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Chapter 5
ANGLE MODULATION:
FREQUENCY and PHASE
MODULATIONS(FM,PM)
Outlines
• Introduction
• Concepts of instantaneous frequency
• Bandwidth of angle modulated signals
• Narrow-band and wid...
Introduction
• Angle modulation: either frequency modulation
(FM) or phase modulation (PM).
• Basic idea: vary the carrier...
• While AM is linear process, FM and PM are
highly nonlinear.
• FM/PM provide many advantages (main –
noise immunity, inte...
Concepts of Instantaneous
Frequency
• A general form of an angle modulated signal is
given by
is the instantaneous angle
i...
• The instantaneous frequency of
• The instantaneous frequency deviation
( ) ( )1 1
( )
2 2
i i
i c
d t d t
f t f
dt dt
θ ...
Example
• for the signal below find the
instantaneous frequency and maximum
frequency deviation.
2
( ) cos(10 )x t A t tπ ...
• For phase modulation (PM), the instantaneous
phase deviation is
•
kp is the phase sensitivity of the PM modulator
expres...
• For Frequency Modulation (FM), the
instantaneous phase deviation is
• kf is the frequency sensitivity of the FM
modulato...
Angle modulation viewed as FM or
PM
Phase
Modulator
Frequency
Modulator
Phase
Modulator∫
Frequency
Modulator
( )m t ( )PMS t
( )m t
( )FMS t
( )m t ( )FMS t
(...
• A PM/FM modulator may be used to
generate an FM/PM waveform
• FM is much more frequently used than PM
• All the properti...
Example 5.1
• Sketch FM and PM waves for the modulating
signal m(t) shown in Fig. 5.4a. The constants kf
and kp are 2πx105...
Example
Bandwidth of Angle Modulated
Signals
1) FM signals
[ ]
2 3
2 3
( ) cos(2 ) ( )sin(2 )
( )cos(2 ) ( )sin(2 ) ...
2! 3!
FM c...
• Narrow-Band Frequency Modulation
(NBFM):
• Narrow-Band Phase Modulation (NBPM):
[ ]( ) cos(2 ) ( )sin(2 )NBFM c f cS t A...
Generation of NBFM
m(t)
Generation of NBPM
m(t)
• If
∆f: maximum carrier frequency deviation
β: deviation ratio or modulation index
• Wide- Band Frequency Modulation (WBF...
• For phase modulation: if
π2
'
ppmk
f =∆
| ( ) | 1Pk m t ?
2( ) 2 ( 1)PMB f B B β= ∆ + = +
' '
max ( )Pm m t=
2WBPMB f= ∆
Single tone modulation
• Let
[ ])2sin(2cos)( tftfAtx mcFM πβπ +=
[ ]∑
∞
−∞=
+=
n
mcnFM tfnfJAtx )(2cos)()( πβ
( ) cos2 mm ...
• The results is valid only for sinusoidal signal
• The single tone method can be used for
finding the spectrum of an FM w...
Example 1
• A single tone FM signal is
Determine
a) the carrier frequency fc
b) the modulation index β
c) the peak frequen...
Example 2
• A 10 MHz carrier is frequency modulated by
a sinusoidal signal such that the peak
frequency deviation is ∆f=50...
Example 3
• An angle modulated signal with carrier
frequency 100kHz is
Find
a) the power of xFM(t)
b) the frequency deviat...
Example 5.3 (Txt book)
a) Estimate BFM and BPM for m(t) when
kf= 2πx105
rad/sV and kp= 5πrad/V
b) Repeat the problem if th...
Features of Angle Modulation
• Channel bandwidth may be exchanged for
improved noise performance. Such trade-off
is not po...
• FM is used for: radio broadcasting, sound
signal in TV, two-way fixed and mobile
radio systems, cellular telephone syste...
Generation of FM Signals
• There are two ways of generating FM
waves:
–Indirect generation
–Direct generation
Indirect Generation of NBFM
m(t)
Indirect Generation of
Wideband FM
• In this method, a narrowband frequency-
modulated signal is first generated and then ...
m(t)
N fc
NBFM
Frequency
Multiplier
BPF
Local Oscillator
(fLo)
xFM(t)
fc
Frequency Converter
m(t)
NBFM
Frequency
Multiplier
x64
Power
Amplifier
Crystal
Oscillator
10.9 MHz
fc1=200 kHz
∆f1= 25 Hz
Frequency
Multiplier...
Direct Generation
• The modulating signal m(t) directly controls
the carrier frequency. [ ]
• A common method is to vary t...
• In Hartley or Colpitt oscillator , the frequency is
given by
• We can show that for k m(t) << C0
LC
1
=ω






+=
...
Varactor Modulator Circuit
• Advantage - Large frequency deviations are
possible and thus less frequency multiplication
is needed.
• Disadvantage - T...
Example 5.6
• Discuss the nature of distortion inherent in the
Armstrong FM generator
–Amplitude distortion
–Frequency dis...
Example
• A given angle modulated signal has a peak
frequency deviation of 20 Hz for an input
sinusoid of unit amplitude a...
Demodulation of FM Signals
• Demodulation of an FM signal requires a
system that produces an output proportional to
the in...
• A frequency-selective network with a transfer
function of the form |H(ω)|= a ω+b over the
FM band would yield an output ...
FM demodulator by direct differentiation
• The basic idea is to convert FM into AM
and then use AM demodulator.
[ ]'
( ) 2...
Bandpass Limiter
• Input-output characteristic of a hard limiter
Hard
Limiter
BPF
• Any signal which exceeds the preset limits are
simply chopped off
Practical Frequency Demodulators
• There are several possible networks for
frequency discriminator
–FM slope detector
–Bal...
FM Slope Detector
FM Slope Detector
FM Slope Detector
Balanced Discriminator
Balanced Discriminator (Cont.)
Balanced Discriminator (Cont.)
Quadrature Demodulator
• FM is converted into PM
• PM detector is used to recover message
signal
Quadrature Demodulator
Transfer function of
Quadrature demodulator
Phase-Locked Loop (PLL)
)sin()( icin tAtv θω +=
)cos()( ocout tBtv θω +=
vout(t)
vin(t) e0(t)x(t) Loop Filter
H(s)
Voltage...
Zero-Crossing Detectors
• Zero-Crossing Detectors are also used
because of advances in digital integrated
circuits.
• Thes...
Summary
• Concepts of instantaneous frequency
• FM and PM signals
• Bandwidth of angle modulated signals
NBFM and WBFM
• G...
Suggested Problems
• 5.1-1 5.1-2 5.1-3 5.2-1 5.2-2
5.2-3 5.2-4 , 5.2-5 5.2-6 .
• 5.2-7 5.3-1 5.3-2 5.4-1 5.4-2
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
Chapter 5
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Chapter 5

  1. 1. Chapter 5 ANGLE MODULATION: FREQUENCY and PHASE MODULATIONS(FM,PM)
  2. 2. Outlines • Introduction • Concepts of instantaneous frequency • Bandwidth of angle modulated signals • Narrow-band and wide-band frequency modulations • Generation of FM signals • Demodulation of FM signals • superhetrodyne FM radio
  3. 3. Introduction • Angle modulation: either frequency modulation (FM) or phase modulation (PM). • Basic idea: vary the carrier frequency (FM) or phase (PM) according to the message signal.
  4. 4. • While AM is linear process, FM and PM are highly nonlinear. • FM/PM provide many advantages (main – noise immunity, interference, exchange of power with bandwidth ) over AM, at a cost of larger transmission bandwidth. • Demodulation may be complex, but modern ICs allow cost-effective implementation. Example: FM radio (high quality, not expensive receivers).
  5. 5. Concepts of Instantaneous Frequency • A general form of an angle modulated signal is given by is the instantaneous angle is the instantaneous phase deviation. • The instantaneous angular frequency of ( ) cos ( ) cos(2 ( ))EM i c iS t A t A f t tθ π φ= = + ( ) ( ) ( ) i i i c d t d t t dt dt θ φ ω ω= = + ( )i tθ ( )i tφ ( )EMS t
  6. 6. • The instantaneous frequency of • The instantaneous frequency deviation ( ) ( )1 1 ( ) 2 2 i i i c d t d t f t f dt dt θ φ π π = = + ( )1 ( ) 2 i i d t f t dt φ π ∆ = ( )EMS t
  7. 7. Example • for the signal below find the instantaneous frequency and maximum frequency deviation. 2 ( ) cos(10 )x t A t tπ π= +
  8. 8. • For phase modulation (PM), the instantaneous phase deviation is • kp is the phase sensitivity of the PM modulator expressed in (rad/ V) if m(t) is in Volts • The instantaneous frequency of ( ) ( )i c p dm t f t f k dt = + Phase modulation (PM) ( ) ( )i t kp m tφ = ( ) cos [2 ( )]PM c pS t A f t k m tπ= + ( )PMS t
  9. 9. • For Frequency Modulation (FM), the instantaneous phase deviation is • kf is the frequency sensitivity of the FM modulator expressed in rad/ V s if m(t) in Volts. • The instantaneous frequency of ( ) cos 2 ( ) t FM c fS t A f t k m dπ α α −∞   = +    ∫ Frequency Modulation (FM) ( ) ( ) t i ft k m dφ α α −∞ = ∫ ( )FMS t ( ) ( ) 2 f i c k f t f m t π = +
  10. 10. Angle modulation viewed as FM or PM
  11. 11. Phase Modulator Frequency Modulator Phase Modulator∫ Frequency Modulator ( )m t ( )PMS t ( )m t ( )FMS t ( )m t ( )FMS t ( )PMS t( )m t d dt
  12. 12. • A PM/FM modulator may be used to generate an FM/PM waveform • FM is much more frequently used than PM • All the properties of a PM signal may be deduced from that of an FM signal • In the remaining part of the chapter we deal mainly with FM signals.
  13. 13. Example 5.1 • Sketch FM and PM waves for the modulating signal m(t) shown in Fig. 5.4a. The constants kf and kp are 2πx105 and 10π, respectively, and the carrier frequency fc is 100 MHz..
  14. 14. Example
  15. 15. Bandwidth of Angle Modulated Signals 1) FM signals [ ] 2 3 2 3 ( ) cos(2 ) ( )sin(2 ) ( )cos(2 ) ( )sin(2 ) ... 2! 3! FM c f c f f c c S t A f t k a t f t k k A a t f t a t f t π π π π = −   + − + +    where ( ) ( ) t a t m dα α −∞ = ∫
  16. 16. • Narrow-Band Frequency Modulation (NBFM): • Narrow-Band Phase Modulation (NBPM): [ ]( ) cos(2 ) ( )sin(2 )NBFM c f cS t A f t k a t f tπ π≈ − ( ) cos(2 ) ( )sin(2 )NBPM c p cS t A f t k m t f tπ π ≈ −  BBNBFM 2= | ( ) | 1fk a t << 2NBPMB B= | ( ) | 1Pk m t <<
  17. 17. Generation of NBFM m(t)
  18. 18. Generation of NBPM m(t)
  19. 19. • If ∆f: maximum carrier frequency deviation β: deviation ratio or modulation index • Wide- Band Frequency Modulation (WBFM) |kf a(t)|>>1 or β>100 fBWBFM ∆= 2 π2 pf mk f =∆ )1(2)(2 +=+∆= βBBfBFM B f∆ =β | ( ) | 1fk a t ? max ( )Pm m t=
  20. 20. • For phase modulation: if π2 ' ppmk f =∆ | ( ) | 1Pk m t ? 2( ) 2 ( 1)PMB f B B β= ∆ + = + ' ' max ( )Pm m t= 2WBPMB f= ∆
  21. 21. Single tone modulation • Let [ ])2sin(2cos)( tftfAtx mcFM πβπ += [ ]∑ ∞ −∞= += n mcnFM tfnfJAtx )(2cos)()( πβ ( ) cos2 mm t f tα π=
  22. 22. • The results is valid only for sinusoidal signal • The single tone method can be used for finding the spectrum of an FM wave when m(t) is any periodic signal. 2 ( 1) 2 FM m f m B f k f f f β α π β = + ∆ = ∆ =
  23. 23. Example 1 • A single tone FM signal is Determine a) the carrier frequency fc b) the modulation index β c) the peak frequency deviation d) the bandwidth of xFM(t) 6 3 FMx (t)=10 cos[ 2 (10 )t+ 8 sin(2 (10 )t)]π π
  24. 24. Example 2 • A 10 MHz carrier is frequency modulated by a sinusoidal signal such that the peak frequency deviation is ∆f=50 KHz. Determine the approximate bandwidth of the FM signal if the frequency of the modulating sinusoid fm is a) 500 kHz, b) 500 Hz, c) 10 kHz.
  25. 25. Example 3 • An angle modulated signal with carrier frequency 100kHz is Find a) the power of xFM(t) b) the frequency deviation ∆f c) The deviation ratio β d) the phase deviation ∆φ e) the bandwidth of xFM(t). EM cx (t)=10 cos[ 2 f t+ 5 sin(3000 t)+10 sin(2000 t) ]π π π
  26. 26. Example 5.3 (Txt book) a) Estimate BFM and BPM for m(t) when kf= 2πx105 rad/sV and kp= 5πrad/V b) Repeat the problem if the amplitude of m(t) is doubled.
  27. 27. Features of Angle Modulation • Channel bandwidth may be exchanged for improved noise performance. Such trade-off is not possible with AM • Angle modulation is less vulnerable than AM to small signal interference from adjacent channels and more resistant to noise. • Immunity of angle modulation to nonlinearities thus used for high power systems as microwave radio.
  28. 28. • FM is used for: radio broadcasting, sound signal in TV, two-way fixed and mobile radio systems, cellular telephone systems, and satellite communications. • PM is used extensively in data communications and for indirect FM. • WBFM is used widely in space and satellite communication systems. • WBFM is also used for high fidelity radio transmission over rather limited areas.
  29. 29. Generation of FM Signals • There are two ways of generating FM waves: –Indirect generation –Direct generation
  30. 30. Indirect Generation of NBFM m(t)
  31. 31. Indirect Generation of Wideband FM • In this method, a narrowband frequency- modulated signal is first generated and then a frequency multiplier is used to increase the modulation index. m(t) NBFM xFM(t) Frequency Multiplier
  32. 32. m(t) N fc NBFM Frequency Multiplier BPF Local Oscillator (fLo) xFM(t) fc Frequency Converter
  33. 33. m(t) NBFM Frequency Multiplier x64 Power Amplifier Crystal Oscillator 10.9 MHz fc1=200 kHz ∆f1= 25 Hz Frequency Multiplier x48 fc2=12.8MHz ∆f2= 1.6 kHz fc3=1.9 MHz ∆f3= 1.6 kHz fc4= 91.2MHz ∆f4= 76.8 kHz Armstrong Indirect FM TransmitterArmstrong Indirect FM Transmitter BPF
  34. 34. Direct Generation • The modulating signal m(t) directly controls the carrier frequency. [ ] • A common method is to vary the inductance or capacitance of a voltage controlled oscillator. ( ) ( )i c ff t f k m t= +
  35. 35. • In Hartley or Colpitt oscillator , the frequency is given by • We can show that for k m(t) << C0 LC 1 =ω       += 02 )( 1 C tmk cωω 0 1 LC c =ω
  36. 36. Varactor Modulator Circuit
  37. 37. • Advantage - Large frequency deviations are possible and thus less frequency multiplication is needed. • Disadvantage - The carrier frequency tends to drift and additional circuitry is required for frequency stabilization. To stabilize the carrier frequency, a phase- locked loop can be used.
  38. 38. Example 5.6 • Discuss the nature of distortion inherent in the Armstrong FM generator –Amplitude distortion –Frequency distortion
  39. 39. Example • A given angle modulated signal has a peak frequency deviation of 20 Hz for an input sinusoid of unit amplitude and a frequency of 50 Hz. Determine the required frequency multiplication factor, N, to produce a peak frequency deviation of 20 kHz when the input sinusoid has unit amplitude and a frequency of 100Hz, and the angle-modulation used is (a) FM; (b) PM
  40. 40. Demodulation of FM Signals • Demodulation of an FM signal requires a system that produces an output proportional to the instantaneous frequency deviation of the input signal. • Such system is called a frequency discriminator. FM Demodulator [ ])(cos)( ttAtx c φω += dt td kty )( )( φ =
  41. 41. • A frequency-selective network with a transfer function of the form |H(ω)|= a ω+b over the FM band would yield an output proportional to the instantaneous frequency. • There are several possible examples for frequency discriminator, the simplest is the FM demodulator by direct differentiation
  42. 42. FM demodulator by direct differentiation • The basic idea is to convert FM into AM and then use AM demodulator. [ ]' ( ) 2 ( ) sin 2 ( ) t c c f c fs t A f k m t f t k m dπ π α α −∞   = − + +    ∫
  43. 43. Bandpass Limiter • Input-output characteristic of a hard limiter Hard Limiter BPF
  44. 44. • Any signal which exceeds the preset limits are simply chopped off
  45. 45. Practical Frequency Demodulators • There are several possible networks for frequency discriminator –FM slope detector –Balanced discriminator – Quadrature Demodulator • Another superior technique for the demodulation of the FM signal is to use the Phased locked loop (PLL)
  46. 46. FM Slope Detector
  47. 47. FM Slope Detector
  48. 48. FM Slope Detector
  49. 49. Balanced Discriminator
  50. 50. Balanced Discriminator (Cont.)
  51. 51. Balanced Discriminator (Cont.)
  52. 52. Quadrature Demodulator • FM is converted into PM • PM detector is used to recover message signal
  53. 53. Quadrature Demodulator
  54. 54. Transfer function of Quadrature demodulator
  55. 55. Phase-Locked Loop (PLL) )sin()( icin tAtv θω += )cos()( ocout tBtv θω += vout(t) vin(t) e0(t)x(t) Loop Filter H(s) Voltage-Controlled Oscillator (VCO) dt td kte i )( )(0 θ =
  56. 56. Zero-Crossing Detectors • Zero-Crossing Detectors are also used because of advances in digital integrated circuits. • These are the frequency counters designed to measure the instantaneous frequency by the number of zero crossings. • The rate of zero crossings is equal to the instantaneous frequency of the input signal
  57. 57. Summary • Concepts of instantaneous frequency • FM and PM signals • Bandwidth of angle modulated signals NBFM and WBFM • Generation of FM signals – Direct and indirect generation • Demodulation of FM signals – frequency discriminator – PLL
  58. 58. Suggested Problems • 5.1-1 5.1-2 5.1-3 5.2-1 5.2-2 5.2-3 5.2-4 , 5.2-5 5.2-6 . • 5.2-7 5.3-1 5.3-2 5.4-1 5.4-2

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