Chapter 3 Amplitude Modulation. Wireless Information Transmission System Lab. Institute of Communications Engineering National Sun Yat-sen University

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1 Chapter 3 Amplitude Modulation Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University

2 Outline 3.1 Introdution 3.2 Amplitude Modulation 3.3 Double Sideband-Suppressed Carrier Modulation 3.4 Quadrature-Carrier Multiplexing 3.5 Single-Sideband and Vestigial-Sideband Methods of Modulation 3.7 Frequeny Translation 2

3 Chapter 3.1 Introdution Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University

4 3.1 Introdution Purpose of a ommuniation system: onvey information through a medium or ommuniation hannel. The information is often represented as a baseband signal ( 基頻訊號 ), i.e. a signal whose spetrum extends from 0 to some maximum frequeny. Proper utilization of the ommuniation hannel often requires a shift of the range of baseband frequenies into other frequeny ranges suitable for transmission, and a orresponding shift bak to the original frequeny range after reeption. A shift of the range of frequenies in a signal is aomplished by using modulation, whih is defined as the proess by whih some harateristi of a arrier is varied in aordane with a modulating wave (signal). 4

5 3.1 Introdution A ommon form of the arrier is a sinusoidal wave, in whih ase we speak of ontinuous-wave modulation. The baseband signal is referred to as the modulating wave, and the result of the modulation proess is referred to as the modulated wave. Modulation is performed at the transmitting end. At the reeiving end, we require the original baseband signal to be restored. This is aomplished by using a proess known as demodulation, whih is the reverse of the modulation proess. CW: ontinuous-wave. 5

6 Chapter 3.2 Amplitude Modulation Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University

7 3.2 Amplitude Modulation A sinusoidal arrier wave: t = Aos 2π ft 3.1 AM is defined as a proess in whih the amplitude of the arrier wave (t) is varied about a mean value, linearly with baseband signal m(t). AM wave, in its most general form s t = A 1 + km a t os 2πft (3.2) Typially, the arrier amplitude A and the message signal m(t) are measured in volts, in whih ase the k a is measured in volt -1. k a : amplitude sensitivity.[volt -1 ] m(t): modulating wave; the baseband signal that arries the message. s(t): modulated wave. m(t) and A are measured in volts. ( ) ( ) ( ) ( ) ( ) ( ) 7 A is the arrier amplitude f is the arrier frequeny Phase is assumed to be 0.

8 3.2 Amplitude Modulation The envelope of s(t) has essentially the same shape as the baseband signal m(t) provided that two requirements are satisfied: 1. The amplitude of k a m(t) is always less than unity, that is, kmt a ( ) < 1 for all t ( 3.3) It ensures that the funtion 1+ k a m(t) is always positive, and sine an envelope is a positive funtion, we may express the envelope of the AM wave s(t) of Eq. (3.2) as A [1+ k a m(t)]. When k a m(t) >1 for any t the arrier wave beomes overmodulated, resulting in arrier phase reversals whenever the fator 1+ k a m(t) rosses zero. (envelope distortion) The absolute maximum value of k a m(t) multiplied by 100 is referred to as the perentage modulation. 8

9 3.2 Amplitude Modulation Baseband signal m(t) AM wave for k a m(t) <1 for all t AM wave for k a m(t) >1 for some t Envelope distortion 9

10 3.2 Amplitude Modulation 2. The arrier frequeny f is muh greater than the highest frequeny omponent W of the message signal m(t), that is f W We all W the message bandwidth. If the ondition of Eq. (3.4) is not satisfied, an envelope an not be visualized satisfatorily. From Eq. (3.2), we find that the Fourier transform of the AM wave 1 s(t) is given by s( t) = A 1 + km a ( t) os( 2π ft ) ( 3.2) os 2π ft δ f f + δ f+ f ( ) ( ) ( ) A ka S f 2 f f f f M f f M f f 2 ( 3.4) a ( ) = δ( ) + δ( + ) + ( ) + ( + ) ( 3.5) 2 10

11 3.2 Amplitude Modulation From the spetrum of S( f ), we note the following: 1. As a result of the modulation proess, the spetrum of the message signal m(t) for negative frequenies extending from W to 0 beomes ompletely visible for positive frequenies, provided that the arrier frequeny satisfies the ondition f >W. 2. For positive frequenies: The spetrum of an AM wave above f is referred to as the upper sideband, below f is referred to as the lower sideband. For negative frequenies: The upper sideband is below f and the lower sideband is above f. The ondition f >W ensures that the sidebands do not overlap. 3. For positive frequenies, the highest frequeny omponent of the AM wave equals f +W, and the lowest frequeny omponent equals f W. The differene between these two frequenies defines the transmission bandwidth B T for an AM wave. BT ( ) = 2 W

12 3.2 Amplitude Modulation Example 3.1 Single-Tone Modulation (1/3) Consider a modulating wave: m(t) = A m os(2πf m t) arrier wave: (t) = A os(2πf t) ( ) = 1 + μ os( 2π ) os( 2π ) ( 3.7) s t A fmt ft where μ = ka To avoid overmodulation μ <1 a m μ :modulation fator (or perentage modulation) Envelope of s(t): A [1+ μos(2πf m t)] ( 1 μ) ( 1 μ) A A + A A = μ= A A A + A max max min min max min A max and A min denote the maximum and minimum values of the envelope of the modulated wave. 12

13 Example 3.1 Single-Tone Modulation (2/3) F 3.2 Amplitude Modulation Eq. (3.7) an be represented in this form: os Aos B= { os( A B) + os( A+ B) } s( t) = A os( 2π ft) + µ A os 2 ( ) os 2 ( ) 2 π f + fm t + µ A 2 π f fm t 1 1 S( f ) = A δ( f f) + δ ( f + f) + µ A δ( f f fm) + δ( f + f + fm) µ A δ( f f + fm) + δ( f + f fm)

14 3.2 Amplitude Modulation Example 3.1 Single-Tone Modulation (3/3) 1 2 Carrier power = A 2 1 Upper side-frequeny power= μ 8 1 Lower side-frequeny power= μ 8 A 2 2 A 2 2 In any ase, the ratio of the total sideband power to the total power in the modulated wave is equal to μ μ 2 ( ) Depend only on the modulation fator μ. If μ=1, the total power in the two side frequenies of the resulting AM wave is only one-third of the total power in the modulated wave. When the perentage modulation is less than 20 perent, the power in one side frequeny is less than 1 perent of the total power in the AM wave. 14

15 Swithing Modulator (1/4) 3.2 Amplitude Modulation One way to generate an AM wave: Swithing Modulator. Assume arrier wave (t) is large in amplitude and the diode ats as an ideal swith. v t = Aos 2π ft + m t 3.8 v 1 2 ( ) ( ) ( ) ( ) v1 ( t), t ( ) > 0 ( t) ( 3.9 ) 0, t ( ) < 0 15

16 Swithing Modulator (2/4) 3.2 Amplitude Modulation From Eq. (3.9), load voltage v 2 (t) varies periodially between the values v 1 (t) and zeros at a rate equal to the arrier frequeny f. By assuming a modulating wave that is weak ompared with the arrier wave, we have effetively replae the nonlinear behavior of the diode by an approximately equivalent pieewise-linear time-varying operation. We may express Eq. (3.9) mathematially as v2 ( t) Aos ( 2π ft ) + m( t) gt ( t) ( 3.10) 0 period T 0 =1/f 16

17 3.2 Amplitude Modulation n n gt ( t) = a anos 2π t + bnsin 2π t n= 1 T0 T0 1 T 2 ( ) T 0 a0 = g T T t dt 0 2 T 2 ( ) 0 an = g T T t π t dt 2 T T 0 0 T 2 ( ) os 2 sin 2 0 bn = g T T t π t dt b n Swithing Modulator (3/4) 0 0 T n T n T n 2 4 T sin 2π t dt 0 T T T = = nπ nπ = os os 0 nπ = 2 2 n os 2π t T n 2π T 0 T 0 4 T a a 0 n T0 1 1 = dt = T 4 T T0 2 n 2 4 T os2π tdt 0 T T T ( m ) ( m ) 2 = = ( m ) n sin 2π t T0 n 2π T ( m ) 0 T0 4 T nπ nπ 2 nπ = sin sin sin nπ = 2 2 nπ π = sin ( 2m 1) π 2 2 = os( mπ) 2 1 π 2 m 2 = ( 1) = π 2 1 π 2 = 2 1 π ( m ) ( 1 ) m 1 ( ) m+ 1

18 Swithing Modulator (4/4) Substituting Eq. (3.11) in (3.10), v 2 (t) onsists of two omponent 3.2 Amplitude Modulation A desired AM wave: Unwanted omponent, the spetrum of whih ontains n= 1 ( 1) n gt ( t) = + os 2πft n 2 π 2n 1 A m( t) os( 2π ft ), ka = 2 πa πa Delta funtion at 0, ±2f, ±4f and so on. Oupy frequeny intervals of width 2W entered at 0, ±3f, ±5f and so on, where W is the message bandwidth. Be removed by using a band-pass filter with mid-band frequeny f and bandwidth 2W, provide that f >2W. 18 ( ) ( ) ( ) ( ) + ( ) ( ) ( ) v2 t Aos 2π ft m t gt t

19 3.2 Amplitude Modulation Envelope Detetor (1/2) The proess of demodulation is used to reover the original modulating wave from the inoming modulated wave. One way to demodulate an AM wave: envelope detetor. Consist of a diode and a resistor-apaitor (RC) filter. (see next page) The operation of envelope detetor: On a positive half-yle of the input signal, the diode is forward-biased and the apaitor C harges up rapidly to the peak value of the input signal. When the input signal falls below this value, the diode beomes reversebiased and the apaitor C disharges slowly through the load resistor R l. The disharging proess ontinues until the next positive half-yle. When the input signal beomes greater than the voltage aross the apaitor, the diode onduts again and the proess is repeated. 19

3.2 Amplitude Modulation Envelope Detetor (2/2) Envelope detetor iruit diagram, assuming the diode is ideal, having a onstant resistane r f when forward biased and infinite resistane when

20 3.2 Amplitude Modulation Envelope Detetor (2/2) Envelope detetor iruit diagram, assuming the diode is ideal, having a onstant resistane r f when forward biased and infinite resistane when reverse-biased. A sinusoidal AM wave with 50 perent modulation. Envelope detetor output ontains a small amount of ripple at the arrier frequeny; this ripple is easily removed by the low-pass filter. 20

Virtues, Limitations, and Modulations of Amplitude Modulation (1/2) AM is the oldest method of performing modulation. Its biggest virtue is the ease with whih it is generated and reversed.

21 Virtues, Limitations, and Modulations of Amplitude Modulation (1/2) AM is the oldest method of performing modulation. Its biggest virtue is the ease with whih it is generated and reversed. In the transmitter: a swithing modulator or a square-law modulator (Problem 3.4). In the reeiver: an envelope detetor or a square-law detetor (Problem 3.6). Its system is relatively heap to build. The reason that AM radio broadasting has been popular for so long. Transmitted power and hannel bandwidth are our two primary ommuniation resoures. Using Eq. (3.2) suffers form limitations. AM is wasteful of power: The arrier wave (t) and baseband signal m(t) are independent. The arrier wave represents a waste of power, whih means that in AM only a fration of the total transmitted power is atually affet by m(t). AM is wasteful of bandwidth: The upper and lower sidebands of an AM wave are uniquely related to eah other by virtue of their symmetry about the arrier frequeny. ( ) = + ( ) ( ) s t A 1 km a t os 2π ft (3.2) 21

22 Virtues, Limitations, and Modulations of Amplitude Modulation (2/2) To overome these limitations, we trade off system omplexity for improved utilization of ommuniation resoures. Three modified forms of amplitude modulation: Double sideband-suppressed arrier (DSB-SC) modulation, in whih the transmitted wave onsists of only the upper and lower sidebands. Transmitted power is saved through the suppression of the arrier. The hannel bandwidth requirement is 2W. Vestigial sideband (VSB) modulation, in whih one sideband is passed almost ompletely and just a trae, or vestige, of the other sideband is retained. The required hannel bandwidth is in exess of the message bandwidth by an amount equal to the width of the vestigial sideband. Suited for the transmission of wideband signals suh as television signals. Single sideband (SSB) modulation, in whih the modulated wave onsists only of the upper sideband or the lower sideband. Suited for the transmission of voie signals by virtue of the energy gap that exists in the spetrum of voie signals between zero and a few hundred hertz. The minimum transmitted power and minimum hannel bandwidth: its prinipal disadvantage is inreased ost and omplexity. 22

23 Spetra of the various modulated signals 23

24 Chapter 3.3 Double Sideband-Suppressed Carrier Modulation Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University

25 3.3 Double Sideband-Suppressed Carrier Modulation Double sideband-suppressed arrier (DSB-SC) modulation. Produt of the message signal m(t) and the arrier wave (t): ( ) = ( ) ( ) = os( 2π ) ( ) ( 3.14) s t t m t A f t m t F The modulated signal s(t) undergoes a phase reversal whenever the message signal m(t) rosses zero. The envelope of a DSB-SC modulated signal is different from the message signal. 1 S f A M f f M f f ( ) = ( ) + ( + ) ( 3.15) 2 limited to the interval -W f W Bandwidth: 2W 25

26 3.3 Double Sideband-Suppressed Carrier Modulation Ring Modulator (1/4) Four diodes form a ring 26

27 3.3 Double Sideband-Suppressed Carrier Modulation Ring Modulator (2/4) Ring modulator is one of the most useful produt modulator, well suited for generating a DSB-SC wave. The diodes are ontrolled by a square-wave arrier (t) of frequeny f, whih is applied longitudinally by means of two enter-tapped transformers. If the transformers are perfetly balaned and the diodes are idential, there is no leakage of the modulation frequeny into the modulation output. The operation of the iruit. Assuming that the diodes have a onstant forward resistane r f when swithed on and a onstant bakward resistane r b when swithed off. And they swith as the arrier wave (t) goes through zero. On one half-yle of the arrier wave, the outer diodes are swithed to their forward resistane r f and the inner diodes are swithed to their bakward resistane r b. On the other half-yle of the arrier wave, the diodes operate in the opposite ondition. 27

28 3.3 Double Sideband-Suppressed Carrier Modulation Ring Modulator (3/4) The output voltage has the same magnitude as the output voltage, but they have opposite polarity. In fat, the ring modulator ats as a ommutator. Square-wave arrier (t) an be represented by a Fourier series: ( ) n ( t) = os 2πft π n= 1 2n 1 2n The ring modulator output is therefore n= 1 ( 1) n 1 It is sometimes referred to as a double-balaned modulator, beause it is balaned with respet to both the baseband signal and the square-wave arrier. 28 ( ) ( ) 4 st ( ) = tmt ( ) ( ) = os 2πft 2n 1 mt 3.17 π 2n 1 ( ) ( ) ( )

29 3.3 Double Sideband-Suppressed Carrier Modulation Ring Modulator (4/4) Assuming that m(t) is limited to the frequeny band -W f W, the spetrum of the modulator output onsists of sidebands around eah of the odd harmonis of the square-wave arrier m(t). To prevent sideband overlap f >W. We an use a band-pass filter of mid-band frequeny f and bandwidth 2W to selet the desired pair of sidebands around the arrier frequeny f. The iruitry needed for the generation of a DSB-SC modulated wave onsists of a ring modulator followed by a band-pass filter. 29

30 3.3 Double Sideband-Suppressed Carrier Modulation Coherent Detetion (1/4) It is assumed that the loal osillator signal is exatly oherent or synhronized, in both frequeny and phase, with arrier wave (t) used in the produt modulator to generate s(t). This method of demodulation is known as oherent detetion or synhronous demodulation. 30

31 3.3 Double Sideband-Suppressed Carrier Modulation Coherent Detetion (2/4) For a more general demodulation proess, we assumeφ is a arbitrary phase differene. υ ' = os 2π ( t) = Aos ( 2πft + φ) s( t) ' = AAos( 2πft) os( 2π ft+ φ ) m( t) ( 3.18) 1 ' 1 = AA os 4πft + m t + AA m t 2 2 ' ( φ) ( ) osφ ( ) ( ) ( ) ( ) s t A ft m t 31

32 3.3 Double Sideband-Suppressed Carrier Modulation Coherent Detetion (3/4) The first term in Eq.(3.18) is removed by low-pass filter, provided that the ut-off frequeny of this filter is greater than W but less than 2f W. This is satisfied by hoosing f >W. Therefore: 1 ' υo( t) = AA os φm( t) ( 3.19) 2 v o (t) is proportional to m(t) when the phase errorφ is a onstant. Attenuated by a fator equal to osφ. 1 ' vo_ max = AAm ( t),when φ=0 2 π vo _ mim = 0, when φ= ± 2 (quadrature null effet) When the phase error φ is onstant, the detetor provides an undistorted version of the original baseband signal m(t). 32

33 3.3 Double Sideband-Suppressed Carrier Modulation Coherent Detetion (4/4) In pratie, we usually find that the phase error φ varies randomly with time, due to random variations in ommuniation hannel. The result is that at the detetor output, the multiplying fator osφ also varies randomly with time, whih is obviously undesired. Provision must be made in the system to maintain the loal osillator in the reeiver in perfet synhronism, in both frequeny and phase, with the arrier wave used to generate the DSB-SC modulated signal in the transmitter. The resulting system omplexity is the prie that must be paid for suppressing the arrier wave to save transmitter power. 33

34 3.3 Double Sideband-Suppressed Carrier Modulation Costas Reeiver (1/2) One method of obtaining a pratial synhronous reeiver system, suitable for demodulating DSB-SC waves. A multiplier followed by a low-pass filter. 34

35 3.3 Double Sideband-Suppressed Carrier Modulation Costas Reeiver (2/2) The frequeny of the loal osillator is adjusted to be the same as the arrier frequeny f, whih is assumed known a prior. The detetor in the upper path is referred to as the in-phase oherent detetor or I-hannel, and that in the lower path is referred to as the quadrature-phase oherent detetor or Q- hannel. These two detetors are oupled together to from a negative feedbak system designed in suh a way as to maintain the loal osillator synhronous with the arrier wave. By ombining the I- and Q-hannel outputs in phase disriminator (whih onsists of a multiplier followed by a lowpass filter), a d ontrol signal is obtained that automatially orrets for loal phase errors in the voltage-ontrolled osillator (VCO). 35

36 3.3 Double Sideband-Suppressed Carrier Modulation Outputs of Produt Modulator I-Channel Q-Channel Outputs of Low-Pass Filter I-Channel Q-Channel Output of Multiplier 1 Aos ( 2π ft ) m( t) os( 2π ft + φ) = Am ( t) os( 4π ft + φ) + osφ 2 { } 1 Aos ( 2π ft ) m( t) sin ( 2π ft + φ) = Am ( t) sin ( 4π ft + φ) + sinφ ( ) Am t ( ) Am t osφ sinφ { } Amt ( ) os ( ) sin ( ) 2 φ Amt φ = A mt sin 2φ

37 Chapter 3.4 Quadrature-Carrier Multiplexing Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University

38 3.4 Quadrature-Carrier Multiplexing Enable two DSB-SC modulated waves to oupy the same hannel bandwidth. It is a bandwidth-onservation sheme. ( ) = ( ) os( 2π ) + ( ) sin( 2π ) ( 3.20) s t Am t ft Am t ft 1 2 in-phase omponent quadrature-phase omponent It is important to maintain the orret phase frequeny relationship between the loal osillators used in the transmitter and reeiver parts of the system. 38

39 Chapter 3.5 Single-Sideband and Vestigial- Sideband Methods of Modulation Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University

3.5 Single-Sideband and Vestigial- Sideband Methods of Modulation With double-sideband modulation, we are transmitting only one suh signal and the question that omes to mind is whether the bandpass

40 3.5 Single-Sideband and Vestigial- Sideband Methods of Modulation With double-sideband modulation, we are transmitting only one suh signal and the question that omes to mind is whether the bandpass bandwidth of 2W is atually required. In atual fat, it an be shown that due to the symmetry of the DSB signal about the arrier frequeny, the same information is transmitted in the upper and lower sidebands, and only one of the sidebands needs to be transmitted. There are two bandwidth onservation methods: Single-sideband (SSB) modulation. Vestigial sideband (VSB) modulation. 40

41 Single-sideband modulation The generation of a SSB signal is straightforward. First, generate a double-sideband signal Then apply an ideal pass-band filter to the result with utoff frequenies of f and f +W (or f W) for the upper sideband (or lower sideband). Pratially, the approximate onstrution of an ideal filter is very diffiult. Voie Signal 41

42 VSB Modulation(1/3) A vestigial-sideband system is a ompromise between DSB and SSB. It inherits the advantages of DSB and SSB but avoids their disadvantages. VSB signals are relatively easy to generate and their bandwidth is only slightly (typially 25 perent) greater than that of SSB signals. In VSB, instead of rejeting one sideband ompletely as in SSB, a gradual utoff of one sideband is aepted. All of the one sideband is transmitted and a small amount (vestige) of the other sideband is transmitted as well. The filter is allowed to have a nonzero transition band. The roll-off harateristi of the filter is suh that the partial suppression of the transmitted sideband in the neighborhood of the arrier is exatly ompensated for by the partial transmission of the orresponding part of the suppressed sideband. 42

43 VSB Modulation(2/3) Our goal is to determine the partiular H( f ) required to produe a modulated signal s(t) with desired spetral harateristis, suh that the original baseband signal m(t) may be reovered from s(t) by oherent detetion. ( ) = ( ) ( ) S f U f H f A = M f f + M f + f H f 2 m(t) F M( f ), u(t) F U( f ) ( ) ( ) ( ) ( 3.21) Figure 3.18:Amplitude response of VSB filter; only positive-frequeny portion is shown. f v : the width of the vestigial sideband 43

44 VSB Modulation(3/3) ' ( ) = os( 2π ) ( ) v t A ft s t ' A V f S f f S f f 2 ' Combine Eq. (3.21) and (3.22) AA V( f ) = M( f ) ( ) ( ) 4 H f f + H f + f ' AA + M f 2 f H f f + M f + 2 f H f + f ( ) = ( ) + ( + ) ( 3.22) ( ) ( ) ( ) ( ) ( ) Low-pass filter ' AA V0 f M f H f f H f f ( ) = ( ) ( ) + ( + ) ( ) To obtain baseband signal m(t) at oherent detetor output, we require V o ( f ) to be a saled version of M( f ). Therefore, we an hoose: Eq. (3.24) beomes 44 F ( ) + ( + ) = 1, ( 3.26) H f f H f f W f W ' AA υ 0 ( t) = mt ( ) baseband M( f ) interval: 4 -W f W

45 Chapter 3.7 Frequeny Translation Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University

46 3.7 Frequeny Translation The basi operation involved in single-sideband modulation is in fat a form of frequeny translation. SSB modulation is sometimes referred to as frequeny hanging, mixing, or heterodyning. The mixer onsists a produt modulator followed by a band-pass filter. Band-pass filter bandwidth: equal to that of the modulated signal s 1 (t) used as input. arrier frequeny f 1 arrier frequeny f 2 46

47 3.7 Frequeny Translation Due to frequeny translation performed by the mixer : We may set f = f + f 2 1 f = f f l l 2 1 assume f 2 >f 1 translated upward or f = f f 2 1 f = f f l l 1 2 assume f 1 >f 2 translated downward ( ) os( 2π ) = ( ) os( 2π ) os( 2π ) s t A ft m t ft A ft 1 l l 1 l l 1 = Am l ( t) os 2π( f + fl) t + f fl t 2 ( 1 ) os( 2π( 1 ) ) The band-pass filter rejets the unwanted frequeny and keeps the desired one. Mixing is a linear operation. 47

3.1 Introduction 3.2 Amplitude Modulation 3.3 Double Sideband-Suppressed Carrier Modulation 3.4 Quadrature-Carrier Multiplexing 3.

3.1 Introduction 3.2 Amplitude Modulation 3.3 Double Sideband-Suppressed Carrier Modulation 3.4 Quadrature-Carrier Multiplexing 3. Chapter 3 Amplitude Modulation Wireless Information Transmission System Lab. Institute of Communications Engineering g National Sun Yat-sen University Outline 3.1 Introduction 3. Amplitude Modulation 3.3