Slide 1

1 Chapter 5 AM,FM, and digital modulation systems Slide 2 2 5.0 Introduction (Chapter objectives) Amplitude modulation and single sideband Frequency and phase modulation Digitally modulated signals(OOK, BPSK, FSK, MSK MPSK, QAM, QPSK, /4QPSK, and OFDM) Spread sprectrum and CDMA system Slide 3 3 5.0 Introduction (the goal of this chapter) Study g(t) and s(t) for various types of analog and digital modulations Evaluate the spectrum for various types of analog and digital modulations Examine some transmitter and receiver structures Learn about spread spectrum systems Slide 4 4 5.0 Introduction (the key of this chapter) Grasping phase modulation and frequency modulation Grasping Binary modulation and Bandpass signaling Grasping Multilevel Modulated bandpass signaling Grasping Minimum-shift keying (MSK)and GMSK Knowing the principle of FDM, OFDM and Spread Spectrum Systems Slide 5 5 5.0 Introduction (band-pass signal and its spectra) Communication system constructure input signal processing carrier circuits Transmission Medium (channel ) transmitter g(t) s(t) carrier circuits signal processing r(t) g(t)output Modulation is the process of imparting the source information onto a Band-pass signal with a carrier frequency f c by the introduction of amplitude or phase perturbations or both. Slide 6 6 5.0 Introduction (band-pass signal and its spectra) Theorem:Any physical band-pass waveform can be representative by g(t) is called the complex envelope of s(t),and f c is carrier frequency (in hertz), c =2f c Notice: The desired type of modulated signal,s(t),is obtained by selecting the appropriate modulation mapping function g[m(t)],where m(t) is the analog or digital base-band signal. The voltage (or current)spectrum of the band-pass signal is and the PSD is Slide 7 7 5.1 Amplitude Modulation The complex envelope of an AM signal is given by Where A c specifies the power level and m(t) is the modulating signal. The representation for AM signal is given by: Fig.5-1 Slide 8 8 5.1 Amplitude Modulation (modulation percentage for AM signal ) Definition %positive modulation= (A max -A c )/ A c 100=max[m(t)] 100 %negative modulation= (A c -A min ) / A c 100=-min[m(t)] 100 %overall modulation= (A max - A min )/ (2A c )100 ={max[m(t)]-min[m(t)]}/2 100 where A max is the maximum value of A c [1+m(t)], and A c is the level of the AM envelope in the absence of modulation. notice:The percentage of modulation can be over100 %(A min will have a negative value).If the transmitter uses a two-quadrant multiplier that produces a zero output when A c [1+m(t)] is negative,the output signal will be: Slide 9 9 5.1 Amplitude Modulation Which is a distorted AM signal which is call as over modulated signal. Its bandwidth is much wider than that of the undistorted AM signal. if the percentage of negative modulation is less than 100%,an envelope detector may be used to recover the modulation without distortion;if the percentage of negative modulation is over 100%,undistorted modulation can still be recovered provided the product detector is used. A product detector is superior to an envelope detector when the input signal-to-noise ratio is small. Slide 10 10 5.1 Amplitude Modulation because the total average normalized power of a band- pass waveform v(t) is given by Where normalized implies that the load is equivalent to 1 ohm. The normalized average power of the AM signal is: If the modulation contains no dc level,then m(t) =0,and the normalized power of the AM signal is Slide 11 11 5.1 Amplitude Modulation modulation efficiency:the percent of the total power of the modulated signal that conveys information. The highest efficiency that can be attained for a 100% AM signal would be 50%.(For the case when square- wave modulation is used). The normalized peak envelope power (PEP)of the AM signal: Slide 12 12 5.1 Amplitude Modulation The voltage spectrum of the AM signal is given by The AM spectrum is just a translated version of the modulation spectral component.The bandwidth is twice that of the modulation Example 5-1 Suppose that a 5000w AM transmitter is connected to a 50 load; If the transmitter is 100% modulated by a 1000Hz test tone. Then compute (1)the total actually average power, (2)actually PEP, (3) The modulation efficiency. Solution: the constant A c is given by (1/2)A c 2 /50=5000, thus peak voltage across the load will be A c =707V during the times when there is no modulation. Slide 13 13 5.1 Amplitude Modulation (2)then across the 50 load, the PEP is: (3)The modulation efficiency would be: (1)the actual average power Slide 14 14 5.1 Amplitude Modulation Slide 15 15 5.1 Amplitude Modulation Fig. 4-2 Spectrum of AM signal Slide 16 16 5.3 Double-sideband Suppressed Carrier A double-sideband suppressed carrier(DSB-SC) signal is an AM signal that has a suppressed discrete carrier. The voltage spectrum of the DSB-SC signal is The percent of modulation of a DSB-SC is :infinite The modulation efficiency of a DSB-SC is 100% A product detector (which is more expensive than an Envelope detector) is required for demodulation of the DSB-SC signal The sideband power of a DSB-SC signal is four times that of a comparable AM signal with the some peak level,that is to say,the DSB-SC signal has a four_fold power advantage over that of an AM signal Slide 17 17 5.3 Double-sideband Suppressed Carrier Spectrum of DSB-CS signal Slide 18 18 5.5Asymmetric sideband signals (Signal sideband) An upper single sideband (USSB) signal has a zero- valued spectrum for|f|f c, where f c is the carrier frequency. SSB-AM:The bandwidth is the same as that of the modulating signal (which is half the bandwidth of an AM or DSB-SC signal). The term SSB refers to the SSB-AM type of signal, unless otherwise denoted. Slide 19 19 5.5Asymmetric sideband signals Theorem:The complex envelope of an SSB signal is given by Which results in the SSB signal waveform: Where the upper(-) sign is used for USSB and the lower (+) sign is used for LSSB. Denotes the Hilbert transform of m(t), which is given by: Where h(t)=1/(t), and H(f)= F [h(t)] corresponds to a -90 0 phase-shift network Slide 20 20 5.5Asymmetric sideband signals Fig.5-4 Spectrum for a USSB signal Proof: Taking the Fourier transform of the complex envelope of an SSB signal, we get: Because of Hilbert transform, we can find that the equation becomes: For USSB case, choose the upper sign, then: Substituting it into eq.(4-15), we have: Slide 21 21 5.5Asymmetric sideband signals The normalized average power of the USSB signal is The SSB signal power is the power of the modulating signal m 2 (t) multiplied by the power gain factor A c. The normalized peak envelope power (PEP) is : Slide 22 22 5.5Asymmetric sideband signals Fig. 5-5 Generation of SSB Slide 23 23 5.5Asymmetric sideband signals SSB signals have both AM and PM. The AM component (real envelope) is: The PM component is SSB signals may be received by using a super- heterodyne receiver that incorporates a product detector with 0 =0, thus the receiver output is: Where K depends on the gain of the receiver and the loss in the channel. In detecting SSB signals with audio modulation, the reference phase 0 does not have to be zero, because the same intelligence is heard regardless of the value of the phase used, For digital modulation, the phase has to be exactly correct so that the digital waveshape is preserved Slide 24 24 5.5Asymmetric sideband signals (Vestigial sideband) Slide 25 25 5.5Asymmetric sideband signals (Vestigial sideband) In certain application, a DSB modulation technique takes too much bandwidth for the channel, and an SSB technique is too expensive to implement, although it takes only half the bandwidth. In this case, a compromise between DSB and SSB, called vestigial sideband(VSB), is often chosen. VSB is obtained by partial suppression of one of the sidebands of a DSB signal. sideband of the DSB signal is attenuated by using a band- pass filter,called a vestigial sideband filter. The VSB signal is given by: Where s(t) is a DSB signal,and h v (t) is the impulse response of the VSB filter.The spectrum of the VSB signal is : Slide 26 26 5.5Asymmetric sideband signals (Vestigial sideband) The modulation on the VSB signal can be recovered by a receiver that uses product detection or, if a large carrier is present, by the use of envelope detection. For recovery of undistorted modulation, the transfer function for VSB filter must satify the constraint: Proof: Thus only when the constraint satisfy, V out (f)=KM(f) hold true. the product detector output is Slide 27 27 Summary AM DSB-SC SSB-AM VSB Slide 28 28 Summary Example 5-2 if linear modulated signal is as following: (1)s 1 (t)=cos( 0 t)cos ( c t) (2)s 2 (t)(1+0.5sin ( 0 t)) cos ( c t) Where c =6 0, please giving their spectrum. Solution : (1) the spectrum is: -7 0 -5 0 5 0 7 0 Slide 29 29 Summary (2) the spectrum is -7 0 -5 0 5 0 7 0 j S 2 (f) Slide 30 30 5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal) PM and FM are special cases of angle-modulated signaling. In this kind signaling the complex envelope is: Here the real envelope R(t)=|g(t)|=A c, is a constant, and the phase (t) is a linear function of the modulating signal m(t). However, g(t) is a nonlinear function of the modulation. The resulting angle-modulated signal is: For PM,the phase is directly proportional to the modulating signal Where the proportionality constant D p is the phase sensitivity of the phase modulator, its units is radians per volt. For FM, the phase is proportional to the integral of m(t), so that: Slide 31 31 5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal) Where the frequency deviation constant D f has units of radians/volt-sencond. From the last two equations, we can see that if we have a PM signal modulated by m p (t), there is also FM on the signal, corresponding to a different modulation waveshape that is given by: Where the subscripts f and p denote frequency and phase. Similarity, if we have an FM signal modulated by m f (t), the corresponding phase modulation on this signal is: Slide 32 32 5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal) Fig. 5-7 Generation of FM from PM, and vice versa Direct PM circuit are realized sinusoidal signal through a time-varying circuit which introduces a phase shift that varies with the applied modulation voltage. Similarly, a direct FM circuit is obtained by varying the tuning of an oscillator tank circuit according to the Modulation voltage. Slide 33 33 5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal) Definition: If a band-pass signal is represented by : Where (t)= c t+(t), then the instantaneous frequency (hertz) of s(t) is: For the case of FM, the instantaneous frequency is: The instantaneous frequency varies about the assigned carrier frequency f c in a manner that is directly proportional to the modulated signal m(t). Slide 34 34 5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal) The frequency deviation from the carrier frequency is: And the peak frequency deviation is : The peak-to-peak deviation is For FM signaling,the peak frequency deviation is related to the peak modulation voltage by: Where V p =max[m(t)] Slide 35 35 5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal) An increase in the amplitude of the modulation signal V p will increase F and the bandwidth of the FM signal. But will not affect the average power level of the FM signal which is A c 2 /2 As V p is increased,spectral components will appear farther and farther away from the carrier frequency,and the spectral components near the carrier frequency will decrease in magnitude,since the total power in the signal remains constant.This situation is distinctly different form AM signaling,where the level of the modulation affects the power in the AM signal,but does not affect it bandwidth. Fig.5-9 Slide 36 36 5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal) The peak phase deviation is defined by: the peak modulation voltage is Where V p =max[m(t)]. Definition: The phase modulation index is given by: Where is the peak phase deviation Definition: The frequency modulation index is given by: Where F is the peak frequency deviation and B is the bandwidth of the modulating signal, which, for the case of sinusoidal modulation, is f m, the frequency of the sinusoid. Slide 37 37 5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals) As the spectrum of the band-pass waveform is Where G(f)= F [g(t)]= F [A c e j(t) ] is the spectra of complex envelope signal. For the type of AM modulation signaling, we able to obtain relatively simple formulas relating S(f) to M(f). For angle modulation signaling, this is not the case, because g(t) is a nonlinear function of m(t), thus, a general formula relating G(f) to M(f) cannot be obtained, because G(f)= F [g(t)]= F [A c e j(t) ] must be evaluated on a case-by-case basic for the particular modulating waveshape of interest. Since g(t) is nonlinear function of m(t), superposition does not hold, and FM spectra for the sum of two modulating waveshape is not the same as summing the FM spectra that were obtained when the individual waveshape were used Slide 38 38 5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals) Example 5-2 spectrum of a PM or FM signal with sinusoidal modulation If the modulation on PM signal is : Then: Where the phase modulation index is p =D p A m = . When m f (t)=A m cos m t in FM modulation, we can get the same phase function. Where = f =D f A m / m. The peak frequency deviation would be F=D f A m /2. The complex envelope is Which is periodic with period T m =1/f m. Its Fourier series can be represented by: Slide 39 39 5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals) Where Here J n () is the Bessel function of the first kind of the nth, and J -n () =(-1) n J n () hold true. Taking the Fourier transform of Eq.(5-55) we get: Fig.5-10 Slide 40 40 5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals) Fig. 5.11 Carsons rule:the bandwidth of the angle-modulated signal depends on the phase modulation index or the frequency modulation index , and bandwidth of the modulating signal. That is : In fact, 98%of the total power is constrained in that bandwidth Slide 41 41 5.6 Phase Modulation and Frequency Modulation (Narrowband Angle Modulation) When (t) is restricted to a small value,say (t)