Chapter 5
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The document discusses angle modulation and demodulation in communication systems, focusing on non-linear modulation, bandwidth analysis, and methods for generating and demodulating FM signals. Key topics include how frequency and phase modulation work, the differences in bandwidth between amplitude modulation (AM) and frequency modulation (FM), and practical approaches to FS wave generation using direct and indirect methods. Additionally, it outlines the challenges related to bandwidth analysis of angle-modulated waves and the necessary techniques for demodulating FM signals.
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![3/23/2014
11
Bandwidth of Angle‐Modulated Waves
• Because n! increases much faster than |kfa(t)|n
Dr. Sarmad Ullah Khan
Narrow Band Angle Modulation
• When kf is very small such that
|k (t)| << 1
0
!
)(
n
tak nn
f
|kfa(t)| << 1
then
• This approximation is linear like AM expression
21
]sin)([cos)( ttaktAt cfcFM
Bandwidth of Angle‐Modulated Waves
• Bandwidth of a(t) is B, bandwidth of is 2B
• Narrow band PM signal is approximated as
Dr. Sarmad Ullah Khan
)(tFM
• Narrow band PM signal is approximated as
• NBPM has approximate bandwidth of 2B
]sin)([cos)( ttmktAt cPcPM
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Chapter 5
- 1. 3/23/2014 1 Communication Systems Instructor: Engr. Dr. Sarmad Ullah Khan Assistant ProfessorAssistant Professor Electrical Engineering Department CECOS University of IT and Emerging Sciences Sarmad@cecos.edu.pk Chapter 5 Dr. Sarmad Ullah Khan Angle Modulation and Demodulation 2
- 2. 3/23/2014 2 Outlines • Non Linear Modulation B d idth f A l M d l t d W Dr. Sarmad Ullah Khan • Bandwidth of Angle‐Modulated Waves • Generating FM Waves • Demodulation of FM Signals 3 Outlines • Non Linear Modulation B d idth f A l M d l t d W Dr. Sarmad Ullah Khan • Bandwidth of Angle‐Modulated Waves • Generating FM Waves • Demodulation of FM Signals 4
- 3. 3/23/2014 3 Non Linear Modulation • Modulation of carrier signal can be achieved by amplitude phase and frequency Dr. Sarmad Ullah Khan amplitude, phase and frequency • Modulating amplitude results in amplitude modulation • Modulating frequency results in frequency modulation • Modulating phase results in phase modulationg p p • Frequency modulation and phase modulation collectively called angle modulation 5 Non Linear Modulation • Noise power reduction • Reduce bandwidth by using modulation schemes Dr. Sarmad Ullah Khan • Reduce bandwidth by using modulation schemes • Bandwidth reduction means more users • FM varies frequency of carrier w.r.t. signal m(t) w(t) = wc(t) + km(t) • If mp is peak amplitude of m(t) M d i l f i f ld b• Max. and min. value of carrier frequency would be wc + kmp , wc - kmp • Spectral component remains with the band of 2kmp 6
- 4. 3/23/2014 4 Non Linear Modulation • Means k control the bandwidth • In practice it was not true Dr. Sarmad Ullah Khan • In practice, it was not true • FM bandwidth is greater than AM bandwidth • AM varies the amplitude of carrier signal while FM varies the instantaneous frequency of carrier signal • Means carrier frequency change continuously• Means carrier frequency change continuously • Consider a sinusoidal signal 7 )(cos)( tAt Non Linear Modulation • (t) = instantaneous phase (radians) • Hypothetical case of (t) Dr. Sarmad Ullah Khan Hypothetical case of (t) • Acos(wct + 0) • (t) tangent to (wct + 0) at ‘t’ • When ∆t→0 Acos(wct + 0) = Acos(t) • Angular frequency of is wc 8 )cos()( 0 tAt c 21 ttt )(t
- 5. 3/23/2014 5 Non Linear Modulation • (t) = instantaneous phase (radians) • (w t + ) is slop to (t) Dr. Sarmad Ullah Khan • (wct + 0) is slop to (t) • Instantaneous frequency wi at any instant is a slop to (t) dt d twi )( • Angle of carrier vary with m(t) 9 dwt t ii )()( Non Linear Modulation • In PM, angle (t) vary linearly with m(t): Dr. Sarmad Ullah Khan • kp is constant and wc is carrier frequency • When 0 = 0 PM )(cos tmktwA pc dtktdd )()()( • The wi varies linearly with the derivative of modulating signal 10 )(twi dt tdm kwc dt tmktwd dt td p pci )()()(
- 6. 3/23/2014 6 Non Linear Modulation • As wi varies linearly with modulating signal, we have FM Dr. Sarmad Ullah Khan have FM )(twi )(tmkw fc )(ti dmktwdw t fc t i )()( FM t fc dmktwA )(cos 11 Non Linear Modulation Dr. Sarmad Ullah Khan )(ti )(tmktw pc PM PM )(twi )(cos tmktwA pc dt tdm kwc dt tmktwd dt td p pci )()()( FM )(twi )(tmkw fc 12TASK: Make block diagrams of PM and FM modulators f )(ti dmktwdw t fc t i )()( FM t fc dmktwA )(cos
- 7. 3/23/2014 7 Non Linear Modulation Dr. Sarmad Ullah Khan )(ti PM )(tmktw pc )(cos tmktwA pc PM PM )(tw i )(pc dt tdm kwc dt tmktwd dt td p pci )()()( Direct Phase modulator PM wave Modulating signal source twAcos 13 twA ccos Indirect Modulating signal source Differentiator Frequency modulator PM wave twA ccos Non Linear Modulation Dr. Sarmad Ullah Khan FM )(twi )(tmkw fc )(ti dmktwdw t fc t i )()( Direct Modulating signal source Frequency modulator FM wave twAcos fci FM t fc dmktwA )(cos 14 Indirect twA ccos Integrator Phase modulator FM wave Modulating signal source twA ccos
- 9. 3/23/2014 9 Outlines • Non Linear Modulation B d idth f A l M d l t d W Dr. Sarmad Ullah Khan • Bandwidth of Angle‐Modulated Waves • Generating FM Waves • Demodulation of FM Signals 17 Bandwidth of Angle‐Modulated Waves • Angle modulation is non linear • Bandwidth analysis cannot be done directly by Dr. Sarmad Ullah Khan • Bandwidth analysis cannot be done directly by Fourier transform • For bandwidth of FM, let a(t) = t dm )( 18 tjwtajktaktwj FM cffc eAeAet )()]([ )( )](Re[)( tt FMFM
- 10. 3/23/2014 10 Bandwidth of Angle‐Modulated Waves • And Dr. Sarmad Ullah Khan • Modulated wave consists of unmodulated carrier plus various amplitude modulated terms 19 Bandwidth of Angle‐Modulated Waves • The signal a(t) is the integral of m(t) • If M(f) is band limited to B then A(f) is also band Dr. Sarmad Ullah Khan • If M(f) is band limited to B, then A(f) is also band limited to B • Spectrum of a2(t) is simply A(f)*A(f) and is band limited to 2B • an(t) is band limited to nB • Hence modulated wave has unmodulated carrierHence modulated wave has unmodulated carrier and spectrum of a(t), a2(t),….., an(t) centered wc • Modulated wave is not band limted • However, in practice bandwidth of FM is finite 20
- 11. 3/23/2014 11 Bandwidth of Angle‐Modulated Waves • Because n! increases much faster than |kfa(t)|n Dr. Sarmad Ullah Khan Narrow Band Angle Modulation • When kf is very small such that |k (t)| << 1 0 ! )( n tak nn f |kfa(t)| << 1 then • This approximation is linear like AM expression 21 ]sin)([cos)( ttaktAt cfcFM Bandwidth of Angle‐Modulated Waves • Bandwidth of a(t) is B, bandwidth of is 2B • Narrow band PM signal is approximated as Dr. Sarmad Ullah Khan )(tFM • Narrow band PM signal is approximated as • NBPM has approximate bandwidth of 2B ]sin)([cos)( ttmktAt cPcPM 22
- 12. 3/23/2014 12 Bandwidth of Angle‐Modulated Waves Wideband FM bandwidth Analysis • FM signal is meaningful if frequency deviation is Dr. Sarmad Ullah Khan • FM signal is meaningful if frequency deviation is large enough • Practically, kf is large such that |kfa(t)| << 1 not satisfied • Hence, we have wideband FM signal (WBFM) • Consider m(t) and its stair case )(tm Consider m(t) and its stair case • Each pulse is called cell 23 )(tm Bandwidth of Angle‐Modulated Waves Wideband FM bandwidth Analysis Dr. Sarmad Ullah Khan 24
- 13. 3/23/2014 13 Bandwidth of Angle‐Modulated Waves Wideband FM bandwidth Analysis • FM signal correspond to single cell has frequency Dr. Sarmad Ullah Khan • FM signal correspond to single cell has frequency wc+kfm(tk) and duration 1/2B • Fourier transform of sinusoidal pulses correspond to a cell is a sinc function • Minimum and maximum frequencies are wc-kfmp and wc+kfmpc f p • Peak frequency deviation and estimate FM bandwidth is 25 Bandwidth of Angle‐Modulated Waves Wideband FM bandwidth Analysis • In NBFM Dr. Sarmad Ullah Khan • In NBFM 26
- 14. 3/23/2014 14 Example Dr. Sarmad Ullah Khan 27 Outlines • Non Linear Modulation B d idth f A l M d l t d W Dr. Sarmad Ullah Khan • Bandwidth of Angle‐Modulated Waves • Generating FM Waves • Demodulation of FM Signals 28
- 15. 3/23/2014 15 Generating FM Waves • Two ways of generating FM waves – Direct Dr. Sarmad Ullah Khan – Direct – Indirect • NBFM Generation 29 Generating FM Waves • Indirect method (Armstrong) – NBFM is converted to WBFM using frequency Dr. Sarmad Ullah Khan – NBFM is converted to WBFM using frequency multiplier – Frequency multiplier is realized by a non linear device followed by bandpass filter 30
- 16. 3/23/2014 16 Generating FM Waves • Indirect method (Armstrong) Dr. Sarmad Ullah Khan – Output spectra will be at wc, 2wc, ….., nwc – Device having nonlinearity and bandpass filter called frequency multiplierfrequency multiplier – Such multiplier increase carrier freq. and freq. deviation – This is basis of Armstrong freq. modulators 31 Generating FM Waves • Indirect method (Armstrong) – Generally freq deviation is increase by factor ‘n’ which Dr. Sarmad Ullah Khan – Generally, freq. deviation is increase by factor n which also increase carrier freq. – Freq. mixing is applied to reduce carrier freq. to desire value 32
- 17. 3/23/2014 17 Generating FM Waves • Direct method Dr. Sarmad Ullah Khan – IN Hartley or Colpitt oscillators, frequency is given by – If C varies by m(t) as 33 Generating FM Waves • Direct method – Then Dr. Sarmad Ullah Khan – Then 34
- 19. 3/23/2014 19 Outlines • Non Linear Modulation B d idth f A l M d l t d W Dr. Sarmad Ullah Khan • Bandwidth of Angle‐Modulated Waves • Generating FM Waves • Demodulation of FM Signals 37 Demodulation of FM Signals Dr. Sarmad Ullah Khan 38