1. Chapter 4Chapter 4
FREQUENCY MODULATIONFREQUENCY MODULATION

2. INTRODUCTIONINTRODUCTION
 3 properties of an analog signal can be modulated by3 properties of an analog signal can be modulated by
information signal:information signal:
o Amplitude - - -> produce AMAmplitude - - -> produce AM
o Frequency - - - > produce FMFrequency - - - > produce FM
o Phase - - - > produce PMPhase - - - > produce PM
 FM & PM are forms ofFM & PM are forms of angle modulationangle modulation and oftenand often
referred as frequency modulation.referred as frequency modulation.

3.  FM is considered to be superior to AM.FM is considered to be superior to AM.
 Transmission efficiency:Transmission efficiency:
 AM use linear amplifier to produced the final RF signal.AM use linear amplifier to produced the final RF signal.
 FM has constant carrier amplitude so it is not necessary to useFM has constant carrier amplitude so it is not necessary to use
linear amplifier.linear amplifier.
 Fidelity (capture effect):Fidelity (capture effect):
 The stronger signal will be capture and eliminate the weaker.The stronger signal will be capture and eliminate the weaker.
 In AM, the weaker signal can be heard in the background.In AM, the weaker signal can be heard in the background.
 Noise immunity (noise reduction):Noise immunity (noise reduction):
 Constant carrier amplitude.Constant carrier amplitude.
 FM receiver have limiter circuitFM receiver have limiter circuit
FM VS AMFM VS AM

4. Disadvantages of FMDisadvantages of FM
 Use too much spectrum space.Use too much spectrum space.
 Requiring a wider bandwidthRequiring a wider bandwidth
 Reduce modulation index to minimize BW but in FMReduce modulation index to minimize BW but in FM
although we reduced the modulation index, BW is still larger.although we reduced the modulation index, BW is still larger.
 typically used at high frequencies (VHF,UHF & microwavetypically used at high frequencies (VHF,UHF & microwave
frequenciesfrequencies
 More complex circuitryMore complex circuitry

5.  Amplitude of the modulated carrier is held constant and either theAmplitude of the modulated carrier is held constant and either the
phase or the time derivative of the phase of the carrier is varied linearlyphase or the time derivative of the phase of the carrier is varied linearly
with the message signal m(t).with the message signal m(t).
 General angle-modulated signal is given byGeneral angle-modulated signal is given by
 In angle modulation,In angle modulation, θθ(t)(t) is prescribed as being a function of theis prescribed as being a function of the
modulating signalmodulating signal
 IfIf vvmm(t)(t) is the modulating signal, angle modulation is expressed asis the modulating signal, angle modulation is expressed as
wherewhere
[ ]( ) ( )mt F v tθ =
( ) sin( )
2
m m m
m m
v t V t
f
ω
ω π
=
=
ANGLE MODULATIONANGLE MODULATION
( ) ( )[ ]ttVtm cc θω += cos

6. FM OR PM ?FM OR PM ?
 Both must occur whenever either form of angle modulation isBoth must occur whenever either form of angle modulation is
performed.performed.
FMFM PMPM
Instantaneous frequencyInstantaneous frequency of the carrier isof the carrier is
varied from its reference value byvaried from its reference value by
an amount proportional to thean amount proportional to the
modulating signal amplitudemodulating signal amplitude
Freq. carrier - - - > directly variedFreq. carrier - - - > directly varied
Phase carrier - - -> indirectly variedPhase carrier - - -> indirectly varied
Phase anglePhase angle of the carrier is variedof the carrier is varied
from its reference value by anfrom its reference value by an
amount proportional to theamount proportional to the
modulating signal amplitudemodulating signal amplitude
Phase carrier - - - > directly variedPhase carrier - - - > directly varied
Freq. carrier - - -> indirectly variedFreq. carrier - - -> indirectly varied

7. Figure 4.1 : Frequency deviation
∆f ∆f
fc-∆f fc fc+∆f f
-Vm 0 +Vm
vm(t) = Vm cos 2πfmt
2∆f

8.  Instantaneous frequency deviationInstantaneous frequency deviation
 Instantaneous change in the frequency of the carrier and is definedInstantaneous change in the frequency of the carrier and is defined
as the first time derivative of the instantaneous phase deviationas the first time derivative of the instantaneous phase deviation
 Instantaneous frequencyInstantaneous frequency
 the precise frequency of the carrier at any given instant of time andthe precise frequency of the carrier at any given instant of time and
is defined as the first time derivative of the instantaneous phaseis defined as the first time derivative of the instantaneous phase
instantaneous frequency deviation '( ) rad/s
'( ) rad/s cycle
or Hz
2 rad/cycle s
t
t
θ
θ
π
=
= = =
[ ]instantaneous frequency ( ) ( )
'( ) rad/s
i c
c
d
t t t
dt
t
ω ω θ
ω θ
= = +
= +
MATHEMATICAL ANALYSISMATHEMATICAL ANALYSIS

9.  Substituting 2Substituting 2ππffcc forfor ωωcc givesgives
 Frequency modulation is angle modulation in which theFrequency modulation is angle modulation in which the
instantaneous frequency deviation,instantaneous frequency deviation, θθ’(t), is proportional to’(t), is proportional to
the amplitude of the modulating signal, and thethe amplitude of the modulating signal, and the
instantaneous phase deviation is proportional to the integralinstantaneous phase deviation is proportional to the integral
of the modulating signal voltage.of the modulating signal voltage.
instantaneous frequency ( )
rad cycles
and ( ) 2 '( ) 2 '( ) rad/s
cycle s
i
i c c
f t
t f t f tω π θ π θ
=
  
= + = + ÷ ÷
  

10. DEVIATION SENSITIVITYDEVIATION SENSITIVITY
 For modulating signalFor modulating signal vvmm(t),(t), the frequency modulation arethe frequency modulation are
frequency modulationfrequency modulation == θθ’(t) = k’(t) = kffvvmm(t)(t) rad/srad/s
wherewhere kkff are constant and are the deviation sensitivities of theare constant and are the deviation sensitivities of the
frequency modulator.frequency modulator.
 Deviation sensitivities are the output-versus-input transferDeviation sensitivities are the output-versus-input transfer
function for the modulators, which gave the relationshipfunction for the modulators, which gave the relationship
between what output parameter changes in respect tobetween what output parameter changes in respect to
specified changes in the input signal.specified changes in the input signal.
 frequency modulator,frequency modulator,
rad/s
V
fk
V
ω∆ 
=  ÷
∆ 

11. FREQUENCY MODULATIONFREQUENCY MODULATION
(FM)(FM)
 VariationVariation ofof ddθθ/dt/dt producesproduces FrequencyFrequency
ModulationModulation
 Frequency modulation implies thatFrequency modulation implies that ddθθ/dt/dt isis
proportional to the modulating signal.proportional to the modulating signal.
 This yieldsThis yields [ ]( ) sin ( )
sin '( )
sin ( )
sin sin ( )
sin cos ( )
FM c c
c c
c c f m
c c f m m
f m
c c m
m
v t V t t
V t t dt
V t k v t dt
V t k V t dt
k V
V t t
ω θ
ω θ
ω
ω ω
ω ω
ω
= +
 = +
 
 = +
 
 = +
 
 
= − 
 
∫
∫
∫

12. Example 4.1Example 4.1
( )
( )
( )
( )
( ) cos ( )
( ) cos
for PM
( ) cos ( )
cos cos( )
c c
m m m
PM c c p m
c c p m m
v t V t t
v t V t
v t V t k v t
V t k V t
ω θ
ω
ω
ω ω
= +
=
= +
= +
( )
( )
( )
for FM
( ) cos ( )
cos cos( )
cos cos( )
cos sin( )
FM c c f m
c c f m m
c c f m m
f m
c c m
m
v t V t k v t dt
V t k V t dt
V t k V t dt
k V
V t t
ω
ω ω
ω ω
ω ω
ω
= +
= +
= +
 
= + ÷
 
∫
∫
∫
Derive the FM signal using both cosine waveDerive the FM signal using both cosine wave
signal.signal.

13. Figure 4.2: Phase and Frequency modulation ; (a) carrier signal (b) modulating
signal (c) frequency modulated wave (d) phase modulated wave
FM WAVEFORMFM WAVEFORM

14.  Carrier amplitude remains constantCarrier amplitude remains constant
 Carrier frequency is changed by the modulating signal.Carrier frequency is changed by the modulating signal.
 amplitude of the information signal varies, the carrier frequency shiftamplitude of the information signal varies, the carrier frequency shift
proportionately.proportionately.
 modulating signal amplitude increases, the carrier frequency increases.modulating signal amplitude increases, the carrier frequency increases.
 modulating signal amplitude varies, the carrier frequency varies below andmodulating signal amplitude varies, the carrier frequency varies below and
above it normal center or resting, frequency with no modulation.above it normal center or resting, frequency with no modulation.
 The amount of the change in carrier frequency produced by theThe amount of the change in carrier frequency produced by the
modulating signal known as frequency deviation fmodulating signal known as frequency deviation fdd..
 Maximum frequency deviation occurs at the maximum amplitudeMaximum frequency deviation occurs at the maximum amplitude
of the modulating signal.of the modulating signal.
 The frequency of the modulating signal determines the frequencyThe frequency of the modulating signal determines the frequency
deviation ratedeviation rate

15. MODULATION INDEXMODULATION INDEX
 Directly proportional to the amplitude of the modulating signalDirectly proportional to the amplitude of the modulating signal
and inversely proportional to the frequency of the modulatingand inversely proportional to the frequency of the modulating
signalsignal
 Ratio of the frequency deviation and the modulating frequencyRatio of the frequency deviation and the modulating frequency
 FM equation :FM equation :
 ββ as modulation index :as modulation index :
 Example:Example:
 Determine the modulation index for FM signal with modulating frequencyDetermine the modulation index for FM signal with modulating frequency
is 10KHz deviated by ±10kHz.is 10KHz deviated by ±10kHz.
 Answer : (20KHz/10KHz) = 2 .0 (unitless)Answer : (20KHz/10KHz) = 2 .0 (unitless)
 The total frequency change, 10kHz x 2 is called theThe total frequency change, 10kHz x 2 is called the carrier swingcarrier swing
[ ]( ) sin cos ( )FM c c mv t V t tω β ω= −
f m c
m m
k V f
f
β
ω
∆
= =

16. Example:Example:
 a simple transmitter with an assigned rest frequency of 100MHza simple transmitter with an assigned rest frequency of 100MHz
deviated by a ±25kHz, the carrier changes frequency with modulationdeviated by a ±25kHz, the carrier changes frequency with modulation
between the limits of 99.975MHz and 100.025MHzbetween the limits of 99.975MHz and 100.025MHz
 The total frequency change, 25kHz x 2 is called theThe total frequency change, 25kHz x 2 is called the carrier swingcarrier swing
 Table 1 display the transmission band that use FM and the legalTable 1 display the transmission band that use FM and the legal
frequency deviation limit for each categoryfrequency deviation limit for each category
 Deviation limits are based on the quality of the intendedDeviation limits are based on the quality of the intended
transmissions, wider deviation results in higher fidelitytransmissions, wider deviation results in higher fidelity
 The frequency deviation is a useful parameter for determining theThe frequency deviation is a useful parameter for determining the
bandwidth of the FM-signalsbandwidth of the FM-signals

17. Specifications for transmission of FM signal

Table 1 display the transmission band that use FM and the legalTable 1 display the transmission band that use FM and the legal
frequency deviation limit for each categoryfrequency deviation limit for each category

18. PERCENT MODULATIONPERCENT MODULATION
 Simply the ratio of the frequency deviation actuallySimply the ratio of the frequency deviation actually
produced to the maximum frequency deviation allowed byproduced to the maximum frequency deviation allowed by
law stated in percent formlaw stated in percent form
 ForFor exampleexample if a given modulating signal produces ±50kHzif a given modulating signal produces ±50kHz
frequency deviation, and the law stated that maximumfrequency deviation, and the law stated that maximum
frequency deviation allowed is ±75kHz, thenfrequency deviation allowed is ±75kHz, then
max
% modulation actualf
f
∆
=
∆
50
% modulation = 100 67%
75
kHz
kHz
× =

19. A 1 MHz carrier freq with a measured sensitivity of 3A 1 MHz carrier freq with a measured sensitivity of 3
kHz/V is modulated with a 2 V, 4 kHz sinusoid.kHz/V is modulated with a 2 V, 4 kHz sinusoid.
DetermineDetermine
1. the max freq deviation of the carrier1. the max freq deviation of the carrier
2. the modulation index2. the modulation index
3. the modulation index if the modulation voltage is3. the modulation index if the modulation voltage is
doubleddoubled
4. the modulation index for v4. the modulation index for vmm(t)=2cos[2π(8kHz)t)]V(t)=2cos[2π(8kHz)t)]V
5. express the FM signal mathematically for a cosine5. express the FM signal mathematically for a cosine
carrier & the cosine-modulating signal of part 4. Carriercarrier & the cosine-modulating signal of part 4. Carrier
amplitude is 10Vamplitude is 10V
Example 4.2Example 4.2

21. FM RADIO FREQUENCYFM RADIO FREQUENCY
 Commercial radio FM band, 88MHz – 108MHzCommercial radio FM band, 88MHz – 108MHz
 Each station allotted to a frequency deviation ofEach station allotted to a frequency deviation of
±75kHz (150 carrier swing) and 25kHz of guard±75kHz (150 carrier swing) and 25kHz of guard
band added above and below the carrierband added above and below the carrier
frequency swingfrequency swing
 Total bandwidth is 200kHzTotal bandwidth is 200kHz
 Therefore, maximum of 100 stations can beTherefore, maximum of 100 stations can be
made availablemade available

22. FREQUENCYFREQUENCY
ANALYSIS OF FMANALYSIS OF FM
WAVESWAVES

23. Tabulated value for Bessel Function for the first kind of the nth
order
BESSEL TABLEBESSEL TABLE
, β

24.  The first column gives the modulation , while the first row gives theThe first column gives the modulation , while the first row gives the
Bessel function.Bessel function.
 The remaining columns indicate the amplitudes of the carrier and theThe remaining columns indicate the amplitudes of the carrier and the
various pairs of sidebands.various pairs of sidebands.
 Sidebands with relative magnitude of less than 0.001 have beenSidebands with relative magnitude of less than 0.001 have been
eliminated.eliminated.
 Some of the carrier and sideband amplitudes have negative signs. ThisSome of the carrier and sideband amplitudes have negative signs. This
means that the signal represented by that amplitude is simply shifted inmeans that the signal represented by that amplitude is simply shifted in
phase 180phase 180°° (phase inversion).(phase inversion).
 The spectrum of a FM signal varies considerably in bandwidthThe spectrum of a FM signal varies considerably in bandwidth
depending upon the value of the modulation index. The higher thedepending upon the value of the modulation index. The higher the
modulation index, the wider the bandwidth of the FM signal.modulation index, the wider the bandwidth of the FM signal.
 With the increase in the modulation index, the carrier amplitudeWith the increase in the modulation index, the carrier amplitude
decreases while the amplitude of the various sidebands increases. Withdecreases while the amplitude of the various sidebands increases. With
some values of modulation index, the carrier can disappear completely.some values of modulation index, the carrier can disappear completely.

25. Bessel Function, Jn(m) vs m

26.  Property - 1:Property - 1:
ForFor nn even,even,
we havewe have JJnn((ββ) = J) = J-n-n((ββ))
ForFor nn odd,odd,
we havewe have JJnn((ββ) = (-1) J) = (-1) J-n-n((ββ))
Thus,Thus,
JJnn((ββ) = (-1)) = (-1)nn
JJ-n-n ((ββ))
 Property - 2:Property - 2:
For small values of the modulation indexFor small values of the modulation index ββ,, we havewe have
JJ00((ββ)) ≅≅ 11
JJ11((ββ)) ≅≅ ββ/2/2
JJ33((ββ)) ≅≅ 00 forfor n > 2n > 2
Property - 3:
2
( ) 1n
n
J β
∞
=−∞
=∑
PROPERTIES OF BESSELPROPERTIES OF BESSEL
FUNCTIONFUNCTION

27. AMPLITUDE SPECTRUMAMPLITUDE SPECTRUM
Amplitude spectrum of different value of β

28. FM BANDWIDTHFM BANDWIDTH
 The total BW of an FM signal can be determined by knowing theThe total BW of an FM signal can be determined by knowing the
modulation index and Bessel function.modulation index and Bessel function.
N = number of significant sidebandsN = number of significant sidebands
ffmm = modulating signal frequency (Hz)= modulating signal frequency (Hz)
 Another way to determine the BW is use Carson’s ruleAnother way to determine the BW is use Carson’s rule
 This rule recognizes only the power in the most significantThis rule recognizes only the power in the most significant
sidebands with amplitude greater than 2% of the carrier.sidebands with amplitude greater than 2% of the carrier.
NfBW m2=

29. Example 4.3Example 4.3
Calculate the bandwidth occupied by a FM signal with aCalculate the bandwidth occupied by a FM signal with a
modulation index of 2 and a highest modulating frequency ofmodulation index of 2 and a highest modulating frequency of
2.5 kHz. Determine bandwidth with table of Bessel functions.2.5 kHz. Determine bandwidth with table of Bessel functions.
Referring to the table, this produces 4 significant pairs ofReferring to the table, this produces 4 significant pairs of
sidebands.sidebands.
2 4 2.5
20kHz
BW = × ×
=

30. CARSON’S RULECARSON’S RULE
ffd (max)d (max) = max. frequency deviation= max. frequency deviation
ffm(max)m(max) = max. modulating frequency= max. modulating frequency
 Carson’s rule always give a lower BW calculated with theCarson’s rule always give a lower BW calculated with the
formula BW = 2fformula BW = 2fmmN.N.
 Consider only the power in the most significant sidebandsConsider only the power in the most significant sidebands
whose amplitudes are greater than 1% of the carrier.whose amplitudes are greater than 1% of the carrier.
 Rule for the transmission bandwidth of an FM signalRule for the transmission bandwidth of an FM signal
generated by a single of frequencygenerated by a single of frequency ffmm as follows:as follows:
][2 (max)(max) md ffBW +=
( )
12 2 2 (1 )
or = 2 1
T m
m
B BW f f f
f
β
β
= ≅ ∆ + = ∆ +
+

31. Example 4.4Example 4.4
For an FM modulator with a modulation indexFor an FM modulator with a modulation index ββ ==
11, a modulating signal, a modulating signal
vvmm(t) = V(t) = Vmmsin(2sin(2ππ1000t) and unmodulated carrier1000t) and unmodulated carrier
vvcc(t) = 10sin(2(t) = 10sin(2ππ500kt), determine500kt), determine
a)a) Number of sets of significant sidebandNumber of sets of significant sideband
b)b) Their amplitudeTheir amplitude
c)c) Then draw the frequency spectrum showing theirThen draw the frequency spectrum showing their
relative amplitudesrelative amplitudes

32. Example 4.5Example 4.5
For an FM modulator with a peak freq deviationFor an FM modulator with a peak freq deviation ΔΔff
= 10kHz, a modulating signal freq f= 10kHz, a modulating signal freq fmm= 10kHz, V= 10kHz, Vcc
=10V and 500kHz carrier, determine=10V and 500kHz carrier, determine
a)a) Actual minimum bandwidth from the BesselActual minimum bandwidth from the Bessel
function tablefunction table
b)b) Approximate minimum bandwidth using Carson’sApproximate minimum bandwidth using Carson’s
rulerule
c)c) Plot the output freq spectrum for the BesselPlot the output freq spectrum for the Bessel
approximationapproximation

33. DEVIATION RATIO (DR)DEVIATION RATIO (DR)
 Minimum bandwidth is greatest when maximum freqMinimum bandwidth is greatest when maximum freq
deviation is obtained with the maximum modulatingdeviation is obtained with the maximum modulating
signal frequencysignal frequency
 Worst case modulation index and is equal to theWorst case modulation index and is equal to the
maximum peak frequency deviation divided by themaximum peak frequency deviation divided by the
maximum modulating signal frequencymaximum modulating signal frequency
 Worst case modulation index produces the widestWorst case modulation index produces the widest
output frequency spectrumoutput frequency spectrum
 Mathematically,Mathematically,
max
(max)
max peak freq deviation
DR
max mod signal freq m
f
f
∆
= =

34. Example 4.6Example 4.6
• Determine the deviation ratio and bandwidth forDetermine the deviation ratio and bandwidth for
the worst case (widest bandwidth) modulationthe worst case (widest bandwidth) modulation
index for an FM broadcast band transmitter with aindex for an FM broadcast band transmitter with a
maximum frequency deviation of 75kHz and amaximum frequency deviation of 75kHz and a
maximum modulating signal frequency of 15kHzmaximum modulating signal frequency of 15kHz
• Determine the deviation ratio and maximumDetermine the deviation ratio and maximum
bandwidth for an equal modulation index with onlybandwidth for an equal modulation index with only
half the peak frequency deviation and modulatinghalf the peak frequency deviation and modulating
signal frequencysignal frequency

35.  The power in an angle-modulated signal is easily computedThe power in an angle-modulated signal is easily computed
P = VP = VCC
22
/2R W/2R W
 Thus the power contained in the FM signal is independentThus the power contained in the FM signal is independent
of the message signal. This is an important differenceof the message signal. This is an important difference
between FM and AM.between FM and AM.
 The time-average power of an FM signal may also beThe time-average power of an FM signal may also be
obtained fromobtained from
( ) cos(2 ( ))FM c cv t V f t tπ θ= +
POWER IN ANGLE-POWER IN ANGLE-
MODULATED SIGNALMODULATED SIGNAL

36. Example 4.7Example 4.7
An FM signal is given as vAn FM signal is given as vFMFM(t)=12cos[(6π10(t)=12cos[(6π1066
t) +t) +
5sin(2π x 1250t)] V. Determine5sin(2π x 1250t)] V. Determine
a.a. freq of the carrier signalfreq of the carrier signal
b.b. freq of the modulating signalfreq of the modulating signal
c.c. modulation indexmodulation index
d.d. freq deviationfreq deviation
e.e. power dissipated in 10 ohm resistor.power dissipated in 10 ohm resistor.

37. Example 4.8Example 4.8
Determine the unmodulated carrier power for theDetermine the unmodulated carrier power for the
FM modulator given thatFM modulator given that ββ ==1, V1, Vcc=10 V, R = 50=10 V, R = 50
Ω. Then, determine the total power in the angle-Ω. Then, determine the total power in the angle-
modulated wave.modulated wave.
Solution:Solution:
 not exactly equal because values in Besselnot exactly equal because values in Bessel
table have been rounded off.table have been rounded off.

38. Example 4.9Example 4.9
An FM signal expressed asAn FM signal expressed as
is measured in a 50 ohm antenna. Determine the following :-is measured in a 50 ohm antenna. Determine the following :-
a.a. total powertotal power
b.b. modulation indexmodulation index
c.c. peak freq deviationpeak freq deviation
d.d. modulation sensitivity if 200 mV is required to achieve part cmodulation sensitivity if 200 mV is required to achieve part c
e.e. amplitude spectrumamplitude spectrum
f.f. bandwidth (99%) and approximate bandwidth by Carson’s rulebandwidth (99%) and approximate bandwidth by Carson’s rule
g.g. power in the smallest sideband of the 99% BWpower in the smallest sideband of the 99% BW
h.h. total information powertotal information power
)102sin5.0102cos(1000)( 47
tttvFM ππ +=

39. Example 4.10Example 4.10
An FM signal with 5W carrier power isAn FM signal with 5W carrier power is
fluctuating at the rate of 10000 times per secondfluctuating at the rate of 10000 times per second
from 99.96 MHz to 100.04 MHz. Findfrom 99.96 MHz to 100.04 MHz. Find
a.a. carrier freqcarrier freq
b.b. carrier swingcarrier swing
c.c. freq deviationfreq deviation
d.d. modulation indexmodulation index
e.e. power spectrumpower spectrum

40. Example 4.11Example 4.11
In an FM transmitter, the freq is changing between 100In an FM transmitter, the freq is changing between 100
MHz to 99.98 MHz, 400 times per seconds. The amplitudeMHz to 99.98 MHz, 400 times per seconds. The amplitude
of the FM signal is 5 V, determine :-of the FM signal is 5 V, determine :-
1.1. carrier and modulating freqcarrier and modulating freq
2.2. carrier freq swingcarrier freq swing
3.3. amplitude spectrumamplitude spectrum
4.4. bandwidth by using Bessel Table and Carson’s rulebandwidth by using Bessel Table and Carson’s rule
5.5. average power at the transmitter if the modulator carrieraverage power at the transmitter if the modulator carrier
power is 5 W.power is 5 W.

41. FM SIGNAL GENERATIONFM SIGNAL GENERATION
 They are two basic methods ofThey are two basic methods of
generating frequency-Modulatedgenerating frequency-Modulated
signals:signals:
 Direct MethodDirect Method
 Indirect MethodIndirect Method

42. DIRECT FMDIRECT FM
 In a direct FM system the instantaneous frequency isIn a direct FM system the instantaneous frequency is
directly varied with the information signal. To vary thedirectly varied with the information signal. To vary the
frequency of the carrier is to use an Oscillator whosefrequency of the carrier is to use an Oscillator whose
resonant frequency is determined by components that canresonant frequency is determined by components that can
be varied. The oscillator frequency is thus changed by thebe varied. The oscillator frequency is thus changed by the
modulating signal amplitude.modulating signal amplitude.
• For example, an electronic Oscillator has an outputFor example, an electronic Oscillator has an output
frequency that depends on energy-storage devices. Therefrequency that depends on energy-storage devices. There
are a wide variety of oscillators whose frequencies dependare a wide variety of oscillators whose frequencies depend
on a particular capacitor value. By varying the capacitoron a particular capacitor value. By varying the capacitor
value, the frequency of oscillation varies. If the capacitorvalue, the frequency of oscillation varies. If the capacitor
variations are controlled by vvariations are controlled by vmm(t),(t), the result is an FMthe result is an FM
( )i c f mf f k v t= +

43. INDIRECT FMINDIRECT FM
 Angle modulation includes frequency modulation FM andAngle modulation includes frequency modulation FM and
phase modulation PM.phase modulation PM.
 FM and PM are interrelated; one cannot change without theFM and PM are interrelated; one cannot change without the
other changing. The information signal frequency alsoother changing. The information signal frequency also
deviates the carrier frequency in PM.deviates the carrier frequency in PM.
 Phase modulation produces frequency modulation. SincePhase modulation produces frequency modulation. Since
the amount of phase shift is varying, the effect is that, as ifthe amount of phase shift is varying, the effect is that, as if
the frequency is changed.the frequency is changed.
 Since FM is produced by PM , the later is referred to asSince FM is produced by PM , the later is referred to as
indirect FM.indirect FM.
 The information signal is first integrated and then used toThe information signal is first integrated and then used to
phase modulate a crystal-controlled oscillator, whichphase modulate a crystal-controlled oscillator, which
provides frequency stability.provides frequency stability.

44. NOISE AND PHASE SHIFTNOISE AND PHASE SHIFT
 The noise amplitude added to an FM signalThe noise amplitude added to an FM signal
introduces a small frequency variation or phaseintroduces a small frequency variation or phase
shift, which changes or distorts the signal.shift, which changes or distorts the signal.
 Noise to signal ratio N/SNoise to signal ratio N/S
 Signal to noise ration S/NSignal to noise ration S/N
deviationallowedMaximum
noisebyproduceddeviationFrequency
S
N
=
S
NN
S 1
=

45. INTERFERENCEINTERFERENCE
 A major benefit of FM is that interfering signals on theA major benefit of FM is that interfering signals on the
same frequency will be effectively rejected.same frequency will be effectively rejected.
 If the signal of one is more than twice the amplitude of theIf the signal of one is more than twice the amplitude of the
other, the stronger signal will "capture" the channel and willother, the stronger signal will "capture" the channel and will
totally eliminate the weaker, interfering signal.totally eliminate the weaker, interfering signal.
 This is known as theThis is known as the capture effectcapture effect in FM.in FM.
 In FM, the capture effect allows the stronger signal toIn FM, the capture effect allows the stronger signal to
dominate while the weaker signal is eliminated.dominate while the weaker signal is eliminated.
 However, when the strengths of the two FM signals beginHowever, when the strengths of the two FM signals begin
to be nearly the same, the capture effect may cause theto be nearly the same, the capture effect may cause the
signals to alternate insignals to alternate in their domination of the frequency.their domination of the frequency.

46.  Despite the fact that FM has superior noise rejectionDespite the fact that FM has superior noise rejection
qualities, noise still interferes with an FM signal. This isqualities, noise still interferes with an FM signal. This is
particularly true for the high-frequency components in theparticularly true for the high-frequency components in the
modulating signal.modulating signal.
 Since noise is primarily sharp spikes of energy, it contains aSince noise is primarily sharp spikes of energy, it contains a
considerable number of harmonics and other high-considerable number of harmonics and other high-
frequency components.frequency components.
 These high frequencies can at times be larger in amplitudeThese high frequencies can at times be larger in amplitude
than the high-frequency content of the modulating signal.than the high-frequency content of the modulating signal.
 This causes a form of frequency distortion that can makeThis causes a form of frequency distortion that can make
the signal unintelligible.the signal unintelligible.
 To overcome this problem Most FM system use aTo overcome this problem Most FM system use a
technique known as Pre-emphasis and De-emphasis.technique known as Pre-emphasis and De-emphasis.