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ANALOG COMMUNICATIONS
LECTURE NOTES-31
UNIT-IV
UNIT-IV
ANGLE MODULATION
Notes-31
Generation of FM Waves:
There are two methods of generating frequency modulating wave namely
indirect FM and Direct FM.
Indirect FM :
In this first consider the generation of a narrow-band FM Wave.
Consider the expression for FM Wave
S1 (t ) = A1 cos[2πf 1t + φ1 (t )]
Where f1 is the carrier frequency and
A1 is the carrier amplitude.
Now the argument φ1(t) is given by
t
φ1

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ANALOG COMMUNICATIONS UNIT-IV LECTURE NOTES-31 D.TIRUMALA RAO ECE GMRIT Page 1 of 3 Ref: Analog & Digital Communications Simon Haykins
UNIT-IV ANGLE MODULATION
Notes-31 Generation of FM Waves:
There are two methods of generating frequency modulating wave namely indirect FM and Direct FM.
Indirect FM :
In this first consider the generation of a narrow-band FM Wave.
Consider the expression for FM Wave
[ ]
)(2cos)(
1111
t t f At S
φ π
+=
Where f
1
is the carrier frequency and A
1
is the carrier amplitude.
Now the argument
φ
1
(t) is given by )2()(2)(
011
−=
∫
t
dt t mK t
φ
Where K
1
is the frequency sensitivity of the modulator And
φ
1
(t) is assumed to small for all t.
[ ][ ]
)4()()(sin
)3(1)(cos
111
−≈−≈
t t and t
φ φ φ
The FM wave equation (1) becomes )5()(2sin22cos
)(2sin2cos)(
01111
111111
−−=−=
∫
dt t mt f At f A
t t f At f At S
t
π π π φ π π
The above narrow band FM wave can be generated as shown in figure below.
The above expression shows difference with standard form in two ways: i. the envelope contains a residual amplitude modulation which varies with time and
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ANALOG COMMUNICATIONS UNIT-IV LECTURE NOTES-31 D.TIRUMALA RAO ECE GMRIT Page 2 of 3 Ref: Analog & Digital Communications Simon Haykins ii. for a sinusoidal modulating wave, the phase of the FM wave contains harmonic distortion in the form of 3
rd
& higher order harmonics of modulation frequency f
m
.
The above two can be reduced by maintaining the modulation index
β
≤
0.3.
Now the narrow band fm wave can be made wideband fm by passing through a frequency multiplier.
The frequency multiplier consists of a non-linear device and a bandpass filter as shown in fig. below.
In this the memory less non-linear device has input-output relation )6()(............)()()(
1212112
−+++=
t S at S at S at S
nn
Where a
1
, a
2
……… a
n
are constant coefficients.
Substituting (5) in (6), the expression S
2
(t) has a dc component and in frequency modulated waves with carrier frequencies f
1
, 2f
2
……nf, and frequency deviations
∆
f
1
, 2
∆
f
2
……n
∆
f
1
respectively.
Here
∆
f
1
can be determined by frequency sensitivity K
1
of narrow-band frequency modulator and maximum amplitude of the modulating wave m(t)
The band-pass filter is used in 2 respects. i. to pass the fm wave centered at the carrier frequency nf1 with frequency deviation n
∆
f
1
ii. to suppress all other FM spectra.
Now the narrow-band frequency modulator and frequency multiplier are connected to produce a wideband frequency modulated wave S(t) with carrier frequency nf1 and frequency deviation
∆
f= n
∆
f
1
as shown in fig. below.
Now the frequency sensitivity of wideband modulator Kf is n times that of a narrow-band modulator.
Crystal oscillator is used for more stability at high frequencies.
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ANALOG COMMUNICATIONS UNIT-IV LECTURE NOTES-31 D.TIRUMALA RAO ECE GMRIT Page 3 of 3 Ref: Analog & Digital Communications Simon Haykins
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