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Chapter 2:Modulation9/18/2016Nurul/DEE 3413/Modulation1

Communication System ChartCommunicationSystemContinuous yModulation(FM)9/18/2016Digital WaveAnalogue PulseModulationDigital PulseModulationPulseModulation(PM)Nurul/DEE 3413/Modulation2

IntroductionWhat is modulation?“Modulation is defined as the process of modifying a carrierwave (radio wave) systematically by the modulating signal(audio)”This process makes the signal suitable for the transmission andcompatible with the channel. The resultant signal is called themodulated signalIn the other words, it is the process of changing/varying one ofthe parameters of the carrier wave by the modulating signal9/18/2016Nurul/DEE 3413/Modulation3

Introduction Modulation is operation performed at the transmitter to achieveefficient and reliable information transmission For analogue modulation, it is frequency translation methodcaused by changing the appropriate quantity in a carrier signal It involves two waveforms: A modulating signal/baseband signal – represents themessage A carrier signal – depends on type of modulation9/18/2016Nurul/DEE 3413/Modulation4

Introduction Analogue modulations - frequency translationmethods caused by changing the appropriatequantity in a carrier ier9/18/2016Nurul/DEE 3413/Modulation5

Introduction9/18/2016Nurul/DEE 3413/Modulation6

Introduction Once this information is received, the low frequency informationmust be removed from the high frequency carrier. This process is known as “ Demodulation”.9/18/2016Nurul/DEE 3413/Modulation7

Types of ModulationThree main type of modulations: Analog Modulation Amplitude modulation Angle modulation (frequency modulation & phase modulation) 9/18/2016Example: Double sideband with carrier (DSB-WC), Doublesideband suppressed carrier (DSB-SC), Single sidebandsuppressed carrier (SSB-SC), Vestigial sideband (VSB)Example: Narrow band frequency modulation (NBFM), Widebandfrequency modulation (WBFM), Narrowband phase modulation(NBPM), Wideband phase modulation (NBPM)Nurul/DEE 3413/Modulation8

Types of Modulation Pulse Modulation Carrier is a train of pulsesExample: Pulse Amplitude Modulation (PAM), Pulse widthmodulation (PWM) , Pulse Position Modulation (PPM)Digital Modulation Modulating signal is analog Modulating signal is digital (binary modulation) 9/18/2016Example: Pulse Code Modulation (PCM), Delta Modulation(DM), Adaptive Delta Modulation (ADM), Differential PulseCode Modulation (DPCM), Adaptive Differential Pulse CodeModulation (ADPCM) etc.Example: Amplitude shift keying (ASK), frequency Shift Keying(FSK), Phase Shift Keying (PSK) etc.Nurul/DEE 3413/Modulation9

Summary of Modulation FSKPSKv(t) V sinDigitalModulation9/18/2016ASK(2 ft )Nurul/DEE 3413/Modulation10

Types of Modulation Changing of the amplitude producesAmplitude Modulation signal Changing of the frequency producesFrequency Modulation signal Changing of the phase producesPhase Modulation signal9/18/2016Nurul/DEE 3413/Modulation11

Modulation 1Analogue ModulationAmplitude Modulation(13-60)9/18/2016Nurul/DEE 3413/Modulation12

Communication System ChartCommunicationSystemContinuous yModulation(FM)9/18/2016Digital WaveAnalogue PulseModulationDigital PulseModulationPulseModulation(PM)Nurul/DEE 3413/Modulation13

Amplitude ModulationVarious forms of Amplitude Modulation Conventional Amplitude Modulation (Alternativelyknown as Full AM or Double Sideband Large carriermodulation (DSBLC) /Double Sideband Full Carrier(DSBFC) Double SidebandmodulationSuppressedcarrier(DSBSC) Single Sideband (SSB) modulation Vestigial Sideband (VSB) modulation9/18/2016Nurul/DEE 3413/Modulation14

Amplitude Modulation DSBFC (Full AM)“Amplitude Modulation is the process of changing theamplitude of the radio frequency (RF) carrier wave by theamplitude variations of modulating signal”The carrier amplitude varied linearly by the modulatingsignal which usually consist of a range of a audiofrequencies. The frequency of the carrier is not affected Application of AM-Frequency range for AMBandwidth-9/18/2016Radio broadcasting, TV pictures(video), facsimile transmission- 535 kHz – 1600 kHz10 kHzNurul/DEE 3413/Modulation15

Amplitude Modulation DSBFC (Full AM)In amplitude modulation, the amplitude of the carrier variesproportional to the instantaneous magnitude of modulating signal Assuming Modulating signal : vm(t) Vm cos wmt carrier signal : vc(t) Vc cos wctmodulatingSignalvm(t)Carrier waveVc cos wct9/18/2016ModulatedSignalAMPLITUDEMODULATIONvAM (t ) Vc Vm cos( mt ) cos( ct )Nurul/DEE 3413/Modulation16

Amplitude Modulation DSBFC (Full AM)Carrier signalvc (t ) Vc cos( c t ) where c 2 f cwhere c 2 f cModulating signalvm (t ) Vm cos mtvam9/18/2016Nurul/DEE 3413/Modulation17

Amplitude Modulation DSBFC (Full AM)V envelope vm1.5VminV envelope Vc vmVmax1Vc max0.5vc instantaneous0-0.5 Vmin-1 Vmax-1.50vam 9/18/201651015amplitude - V envelopefrequency - carrier202530354045V modulated signal vamNurul/DEE 3413/Modulation18

Amplitude Modulation DSBFC (Full AM)Carrier signalvc (t ) Vc cos( c t ) where c 2 f cModulating signalvm (t ) Vm cos mt9/18/2016Nurul/DEE 3413/Modulation19

Amplitude Modulation DSBFC (Full AM)The amplitude-modulated wave can then be expressed asv AM (t ) Vc cos( c t ) vm (t ) cos( c t ) v AM (t ) Vc vm (t ) cos( c t )v AM (t ) Vc Vm cos( mt ) cos( ct )Vmv AM (t ) Vc cos( c t ) 1 cos m t Vcv AM (t ) Vc cos( ct ) 1 ma cos m t 9/18/2016Nurul/DEE 3413/Modulation20

Amplitude Modulation DSBFC (Full AM)where notation m is termed the modulation index. It issimply a measurement for the degree of modulation andbears the relationship of Vm to VcVmma VcTherefore the full AM signal may be written asvAM (t ) Vc cos( ct ) 1 ma cos( m t 9/18/2016Nurul/DEE 3413/Modulation21

Amplitude Modulation DSBFC (Full AM)Usingcos A cos B 1 / 2[cos( A B) cos( A B)]maVcmaVcv Am (t ) Vc (cos ct ) cos( c m )t cos( c m )t22CarriercomponentUpper sidebandcomponentLower sidebandcomponentSo, with the modulating process, the original modulatingsignal is transferred to a different frequency spectrum with ahigher value frequency9/18/2016Nurul/DEE 3413/Modulation22

Amplitude Modulation DSBFC (Full AM)The frequency spectrum of AM waveform contains 3 parts: A component at the carrier frequency fc An upper sideband (USB), whose highest frequencycomponent is at fc fm A lower sideband (LSB), whose highest frequencycomponent is at fc-fm The bandwidth of the modulated waveform is twice theinformation signal bandwidth.# sideband is a component above and below centre frequency# Every sideband contains all the original message, but not thecarrier9/18/2016Nurul/DEE 3413/Modulation23

Amplitude Modulation DSBFC (Full AM)DSBFC Frequency SpectrumWith single frequency fmB Maximum freq. - minimum freq. (fc fm)-(fc-fm) fc fm-fc fm 2fmVcmaVc2maVc2freqfc-fmfCfc fm2fm9/18/2016Nurul/DEE 3413/Modulation24

Amplitude Modulation DSBFC (Full AM)If fm consists of a range frequencies f1 to f2, thecomponent of the sidebands become:Upper sideband (USB) range is from (fc f1) to (fc f2)Lower sideband (LSB) range is from (fc-f2) to (fc-f1)Amplitude,VAmplitude,VBaseband signalf1f2freqlower sidebandfc-f2fc-f1Modulatedsignalupper sidebandfc f1fc f2freqAM spectrum when the modulating signal is a baseband signal from frequency f1 to f29/18/2016Bandwidth for this case,B (fc f2) - (fc-f2)Nurul/DEE 3413/Modulation2f225

Amplitude Modulation DSBFC (Full AM) For example, if voice signal with the band of frequency of0 – 4 kHz is transmitted using a carrier of 100 kHz, themodulated signal consists ofCarrier signal with frequency of 100 kHz upper side band with frequency of range of 100 – 104 kHz lower side band with frequency of range 96 – 100 kHz The bandwidth is 104 – 96 8 kHz9/18/2016Nurul/DEE 3413/Modulation26

Modulation Index m (Coefficient of Modulation)m is merely defined as a parameter, which determines theamount of modulation.What is the degree of modulation required to establish adesirable AM communication link?Answer is to maintain m 1.0 (m 100%).This is important for successful retrieval of the originaltransmitted information at the receiver end.9/18/2016Nurul/DEE 3413/Modulation27

Modulation Index m9/18/2016Nurul/DEE 3413/Modulation28

Modulation Index m9/18/2016Nurul/DEE 3413/Modulation29

Modulation Index mm must have a value between 0 and 1 to avoid over-modulationThis modulation is known as double sideband with carrier9/18/2016Nurul/DEE 3413/Modulation30

Modulation Index mIf the amplitude of the modulating signal is higher than thecarrier amplitude, which in turn implies the modulation indexm 1.0(100%).This willcausesevere distortionto themodulated signal.9/18/2016Nurul/DEE 3413/Modulation31

Modulation Index mThe ideal condition for amplitude modulation (AM) is whenm 1, which also means Vm Vc.This will give rise to the generation of the maximummessage signal output at the receiver without distortion.9/18/2016Nurul/DEE 3413/Modulation32

Modulation Index mIf the modulating signal is pure, single-frequency sinewave and the modulation process is symmetrical (i.e., thepositive and negative excursion of the envelope'samplitude are equal), then percent modulation as follows:Vm ½ (Vmax – Vmin) and Vc ½ (Vmax Vmin)1 / 2(V max V min)(V max V min)x100Therefore, m 1 / 2(V max V min) (V max V min) x1001 / 2(V max V min) 1 (V max V min)249/18/2016Nurul/DEE 3413/Modulation33

Modulation Index mThe peak change in the amplitude of the output wave(Vm) is the sum of the voltage from the upper and lowerside frequencies. ThereforeSinceVm Vusf Vlsf and Vusf Vlsf , thenVusf Vlsf Vm/2 Vusf peak amplitude of the upper sidefrequency (volts)Vlsf peak amplitude of the lower sidefrequency (volts)9/18/2016Nurul/DEE 3413/Modulation34

Modulation Index m1.5VminVmax1Vm0.5Vc0-0.5 Vmin-1 Vmax-1.509/18/2016510152025Nurul/DEE 3413/Modulation3035404535

Modulation Index mThe modulation index can be determined by measuring theactual values of the modulation voltage and the carrier voltageand computing the ratio.VV Vmmaxminma VV Vcmaxmin9/18/2016V max Vc VmV min Vc VmNurul/DEE 3413/Modulation36

Modulation Index mTrapezoid waveform can be obtained from by connectingthe modulating signal to x-axis of an oscilloscope andmodulated signal to y-axis of the oscilloscopebam 0m 10 m 1Thus, m can be calculated as9/18/2016m 1ma a ba bNurul/DEE 3413/Modulation37

AM Power DistributionmaVcmaVcv Am (t ) Vc (cos ct ) cos( c m )t cos( c m )t22 For a single frequency signal, average power for eachcomponent is (assume transmission impedance is R):9/18/2016Nurul/DEE 3413/Modulation38

AM Power DistributionCarrier power :Vc2Pc 2RSideband power: PUSB22ma Vc2 ma Pc PLSB 8R42ma PcPSB PUSB PLSB 2The total transmitted power isPtotal Pc PUSB pLSBthe sum of the carrier power Pc PSBand the power in the ma 2 Pc 1 2 sidebands.9/18/2016Nurul/DEE 3413/Modulation39

AM Power DistributionThe efficiency of the AM in term of power consumption is2Pm SB 2 aPTma 2Thus, at optimum operation (m 100%), only 33% ofpower is used to carry informationFrom previous equation, total current flow in AM is2m PPSB PUSB PLSB a c29/18/2016Nurul/DEE 3413/Modulation40

Generation and Detection of Full AM Both generation and detection require multiplication tobe performed. The multiplication is achieved by using a network with anonlinear characteristic. Nonlinear networks are not true multipliers because othercomponents are produced and need to be filtered out.9/18/2016Nurul/DEE 3413/Modulation41

Square-Law Modulator Consists of a summer (summing the carrier andmodulating signal), nonlinearity (square-law) block and aband pass filter (BPF) of bandwidth (2B) centered at fc toextract the desired modulation products.9/18/2016Nurul/DEE 3413/Modulation42

Square-Law ModulatorSquare law of nonlinearity:v2(t) a1v1(t) a2v12(t)where, a1 and a2 are constants and v1 is the inputvoltage signal consist of the carrier plus the modulationsignalv1(t) Sc(t) Sm(t) Vc cos(wct) Sm(t)v2(t) a1Vc(1 2a2/a1 Sm(t)) cos(wct) a1Sm(t) a2Sm2(t) a2Ac2cos2wctBy letting a1 1 , a2 ½ Acvo Ac (1 mcos(wmt)) cos(wct) ---------Full AM signal9/18/2016Nurul/DEE 3413/Modulation43

Square-Law Detector Although above is described as a modulator, it can alsobe used as a demodulator provided that the BPF isreplaced by a low pass filter (LPF) with cutofffrequency at fm (i.e.; bandwidth of B) and a localcarrier signal oscillator.9/18/2016Nurul/DEE 3413/Modulation44

Envelope Detector However, envelope detector is yet another full AMdetector commonly employed to replace the square-lawdetector. Since it is more simple and highly effectivedevice produces a waveform at its output that isproportional to the real envelope of its input;i.e. the output of the detector simply follows theenvelope of the input signal.9/18/2016Nurul/DEE 3413/Modulation45

Envelope Detector - OperationMake an initial assumption that the input (AM signal) is of fixedamplitude and ignore the present of the resistor R. Followingthis, the capacitor C charges to the peak positive voltage of thecarrier. It capacitor) then holds this peak voltage, results thediode stop conducting. Suppose now that the input-carrieramplitude is made to increase. Again, the diode resumesconduction, and the capacitor charges to a new higher carrierpeak. To ensure that the capacitor voltage vc to follow thecarrier peaks when the carrier amplitude is decreasing, it isrequired to include the resistor R, so the capacitor C maydischarge. In this case the capacitor voltage vc has the formshown in (AM waveform); i.e. the positive portion of themodulated signal envelope approximates the modulatinginformation signal. An additional LPF might be needed toeffectively smoothen out the saw tooth distortion of theenvelope waveform shown in figure (AM waveform) after theenvelope detector.9/18/2016Nurul/DEE 3413/Modulation46

m for Complex SignalAs most of the signals are complex and can berepresented by combination of various sine waves, m can bedetermined by ma meff m12 m22 m32 . Thus, total power for this complex signal isPT Pc [1 9/18/20162meff2]Nurul/DEE 3413/Modulation47

Amplitude Modulation Double Sideband Suppress Carrier (DSBSC)The previous modulated signal (DSBFC) has twodrawbacks; it waste power and bandwidth Powersent as the carrier contains no information and eachsideband carries the same information independently Thedouble sideband suppressed carrier (DSBSC) isintroduced to eliminate carrier hence improve powerefficiencyIt is a technique where it is transmitting both the sidebandswithout the carrier (the carrier is being suppressed) 9/18/2016Nurul/DEE 3413/Modulation48

Amplitude Modulation DSBSC The equation, then is simplified toVcVm cos( c m )t cos( c m )t vDSBSC (t ) VcVm cos c t cos mt 2LSBfc-fmfc fmUSBfreqfreqFrequency spectrum of a DSBSC systemTotal power in DSBSCPtotal PUSB p LSB Although, the power is improved, the bandwidth remain unchanged,that is BW 2B 2 fmax9/18/2016Nurul/DEE 3413/Modulation49

Amplitude Modulation DSBSC Thesuppressed carrier is further improved by sending onlyone sideband Thisnot only uses less power but also only half of thebandwidth and it is called single sideband suppressed carrier(SSBSC) There are two possible of SSBSCthe lower sideband VLSB Vm cos (wc-wm)tthe upper sideband VUSB Vm cos (wc wm)t9/18/2016Nurul/DEE 3413/Modulation50

Amplitude Modulation Single Sideband (SSB) As both DSB and standard AM waste a lot of power andoccupy large bandwidth, SSB is adopted SSB is a process of transmitting one of the sidebands of thestandard AM by suppressing the carrier and one of thesidebands (only transmits upper or lower sideband of AM) Reduces bandwidth by factor of 2USBLSBLSBfcfcTotal power in SSB9/18/2016USBFrequency spectrum of a SSB systemPtotal PUSB pLSBNurul/DEE 3413/Modulation51

Amplitude Modulation Single Sideband (SSB)SSB Applications: SSB is used in the systems which require minimumbandwidth such as telephone multiplex system and it isnot used in broadcasting Point to point communications at frequency below 30MHz – mobile communications, military, navigation radioetc where power saving is needed9/18/2016Nurul/DEE 3413/Modulation52

Amplitude Modulation Vestigial SidebandVSB is a technique AM transmission where the carrier, onesideband and a part of the other sideband are transmitted VSB application:VSB is mainly used in TV broadcasting for their videotransmissions. TV signal consists of:Audio signal – is transmitted by FMVideo signal – is transmitted by VSB9/18/2016Nurul/DEE 3413/Modulation53

Amplitude Modulation Vestigial SidebandA video signal consists of range of frequencies and maximumfrequency is as high as 4.5Mhz.If it is transmitted using the conventional AM system, therequired bandwidth is 9.0 Mhz (B 2fm). But according to thestandardization, TV signal is limited to 6MHz only.So, to reduce to 6Mhz bandwidth, a part of the LSB is nottransmitted. In this case SSB transmission is not applied as itis very difficult to suppress a sideband accurately at highfrequency.9/18/2016Nurul/DEE 3413/Modulation54

Amplitude Modulation Vestigial SidebandCarrierfor videoLowerSidebandfc-1.25Carrierfor audioAudioSignal(FM)Upper sidebandfc4.5 MHzfc 4.5Frequency spectrum of a Vestigial Sideband9/18/2016Nurul/DEE 3413/Modulation55

Conclusion Only sidebands contain the information Lower and upper sideband are identical. Only one sidebandis enough to recover the original signal Carrier component does not contain any information butconstitute 2/3 of the total power, at full modulation (ma 1)9/18/2016Nurul/DEE 3413/Modulation56

Advantages and Disadvantages of AM Advantages: simple with proven reliability low cost Disadvantages: wastage of power as most of the transmitted power are inthe carrier component which does not contain information.When ma 1, 2/3 of the power is wasted AM requires a bandwidth which is double to audiofrequency Noisy9/18/2016Nurul/DEE 3413/Modulation57

AM Communication ChartContinuous l/DEE 3413/ModulationPhaseModulation(PM)58

Examples2.1(i)(ii)For an AM modulator with carrier frequency of 150 kHz and a modulating signal frequency of10 kHz, determine the:Freq for the upper and lower sidebandbandwidthSketch the output frequency spectrumSolution:i)The lower and upper side band frequencyfLSB fc – fm 150 kHz – 10 kHz 140 kHz160 kHzi)fUSB fc fm 150 kHz 10 kHz BandwidthB 2fm 2 (10) kHz 20 kHzThe output frequency spectrum is as shown:Vc(maVc)/29/18/2016140(maVc)/2160B 20kHz 150Nurul/DEE3413/Modulationf (kHz)59

Examples2.2(i)(ii)(iii)For an AM wave with a peak unmodulated carrier voltage Vc 20 V, a load resistance RL 20 ohm and a modulation index ma 0.2, determine :Power contained in the carrier and the upper and lower sidebandsTotal sideband powerTotal power of the modulated powerSolution:(i)The carrier power is2 222mVmPV220a ca cc Pc 10W PLSB PUSB 8R42R2 ( 20 )(i)( 0.2 ) 2 (10 ) 0.1w4The total sideband2mp( 0.2 ) 2 (10 )acPSB 0.2 w22(i) ORPSB PUSB PLSB 0.1 0.1 0.2 wThe total power in the modulated wave:maPT P [1 c29/18/20162] 10[1 ( 0.2 ) 22] 10.2WORPT Pc PSB 10 0.2 10.2 wNurul/DEE 3413/Modulation60

Modulation 2Analogue ModulationAngle Modulation(62-112)9/18/2016Nurul/DEE 3413/Modulation61

Communication System ChartCommunicationSystemContinuous yModulation(FM)9/18/2016Digital WaveAnalogue PulseModulationDigital PulseModulationPulseModulation(PM)Nurul/DEE 3413/Modulation62

Types of Modulation Process9/18/2016Nurul/DEE 3413/Modulation63

Types of Modulation Process9/18/2016Nurul/DEE 3413/Modulation64

AnalogModulation9/18/2016Nurul/DEE 3413/Modulation65

Types of angle modulation1. FREQUENCY MODULATION (FM)2. PHASE MODULATION (PM).9/18/2016Nurul/DEE 3413/Modulation66

FM Communication ChartContinuous l/DEE 3413/ModulationPulseModulation(PM)67

Angle Modulation9/18/2016FMNurul/DEE 3413/ModulationPM68

FREQUENCY-MODULATION SYSTEMAngle ModulationIn angle modulation, the amplitude of the modulated carrieris held constant and either the phase or the time derivativeof the phase of the carrier is varied linearly with themessage signal vm(t).9/18/2016Nurul/DEE 3413/Modulation69

Frequency ModulationIntroduction As in Chapter 1, the need for modulation arises becausethe range of frequencies contained in a baseband signalis not, in general, the same as the range of frequencieswhich can be transmitted by the communicationschannel. 9/18/2016AM – amplitude modulation medium wave (300 kHz to 3 MHz), short wave(3–30 MHz)FM – frequency modulation VHF (30 – 300 MHz )Nurul/DEE 3413/Modulation70

Frequency Modulation (FM)Introduction FM is the process of varying the frequency of a carrierwave in proportion to a modulating signal.The amplitude of the carrier is constant while itsfrequency and rate of changes varied by the modulatingsignalFM modulatorFM signalFrequency modulated signal9/18/2016Nurul/DEE 3413/Modulation71

Frequency Modulation (FM)Introduction The FM modulator receives two signals, theinformation signal from an external source and thecarrier signal from a built in oscillator. The modulator circuit combines the two signalsproducing a FM signal which is passed on to thetransmission medium.9/18/2016Nurul/DEE 3413/Modulation72

Frequency Modulation Waveform Point A, C and E are where the informationsignal is at 0V.Point B is where the information signal isat the max. positive amplitude, point D iswhere the information signal is at the max.negative amplitude.During the time from point A to B, the FMsignal increases in freq.to its max. value at point B.From point B to C, the FM signal freq.decrease until reaching the freq. of thecarrier signal which calledthe center frequency.9/18/2016Nurul/DEE 3413/Modulation73

Frequency Modulation Waveform At point D is where the info signal has the max.negative amplitude. From point D to E, the FM signal increases untilreaching the centre frequency.9/18/2016Nurul/DEE 3413/Modulation74

Frequency Modulation (FM)The important features about FM waveforms are:i.The frequency variesii.The rate of change of carrier frequency changes is thesame as the frequency of the information signaliii. The amount of carrier frequency changes is proportional tothe amplitude of the information signaliv. The amplitude is constant9/18/2016Nurul/DEE 3413/Modulation75

FM AnalysisAssume : Carrier signal:Information signal:vc (t ) Vc cos( ct )vm (t ) Vm cos mtIn FM, frequency changes with the change of theamplitude of the information signal9/18/2016Nurul/DEE 3413/Modulation76

FM Analysis Thus, the instantaneous modulated frequency,Vm c kvm (t )f fc kcos m tor2 c kVm cos mtf f c f cos m tk is constant proportionalitykVm f 2 f k f Vm f frequency deviationk f frequency deviation constant(deviation sensitivity, Hz/V)9/18/2016Nurul/DEE 3413/Modulation77

Analysis of FMThe wave equation of the frequency modulation is:vF M ( t ) V cc o s θT h e a n g l e i so b t a i n eads : wdt wc kVm cos w m t dt w ct kVmsin w m t wmAssu min g 0 kVmvF M ( t ) V c c o s w c t sin w m t wm 9/18/2016Nurul/DEE 3413/Modulation78

Analysis of FMvFM (t ) Vc cos( c t mf sin m t )wheremf kVm m kVm2 f m f kVm2 FM modulation index m f ffmIn the FM, the value of modulation index, mf can be any valuefrom zero to infinity 0 mf 9/18/2016Nurul/DEE 3413/Modulation79

Carrier Frequency (fc) As in AM, the carrier frequency in FM system must behigher than the information signal frequency.FM radio : Uses carrier frequenciesbetween 88 MHz and 108 MHz.Television: Frequency range 54 MHz – 806 MHzNo. of channels 67 channelsBandwidth 6 MHzVHF: 54 MHz – 216 MHz (channel 2 – channel 13)UHF: 470 MHz – 806 MHz (channel 14 – channel 69)608 MHz – 614 MHz ( Radio Astronomy )9/18/2016Nurul/DEE 3413/Modulation80

Frequency Deviation Frequency deviation represents the maximum change ofthe instantaneous frequency of the FM signal from thecarrier frequency. A fundamental characteristic of an FM signal is that thefrequency deviation is proportional to the amplitude ofthe modulating signal, Vm and independent of themodulating frequency, fmkVm f 2 9/18/2016or f VmNurul/DEE 3413/Modulation81

Frequency DeviationThe highest frequency for FM wave isf max f c fThe minimum frequency for FM wave isf min f c fThe total change of the frequency from minimum frequencyto the maximum frequency is called frequency carrierswing, fcsf cs 2 f9/18/2016Nurul/DEE 3413/Modulation82

FM Frequency SpectrumAs obtained, the FM signal isvFM (t ) Vc cos( ct m f sin mt )v FM ( t ) V (cos t[m (sin t )] sin t[m sin t ])ccfmcfm9/18/2016Nurul/DEE 3413/Modulation83

FM Frequency SpectrumBy using mathematical expressions:v FM ( t ) V {cos t[ J J cos 2 t J cos 4 t.]cc 02m4m sin t[ J sin t J sin 3 t.]}c 1m3mv FM ( t ) V {J cos t J [cos( ) t cos( ) t ]c 0c1cmcm J [cos( 2 ) t cos( 2 ) t ]. J .}2cmcm5 Where Jn is a Bessel Function from first type, nth orderJ0 - will give the amplitude of the carrierJn – will give the amplitude of the sidebands, withfrequency ( n )c9/18/2016mNurul/DEE 3413/Modulation84

FM frequency spectrumFrom above equation, the FM waveform has a component atthe carrier frequency and an unlimited series of frequency,above and below the carrier frequency as below figure.An important characteristic of Bessel function: 2 1J n nJ ( n ) ( 1) n J n9/18/2016or 2Jn2 Vc2( power)V n cActual amplitude for the sideband Jn x VcRelative amplitude for the sideband JnNurul/DEE 3413/Modulation85

FM frequency spectrum Jn J0J1J1J2J2J3fc-3fmJ3fc-2fm fc-fmfcfc fm fc 2fm fc 3fmAn FM frequency spectrum9/18/2016Nurul/DEE 3413/Modulationfreq86

Bessel Functions9/18/2016Nurul/DEE 3413/Modulation87

TABLE OF BESSEL FUNCTIONS9/18/2016Nurul/DEE 3413/Modulation88

Bessel Functions The first column gives the sideband number,while the first row gives the modulation index. The remaining columns indicate the amplitudesof the carrier and the various pairs of sidebands. Sidebands with relative magnitude of less than0.001 have been eliminated.9/18/2016Nurul/DEE 3413/Modulation89

Bessel FunctionsSome of the carrier and sideband amplitudes have negativesigns. This means that the signal represented by thatamplitudeissimplyshiftedinphase180 (phaseinversion). As you can see, the spectrum of a FM signalvaries considerably in bandwidth depending upon the valueof the modulation index. The higher the modulation index,the wider the bandwidth of the FM signal.9/18/2016Nurul/DEE 3413/Modulation90

Bessel FunctionsWith the increase in the modulation index, the carrieramplitude decreases while the amplitude of the varioussidebands increases. With some values of modulation index,the carrier can disappear completely.9/18/2016Nurul/DEE 3413/Modulation91

FM Bandwidth Theoretically, a FM signal contains an infinite number of sidefrequencies so that the bandwidth required to transmit suchsignal is infinite. However, since the values of Jn( ) become negligible forsufficiently large n, the bandwidth of an angle-modulatedsignal can be defined by considering only those terms thatcontain significant power.9/18/2016Nurul/DEE 3413/Modulation92

FM BandwidthFrom Bessel table:B.W 2nf m(max)actual bandwidthn number of significant sidebandCarson's rule is given by the expressionBW 2( f f m)approximate bandwidthCarson’s rule is an approximation and givestransmission bandwidth that are slightly narrower thanthe bandwidths determined using the Bessel table.9/18/2016Nurul/DEE 3413/Modulation93

ExamplesCalculate the bandwidth occupied by a FM signal with amodulation index of 2 and a highest modulating frequency of2.5 kHz.Solution:B.W 2nf m(max)B.W . 2 6 2.5 30kHzExample:Assuming a maximum frequency deviation of 5 kHz and amaximum modulating frequency of 2.5 kHz, the bandwidthwould beSolution:B.W . 2( 2.5kHz 5kHz) 2 7.5kHz 15kHz9/18/2016Nurul/DEE 3413/Modulation94

Power in FMIn FM, the amplitude of the modulated signal is the same asthe amplitude of the un-modulated carrier signal. Power of FMwave dissipated in a load, R is:V2V2P rms cFMR2RPFM PcBut the power in the carrier is distributed over the variousFM sidebands that results from the modulation. This poweris contained at the various frequency Spectrumcomponents, in amounts determined by the mf and thecorresponding Bessel Function9/18/2016Nurul/DEE 3413/Modulation95

Power in FMThe FM average power is:2P P [J 2Tc 0n J n2 ]n 1wherePc carrier powern number of pairs ofsignificant sidebandsThe average power of the modulated carrier (PT) mustbe equal to the average power of the un-modulatedcarrier9/18/2016Nurul/DEE 3413/Modulation96

Narrow Band FM (NBFM)1. Modulation index approximates to 12. The frequency modulation is between 5 kHz to 10khz3. Bandwidth : 10 – 30kHz4. The maximum mod

9/18/2016 9Nurul/DEE 3413/Modulation Types of Modulation Pulse Modulation Carrier is a train of pulses Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) , Pulse Position Modulation (PPM) Digital Modulation Modulating signal is analog Example: Pulse Code Modulation (PCM), Delta Modulation (DM), Adaptive Delta Modulation (ADM), Differential Pulse

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