EKT358 Communication Systems

Transcription

1 EKT358 Communiation Systems

2 Chapter 2 Amplitude Modulation

3 Topis Covered in Chapter 2 2-1: AM Conepts 2-2: Modulation Index and Perentage of Modulation 2-3: Sidebands and the Frequeny Domain 2-4: Single-Sideband Modulation 2-5: AM Power

4 2-1: AM Conepts In the modulation proess, the voie, video, or digital signal modifies another signal alled the arrier. In amplitude modulation (AM) the information signal varies the amplitude of the arrier sine wave. The instantaneous value of the arrier amplitude hanges in aordane with the amplitude and frequeny variations of the modulating signal. An imaginary line alled the envelope onnets the positive and negative peaks of the arrier waveform.

5 2-1: AM Conepts

6 2-1: AM Conepts Figure 1-1: Amplitude modulation. (a) The modulating or information signal.

7 2-1: AM Conepts Figure 1-2: Amplitude modulation. (b) The modulated arrier.

8 2-1: AM Conepts In AM, it is partiularly important that the peak value of the modulating signal be less than the peak value of the arrier. V m < V Distortion ours when the amplitude of the modulating signal is greater than the amplitude of the arrier. A modulator is a iruit used to produe AM. Amplitude modulators ompute the produt of the arrier and modulating signals.

9 2-1: AM Conepts Figure 1-3: Amplitude modulator showing input and output signals.

10 The Mathematial Representation and Analysis of AM Representing both the modulating signal V m (t) and the arrier signal V (t) in trigonometri funtions. The AM DSBFC modulator must be able to produe mathematial multipliation of these two analog signals v m ( t) V sin (2 f t) m m v am ( t) [ V V sin (2 f t)] sin (2 f t) m m v ( t) V sin (2 f t) EKT343 Priniple of Communiation Engineering 10

11 Cont d Substituting V m = mv gives: v am ( t) [ V [1 m mv sin (2 f sin (2 f m m t)] V t)] sin (2 f t)] sin (2 f t)] Constant + mod. signal Unmodulated arrier EKT343 Priniple of Communiation Engineering 11

12 Cont d The onstant in the first term produes the arrier freq while the sinusoidal omponent in the first term produes side bands frequenies v am ( t) Carrier frequeny signal (volts) V V sin (2 f t) [ mv sin (2 f t) mv 2 os[2 ( f mv 2 Lower side frequeny signal (volts) sin (2 f os[2 ( f f m ) t] m t)][sin (2 f t)] f m ) t] Upper side frequeny signal (volts) EKT343 Priniple of Communiation Engineering 12

13 Cont d From the equation it is obvious that the amplitude of the arrier is unaffeted by the modulation proess. The amplitude of the side frequenies depend on the both the arrier amplitude and modulation index. At 100% modulation the amplitudes of side frequenies are eah equal to one-half the amplitude of the arrier. EKT343 Priniple of Communiation Engineering 13

14 2-2: Modulation Index and Perentage of Modulation Figure 1-5: AM wave showing peaks (V max ) and troughs (V min ).

15 2-2: Modulation Index and Perentage of Modulation The modulation index (m) is a value that desribes the relationship between the amplitude of the modulating signal and the amplitude of the arrier signal. It is the term used to desribe the amount of amplitude hange(modulation) present in the an AM waveform. m = V m / V This index is also known as the modulating fator or oeffiient, or the degree of modulation. Multiplying the modulation index by 100 gives the perentage of modulation.

16 2-2: Modulation Index and Perentage of Modulation Perentage of Modulation The modulation index is ommonly omputed from measurements taken on the omposite modulated waveform. Using osillosope voltage values: Vm = V max V min 2 The amount, or depth, of AM is then expressed as the perentage of modulation (100 m) rather than as a fration.

17 Determining modulation index from V max and V min EKT343 Priniple of Communiation Engineering 17

18 Cont d Mathematially, the modulation index is m = modulation index E m = peak hange in the amplitude output waveform (sum of voltages from upper and lower side frequenies) E = peak amplitude of the unmodulated arrier m E E m And the perentage of modulation index is Em % m x100% E EKT343 Priniple of Communiation Engineering 18

19 Cont d If the modulating signal is a pure, single-freq sine wave and the proess is symmetrial then the modulation index an be derived as follows: Therefore, E E m ( V ( V max max V V min min ) ) m ( V ( V max max V V min min ) ) ( V ( V max max V V min min ) ) EKT343 Priniple of Communiation Engineering 19

20 Cont d Sine the peak hange of modulated output wave E m is the sum of the usf and lsf voltages hene, E E E where E E m usf lsf usf lsf Then E usf E lsf Em ( V 1 2 max ( V max V 2 min V ) min ) E usf = peak amplitude of the upper side frequeny (volts) E lsf = peak amplitude of the lower side frequeny (volts) EKT343 Priniple of Communiation Engineering 20

21 2-2: Modulation Index and Perentage of Modulation Overmodulation and Distortion The modulation index should be a number between 0 and 1. If the amplitude of the modulating voltage is higher than the arrier voltage, m will be greater than 1, ausing distortion. If the distortion is great enough, the intelligene signal beomes unintelligible.

22 2-2: Modulation Index and Perentage of Modulation Overmodulation and Distortion Distortion of voie transmissions produes garbled, harsh, or unnatural sounds in the speaker. Distortion of video signals produes a srambled and inaurate piture on a TV sreen.

23 2-2: Modulation Index and Perentage of Modulation Figure 1-4: Distortion of the envelope aused by overmodulation where the modulating signal amplitude V m is greater than the arrier signal V.

24 2-3: Sidebands and the Frequeny Domain Side frequenies, or sidebands are generated as part of the modulation proess and our in the frequeny spetrum diretly above and below the arrier frequeny.

25 Sideband Calulations 2-3: Sidebands and the Frequeny Domain Single-frequeny sine-wave modulation generates two sidebands. Complex wave (e.g. voie or video) modulation generates a range of sidebands. The upper sideband (f USB ) and the lower sideband (f LSB ) are alulated: f USB = f + f m and f LSB = f f m

26 2-3: Sidebands and the Frequeny Domain Figure 1-6: The AM wave is the algebrai sum of the arrier and upper and lower sideband sine waves. (a) Intelligene or modulating signal. (b) Lower sideband. ( ) Carrier. (d ) Upper sideband. (e ) Composite AM wave.

27 2-3: Sidebands and the Frequeny Domain Frequeny-Domain Representation of AM Observing an AM signal on an osillosope, you see only amplitude variations of the arrier with respet to time. A plot of signal amplitude versus frequeny is referred to as frequeny-domain display. A spetrum analyzer is used to display the frequeny domain as a signal. Bandwidth is the differene between the upper and lower sideband frequenies. BW = f USB f LSB = [f + f m(max) ] [f f m(max) ] = 2f m(max)

28 2-3: Sidebands and the Frequeny Domain Figure 1-8: The relationship between the time and frequeny domains.

29 2-3: Sidebands and the Frequeny Domain Frequeny-Domain Representation of AM Example 1: For a onventional AM modulator with a arrier freq of f = 100 khz and the maximum modulating signal frequeny of f m(max) = 5 khz, determine: a) Freq limits for the upper and lower sidebands. b) Bandwidth. ) Upper and lower side frequenies produed when the modulating signal is a single-freq 3-kHz tone. d) Draw the output freq spetrum.

30 Solution: Example 1

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32 Example 2 Suppose that V max value read from the gratiule on an osillosope sreen is 4.6 divisions and V min is 0.7 divisions. Calulate the modulation index and perentage of modulation. EKT343 Priniple of Communiation Engineering 32

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34 Example 3 For the AM waveform shown in Figure below, determine a) Peak amplitude of the upper and lower side frequenies. b) Peak amplitude of the unmodulated arrier. ) Peak hange in the amplitude of the envelope. d) Modulation index. e) Perent modulation. EKT343 Priniple of Communiation Engineering 34

35 AM Envelope for Example 3 EKT343 Priniple of Communiation Engineering 35

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37 Generation of AM DSBFC envelope showing the timedomain of the modulated wave, arrier & sideband signals EKT343 Priniple of Communiation Engineering 37

38 Voltage spetrum for an AM DSBFC wave EKT343 Priniple of Communiation Engineering 38

39 Example 4 One input to a onventional AM modulator is a 500-kHz arrier with an amplitude of 20 V p. The seond input is a 10-kHz modulating signal that is of suffiient amplitude to ause a hange in the output wave of ±7.5 V p. Determine a) Upper and lower side frequenies. b) Modulation index and perentage modulation. ) Peak amplitude of the modulated arrier and the upper and lower side frequeny voltages. d) Maximum and minimum amplitudes of the envelope. e) Expression for the modulated wave. EKT343 Priniple of Communiation Engineering 39

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42 2-3: Sidebands and the Frequeny Domain Pulse Modulation When omplex signals suh as pulses or retangular waves modulate a arrier, a broad spetrum of sidebands is produed. A modulating square wave will produe sidebands based on the fundamental sine wave as well as the third, fifth, seventh, et. harmonis. Amplitude modulation by square waves or retangular pulses is referred to as amplitude shift keying (ASK). ASK is used in some types of data ommuniations.

43 2-3: Sidebands and the Frequeny Domain Figure 1-11: Frequeny spetrum of an AM signal modulated by a square wave.

44 2-3: Sidebands and the Frequeny Domain Figure 1-12: Amplitude modulation of a sine wave arrier by a pulse or retangular wave is alled amplitude-shift keying. (a) Fifty perent modulation. (b) One hundred perent modulation.

45 Pulse Modulation 2-3: Sidebands and the Frequeny Domain Continuous-wave (CW) transmission an be ahieved by turning the arrier off and on, as in Morse ode transmission. Continuous wave (CW) transmission is sometimes referred to as On-Off keying (OOK). Splatter is a term used to desribe harmoni sideband interferene.

46 2-4: Single-Sideband Modulation In amplitude modulation, two-thirds of the transmitted power is in the arrier, whih onveys no information. Signal information is ontained within the sidebands. Single-sideband (SSB) is a form of AM where the arrier is suppressed and one sideband is eliminated.

47 2-4: Single-Sideband Modulation DSB Signals The first step in generating an SSB signal is to suppress the arrier, leaving the upper and lower sidebands. This type of signal is alled a double-sideband suppressed arrier (DSSC) signal. No power is wasted on the arrier. A balaned modulator is a iruit used to produe the sum and differene frequenies of a DSSC signal but to anel or balane out the arrier. DSB (or DSSC) is not widely used beause the signal is diffiult to demodulate (reover) at the reeiver.

48 2-4: Single-Sideband Modulation Figure 1-16: A frequeny-domain display of DSB signal.

49 2-4: Single-Sideband Modulation SSB Signals One sideband is all that is neessary to onvey information in a signal. A single-sideband suppressed arrier (SSSC) signal is generated by suppressing the arrier and one sideband.

50 2-4: Single-Sideband Modulation SSB Signals SSB signals offer four major benefits: 1. Spetrum spae is onserved and allows more signals to be transmitted in the same frequeny range. 2. All power is hanneled into a single sideband. This produes a stronger signal that will arry farther and will be more reliably reeived at greater distanes. 3. Oupied bandwidth spae is narrower and noise in the signal is redued. 4. There is less seletive fading over long distanes.

51 2-4: Single-Sideband Modulation Disadvantages of DSSC and SSBSC Single and double-sideband SC s are not widely used beause the signals are diffiult to reover (i.e. demodulate) at the reeiver. A low power, pilot arrier is sometimes transmitted along with sidebands in order to more easily reover the signal at the reeiver.

52 2-4: Single-Sideband Modulation Signal Power Considerations In SSB, the transmitter output is expressed in terms of peak envelope power (PEP), the maximum power produed on voie amplitude peaks. Appliations of DSB and SSB A vestigial sideband signal (VSB) is produed by partially suppressing the lower sideband. This kind of signal is used in TV transmission.

53 2-5: AM Power In radio transmission, the AM signal is amplified by a power amplifier. A radio antenna has a harateristi impedane that is ideally almost pure resistane. The AM signal is a omposite of the arrier and sideband signal voltages. Eah signal produes power in the antenna. Total transmitted power (P T ) is the sum of arrier power (P ) and power of the two sidebands (P USB and P LSB ).

54 2-5: AM Power When the perentage of modulation is less than the optimum 100, there is muh less power in the sidebands. Output power an be alulated by using the formula P T = (I T ) 2 R where I T is measured RF urrent and R is antenna impedane

55 2-5: AM Power The greater the perentage of modulation, the higher the sideband power and the higher the total power transmitted. Power in eah sideband is alulated P SB = P LSB = P USB = P m 2 / 4 Maximum power appears in the sidebands when the arrier is 100 perent modulated.

56 AM Power Review: onventional AM(DSB-FC) Frequeny spetrum: f -f m f f +f m Bandwidth=2 x f mmax Total Power=P arrier +P usb +P lsb EKT343 Priniple of Communiation Engineering 56

57 DSB FULL CARRIER

58 Two major Drawbaks of DSBFC Large power onsumption, where arrier power onstitutes >2/3 transmitted power.{remember : arrier does not ontain any information} Utilize twie as muh bandwidth both the upper and lower sideband atually ontains same information (redundant). Thus, DSBFC is both power and bandwidth ineffiient EKT343 Priniple of Communiation Engineering 58

59 Double side band suppressed arrier(dsb-sc) Frequeny spetrum: f -f m f f +f m Bandwidth:2 x f mmax Total Power= P usb + P lsb EKT343 Priniple of Communiation Engineering 59

60 Single-Sideband (SSB) The arrier is transmitted at full power but only one sideband is transmitted requires half the bandwidth of DSBFC AM Carrier power onstitutes 80% of total transmitted power, while sideband power onsumes 20% SSBFC requires less total power but utilizes a smaller perentage of the power to arry the information EKT343 Priniple of Communiation Engineering 60

61 Single Side Band Full Carrier (SSB-FC) Frequeny spetrum: f -f m f f +f m Bandwidth=f mmax Total Power=P arrier +P usb EKT343 Priniple of Communiation Engineering 61

62 AM Single-Sideband Suppressed Carrier (SSBSC) The arrier is totally suppressed and one sideband is removed requires half the bandwidth of DSBFC AM Considerably less power than DSBFC and SSBFC shemes Sideband power makes up 100% of the total transmitted power The wave is not an envelope but a sine wave at frequeny equal to the arrier frequeny ±modulating frequeny (depending on whih sideband is transmitted) EKT343 Priniple of Communiation Engineering 62

63 Single Side band Suppress Carrier (SSB-SC) Frequeny spetrum: f -f m f f +f m Bandwidth=f mmax Total Power=+P usb EKT343 Priniple of Communiation Engineering 63

64 AM Single-Sideband Redued Carrier (SSBRC) One sideband is totally removed and the arrier voltage is redued to approximately 10% of its unmodulated amplitude requires half the bandwidth of DSBFC AM Less transmitted power than DSBFC and SSBFC but more power than SSBSC As muh as 96% of the total transmitted power is in the sideband The output modulated signal is similar to SSBFC but with redued maximum and minimum envelope amplitudes EKT343 Priniple of Communiation Engineering 64

65 Comparison of time domain representation of three ommon AM transmission systems: Tomasi Eletroni Communiations Systems, 5e EKT343 Priniple of Communiation Engineering 65

66 Example 5 For an AM DSBFC wave with a peak unmodulated arrier voltage V = 10Vp, frequeny of 100kHz, a load resistor of RL = 10, frequeny of modulating signal of 10kHz and m = 1, determine the following i) Powers of the arrier and the upper and lower sidebands. ii) Total power of the modulated wave. iii) Bandwidth of the transmitted wave. iv) Draw the power and frequeny spetrum. EKT343 Priniple of Communiation Engineering 66

67 Example 5..ont d Solution for DSBFC; i) ii) P P usb ( V P lsb / R ) V (10) 2R m P 1.25W 4 5W P t 2 m P P (5) 4 4 m 4 2 (5) P 7.5W iii) Bandwidth=2xf mmax =2(10kHz)=20kHz EKT343 Priniple of Communiation Engineering 67

68 Example 5..ont d For the same given values, determine questions (ii)-(iv) for a AM DSB-SC, AM SSB-FC and AM SSB-SC systems. Determine also the perentage of power saved in eah of the system design. EKT343 Priniple of Communiation Engineering 68

69 Example 5..ont d Solution: For DSB-SC ii) P t m m P P (5) (5) 4 2.5W Power 5W saved % Power 66.67% saved 7.5W 2.5W 5W x100% 7.5W iii)bandwidth=2xf mmax =2(10kHz)=20kHz iv) 90kHz 110kHz EKT343 Priniple of Communiation Engineering 69

70 Example 5..ont d Solution:For SSB-FC ii) P t 2 m P P (5) W Power saved 1.25W % Power 16.67% saved 7.5W 6.25W 1.25W x100% 7.5W iii)bandwidth=f mmax =10kHz iv) f -f m 100kHz 110kHz EKT343 Priniple of Communiation Engineering 70

71 Example 5..ont d Solution:For SSB-SC ii) P t 2 m P (5) W Power saved 6.25W % Power 83.33% saved 7.5W 1.25W 6.25W x100% 7.5W iii)bandwidth=f mmax =10kHz iv) f -f m f 110kHz EKT343 Priniple of Communiation Engineering 71

72 Exerises 1. An audio signal 15sin2π (1500t ). Amplitude modulates a arrier 60sin2π (100000t). a) Sketh the audio signal b) Sketh the arrier ) Construt the modulated wave d) Determine the modulation index and perent modulation e) What are the frequenies of the audio signal and the arrier f) What frequenies would show up in the spetrum analysis of the modulated wave.

73 Exerises 2. The total power ontent of an AM wave is 600W. Determine the perent modulation of the signal if eah of the sidebands ontains 75W. 3. Determine the power ontent of the arrier and eah of the sidebands for an AM signal having a perent modulation of 80% and the total power of 2500W

74 Methods of Generating SSB 2 methods, i) Filtering method A filter removes the undesired sideband produing SSB. Quartz rystal filters are the most widely used sideband filters sine they are very seletive and inexpensive. ii) Phasing method A balaned modulator eliminates the arrier and provides DSB. EKT343 Priniple of Communiation Engineering 74

75 Filtering method Carrier osillator Mirophone Audio amplifier Balaned modulator DSB signal Sideband filter Lower Upper sidebands sidebands SSB signal Linear amplifier Filter response urve Antenna EKT343 Priniple of Communiation Engineering 75

76 Phasing methods-using two balane modulator Another way to produe SSB uses a phase shift method to eliminate one sideband. Two balaned modulators driven by arriers and modulating signals 90º out of phase produe DSB. Adding the two DSB signals together results in one sideband being anelled out. EKT343 Priniple of Communiation Engineering 76

77 Phasing method..ont d Information signal Am os wmt Carrier signal Balaned Modulator 1 Phase shifter A 1 (t) A os (wt + 90) + Output Signal, a o t Phase shifter Am os (wmt + 90) Balaned Modulator 2 A 2 (t) EKT343 Priniple of Communiation Engineering 77

78 Phasing method..ont d a ( t) 0 a ( t) a ( t) a ( t) a 1 A 2 os( w t ( t) 90 0 )* A (1) os w t 0 0 A A os( w t 90 w t) A A os( w t 90 w t) (2) m A os( w t)* A m m os( w t m A A os( w t 90 w t) A A os( w t 90 w t) (3) m a 0 ( t) A A m m (2) m m (3) os( w t m 0 m ) 90 0 w t) m m m EKT343 Priniple of Communiation Engineering 78

79 Advantages/Disadvantages of SSB Advantages Power onsumption - Muh less total transmitted power is neessary to produe the same quality signal as ahieved with DSBFC AM Bandwidth onservation Seletive fading - arrier phase shift and arrier fading an not our, thus smaller distortion is expeted. Noise redution - thermal noise power is redued Disadvantages Complex reeivers Tuning diffiulties requires more omplex and preise than DSB EKT343 Priniple of Communiation Engineering 79

80 VESTIGIAL SIDEBAND (VSB) VSB is similar to SSB but it retains a small portion (a vestige) of the undesired sideband to redue DC distortion. VSB signals are generated using standard AM or DSBSC modulation, then passing modulated signal through a sideband shaping filter. Demodulation uses either standard AM or DSBSC demodulation. EKT343 Priniple of Communiation Engineering 80

81 Cont d Also alled asymmetri sideband system. Compromise between DSB & SSB. Easy to generate. Bandwidth is only ~ 25% greater than SSB signals. Derived by filtering DSB, one pass band is passed almost ompletely while just a trae or vestige of the other sideband is inluded. EKT343 Priniple of Communiation Engineering 81

82 Cont d AM wave is applied to a vestigial sideband filter, produing a modulation sheme VSB + C Mainly used for television video transmission. VSB Frequeny Spetrum Carrier VSB LSB MSB f EKT343 Priniple of Communiation Engineering 82