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 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-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 ) 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-negative +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 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 than 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 carrier 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 sideband 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. components. 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 transfer 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: 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 filter 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 amplitude, 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 - angular 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 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 phase modulation linearly varies with the derivative of the modulating signal.,18,Defi