This document discusses Frequency Modulation (FM) and methods for generating wideband FM signals. It begins by explaining Carson's Bandwidth Rule, which defines the approximate bandwidth requirements for an FM signal based on its peak frequency deviation and highest modulating frequency. It then describes the direct and indirect (Armstrong) methods for generating FM signals. The indirect method uses an integrator and Armstrong phase modulator to approximate FM for small modulation indices. To achieve wider modulation indices, the signal can pass through nonlinear devices and bandpass filters to multiply the carrier frequency and modulation index. This allows for excellent frequency stability by using a crystal oscillator as the carrier source.

1. EC403: Communication Systems
Term paper
Frequency Modulation
Prepared by:
GEET PATEL (13BEC072)
DARP RAITHATHA (13BEC084)

2. Carson’s Bandwidth rule:-
 In telecommunicationCarson’sbandwidthrule definesapproximate bandwidthrequirementsof
the communicationsystemcomponentsforacarriersignal that isfrequencymodulatedbya
continuousorbroad spectrumfrequenciesratherthanasingle frequency.
 Carson’srule doesnotapplywell whenthe modulatingsignalscontaindiscontinuities,suchasa
square wave.
 Carson’srule originatesfromJohnRenshaw Carson’s1922 paper.
Carson’s bandwidth rule can be expressed as follows:-
CBR = 2( Δf + fm)
Where:
CBR = Bandwidthrequirement
Δf = peak frequencydeviation
fm = Highestfrequencyinthe modulatingsignal
 For example,anFMsignal with5 kHz peakdeviation,andamaximumaudiofrequencyof 3 kHz,
wouldrequire anapproximate bandwidth2(5+3) = 16 kHz.
 For example,standardbroadcastFMhas a peakdeviationof 75 kHz above andbelow the
carrier.With stereoFM.,the highestmodulatingfrequency(whichcombinesL+Rand L-R) is 53
kHz. Somost of the energyof standardstereoFMfallsinan approximate bandwidthof 2(75+53)
= 256 kHz. (Geographicallyclose FMbroadcasttransmittersare almostalwaysassignednominal
centerfrequenciesatleast500 kHz apart)
 Thisrule is basedonexperimental resultsthatprovedthatthere are limitednumberof side
bandsaround the carrierfrequency,whichcontainapproximately98percentof the total power
of an FMsignal.All the remainingside handsinthe frequencyspectrumcontainonly2percent
of the total power.Thus,itis obviousthatthe bandwidthof anFM systemcanbe reducedtoa
practically feasible limitatthe expenseof 2percentof the total power.

3.  The lossof 2 percentof total powerisa wise trade betweenthe qualitiesof the received.Signal
and the bandwidth,asinfinite bandwidthisrequiredtotransmittotal powerof anFM signal.
 It isalso observedthatif onlyafew side bandsare transmittedthroughlimitedbandwidth,then,
the distortionproducedinthe recoveredbasebandsignalatthe receiverisnegligible andthe
qualityof the recoverysignal isnotseverelydegraded.Therefore,the bandwidthof anFM
systemisbroughtwithinpracticallyfeasible limitsbytransmitting,onlythoseside bandsthat
contain98 percentof the total powersystem.
 Applications:- Designingtransmitters,antennas,optical sources,receivers, photodetectors and
othercommunicationsystemcomponents.
Armstrong method of generating WB FM:-
 There are mainlytwotypesof methodforFMgeneration.
o Directmethod
o IndirectmethodorArmstrong method
Direct method:-
 Thismethodissimple inthe sense thatitusesa single component:the voltage-controlled
oscillator(VCO).Asdescribedinthe sectionof CarrierAcquisitionforDSBSCsystems,VCOsare
devicesthatproduce a sinusoidwithafrequencythatisproportional tothe inputsignal.So,if
the inputsignal toa VCOisthe message signal,the outputof the VCOwill be anFMmodulated
signal of the message signal since the frequencyof thisFMsignal changesaccordingto the input
message signal.
 Features:- 1. Poor frequencystability.(canbe improvedusingfeedback.) (-ve feature)
2. Lessmultiplicationrequirementsascomparedtothe indirectmethodaswill be seen
(+ve feature)

4. Indirect methodor Armstrong method:-
 In thisindirectmethod,the messagesignal isintegrated;thisproducesanew signal whose
derivative isthe originalmessagesignal.
 Phase modulationof thisnewsignal ontothe carrierproducesthe FM.
 Here a special type of phase modulator,calledthe Armstrongmodulator,isused.
 This phase modulatorisonlyanapproximationtoatrue phase modulator;however,itisagood
approximationforsmall modulationindices.
 The combinationof anintegratorandan Armstrongmodulatorisillustratedbelow;this
representsanapproximationtoafrequencymodulator.
 The weightingfactorsinthe weightedadderare shownexplicitlyasamplifiers.
 In the TIMS weightedadder,the gainsof bothof these amplifiersare negative.
 This can be neutralizedbyplacing anamplifierwithnegativegainatthe outputof the weighted
adder.
The outputof the integratoris,
 If the message signal isasinusoid,the integratoroutputisa sinusoidhavingthe same
frequency;butthe (inputandoutput) amplitudesare differentandthe phasesare different.
 The Armstrongphase modulatorlookssimilartoa modulatorforAM. For bothmodulators,a
double-sidebandtermandaresidual carrierare addedtogether.
 Furthermore,the spectrumof the outputfromthe Armstrongmodulatorlookssimilartothe
spectrumof AM. For a sinusoidalmessagesignal,there are three spectral lines:one fromthe
residual carrierandtwofrom the double-sidebandterm.
 However,anArmstrongmodulatordoesnotproduce anAM carrier.In the Armstrong
modulatorthe phase shifter(whichdelaysthe residual carrierbyπ⁄ 2 radians) makesthe
difference.
The outputof the Armstrongmodulatorisof the form,

5. Thissignal showsbothamplitude andangle modulation.
Equationcan be approximatedas follows
Where,
OR
Where,
β = Modulationindex
VDSB = rms voltage of double-sideband(DSB) componentatmodulatoroutput
Vc = rms voltage of residual carrier(C) componentatmodulatoroutput
 An integratorfollowedbyanArmstrongphase modulatorcanproduce a goodapproximationof
FM whenthe desiredmodulationindex βissmall.ThisiscallednarrowbandFM,owingtothe
fact that the modulationindex andtherefore the bandwidthissmall.However,the well-known
performance advantage of FMover AMoccurs onlywhen βis large.However,there isawayto
use an Armstrongmodulatorandyetstill achieve alarge β . Thisisillustratedbelow.(Forthe
sake of havinga definite example,the illustrationbelow assumesthe messagesignal isa
sinusoid.)

6.  In words,the FMis generatedwithanintegratorfollowedbyanArmstrongphase modulator.
 The carrier frequency f0 andthe modulationindex β0 atthe outputof the Armstrongmodulator
are bothsmallerthandesired.
 ThisnarrowbandFM signal isplacedatthe inputof a (memoryless) nonlineardevice (suchasa
clipper),whichgeneratesharmonics.
 Thenthe m-th harmonicisselectedbyabandpass filter,havingapassbandcenteredat mf0 .
 The outputof thisbandpassfilterisa carrierof frequency,havingFMwithmodulationindex
mβ0.
 The combinationof the nonlineardevice andthe bandpassfilteriscalledafrequencymultiplier.
 The truth be told,angle multiplierwouldbe abettername,because itisthe angle (the
argumentof the carriersinusoid) thatismultiplied.
 A secondfrequencymultipliercanbe usedto furtherincrease boththe modulationindex and
the carrier frequency.
 If the secondfrequencymultiplieremploysafactor k (selectsthe –kth
harmonic),thenthe
outputof thissecondfrequencymultiplierisacarrierof frequency kmf0 ,havingFMwith
modulationindex kmβ0 .
 The followingequationssummarizethe effectof the frequencymultiplications:
fc = kmf0
β = kmβ0
 In thisway,quite large modulationindicescanbe achieved.Because thisisthe indirectmethod
for generatingFM,whichpermitsuse of acrystal oscillatorforthe frequency f0,the carriercan
have excellentfrequencystability.
 Advantage:-The generationof FMby the indirectmethod,employinganintegratorandphase
modulator,hasan importantpractical advantage overthe directmethod.A VCOtypicallyhas
poor frequencystability,soacarrier generated fromaVCO(directmethod) exhibitsfrequency
drift.Withthe 10 indirectmethodsaverystable oscillator(usuallyacrystal oscillator) canbe
usedas the source of the carrier.