Diese Präsentation wurde erfolgreich gemeldet.
Wir verwenden Ihre LinkedIn Profilangaben und Informationen zu Ihren Aktivitäten, um Anzeigen zu personalisieren und Ihnen relevantere Inhalte anzuzeigen. Sie können Ihre Anzeigeneinstellungen jederzeit ändern.
Nächste SlideShare
×

# Chapter 5

9.855 Aufrufe

Veröffentlicht am

Frequency Modulation

Veröffentlicht in: Bildung
• Full Name
Comment goes here.

Are you sure you want to Yes No

Sind Sie sicher, dass Sie …  Ja  Nein
Ihre Nachricht erscheint hier

### 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