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1、1,3.1 Introduction Analog modulation: modulation of a carrier by a source baseband analog signal Carrier: a deterministic periodic waveform cosinusoidal where, A - amplitude 0 - angular frequency of carrier 0 - initial phase Definition: Modulating signal m(t) signal from the source Modulated signal
2、s(t) signal after being modulated Modulator the device for modulation,Chapter 3 Analog modulation system,2,Purpose of modulation Frequency spectrum movement - for accommodating the requirement of channel transmission or for combining several signals for multi-channel transmission Improvement of anti
3、-jamming ability Classification of analog modulation: Linear modulation: AM, SSB, DSB, VSB, Nonlinear modulation (angular modulation): FM, PM,3,3.2 Linear modulation 3.2.0 Basic concept Assume: the carrier is: c(t) = Acos0 t = Acos2 f0t modulating signal is a energy signal m(t), its spectrum is M(f
4、) carrier: c(t) multiplication result: s(t) filter output: s(t) “” is used to express Fourier transform: where,4,3.2.1 AM Basic principles Let: m(t) = 1+m(t)， |m(t)| 1， m(t)|max = m modulation index, then we have the AM signal s(t) = 1+m(t)Acos0t， where, 1+m(t) 0, i.e., the envelope of s(t) is non-n
5、egative +1 = =,m(t),5,Frequency density Contain discrete carrier component When m(t) is cosinusoidal, and m100, sum of the two side band power half of carrier power,6,Reception of AM signal: envelope detecton Principle: Characteristics: assume the input voltage is where is the input noise voltage of
6、 the detector The envelope of y(t): For large S/N:,7,After detection (D.C. component has been filtered): Signal to noise power ratio of output signal: signal to noise power ratio before detection equals Ratio of S/N before and after detection: Since m(t) 1，obviously the above ratio r0/ri is less tha
7、n 1, i.e., the S/N decreased after detection.,8,3.2.2 DSB modulation Principle: when the modulation signal m(t) has no D.C. component, DSB signal is obtained. Frequency spectrum: the two sidebands contain identical information.,9,Demodulation: need local carrier Let received DSB signal be local carr
8、ier of receiver be Product of the above two voltages is After low-pass filtered, we obtain The output signal equals m(t) / 2, only if the local carrier has no frequency and phase error. Advantage it is equivalent to convolution of carrier and signal spectra in frequency domain.,11,To use upper sideb
9、and as example shows demodulated signal after low-pass filtering. Advantages of SSB: smaller transmitting power and bandwidth than DSB signal.,12,3.2.4 VSB modulation Advantages of VSB: During demodulation, no local carrier is necessary; modulating signal may contain very low frequency and D.C. comp
10、onents. Principles: VSB is still linear modulation. The frequency spectrum of the modulated signal is Assume the transfer function of the filter of modulator is H( f )，then the frequency spectrum of the modulated signal after filtering is,13,Lets find the condition which should be satisfied by trans
11、fer function H( f ) in the figure. In the figure, the received signal is multiplied by the local carrier, and the frequency spectrum of the resultant signal r (t) is: Substituting the frequency spectrum of the modulated signal into the above equation, the frequency spectrum of r (t) is obtained as:
12、M(f + 2f0) and M(f 2f0) in the above equation may be filtered out by the low-pass filter, hence the spectral density of the demodulated signal from filtering is:,14,For distortionless transmission, require Since The above equation can be rewritten as The above equation is a prerequistie for the filt
13、er characteristic to produce VSB signal.,15,The above equation requires that the cut-off characteristic of the filter is complementary symmetry with respect to the f0.,16,3.3 Nonlinear modulation 3.3.1 Basic principles Concept of frequency: strictly speaking, only the sinusoidal wave with constant a
14、mplitude, constant phase, and infinite length has single frequency. A carrier after modulated no longer has single frequency. Concept of “instantaneous frequency”: let a carrier can be expressed as where, 0 - initial phase of carrier (t) = 0t + 0 - instantaneous phase of carrier 0 = d(t)/dt - angula
15、r frequency of carrier Define instantaneous frequency as: The above equation can be written as:,17,Definition of angular modulation: As can be seen from the following equation, (t) is the phase of carrier. If it varies with modulating signal m(t) according to certain mode, then it is called angular
16、modulation. Definition of phase modulation: If phase (t) linearly varies with m(t), i.e., let then it is called phase modulation. Thus, the expression of the modulated signal is Now, the instantaneous frequency of the modulated carrier is: The above equation shows that the instantaneous frequency in
17、 phase modulation linearly varies with the derivative of the modulating signal.,18,Definition of frequency modulation: If instantaneous frequency linearly varies with the modulating signal, then frequency modulation is obtained. Now instantaneous angular frequency is and instantaneous phase is In th
18、is way, the expression of the modulated signal obtained is: As can be seen from the above equation, the phase of the carrier is linearly varies with the integration of modulating signal.,19,Comparison of phase modulation and frequency modulation: The carrier phase (t) in phase modulation linearly va
19、ries with the modulating signal m (t), and the carrier phase (t) in frequency modulation linearly varies with the integral of the modulating signal m (t). If m (t) is integrated first, and the phase of carrier is modulated, then frequency modulated signal is obtained. Similarly, if m (t) is differen
20、tiated first, and frequency of carrier is modulated, then phase modulated signal is obtained. It is impossible to distinguish them by modulated signal waveforms.,20,Waveform of angular modulation If m(t) linearly varies, then the modulated signal is frequency modulated signal. If m(t) varies with t
21、2, then the modulated signal is phase modulated signal.,21,3.3.2 Frequency spectrum and bandwidth of modulated signal Assume：modulating signal m(t) is a cosinusoidal wave: It is used to modulate the frequency of the carrier, then the instantaneous frequency of the carrier is where, kf = max. angular
22、 frequency deviation Expression of modulated signal: where, mf / fm - ratio of max. frequency deviation to baseband signal frequency, it is called modulation index mf , i.e.,22,is a cosine function containing sine functions. Its expansion is: where, Jn(mf) is the Bessel function of first kind of n-t
23、h order. It has the following characteristics: Hence, the above equation can be rewritten as: Final expression,23,Characteristics of the frequency spectrum Side frequencies in pair Most part of power concentrates in a finite bandwidth. When mf 1, B： where f frequency deviation fm frequency of modulation signal,24,3.3.3 Reception of angular modulated signal 3.4 Brief summary,