM EEN303 Communication Systems
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Chapter ContentsChapter Contents
•• CH4: CH4: Fundamentals of Frequency Fundamentals of Frequency
ModulationModulation
1. Angle Modulation
2. Basic principle of Frequency modulation
3. Principle of Phase modulation
4. Modulation index and sidebands
5. Noise suppression effects of FM
6. FM versus AM
7. Disadvantages of FM
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CH:4 FM EEN303 Communication Systems
Angle ModulationAngle Modulation
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CH:4 FM EEN303 Communication Systems
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Angle ModulationAngle ModulationThree parameters of a carrier sinusoid can be varied to allow it to carry a low
frequency intelligence signal:
1. Amplitude
2. Frequency
3. Phase
1. Amplitude modulation
2.3. Angle modulation
Angle Modulation:
Super imposing the intelligence signal on a
high frequency carrier so that its phase angle
or frequency is altered as a function of
amplitude of intelligence signal
Types of Angle Modulation:
a. Frequency modulation
b. Phase modulation4-Dec-09
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CH:4 FM EEN303 Communication Systems
Fig. 4-1: AM, FM & PM
Angle ModulationAngle ModulationFrequency Modulation:
‘An angle modulation in which an information signal changes the frequency of a
carrier proportional to its amplitude’
Phase Modulation:
‘An angle modulation where the phase angle of a carrier is caused to depart from its
reference value by an amount proportional to the modulating signal’s amplitude’
• Usually PM is not used as the transmission signal , but
– Helps in generating FM
– Helps to understand noise characteristics of FM as compared to AM
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CH:4 FM EEN303 Communication Systems
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FM: Basic PrincipleFM: Basic Principle
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CH:4 FM EEN303 Communication Systems
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Fig. 4-2: AM & FM Techniques
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Fig. 4-3: Modulation Techniques: AM & FM (constant amplitude
intelligence)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1
-0.5
0
0.5
1
Inte
lligenc
e
Time domain AM & FM waveforms
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1
-0.5
0
0.5
1
AM
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1
-0.5
0
0.5
1
FM
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Fig. 4-4: FM: Variable amplitude intelligence
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• In FM, the carrier amplitude remains constant & the carrier frequency is
changed by the modulating signal
• As the amplitude of the intelligence signal varies, the carrier frequency shift
proportionally
• if vm(t) ↑ => the fc ↑ & if vm(t) ↓ => the fc ↓ (Note: The reverse
relationship is also allowed)
• When intelligence signal = 0 => fc = fc = centre or resting frequency of carrier
frequency
• As the modulating signal’s amplitude varies between +ve & -ve peaks,
passing via zero values, carrier frequency changes above & below its normal,
‘centre’, or ‘resting’ value
Frequency deviation
• The amount of change in carrier frequency occurs due to modulating signal
(max deviation @ maximum amplitude)
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Frequency deviation rate:
• How many times per second the carrier frequency deviates above & below the
carrier/centre frequency
• fm determines fd i.e.,
if modulating signal: fm , then,
fc shifts above & below the centre
frequency, fm times per second
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1
0
1Time domain FM signals
Info
rmation
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1
0
1
Carr
ier
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1
0
1
FM
Fig. 4-5: FM
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A simple FM generator:
• Simple FM transmitter
• Components:
i. LC tank circuit
ii. Oscillator
iii. FM transmitting antenna
• The capacitance of LC tank circuit is not a standard capacitor, but a capacitor
microphone (or condenser mike i.e., a variable capacitor)
• With no sound waves at mike, its capacitor remains constant while for sound
waves, its plates move in and out alternatively and its capacitance goes up and
down around its centre value
• The rate of capacitance change is equal to frequency of the sound waves
striking the mike and the amount of capacitance change is proportional to the
amplitude of the sound waves
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
OscillatorOscillator
Fig. 4-6: Modulation Techniques
FM Generation Mechanism:
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Fig. 4-6 (a):
FM Generation mechanism
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FM Generation Mechanism:
Time: 0 – T1:
• Intelligence signal = zero amplitude
• Carrier remains unchanged
Time: T1 – T2:
• Intelligence signal’s amplitude: zero to +ve peak
• Oscillator’s frequency changes from its centre value to highest value
respectively
Time: T2 – T3:
• Intelligence signal’s amplitude gradually decreases from +ve peak to zero
• Oscillator's frequency its highest value to centre value
Time: T3 – T4:
• Intelligence signal’s amplitude goes from zero to –ve peak
• Oscillator's frequency gradually decreases from centre value to a lowest value
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
FM Generation Mechanism (contd..):
Time: T4 – T5:
• Intelligence signal’s amplitude goes zero again
• Oscillator's frequency gradually goes to its central value
• The relationship of FM generation with capacitor microphone is:
• k : “how much the carrier frequency will deviate for a given modulating input
voltage level” (kHz/volt)
• k vm = total deviation
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
out c mf f kv= +instantaneous
output frequency
carrier frequency
deviation constant
intelligence signal
. . . . . (4-1)
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FM Generation Mechanism:
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Fig. 4-6 (b): FM signal
with square wave as intelligence
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-1
-0.5
0
0.5
1
Inte
lligence
Time domain AM & FM waveforms
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-1
-0.5
0
0.5
1
FM
FM Generation Mechanism:
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Fig. 4-6 (c): FM signal with variable square wave
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FM Generation Mechanism:
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
Fig. 4-6 (d): FM signal
with saw tooth wave as intelligence
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-1
-0.5
0
0.5
1
Inte
lligence
Time domain FM waveform
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-1
-0.5
0
0.5
1
FM
ExampleExample ((44--11)):: (Miller)(Miller)
A 25-mV sinusoid at a frequency of 400 Hz is applied to a capacitor microphone
FM generator. If the deviation constant for the capacitor microphone FM generator
is 750 Hz/10mV, determine:
(a) The frequency deviation generated by an input level of 25 mV
(b) The rate at which the carrier frequency is being deviated
(c) Output frequency, if fc = 50 kHz
ExampleExample ((44--22)):: ((FrenzelFrenzel 22/e/e pp..7171))
For a carrier of 50 MHz, find the total frequency deviation, if the peak amplitude of
the modulating signal causes a maximum frequency shift of 200 kHz.
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
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ExampleExample ((44--33)):: ((FrenzelFrenzel 33/e)/e) pp..153153
A transmitter operates on a frequency of 915 MHz. The maximum FM deviation is
+/- 12.5 kHz. What are the maximum and minimum frequencies that occur during
Modulation?
ExampleExample ((44--44))::
An FM signal has a centre frequency of 100 MHz, but is swinging between 100.001
MHz & 99.999 MHz at a rate of 100 times per second. Determine:
(a) fm
(b) Vm
(c) What happens to amplitude of intelligence if the frequency deviation changes
to between 100.002 & 99.998 MHz.
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CH:4 FM EEN303 Communication Systems
Basics Principle of FMBasics Principle of FM
PM: Basic PrinciplePM: Basic Principle
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CH:4 FM EEN303 Communication Systems
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• A method to produce FM, by varying the amount of phase shift of a constant
frequency carrier in accordance with a modulating signal
• Phase shift: a time separation between two (sine) waves of same frequency
• A Phase modulator is a circuit that causes a phase shift in a sinusoid in
accordance with the amplitude of a modulating signal such that
• The amplitude of the intelligence ↑, the phase shift ↑ and vise versa
• Further, for positive amplitudes of modulating signal: lagging phase shift and,
for negative values, a leading phase shift
• In other words, the output of a phase shifter (PM) is delayed, delay increases
with the amplitude of modulating signal, if the input is a ‘constant-frequency-
constant-amplitude’ sinusoid carrier
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CH:4 FM EEN303 Communication Systems
Basics Principle of PMBasics Principle of PM
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CH:4 FM EEN303 Communication Systems
Basics Principle of PMBasics Principle of PM
Fig. 4-7: PM
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CH:4 FM EEN303 Communication Systems
Basics Principle of PMBasics Principle of PM
Fig. 4-8: Modulations: (a) AM (b) FM (c) PM
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CH:4 FM EEN303 Communication Systems
Basics Principle of PMBasics Principle of PM
Fig. 4-9: PM: variable amplitude intelligence
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Modulation Index & Modulation Index &
SidebandsSidebands
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CH:4 FM EEN303 Communication Systems
FrequencyFrequency SpectrumSpectrum ofof FMFM::
• All modulation processes produce sidebands
• Like AM, in FM/PM, side bands are ‘sum & difference of the carrier &
modulating frequencies’
• Other (theoretical) infinite pairs of upper & lower side bands
• FM/PM wider than equivalent AM (broadband FM)
• Special signal, whose BW slightly wider than that of AM (Narrowband FM)
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
Carrier
fc
LSBs USBs
fc-7fm fc-5fm fc-3fm fc - fm fc+2fm fc+4fm fc+6fm
Fig. 4-10 : Frequency spectrum of FM signal (single frequency modulating)
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FrequencyFrequency SpectrumSpectrum ofof FMFM (Contd(Contd....))::
• Frequency will change if the amplitude of modulating signal varies
• Number of side bands produced , their amplitudes & their spacing depend on:
i. Frequency deviation (δ)
ii. Modulating signal’s frequency ( fm )
• Among infinite number of side bands, only larger amplitude side bands carry
useful information
• An insignificant side band’s amplitude < 1% of un-modulated carrier’s amplitude
• The above fact narrows the FM spectrum to a finite extent
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
ModulationModulation IndexIndex ofof FMFM ::
• The ratio of frequency deviation (δ) to the modulating frequency ( fm )
• ↑ mf, wider the FM band width
• Modulation index is called ‘deviation ration’ if computer using equation (4-2)
• If mf is known, amplitudes and number of significant side bands can be
computed, using ‘Bessel function’
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
f
m
mf
δ=
Maximum frequency shift in
carrier caused by intelligence
Modulating frequency
Modulation Index
. . . . . . . . . (4-2)
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BesselBessel functionfunction::
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
Table 4-1 : Bessel function based carrier & side band amplitudes for different values of mf
TotalTotal bandband widthwidth ofof FMFM ::
• Two methods:
i. Total bandwidth of an FM signal can be determined by mf & ‘Bessel function
table’
ii.ii. Carson’sCarson’s rulerule::
An equation to approximate the bandwidth of an FM signal:
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
max2 mBW Nf= . . . . . . . . . (4-3)
N : number of significant side bands
( )maxmax
2m
BW fδ +
max. frequency shift caused
by the intelligence signal
. . . . . . . . (4-4)
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MeasurementMeasurement ofof frequencyfrequency deviationdeviation::
• Method is called ‘zerozero carriercarrier amplitudeamplitude’
• Generated FM is observed on spectrum analyzer
• At the point where carrier’s amplitude becomes zero, number of side bands are
noted down
• Number of side bands -> Modulation index (Bessel function table)
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
mf = 0.5
Carrier
mf = 1.0
Carrier
mf = 2.0Carrier
Fig. 4-11: FM Spectrum
ExampleExample ((44--55))::
Highest modulating frequency = 2 kHz, carrier deviation = 5 kHz. Find the number of
usable side bands.
ExampleExample ((44--66)):: FrenzelFrenzel
Find the modulation Index:
(a) The maximum frequency deviation of a carrier in FM is ± 25 kHz with
modulating frequency is 10 kHz .
(b) The maximum frequency deviation of a carrier in FM is ± 75 kHz with
modulating frequency is 15 kHz .
ExampleExample ((44--77)):: FrenzelFrenzel
Highest modulating frequency = 2.5 kHz, modulation index = 2. Find the total
bandwidth occupied by FM signal.
ExampleExample ((44--88))::
In zero carrier amplitude method, 9 side bands are visible on a spectrum analyzer
showing FM signal. If modulating frequency = 100 kHz, find frequency deviation.
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
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ExampleExample ((44--99))::
Determine the bandwidth required to transmit an FM signal, if maximum deviation
δ = 20 kHz : (a) fm = 10 kHz (b) fm = 5 kHz
ExampleExample ((44-- 1010)):: For broadcast FM radio, compute DR.
ExampleExample ((44--1111))::
(a) Determine the permissible range in maximum modulation index for
commercial FM that has 30 Hz – 15 kHz modulating frequencies
(b) Repeat for a narrow band system that allows a maximum deviation of 1 kHz
and 100 Hz to 2 kHz modulating frequency
(c) Determine the deviation ratio for the system in part (b)
ExampleExample ((44--1212))::
Determine the relative and total power of the carrier & side frequency bands when
mf = 0.25 for a 10 kW FM transmitter.
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CH:4 FM EEN303 Communication Systems
Modulation Index & SidebandsModulation Index & Sidebands
BroadbandBroadband FMFM (BBFM/WBFM)(BBFM/WBFM)::
• Standard FM broadcast bandwidth: 200 kHz for each station (one FM band may
contain many AM channels)
• Such a large allocation is needed:
– High Fi modulating signal up to 15 kHz
– Having superior noise performance
• Maximum allowed deviation in fc : ± 75 kHz for significant side bands
• Guard bands” to help minimizing inter-channel interference: 25 kHz
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CH:4 FM EEN303 Communication Systems
FM ClassificationFM Classification
Fig. 4-12: Commercial FM bandwidth allocation for two adjacent stations
200 kHz 200 kHz
-75 kHz Carrier 1 +75 kHz Carrier 2 +75 kHz-75 kHz
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BroadbandBroadband FMFM (contd(contd....))::
• DR: (deviation ratio): maximum possible frequency deviation over the maximum
input frequency:
• If DR > 1 => wideband FM system
• If DR < 1 => narrow band FM system
NarrowbandNarrowband FMFM (NBFM)(NBFM)::
• Band allocation : 10-30 kHz
• Modulation index: 0.5 – 1.0
• Use for voice transmission (intelligence of 3 kHz) in systems such as
Applications:
Police help line, Aircrafts, Taxi cabs, Weather services, Private industrial
networks
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CH:4 FM EEN303 Communication Systems
FM ClassificationFM Classification
(max)
max. .
. . m
max possible freq deviationDR
max input freq f
δ= = . . . . . . . . (4-4)
Analysis of FM & PMAnalysis of FM & PM
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CH:4 FM EEN303 Communication Systems
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CH:4 FM EEN303 Communication Systems
Analysis of FM & PMAnalysis of FM & PM
( ) sin( sin )p c p m
v t A t mφ ω ω= +Phase modulated
instantaneous voltage
Peak value of
un-modulated carrier
Carrier frequency
(radians)
Maximum phase shift by
the intelligence signal (radians)
Modulating frequency
(radians)
. . . . . . . (4-5)
( ) sin( sin )FM p c f m
v t A t mω ω= +Frequency modulated
instantaneous voltage
Peak value of
un-modulated carrier
Carrier frequency
(radians)
Modulating index of FM (measure of maximum
frequency phase shift in carrier’s frequency)
Modulating frequency
(radians)
. . . . . . . (4-6)
f
i
mf
δ=
Maximum frequency shift in
carrier caused by intelligence
• FM is not sensitive to intelligence signal’s frequency but PM
• In FM the amount of frequency deviation produced in carrier, does not
depend on the intelligence’s frequency but in PM
• The amount of deviation is proportional to the intelligence signal’s amplitude
for both PM & FM
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CH:4 FM EEN303 Communication Systems
Analysis of FM & PMAnalysis of FM & PM
Dev
iati
on
(δ)
f
Vm0
Dev
iati
on
(δ)
f
fm0
FM
Fig. 4-11: Relationship b/w deviation & modulating
signal amplitude & frequency for FM & PM
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ExampleExample ((44--1313))::
An FM signal, 2000 sin(2π 108 t + 2 sin (π 104 t)), is applied to a 50-Ω antenna.
Determine:
(a) fc
(b) fm
(c) PT
(d) mf
(e) BW
(f) Power in the largest & smallest sidebands predicted by table (4-1)
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CH:4 FM EEN303 Communication Systems
Analysis of FM & PMAnalysis of FM & PM
Noise Suppression Noise Suppression
Effects of FM Effects of FM
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CH:4 FM EEN303 Communication Systems
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• Noise : an interference by:
– Lightning
– Motors
– Automotive ignition systems
– Transient signals by power line switching
• Such noise is typically narrow spikes of voltage with very high frequencies
• Add to a signal and interfere with it
• Usually changes its amplitude
• FM has superior noise characteristics than AM
• e.g., static noise is rarely heard on FM (although quite common in AM)
FM limiters:
• A stage in FM receivers that removes any amplitude variations of the received
signal before next stage
• If limiters do not remove all noise completely, the remaining noise spikes
produce a small frequency variations or phase shifts
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CH:4 FM EEN303 Communication Systems
Noise Suppression Effects of FMNoise Suppression Effects of FM
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CH:4 FM EEN303 Communication Systems
Noise Suppression Effects of FMNoise Suppression Effects of FM
FM FM
Limiter/Limiter/
DetectorDetector
AM AM
DetectorDetector
Fig. 4-12: FM, AM noise comparison
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• This unwanted noise produces PM, which in terns produce unwanted FM
• The amount of frequency deviation (FM) caused by PM is:
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CH:4 FM EEN303 Communication Systems
Noise Suppression Effects of FMNoise Suppression Effects of FM
mfδ φ= ×
Frequency
deviation
Phase shift
in radians
Modulating
frequency
. . . . . . . (4-7)
S : desired signal
N : noise signal = ½ S => S/N = 2:1
R : resultant signal
• The phase shift b/w noise and signal is given by:
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CH:4 FM EEN303 Communication Systems
FM Noise analysisFM Noise analysis
Fig. 4-13: (a) Phase shift as a result of noise (b) Maximum phase shift condition
S
Φ
½ S
S
Φ
Rotating vector
1sin
N
Sφ − =
. . . . . . . (4-8)
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General equation for phase shift:
The maximum phase shift occurs when the noise & signal phasors are at a right angle
to each other (worst case):
Then,
worst case frequency deviation (from eq(4-7)):
For improved SNR of an FM system:
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CH:4 FM EEN303 Communication Systems
FM Noise analysisFM Noise analysis
( )1 1sin 30 0.5236 2
oradφ −= = =
( ) 0.5236worst mfδ = . . . . . . . (4-9-a)
. .
. .
N freq dev produced by noise
S max allowed dev= . . . . . . . (4-10)
( ) ( )worst rad mfδ φ= . . . . . . . (4-9
ExampleExample ((44--1414))::
If modulating frequency = 15 kHz, find worst case deviation in FM system, if input
SNR is 2.
ExampleExample ((44--1515))::
Modulating frequency = 800 Hz. The SNR = 3:1. Determine the frequency deviation
produced.
ExampleExample ((44--1616))::
Determine the worst case output SNR for a broadcast FM that has a maximum
modulating frequency of 5 kHz. The input SNR is 2.
ExampleExample ((44--1717))::
The input SNR of an FM receiver is 2.8. the modulating frequency is 1.5 kHz. The
maximum permitted deviation is 4 kHz. Find:
(a) Frequency deviation caused by the noise
(b) The improved output SNR
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CH:4 FM EEN303 Communication Systems
FM Noise analysisFM Noise analysis
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• A voice signal is band limited to 3 kHz (low frequency)
• Musical instruments have almost low frequency components but some of them
contain high frequency components as well
• Thus an audio Hi Fi system must have wider band width to represent all
• Noise interfere FM signal, particularly at higher frequencies
• Noise primarily is sharp spikes of energy, it contains a lot of harmonics & other
high frequency components
• These components are larger in magnitude than the high frequency components
of modulating signal
• High frequency components of information signals are usually at low amplitude
levels
• To overcome this problem, most FM systems use a technique ‘Pre-Emphasis’ to
deal with high frequency noise problem
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CH:4 FM EEN303 Communication Systems
PrePre--EmphasisEmphasis
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CH:4 FM EEN303 Communication Systems
PrePre--EmphasisEmphasis
FMFM
ModulatorModulator
Pre-emphasis
FM output
Fig. 4-14: (a) FM with pre-emphasis circuit
3 dB
0 dB
dB/octave
A(dB)
f (Hz)fu
Fig. 4-14 (b) :
Pre-emphasis curve
C
R1 R21 2
1 22u
R Rf
R R Cπ+
=
f1
Pre-emphasis
circuit
≥ 30 kHz
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CH:4 FM EEN303 Communication Systems
PrePre--EmphasisEmphasis
-3 dB
0 dB
A(dB)
f (Hz)fL
Fig. 4-15 (b) :
De-emphasis curve
FM inFMFM
demodulatordemodulator
Audio out
De-emphasis
circuit
Fig. 4-15 (a) : FM demodulator with De-emphasis circuit
C
R
1
2Lf
RCπ=
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CH:4 FM EEN303 Communication Systems
PrePre--EmphasisEmphasis
-3 dB
0 dB
A(dB)
f (Hz)fa
Fig. 4-16: Combined frequency response
+3 dB