f9-cs-ch4-fm- part 1-3

12/4/2009

1

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

4-Dec-09

2

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

12/4/2009

2

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

4-Dec-09

3


Angle ModulationAngle Modulation

4-Dec-09

4


12/4/2009

3

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

5


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

4-Dec-09

6


12/4/2009

4

FM: Basic PrincipleFM: Basic Principle

4-Dec-09

7


4-Dec-09

8


Basics Principle of FMBasics Principle of FM

Fig. 4-2: AM & FM Techniques

12/4/2009

5

4-Dec-09

9



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

4-Dec-09

10



Fig. 4-4: FM: Variable amplitude intelligence

12/4/2009

6

• 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)

4-Dec-09

11



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

4-Dec-09

12



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

12/4/2009

7

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

4-Dec-09

13



OscillatorOscillator

Fig. 4-6: Modulation Techniques

FM Generation Mechanism:

4-Dec-09

14



Fig. 4-6 (a):

FM Generation mechanism

12/4/2009

8


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

4-Dec-09

15



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

4-Dec-09

16



out c mf f kv= +instantaneous

output frequency

carrier frequency

deviation constant

intelligence signal

. . . . . (4-1)

12/4/2009

9


4-Dec-09

17



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


4-Dec-09

18



Fig. 4-6 (c): FM signal with variable square wave

12/4/2009

10


4-Dec-09

19



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.

4-Dec-09

20



12/4/2009

11

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.

4-Dec-09

21



PM: Basic PrinciplePM: Basic Principle

4-Dec-09

22


12/4/2009

12

• 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

4-Dec-09

23


Basics Principle of PMBasics Principle of PM

4-Dec-09

24



Fig. 4-7: PM

12/4/2009

13

4-Dec-09

25



Fig. 4-8: Modulations: (a) AM (b) FM (c) PM

4-Dec-09

26



Fig. 4-9: PM: variable amplitude intelligence

12/4/2009

14

Modulation Index & Modulation Index &

SidebandsSidebands

4-Dec-09

27


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)

4-Dec-09

28


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)

12/4/2009

15

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

4-Dec-09

29



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’

4-Dec-09

30



f

m

mf

δ=

Maximum frequency shift in

carrier caused by intelligence

Modulating frequency

Modulation Index

. . . . . . . . . (4-2)

12/4/2009

16

BesselBessel functionfunction::

4-Dec-09

31



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:

4-Dec-09

32



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)

12/4/2009

17

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)

4-Dec-09

33



mf = 0.5

Carrier

mf = 1.0

Carrier

mf = 2.0Carrier

Fig. 4-11: FM Spectrum


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.


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.

4-Dec-09

34



12/4/2009

18


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.


(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)


Determine the relative and total power of the carrier & side frequency bands when

mf = 0.25 for a 10 kW FM transmitter.

4-Dec-09

35



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

4-Dec-09

36


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

12/4/2009

19

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

4-Dec-09

37


FM ClassificationFM Classification

(max)

max. .

. . m

max possible freq deviationDR

max input freq f

δ= = . . . . . . . . (4-4)

Analysis of FM & PMAnalysis of FM & PM

4-Dec-09

38


12/4/2009

20

4-Dec-09

39



( ) 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)


(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)


(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

4-Dec-09

40



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

12/4/2009

21


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)

4-Dec-09

41



Noise Suppression Noise Suppression

Effects of FM Effects of FM

4-Dec-09

42


12/4/2009

22

• 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

4-Dec-09

43


Noise Suppression Effects of FMNoise Suppression Effects of FM

4-Dec-09

44



FM FM

Limiter/Limiter/

DetectorDetector

AM AM

DetectorDetector

Fig. 4-12: FM, AM noise comparison

12/4/2009

23

• This unwanted noise produces PM, which in terns produce unwanted FM

• The amount of frequency deviation (FM) caused by PM is:

4-Dec-09

45



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:

4-Dec-09

46


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)

12/4/2009

24

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:

4-Dec-09

47



( )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


If modulating frequency = 15 kHz, find worst case deviation in FM system, if input

SNR is 2.


Modulating frequency = 800 Hz. The SNR = 3:1. Determine the frequency deviation

produced.


Determine the worst case output SNR for a broadcast FM that has a maximum

modulating frequency of 5 kHz. The input SNR is 2.


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

4-Dec-09

48



12/4/2009

25

• 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

4-Dec-09

49


PrePre--EmphasisEmphasis

4-Dec-09

50



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

12/4/2009

26

4-Dec-09

51



-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=

4-Dec-09

52



-3 dB

0 dB

A(dB)

f (Hz)fa

Fig. 4-16: Combined frequency response

+3 dB

f9-cs-ch4-fm- part 1-3

Documents