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Lecture 1.7. AM FM PM OOK BPSK FSK

Lecture 1.7. AM FM PM OOK BPSK FSK. AM, FM, and Digital Modulated Systems Amplitude Modulation (AM) Double Sideband Suppressed carrier (DSSC) Assymetric Sideband Signals Single sideband signals (SSB) Frequency Division Multiplexing (FDM). Bandpass Signaling Review. Where. Where.

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Lecture 1.7. AM FM PM OOK BPSK FSK

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  1. Lecture 1.7.AM FM PMOOK BPSK FSK

  2. AM, FM, and Digital Modulated Systems • Amplitude Modulation (AM) • Double Sideband Suppressed carrier (DSSC) • Assymetric Sideband Signals • Single sideband signals (SSB) • Frequency Division Multiplexing (FDM)

  3. Bandpass Signaling Review Where Where • The modulated bandpass signal can be described by Modulation Mapping function:Convert m(t) →g(t) Ref :Table4-1 • The voltage spectrum of the bandpass signal is • The PSD of the bandpass signal is

  4. Amplitude Modulation • The Complex Envelope of an AM signal is given by Ac indicates the power level of AM and m(t) is the Modulating Signal • Representation of an AM signal is given by • Ac[1+m(t)] In-phase component x(t) • If m(t) has a peak positive values of +1 and a peak negative value of -1 AM signal  100% modulated • Envelope detection can be used if % modulation is less than 100%.

  5. Amplitude Modulation An Example of a message signal m(t) Waveform for Amplitude modulation of the message signal m(t)

  6. Amplitude Modulation B An Example of message energy spectral density. Carrier component together with the message 2B Energy spectrum of the AM modulated message signal.

  7. AM – Percentage Modulation • Definition: The percentage of positive modulation on an AM signal is • The percentage of negative modulation on an AM signal is • The percentage of overall modulation is If m(t) has a peak positive values of +1 and a peak negative value of -1 AM signal  100% modulated

  8. AM Signal Waveform % Positive modulation= 50% % Negative modulation =50% Overall Modulation = 50% Amax = 1.5Ac Amin = 0.5 Ac

  9. AM – Percentage Modulation Under modulated (<100%) 100% modulated Over Modulated (>100%) Envelope Detector Can be used Envelope Detector Gives Distorted signal

  10. AM – Normalized Average Power The normalized average power of the AM signal is If the modulation contains no dc level, then The normalized power of the AM signal is Discrete Carrier Power Sideband power

  11. AM – Modulation Efficiency • Definition : The Modulation Efficiency is the percentage of the total power of the modulated signal that conveys information. Only “Sideband Components” – Convey information Modulation Efficiency: Highest efficiency for a 100% AM signal : 50% - square wave modulation Normalized Peak Envelope Power (PEP)of the AM signal: Voltage Spectrum of the AM signal: Unmodulated Carrier Spectral Component Translated Message Signal

  12. The peak envelope power (PEP) is Example 5-1. Power of an AM signal Suppose that a 5000-W AM transmitter is connected to a 50 ohm load; Without Modulation Then the constant Acis given by If the transmitter is then 100% modulated by a 1000-Hz test tone , the total (carrier + sideband) average power will be The peak voltage (100% modulation) is (2)(707) = 1414 V across the 50 ohm load. The modulation efficiency would be 33% since < m2(t) >=1/2

  13. Carrier Power Sideband power Spectrum  Modulation Efficiency  Double Side Band Suppressed Carrier (DSBSC) • Power in a AM signal is given by • DSBSC is obtained by eliminating carrier component • If m(t) is assumed to have a zero DC level, then Power  • Disadvantages of DSBSC: • Less information about the carrier will be delivered to the receiver. • Needs a coherent carrier detector at receiver

  14. DSBSC Modulation B An Example of message energy spectral density. No Extra Carrier component 2B Energy spectrum of the DSBSC modulated message signal.

  15. Carrier Recovery for DSBSC Demodulation • Coherent reference for product detection of DSBSC can not be obtained by the use of ordinary PLL because there are no spectral line components at fc.

  16. Carrier Recovery for DSBSC Demodulation • A squaring loop can also be used to obtain coherent reference carrier for product detection of DSBSC. A frequency divider is needed to bring the double carrier frequency to fc.

  17. LSSB USSB Single Sideband (SSB) Modulation • An upper single sideband (USSB) signal has a zero-valued spectrum for • A lower single sideband (LSSB) signal has a zero-valued spectrum for • SSB-AM – popular method ~ BW is same as that of the modulating signal. Note: Normally SSB refers to SSB-AM type of signal

  18. –Hilbert transform of m(t)  Where and H(f) j f -j Single Sideband Signal • Theorem :A SSB signal has Complex Envelopeand bandpass form as: Upper sign (-)  USSB Lower sign (+)  LSSB Hilbert Transform corresponds to a -900phase shift

  19. Using Recall from Chapter 4 Single Sideband Signal Proof: Fourier transform of the complex envelope Upper sign  USSB Lower sign  LSSB Upper sign  USSB If lower signs were used  LSSB signal would have been obtained

  20. Single Sideband Signal

  21. SSB - Power The normalized average power of the SSB signal Hilbert transform does not change power. SSB signal power is: Power of the modulating signal Power gain factor The normalized peak envelope (PEP) power is:

  22. Generation of SSB SSB signals have bothAM and PM. The complex envelope of SSB: For the AM component, For the PM component, Advantages of SSB • Superior detected signal-to-noise ratio compared to that of AM • SSB has one-half the bandwidth of AM or DSB-SC signals

  23. Generation of SSB • SSB Can be generated using two techniques • Phasing method • Filter Method • Phasing method This method is a special modulation type of IQ canonical form of Generalized transmitters discussed in Chapter 4 ( Fig 4.28)

  24. Generation of SSB • Filter Method The filtering method is a special case in which RF processing (with a sideband filter) is used to form the equivalent g(t), instead of using baseband processing to generate g(m) directly. The filter method is the most popular method because excellent sideband suppression can be obtained when a crystal oscillator is used for the sideband filter. Crystal filters are relatively inexpensive when produced in quantity at standard IF frequencies.

  25. Weaver’s Method for Generating SSB.

  26. Generation of VSB

  27. Frequency Divison Multiplexing

  28. AM, FM, and Digital Modulated Systems • Phase Modulation (PM) • Frequency Modulation (FM) • Generation of PM and FM • Spectrum of PM and FM • Carson’s Rule • Narrowband FM

  29. AM and FM Modulation (a) Carrier wave. (b) Sinusoidal modulating signal. (c) Amplitude-modulated signal. (d) Frequency modulated signal.

  30. Angle Modulation • We have seen that an AM signal can be represented as Note that in this type of modulation the amplitude of signal carries information. • Now we will see that information can also be carried in the angleof the signal as Here the amplitude Ac remains constant and the angle is modulated. This Modulation Technique is called the Angle Modulation Angle modulation: Vary either the Phase or the Frequency of the carrier signal • Phase Modulation and Frequency Modulation are special cases of Angle Modulation

  31. The Complex Envelope for an Angle Modulation is given by Is a constant Real envelope, The Angle-modulated Signal in time domain is given by Angle Modulation Representation of PM and FM signals: θ(t) - linear function of the modulating signal m(t) g(t) - Nonlinearfunction of the modulation. Special Case 1: For PM the phase is directly proportional to the modulating signal. i.e.; Where Dpis the Phase sensitivity of the phase modulator, having units of radians/volt. Special Case 2: For FM, the phase is proportional to the integral of m(t) so that where the frequency deviation constant Dfhas units of radians/volt-sec.

  32. Resulting PM wave: • Frequency Modulation occurs when the instantaneous frequency is varied linearly with the message signal. Dfis the frequency deviation constant Resulting FM wave: Angle Modulation • Instantaneous Frequency (fi) of a signal is defined by • Phase Modulationoccurs when the instantaneous phase varied in proportion to that of the message signal. Dp is the phase sensitivity of the modulator

  33. Phase Modulation Frequency Modulation Phase and Frequency Modulations Comparing above two equations , we see that if we have a PM signal modulated by mp(t), there is also FM on the signal, corresponding to a different modulation wave shape that is given by: Similarly if we have a FM signal modulated by mf(t),the corresponding phase modulation on this signal is: Where f and pdenote frequency and phase respectively.

  34. Generation of FM from PM and vice versa Generation of FM using a Phase Modulator: Integrator Phase Modulator (Carrier Frequency fc) FM Signal Generation of PM using a Frequency Modulator: Differentiator Frequency Modulator (Carrier Frequency fc) PM signal

  35. FM with sinusoidal modulating signal If a bandpass signal is represented by: ∆F is related to the peak modulating voltage by Where • The Peak-to-peak Deviationis given by • The Instantaneous Frequency of the FM signal is given by: • The Frequency Deviationfrom the carrier frequency: • The Peak Frequency Deviation is given by:

  36. FM with sinusoidal modulating signal Vp BW   But,  Average Power does not change with modulation

  37. Angle Modulation • Advantages: • Constant amplitude means Efficient Non-linear Power Amplifiers can be used. • Superior signal-to-noise ratio can be achieved (compared to AM) if bandwidth is sufficiently high. • Disadvantages: • Usually require more bandwidth than AM • More complicated hardware

  38. ∆θ is related to the peak modulating voltage by: Where Where ∆θis the peak phase deviation • The Phase Modulation Indexis given by: • The Frequency Modulation Indexis given by: ∆F Peak Frequency Deviation B Bandwidth of the modulating signal Modulation Index • The Peak Phase Deviationis given by:

  39. Spectrum of Angle modulated signal Where Spectra of Angle modulated signals • Spectra for AM, DSB-SC, and SSB can be obtained with simple formulas relating S(f) to M(f). • But for angle modulation signaling, because g(t) is a nonlinear function of m(t). Thus, a general formula relating G(f) to M(f) cannot be obtained. • To evaluate the spectrum for angle-modulated signal, G(f) must be evaluated on a case-by-case basis for particular modulating waveshape of interest.

  40. Then Where is the phase Modulation Index. which is periodic with period Spectrum of PM or FM Signal with Sinusoidal Modulating Signal • Assume that the modulation on the PMsignal is Same θ(t) could also be obtained if FM were used where and The peak frequency deviation would be The Complex Envelope is:

  41. Spectrum of PM or FM Signal with Sinusoidal Modulating Signal Where Which reduces to Is a special property of Bessel Functions or Using discrete Fourier series that is valid over all time, g(t) can be written as Jn(β) – Bessel function of the first kind of the nth order Taking the fourier transform of the complex envelopeg(t), we get

  42. Bessel Functions of the First Kind J0(β)=0 at β=2.4, 5.52 & so on

  43. Bessel Functions of the First Kind

  44. Frequency spectrum of FM • The FM modulated signal in time domain Observations: • From this equation it can be seen that the frequency spectrum of an FM waveform with a sinusoidal modulating signal is a discrete frequency spectrum made up of components spaced at frequencies of c± nm. • By analogy with AM modulation, these frequency components are called sidebands. • We can see that the expression for s(t) is an infinite series. Therefore the frequency spectrum of an FM signal has an infinite number of sidebands. • The amplitudes of the carrier and sidebands of an FM signal are given by the corresponding Bessel functions, which are themselves functions of the modulation index

  45. Spectra of an FM Signal with Sinusoidal Modulation • The following spectra show the effect of modulation index, , on the bandwidth of an FM signal, and the relative amplitudes of the carrier and sidebands 1.0 f BT

  46. Spectra of an FM Signal with Sinusoidal Modulation J0(1.0) 1.0 J1(1.0) J2(1.0) f BT

  47. Spectra of an FM Signal with Sinusoidal Modulation 1.0 f BT

  48. Carson’s rule • Although the sidebands of an FM signal extend to infinity, it has been found experimentally that signal distortion is negligible for a bandlimited FM signal if 98% of the signal power is transmitted. • Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+ on each side. (1+b)fm

  49. For sinusoidal modulation Note: When β =0 i.e. baseband signals Carson’s rule • Therefore the Bandwidth required is given by β – phase modulation index/ frequency modulation index B – bandwidth of the modulating signal • Carson’s rule :Bandwidth of an FM signal is given by

  50. Narrowband Angle Modulation • Narrowband Angle Modulation is a special case of angle modulation where θ(t) is restricted to a small value. • The complex envelope can be approximated by a Taylor's series in which only first two terms are used. becomes • The Narrowband Angle Modulated Signal is • The Spectrum of Narrowband Angle Modulated Signal is PM where FM

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