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1、3.1 Introductionl lAnalog modulation: modulation of a carrier by a source Analog modulation: modulation of a carrier by a source baseband analog signalbaseband analog signall lCarrier: a deterministic periodic waveform Carrier: a deterministic periodic waveform cosinusoidal cosinusoidalwhere, where,
2、 A A - amplitude- amplitude 0 0 - angular frequency - angular frequency of carrierof carrier 0 0 - initial phase - initial phasel lDefinition:Definition:Modulating signal Modulating signal m(tm(t) ) signal from the sourcesignal from the sourceModulated signal Modulated signal s s( (t t) ) signal aft
3、er being modulated signal after being modulatedModulator Modulator the device for modulation the device for modulation Figure 3.1.1 ModulatorModulatorModulatedsignal s(t)Modulating signal m(t)Chapter 3 Analog modulation system1l lPurpose of modulationPurpose of modulationFrequency spectrum movement
4、- for accommodating the Frequency spectrum movement - for accommodating the requirement of channel transmission or for combining requirement of channel transmission or for combining several signals for multi-channel transmissionseveral signals for multi-channel transmissionImprovement of anti-jammin
5、g abilityImprovement of anti-jamming abilityl lClassification of analog modulation:Classification of analog modulation:Linear modulation: AM, SSB, DSB, VSB, Linear modulation: AM, SSB, DSB, VSB, Nonlinear modulation (angular modulation): FM, PMNonlinear modulation (angular modulation): FM, PM2(a) Fr
6、equency spectral density of input signalS (f)f0f-f00M(f)f0(b) Frequency spectral density of output signal3.2 Linear modulation3.2.03.2.0 Basic concept Basic conceptAssume: the carrier is: Assume: the carrier is: c(c(t t) = ) = A Acoscos 0 0 t t = = A Acos2cos2 f f0 0t tmodulating signal is a energy
7、signal modulating signal is a energy signal m(tm(t), its spectrum is M(), its spectrum is M(f f ) ) carrier: c(carrier: c(t t) )multiplication result: multiplication result: s s ( (t t) ) filter output: filter output: s s( (t t) ) “ “” is used to express Fourier transform:” is used to express Fourie
8、r transform: where, where, H(f)s (t)Modulated signals(t)Modulatingsignalm(t)Acos 0t33.2.1 AMl lBasic principlesBasic principlesLet: Let: mm( (t t) = 1+) = 1+mm ( (t t) )， | |mm ( (t t)| )| 1 1， mm ( (t t)| )|maxmax = = mm modulation index, then we have the AM modulation index, then we have the AM si
9、gnalsignals s ( (t t) = 1+) = 1+mm ( (t t) )A Acoscos 0 0t t，where, 1+where, 1+mm ( (t t) ) 0, i.e., the envelope of 0, i.e., the envelope of s s ( (t t) is non-) is non-negativenegative +1 =+1 = = =m (t)101+m (t)101+m (t)4l lFrequency densityFrequency density Contain discrete carrier component Cont
10、ain discrete carrier componentWhen When mm ( (t t) is cosinusoidal, and ) is cosinusoidal, and mm100100, , sum of the two side band power sum of the two side band power half of carrier power half of carrier powerFigure 3.2.3 Waveform and spectrum of modulated signalm(t)s(t)M(f)C(f)c(t)A-Atfm-fmf0-f0
11、2fmS (f)2fm-f0f0ffftt5l lReception of AM signal: envelope detectonReception of AM signal: envelope detectonPrinciple:Principle:Characteristics: assume the input voltage isCharacteristics: assume the input voltage iswherewhereis the input noise voltage of the detectoris the input noise voltage of the
12、 detector The envelope of The envelope of y y( (t t): ):For large S/N:For large S/N:RectifierLow-pass filterFigure 3.2.4 Envelope detector6After detection (D.C. component has been filtered):After detection (D.C. component has been filtered):Signal to noise power ratio of output signal:Signal to nois
13、e power ratio of output signal:signal to noise power ratio before detection equalssignal to noise power ratio before detection equals Ratio of S/N before and after detection: Ratio of S/N before and after detection: Since Since mm ( (t t) ) 1 1，obviously the above ratio obviously the above ratio r r
14、0 0/ /r ri i is less than 1, is less than 1, i.e., the S/N decreased after detection. i.e., the S/N decreased after detection. 73.2.2 DSB modulationl lPrinciple: when the modulation signal Principle: when the modulation signal mm( (t t) has no D.C. ) has no D.C. component, DSB signal is ponent, DSB
15、signal is obtained.l lFrequency spectrum: the two sidebands contain identical Frequency spectrum: the two sidebands contain identical information.information.M(f)f0f00-f0fS(f)(a) Frequency spectral density of modulating signal Figure 3.2.5 Spectrum of double-sideband modulation signalUpper-sideband(
16、b) Frequency spectral density of modulated signalUpper-sidebandLower-sideband8l lDemodulation: need localDemodulation: need localcarriercarrierLet received DSB signalLet received DSB signalbe be local carrier of receiver local carrier of receiver be be Product of the above two voltages is Product of
17、 the above two voltages is After low-pass filtered, we obtain After low-pass filtered, we obtainThe output signal equals The output signal equals mm ( (t t) / 2, only if the local carrier has ) / 2, only if the local carrier has no frequency and phase error.no frequency and phase error.l lAdvantage
18、& disadvantage: DSB signal can save transmitting Advantage & disadvantage: DSB signal can save transmitting power, but the receiving circuit will be rather complicated.power, but the receiving circuit will be rather complicated.Figure 3.2.6 Block diagram of DSB signal demodulatorBaseband signalm(t)R
19、eceived signals(t)cos0tr(t) H(f)93.2.3 3.2.3 SSB modulationSSB modulationl lPrinciples:Principles:Two sidebands contain Two sidebands contain identical informationidentical informationOnly one sidaband Only one sidaband should be transmittedshould be transmittedToo low frequencyToo low frequency com
20、ponents in components in mm( (t t) is) is not allowed not allowedl lDemodulation: local carrierDemodulation: local carrier is needed is neededSince, ifSince, if z z( (t t) = ) = x x( (t t) ) y y( (t t) ) ， then, we have then, we haveZ Z( ( ) = ) = X X( ( ) ) Y Y( ( ) ) During demodulation of SSB sig
21、nal, the carrier cosDuring demodulation of SSB signal, the carrier cos 0 0t t is is multiplied with the received signal; it is equivalent to multiplied with the received signal; it is equivalent to convolution of carrier and signal spectra in frequency convolution of carrier and signal spectra in fr
22、equency domain.domain.Figure 3.2.7 Frequency spectrum of single-sideband signal(b)Upper-sideband filter characteristic and signal frequency spectrumf00f-f00ff0-f0HH(f)HH(f)S(f)Upper-sidebandUpper-sideband(c)Lower-sideband filter characteristic and signal frequency spectrum-f0f0fHL(f)S(f)Lower-sideba
23、nd(a)Signal frequency spectrum before filteringUpper-sidebandS(f)Upper-sidebandLower-sideband10To use upper sideband as example shows demodulated signal To use upper sideband as example shows demodulated signal after low-pass filtering.after low-pass filtering.l lAdvantages of SSB: smaller transmitt
24、ing power and Advantages of SSB: smaller transmitting power and bandwidth than DSB signal.bandwidth than DSB signal.Figure 3.2.7 Frequency spectrum of single-sideband signal(b) Upper-sideband filter characteristic and signal frequency spectrumf00f-f00ff0-f0HH(f)HH(f)S(f)Upper-sidebandUpper-sideband(
25、c) Lower-sideband filter characteristic and signal frequency spectrum-f0f0fHL(f)S(f)Lower-sideband(a) Signal frequency spectrum before filteringUpper-sidebandS(f)Upper-sidebandLower-sideband113.2.4 VSB modulationl lAdvantages of VSB: During demodulation, no local carrier is Advantages of VSB: During
26、 demodulation, no local carrier is necessarynecessary; modulating signal may contain very low frequency ; modulating signal may contain very low frequency and D.C. components.and D.C. components.l lPrinciples: VSB is still linear modulation.Principles: VSB is still linear modulation. The frequency s
27、pectrum of the modulated signal is The frequency spectrum of the modulated signal isAssume the transfer function of the filter of modulator is Assume the transfer function of the filter of modulator is HH( ( f f ) )，then the frequency spectrum of the modulated signal after then the frequency spectru
28、m of the modulated signal after filtering isfiltering iss (t)A Acoscos 0 0t tH H( (f f) )DemoduDemodulated lated signalsignals s( (t t) )Modulating Modulating signalsignalm m( (t t) )12 Lets find the condition Lets find the condition which should be satisfied by which should be satisfied by transfer
29、 function transfer function HH( ( f f ) in the) in the figure. figure. In the figure, the received signal is multiplied by the local In the figure, the received signal is multiplied by the local carrier, and the frequency spectrum of the resultant signal carrier, and the frequency spectrum of the re
30、sultant signal r r ( (t t) is:) is:Substituting the frequency spectrum Substituting the frequency spectrum of the modulated signal into the above equation, the frequency of the modulated signal into the above equation, the frequency spectrum of spectrum of r r ( (t t) is obtained as:) is obtained as
31、: M M( (f f + 2 + 2f f0 0) and ) and MM( (f f 2 2f f0 0) in the above equation may be filtered out ) in the above equation may be filtered out by the low-pass filter, hence the spectral density of the by the low-pass filter, hence the spectral density of the demodulated signal from filtering is:demo
32、dulated signal from filtering is:Baseband Baseband signalsignalm m( (t t) )Received Received signalsignals s( (t t) )coscos 0 0t tr (t) H H( (f f) )13 For distortionless transmission, require For distortionless transmission, requireSinceSince The above equation can be rewritten as The above equation
33、 can be rewritten as The above equation is a prerequistie for the filter The above equation is a prerequistie for the filter characteristic to produce VSB signal.characteristic to produce VSB signal.14 The above equation requires that the cut-off characteristic of The above equation requires that th
34、e cut-off characteristic of the filter is complementary symmetry with respect to thethe filter is complementary symmetry with respect to the f f0 0. .H(f + f0)-(f0+fm)0000ffff0-f0f0+fm-2f02f0-2f02f0fm-fmfmfH(f)H(f - f0)H(f + f0) + H(f f0)153.3 Nonlinear modulation3.3.1 3.3.1 Basic principlesBasic pr
35、inciplesl lConcept of frequency: strictly speaking, only the sinusoidal Concept of frequency: strictly speaking, only the sinusoidal wave with constant amplitude, constant phase, and infinite wave with constant amplitude, constant phase, and infinite length has single frequency. A carrier after modu
36、lated no length has single frequency. A carrier after modulated no longer has single frequency.longer has single frequency.l lConcept of “instantaneous frequency”: let a carrier can be Concept of “instantaneous frequency”: let a carrier can be expressed asexpressed aswhere, where, 0 0 - initial phas
37、e of carrier - initial phase of carrier ( (t t) =) = 0 0t t + + 0 0 - instantaneous phase of carrier- instantaneous phase of carrier 0 0 = d= d ( (t t)/d)/dt - t - angular frequency of carrierangular frequency of carrier Define instantaneous frequency as: Define instantaneous frequency as: The above
38、 equation can be written as:The above equation can be written as:16l lDefinition of angular modulation:Definition of angular modulation:As can be seen from the following equation, As can be seen from the following equation, ( (t t) is the phase of carrier. If it varies with modulating signal ) is th
39、e phase of carrier. If it varies with modulating signal mm( (t t) according to certain mode, then it is called angular ) according to certain mode, then it is called angular modulation.modulation.Definition of phase modulation: If phase Definition of phase modulation: If phase ( (t t) linearly varie
40、s ) linearly varies with with mm( (t t), i.e., let), i.e., let then it is called phase modulation. Thus, the expression of then it is called phase modulation. Thus, the expression of the modulated signal isthe modulated signal isNow, the instantaneous frequency of the modulated carrier Now, the inst
41、antaneous frequency of the modulated carrier is:is: The above equation shows that the instantaneous frequency The above equation shows that the instantaneous frequency in phase modulation linearly varies with the derivative of in phase modulation linearly varies with the derivative of the modulating
42、 signal. the modulating signal. 17Definition of frequency modulation: If instantaneous Definition of frequency modulation: If instantaneous frequency linearly varies with the modulating signal, then frequency linearly varies with the modulating signal, then frequency modulation is obtained. Now inst
43、antaneous frequency modulation is obtained. Now instantaneous angular frequency isangular frequency isand instantaneous phase isand instantaneous phase isIn this way, the expression of the modulated signal obtained In this way, the expression of the modulated signal obtained is:is:As can be seen fro
44、m the above equation, the phase of the As can be seen from the above equation, the phase of the carrier is linearly varies with the integration of modulating carrier is linearly varies with the integration of modulating signal.signal.18Comparison of phase modulation and frequency Comparison of phase
45、 modulation and frequency modulation:modulation:n nThe carrier phase The carrier phase ( (t t) in phase modulation ) in phase modulation linearly varies with the modulating signal linearly varies with the modulating signal m m ( (t t), ), and the carrier phase and the carrier phase ( (t t) in freque
46、ncy ) in frequency modulation linearly varies with the integral of modulation linearly varies with the integral of the modulating signal the modulating signal m m ( (t t). ).n nIf If m m ( (t t) is integrated first, and the phase of ) is integrated first, and the phase of carrier is modulated, then
47、frequency modulated carrier is modulated, then frequency modulated signal is obtained. Similarly, if signal is obtained. Similarly, if m m ( (t t) is ) is differentiated first, and frequency of carrier is differentiated first, and frequency of carrier is modulated, then phase modulated signal is mod
48、ulated, then phase modulated signal is obtained.obtained.n nIt is impossible to distinguish them by modulated It is impossible to distinguish them by modulated signal waveforms.signal waveforms.19Waveform of angular modulationWaveform of angular modulationn nIf If mm( (t t) linearly varies, then the
49、 modulated signal is ) linearly varies, then the modulated signal is frequency modulated signal.frequency modulated signal.n nIf If mm( (t t) varies with ) varies with t t 2 2, then the modulated signal is phase , then the modulated signal is phase modulated signal.modulated signal. i203.3.2 3.3.2 F
50、requency spectrum and bandwidth of modulated Frequency spectrum and bandwidth of modulated signal signalAssumeAssume：modulating signal modulating signal mm( (t t) is a cosinusoidal wave:) is a cosinusoidal wave:It is used to modulate the frequency of the carrier, then the It is used to modulate the
51、frequency of the carrier, then the instantaneous frequency of the carrier isinstantaneous frequency of the carrier is where, where, k kf f = = max. angular frequency deviationmax. angular frequency deviationExpression of modulated signal: Expression of modulated signal: where, where, mm f f / / f fm
52、m - ratio of max. frequency deviation to - ratio of max. frequency deviation to baseband signal frequency, it is called modulation index baseband signal frequency, it is called modulation index mmf f , , i.e.i.e.21 is a cosine function containing sine functions. Its expansion is: is a cosine functio
53、n containing sine functions. Its expansion is: where, where, J Jn n( (mmf f) ) is the Bessel function of first kind of is the Bessel function of first kind of n n-th order.-th order.It has the following characteristics:It has the following characteristics:Hence, the above equation can beHence, the a
54、bove equation can be rewritten as: rewritten as: Final expression Final expressionx22Characteristics of the frequency spectrumCharacteristics of the frequency spectrumn nSide frequencies in pairSide frequencies in pairn nMost part of powerMost part of power concentrates in a finite concentrates in a
55、 finite bandwidth.bandwidth.n nWhen When mmf f 1, 1, 1, B B： wherewhere f f frequency deviationfrequency deviationf fmm frequency of modulation signalfrequency of modulation signalmkHzkHzkHzkHz作kHzkHzkHzkHz23 3.3.3 3.3.3 Reception of angular modulated signalReception of angular modulated signal 3.4 3.4 Brief summaryBrief summary24
