1-B.P. Lathi, Modern Digital and Communication Systems, Fourth Edition, Oxfodr university press, 2009.

Transcription

1 Items : 1-Introduction to Communication Systems 2-Amplitude Modulation 3- Angle Modulation 4-Detectors and Receivers. 5- Pulse Modulation. 6-Noise in Communication Systems 7- Transmission Line Theory. Reference : 1-B.P. Lathi, Modern Digital and Communication Systems, Fourth Edition, Oxfodr university press, Rodger E. Ziemer and William H. Tranter, Principles of Communications systems, modulation and noise, sixth edition, john Wiley and Sons, Inc., Simon Haykin, Communication Systems, fourth Edition, John Wiley and Sons, Inc., Eerrel G. Steremler," Introduction to Communication Systems", second edition, part one, part two and part three, سيد احمد مرعي," اساسيا ت الاتصالات ", مديرية دار الكتب للطباعة والنشر, جامعة الموصل, كانون الثاني

2 Item 1 : Introduction to Communication Systems Transmitted Message x(t) Information Image video audio speech Channel Encoder Transmitter Tx message thought put into words ( verbal symbols or any the symbolic form of expression ) Modulation Tx signal Channel h(t) Noise and Distortion Channel Decoder Received Messages y(t)=x(t) h(t) Receiver Rx Demodulation Rx signal Communications system block diagram Transmitter (Tx). 1-The transmitter puts the information from the source (meant for the receiver) on to the channel. The information can be represented using the signals. A signal is formally defined as a function of one or more variables that conveys information on the nature of a physical phenomenon. The signals can be classified in various ways such as: a)power or Energy. b) Deterministic or Random. c) Real or Complex. d) Periodic or a periodic. f) continues time signal and discrete time signal. h) Analog signal and digital signal. 2

3 2-converts electrical signal into a form suitable for transmission through the channel 3- conversion is made through modulation : amplitude (AM), frequency (FM)and phase (PM). Example : AM, FM radio broadcast. 4-other function : filtering, amplification, radiation. Modulation: Modulation is defined as the process by which some characteristics (i.e. amplitude, frequency, and phase) of a carrier are varied in accordance with a modulating wave. Channel. The channel is the medium connecting the transmitter and the receiver and the transmitted information travels on this channel until it reaches the destination. Channels can be of two types: 1) wired channels : telephone line Twisted pair telephone channels Coaxial cables Fiber optic cable 2) wireless channels: radio earth s atmosphere (enabling the propagation of ground wave and sky wave Satellite channel Laser beam. Radio wave. Sea water etc. For efficient radiation, the size of the antenna should be λ/ 10 or more (preferably around λ/ 4 ), where λ is the wavelength of the signal to be radiated. Take the case of audio, which has spectral components almost from DC up to 20 khz. Assume that we are designing the antenna for the mid frequency; that is,10 khz. Then the length of the antenna that is required, even for the λ/ 10 situation is: c/ f 10= / = meters, c being the velocity of light. 3

4 Even an antenna of the size of 3 km, will not be able to take care of the entire spectrum of the signal because for the frequency components around 1 khz, the length of the antenna would be λ/ 100. Challenges. a) the transmitted signals may have to travel long distances (there by undergoing severe attenuation) before they can reach the receiver. b) of imperfections of the channel over which the signals have to travel. c) of interference due to other signals sharing the same channel and d) of noise at the receiver input1. The term noise is present unwanted signals that tend to disturb the transmission and processing of signals in communication systems and over which we have incomplete control. In practice, we find that there are many potential sources of noise in a communication system. The sources of noise : 1- external to the system ( atmospheric noise, galactic noise, man-made noise), 2- internal to the system.( white noise, thermal noise,..) The second category includes an important type of noise that arises from spontaneous fluctuations of current or voltage in electrical circuits. Receiver (Rx). 1- main function : to recover the message from the received signal. 2- Demodulation : inverse of the modulation. 3- Operates in the presence of noise and interference. 4- Filtering, suppression of noise and interference. Demodulation is the reverse process of modulation, which is used to get back the original message signal. Modulation is performed at the transmitting end whereas demodulation is performed at the receiving end. In analog modulation sinusoidal signal is used as carrier where as in digital modulation pulse train is used as carrier. 4

5 Type of Communication Systems. 1- Types of communication systems : wire line and wireless, RF and optical, digital and analog, point-to-point and broadcasting, low frequency / high frequency 2- Example : telephone, cell phone, TV, internet, hard disk in a PC. Aim of communications Engineer. To design transmitter and receivers that are : 1- Cost efficient 2- Bandwidth efficient. 3- Maximize information transfer (message at sink is a faithful representation of the source message). 4- Power efficient (uses little power necessary) Many of the above goals are contrary to one another : 1- For example, one way to improve message fidelity at the receiver is to increase transmit power. 2- Therefore tradeoffs are required. 5

6 Item 2 : Amplitude Modulation Causes of modulation in communication systems : 1) To send a signal over long distance it requires more energy. E = hv; E = Energy of the signal,h = plancks constant,v = frequency of the signal Modulation is the process of increasing the frequency content of a signal ( indirectly increasing the energy of the signal to enable it to travel long distance). Demodulation is the exactly opposite process to it (Decreasing the frequency content of the signal) 2) to decrease antenna height. For transmitting a signal of wavelength λ the antenna height must be λ/4. So if we want to send a 1 Hz (λ=3*10^8 m) signal ( very low frequency) using an antenna, its height must be 75,000 Km ( impossible to build such a huge antenna ). If the same signal is modulated to some high frequency say 88 MHZ ( λ = 3.4 m ), antenna height needed is m (88 MHZ is the starting range of Frequency modulation which exists up to 108 MHZ). 3-modulation is a process in which the characteristics like frequency, time, amplitude and phase of a carrier signal is changed according to message signal. 6

7 Modification of Amplitude Modulation (AM). Amplitude modulation results when a DC bias A is added to m(t) prior to the modulation process. The result of the DC bias is that a carrier component is present in the transmitted signal. For AM, the transmitted signal is typically defined as y(t) =x(t) cos(ω c t) in which Ac is the amplitude of the un modulated carrier A cos (ω c t) is the normalized message signal to be discussed in the following paragraph, and the parameter a 1 is known as the modulation index.1 We shall assume that m(t) has zero DC value so that the carrier component in the transmitted signal arises entirely from the bias. x(t) y(t) =x(t) cos(ω c t) Carrier signal cos(ω c t) 2222ff cc carrier frequency Multiplying a signal by a sinusoidal carrier signal is called amplitude modulation. The signal modulates the amplitude of the carrier. 7

8 There are three types of linear modulation involving a single message signal: 1. Double sideband-suppressed carrier (DSB-SC) modulation, where only the upper and lower sidebands are transmitted. 2. Single sideband (SSB) modulation, where only one sideband (the lower sideband or the upper sideband) is transmitted. 3. Vestigial sideband (VSB) modulation, where only a vestige of one of the sidebands and a correspondingly modified version of the other sideband are transmitted. AMPLITUDE MODULATION DOUBLE-SIDEBAND-SUPPRESSED CARRIER.(AM-DSB/SC) This form of linear modulation is generated by using a product modulator that simply multiplies the message signal m(t) by the carrier wave Ac cos(2πfct). (a) Block diagram of product modulator. (b) Baseband signal. (c) DSB- SC modulated wave 8

9 As DSB-SC modulation involves just the multiplication of the message signal and the carrier, this scheme is also known as product modulation m(t) s(t) A c cos ω c t s(t) = A c m(t) cos(2πfct) For double-sideband (DSB) modulation, A = 0 and Sc(t) = m(t) cos 2πfct The Fourier transform of s(t) is obtained as ss(ff) = 1 2 AA cc [MM(ff ff cc ) + MM(ff + ff cc )] Where M(f): Fourier transform Lower Side Band Lower Side Band Lower Side Band Upper Side Band (a) Spectrum of baseband signal. (b) Spectrum of DSB-SC Power calculation of DSB-SC. Total power P T =P LSB + P USB +Pc Total power P T =A c 2 A m 2 /8+ A c 2 A m 2 /8+Pc 9

10 Total power P SB =A c 2 A m 2 /4 Exercise An antenna has an impedance of An un modulated AM signal produces a current of 4.8 A. The modulation is 90 percent. Calculate (a) the carrier power, (b) the total power, and (c) the sideband power. Example1: Draw the modulated output signal for a< 1, of message signal as show in fig.(a) and the modulator show in fig.(c). m n (t) am n (t) 1+am n (t) X c (t) + a 1 A c cos(2πf c t) (c) 10

11 Example 2 Let m(t) be real signal with the spectrum M(f),f c =100KHz.A c /2=1. Draw the shifted spectrum. Baseband spectrum (real signal) Shifted spectrum Example 3: Let m(t) be a complex signal with M(f) as shown. draw the shifted spectrum at f c =100KHz. Baseband spectrum (complex) USB LSB LSB USB Shifted spectrum 11

12 Any one of these two sidebands has the complete information about the message signal. As we shall see later, SSB modulation conserves the bandwidth by transmitting only one sideband and recovering the m(t ) with appropriate demodulation. Example 4: consider the scheme shown in Fig. The ideal HPF has the cutoff frequency at 10 khz. Given that f1 = 10 khz and f2 = 15 khz, let us sketch Y (f ) for the X (f ) given at (b). We have V (f ) = X (f f1) + X (f + f1), which is as shown in (a). The HPF eliminates the spectral components for f 10 khz. Hence W (f ) is shown in (b) Y (f ) = W (f f2 ) + W (f + f2 ). This is shown in (c). 12

13 AMPLITUDE MODULATION SINGLE -SIDEBAND-SUPPRESSED CARRIER.(AM-SSB/SC) the USB and LSB have even amplitude and odd phase symmetry about the carrier frequency Thus transmission of both sidebands is not necessary because the transmitted information in LSB same with transmitted information USB. when one of the sideband has been separated and the same information can be transmitted in ½ BW. AM-SS/Sc Signal a)signal spectrum b) modulated signal spectrum 13

14 VESTIGIAL SIDE BAND MODULATION. In vestigial sideband (VSB) modulation, one of the sidebands is partially up pressed and a vestige of the other sideband is transmitted to compensate for that suppression. frequency discrimination method can be used to generating a VSBmodulated wave is to use the. We generate a DSB-SC modulated wave and then pass it through a band pass filter, as shown in Figure, it is the special design of the band-pass filter that distinguishes VSB modulation from SSB modulation. Assuming that a vestige of the lower sideband is transmitted. The frequency response H(f) of the band-pass filter takes the form shown in Figure.at the carrier frequency fc, the H(fc) = 1/2. The cutoff portion of the frequency response around the carrier frequency fc exhibits odd symmetry. That is, inside the transition interval fc - fv f fc + fv: 1. The sum of the values of the magnitude response H(f) at any two frequencies equally displaced above and below fc is unity. 2. The phase response H(f) is linear: H(f fc) +H ( f + fc)=1 for W f W 14

15 The transmitted band width of VSB modulation is B T =W +f v W: message band width./ f v : the width of the vestigial sideband. The VSB modulated wave in time domain : ss(tt) = 1 2 AA ccmm(tt) cos(2ππff cc tt) 1 2 AA ccmm (tt) sin(2ππff cc tt) Spectra of AM signals. Taking the Fourier transform: [ss(ff)] AAAA = AA cc 2 [δδ(ff ff cc) + δδ(ff + ff cc )] + AA cc 2 [MM(ff ff cc) + MM(ff + ff cc )] Baseband message spectrum M(f ) Upper sideband Lower sideband Lower sideband Upper sideband Spectrum of the AM signal 15

16 1-The spectrum has two sidebands, the USB [between fc to fc + W, and ( fc W) to fc] and the LSB[ ( fc W to fc and fc to ( fc + W) ]. 2-If the baseband signal has bandwidth W, then the AM signal has bandwidth 2W. That is, the transmission bandwidth BT, required for the AM signal is 2W. 3-Spectrum has discrete components at f = ± fc, indicated by impulses of area A c /2. 4-In order to avoid the overlap between the positive part and the negative part of S(f ), fc > W (In practice, fc >> W, so that s (t ) is a narrowband signal) The discrete components at f = ± fc, do not carry any information and as such AM does not make efficient use of the transmitted power. Example 5 : For AM with tone modulation, let us find ηη = of modulation index µ. for tone modulation tttttttttt ssssssssssssssss pppppppppp tttttttttt pppppppppp as a function Carrier term =AA cc cos(ωω mm tt) ss(tt) = AA cc [1 + μμ cos(ωω mm tt)] cos(ωω mm tt) Carrier power= AA cc 2 2 USB term= AA ccμμ 2 cos(ωω cc + ωω mm )tt Power in USB= AA ccμμ = AA cc 2 μμ 2 8 Power in LSB=power in USB Total sideband power = 2 AA cc 2 μμ 2 Total power = AA cc 2 + AA cc 2 μμ = AA cc 2 2 = AA cc 2 μμ μμ 2 2 = AA cc 2 (2+μμ 2 ) 4 16

17 ηη = AA cc 2 μμ 2 4 AA cc 2 (2 + μμ 2 ) 4 = μμ2 2 + μμ 2 μ η ss(tt) = AA cc [1 + μμ cos(ωω mm tt)]cccccc(ωω mm tt) RRRR{AA cc ee jjjj cctt + AA ccμμ 2 eejj (ωω cc +ωω mm } tt + ee jj (ωω cc ωω mm } tt } [ss(tt)] cccc = AA cc + AA ccμμ 2 eejj ωω mm tt + AA ccμμ 2 ee jj ωω mm tt Pharos diagram for AM with tone modulation Pharos diagrams such as the one shown in Fig. are helpful in the study of unequal attenuation of the sideband components. 17

18 Example 6 : Let Ac = 1, μ = 1 /2 and let the upper sideband be attenuated by a factor of 2. Let us find the expression for the resulting envelope, A(t ). Phasor diagram for an AM signal with unequal sidebands the sidebands is no longer collinear with the carrier [ss(tt)] cccc = cos(ωω mmtt) + jjjjjjjj(ωω mm tt) cos(ωω mmtt) jjjjjjjj(ωω mm tt) = cos(ωω mmtt) jj 1 8 ssssss(ωω mmtt) AA(tt) = [( cos(ωω mmtt)) jjjjjjjj(ωω mmtt) ] 1 2 The AM signal is really a composite of several signal voltages, namely, the carrier and the two sidebands, and each of these signals produces power in the antenna. The total transmitted power P T is simply the sum of the carrier power P c and the power in the two sidebands P USB and P LSB : PT=P c + P USB + P LSB vv AAAA = VV cc sin 2ππff cc tt + VV mm 2 cos 2ππππ( ff cc ff mm ) VV mm 2 cos 2ππππ( ff cc + ff mm ) Carrier lower sideband upper sideband 18

19 VV cc and VV mm are peak values of the carrier and modulating sine waves. The rms carrier and sideband voltages : vv AAAA = VV cc 2 sin 2ππff cctt + VV mm 2 2 cos 2ππππ( ff cc ff mm ) VV mm 2 2 cos 2ππππ( ff cc + ff mm ) The power in the carrier and sidebands can be calculated by using the power formula P=V 2 /R where P is the output power, V is the rms output voltage, and R is the resistive part of the load impedance, which is usually an antenna. VV mm ( VV cc PP TT = 2 )2 ( RR )2 + RR ( VV mm 2 2 )2 RR = VV cc 2 2RR + VV 2 mm 8RR + VV mm 8RR 2 β= VV mm VV cc VV mm = mmvv cc PP TT = (VV cc ) 2 RR + (mmmm cc ) 2 8RR + (mmmm cc ) 2 8RR = VV cc 2RR + mm2 VV cc 8RR mm2 VV cc 8RR 2 VV cc 2 2RR = rrrrrr cccccccccccccc pppppppppp PPPP PP TT = (VV cc ) 2 (mm)2 (1 + RR 4 + (mm)2 4 the total power in an AM signal when the carrier power and the percentage of modulation are known: PP TT = PP cc (1 + (mm)2 2 ) P T =I T 2 R II TT = IIII (1 + mm 2 /2) mm = 2 II 2 TT 1 II cc 19

20 Generation of AM : We shall discuss two methods of generating AM signals, one using a nonlinear element and the other using an element with time-varying characteristic. 1-Square law product consider the scheme shown below : V 1 (t) V 2 (t) A circuit with a nonlinear element v-j characteristic of the diode For small variations of v around a suitable operating point, v2 (t ) vv oo (tt) = αα 1 vv ii (tt) + αα 2 vv 2 ii (tt) αα 1 aaaaaa αα 2 : constant vv ii (tt) = AA cc cos(2ππff cccc ) + mm(tt) 20

21 vv oo (tt) = αα 1 AA cc 1 + 2αα 2 mm(tt) cos(2ππff cccc ) + αα 1 mm(tt) + αα 2 mm 2 (tt) αα 1 + αα 2 AA 2 cccccccc 2 (2ππff cccc ) Spectra of the components of v2 (t ) component AA cc cos(2ππff cccc ) 2αα 2 AA cc mm(tt)cccccc 2 (2ππff cccc ) αα 1 mm(tt) αα 2 mm 2 (tt) αα 2 AA 2 cccccccc 2 (2ππff cccc ) Spectrum A B C D E then the required AM signal would be available at the output of the filter. This is possible by placing a BPF with centre at fc and bandwidth 2W provided ( fc W )> 2W or fc > 3W. The disadvantages. 1) The required square-law nonlinearity of a given device would be available only over a small part of the (v i ) characteristic. Hence, it is possible to generate only low levels of the desired output. 2) If fc is of the order of 3W, then we require a BPF with very sharp cut off characteristics. Spectrum of message signal Spectrum of AM signal 21

22 2- Switching modulator In this method, diode will be used as a switching element. As such, it acts as a device with time-varying characteristic (a) Switching modulator (b) Switching characteristic of the diodeload combination. If we assume that m(t) max << Ac vv 1 (tt) = cc(tt) + mm(tt) = AA cc cos(2ππff cccc ) + mm(tt) vv 2 (tt) = vv 1(tt) cc(tt) > 0 0 cc(tt) 0 vv 2 (tt) = vv 1 (tt)xx pp (tt) Where xx pp (tt) is the periodic rectangular pulse train When f 0 =f c xx pp (tt) = 1 iiii cc(tt) > 0 (pppppppppppppppp haaaaaa cccccccccc oooo cc(tt)) 0 iiii cc(tt) < 0( nnnnnnnnnnnnnnnn haaaaaa cccccccccc oooo cc(tt)) xx pp (tt) = xx nn ee jj 2ππππ ff cctt nn= Where xx nn = 1 2 sin nn 2 xx nn = 0 ffffff nn = ±2, ±4. xx pp (tt) = ππ cos( 2ππff cctt) + ( 1)nn 1 cos [2ππ(2nn 1)ff 2nn 1 cc tt nn=2 22

23 vv oo (tt) = AA cc / ππaa cc mm(tt) cos(2ππff cc tt) + mm(tt) 2 + 2AA cc/ππcccccc 2 (2ππff cc tt). switching modulator advantages: a) Generated AM signals can have larger power levels. b) Filtering requirements are less stringent because we can separate the desired AM signal if fc > 2W. Spectrum of message signal Spectrum of AM signal 23

24 balanced modulator 1-A balanced modulator is a circuit that generates a DSB signal, suppressing the carrier and leaving only the sum and difference frequencies at the output. 2-The output of a balanced modulator can be further processed by filters or phase-shifting circuitry to eliminate one of the sidebands, resulting in a SSB signal. SS 1 (tt) = AA cc [1 + kk aa mm(tt)]cccccc 2ππff cc tt SS 2 (tt) = AA cc [1 kk aa mm(tt)]cccccc 2ππff cc tt SS(tt) = SS 1 (tt) SS 2 (tt) = 2AA cc kk aa mm(tt)cccccc 2ππff cc tt SS(ff) = kk aa AA cc [MM(ff ff cc ) + MM(ff + ff cc )] Spectrum of message signal Spectrum of AM signal 24

25 3- Transistor linear modulation Low-Level AM: Transistor Modulator: 1-Transistor modulation consists of a resistive mixing network, a transistor, and an LC tuned circuit. 2-The emitter-base junction of the transistor serves as a diode and nonlinear device. 3-Modulation and amplification occur as base current controls a larger collector current. 4-The LC tuned circuit oscillates (rings) to generate the missing half cycle. +v cc Carrier AM Modulation signal Simple transistor modulator 25

26 AM Transmitter Principles An AM transmitter can be divided into two major sections according to the frequencies at which they operate, radio-frequency and audio-frequency units. 1-The radio-frequency unit is the section of the transmitter used to generate the radio-frequency carrier wave. oscillator stage where it is generated as a constantamplitude, constant-frequency sine wave. The carrier is not of sufficient amplitude and must be amplified in one or more stages before it attains the high power required by the antenna. With the exception of the last stage, the amplifiers between the oscillator and the antenna are called INTERMEDIATE POWER AMPLIFIERS (IPA) The final stage, which connects to the antenna, is called the FINAL POWER AMPLIFIER (FPA). Block diagram of an AM Modulation 2-The second section of the transmitter contains the audio circuitry. This section of the transmitter takes the small signal from the microphone and increases its amplitude to the amount necessary to fully modulate the carrier. The last audio stage is the MODULATOR. It applies its signal to the carrier in the final power amplifier.. 26

27 Single Sideband Transmitter 160m 20w AM Transmitter Advantages of Amplitude modulation:- Generation and detection of AM signals are very easy It is very cheap to build, due to this reason it I most commonly used in AM radio broad casting Disadvantages of Amplitude of modulation:- Amplitude modulation is wasteful of power Amplitude modulation is wasteful of band width Application of Amplitude modulation: - AM Radio Broadcasting 27

28 Introduction. UItem 3 : Angle Modulation It is another method of modulating a sinusoidal carrier wave, namely, angle Modulation in which either the phase or frequency of the carrier wave is varied according to the message signal. there are two types of Angle modulation techniques namely: 1. Phase modulation 2. Frequency modulation e(t) = A cos (ωt + φ) Angle modulation : phase- frequency modulation 28

29 Phase Modulation PM θθ ii (tt) = 2ππff cc tt + kk pp mm(tt) 2ππff cc :phase of un modulated carrier signal kk pp : modulator constant rad/volt mm(tt):modulation signal volt ee(tt) PPPP = AA cc cos [2ππff cc + kk pp mm(tt)] Frequency Modulation FM ff ii (tt) = ff cc + kk ff mm(tt)] ff cc :frequency of un modulated carrier signal kk ff : modulator constant Hz/volt tt θθ ii (tt) = 2ππππ cc tt + 2ππ kk ff mm(tt) 0 Modulating wave tt ee(tt) FFFF = AA cc cos [2ππff cc tt + 2ππππ ff mm(tt)dddd] 0 Differentiator Frequency modulator PM signal AA cc cos (2ππff cc ) Generation of PM signal using frequency modulator Modulating wave Integration Phase modulator FM signal AA cc cos (2ππff cc ) Generation of FM signal using phase modulator 29

30 Single Tone Frequency Modulation m(t) = A m cos (2πf m t) ff:frequency deviation ff ii (tt) = ff cc + ffcccccc (2ππff mm tt) ff = kk ff AA mm θθ ii (tt) = 2ππff cc tt + ββsin (2ππff mm tt) ββ = ff ff mm ee(tt) FFFF = AA cc cos [ωω cc tt + ββ sin(ωω mm tt)] Where β= f/fm= modulation index of the FM wave 1- When β<<1 radian then it is called as narrowband FM consisting essentially of a carrier, an upper side-frequency component, and a lower side-frequency component. 2- When β>>1 radian then it is called as wideband FM which contains a carrier and an infinite number of side-frequency components located symmetrically around the carrier. Multi Tone Frequency Modulation Let mm(tt) = AA 1 cos(ωω 1 tt) + AA 2 cos(ωω 2 tt) Where ff 1 and ff 2 are arbitrary. ss pppp (tt) = AA cc ee jj ββ 1sin (ωω 1 tt)] ee jj ββ 1 sin (ωω 2 tt)] ee jj ωω cctt ββ 1 = AA 1kk ff ff 1 and ββ 2 = AA 2kk ff ff 2 ss pppp (tt) = AA cc JJ mm (ββ 1 ) ee jj mmmm 1tt ][ JJ nn (ββ 2 ) ee jj nnnn 2tt ]}ee jj ωω cctt mm nn ss pppp (tt) = AA cc JJ mm mm nn (ββ 1 )JJ nn (ββ 2 )cccccc [(ωω cc + mmmm 1 + nnωω 2 )tt] 30

31 1- Narrow Band Frequency Modulation (NBFM). xx(tt) FFFF = AA cc cos(ωωωω) cos [ββ sin(ωωωωωω)] AAAAAAAA(ωω cc tt)sin [ββsin ( ωωωωωω)] For study case, assume : cos [ββ sin(ωωωωωω)] 1 sin [ββ sin(ωωωωωω)] ββ sin(ωωωωωω) xx(tt) FFFF = AA cc cos(ωω cc tt) ββaa cc ssssss(ωω cc tt)sin ( ωωωωωω) m(t) ʃdt FM PM Parallel modulator + NBFM Phase shift 90 o Oscillator cos(ωω cc tt) Generation of NBFM signal xx(tt) FFFF = AA cc cos(ωω cc tt) ββaa cc[cos(ωω cc + ωωωω) tt cccccc ( ωω cc ωωωω)tt] xx(tt) AAAA = AA cc cos(ωω cc tt) ββaa cc[cos(ωω cc + ωωωω) tt + cccccc ( ωω cc ωωωω)tt] 31

32 A pharos comparison of narrowband FM and AM waves for sinusoidal modulation. (a) Narrowband FM wave. (b) AM wave. 32

33 2-Wide Band Frequency Modulation (WBFM). The spectrum of single-tone FM signal, the modulation index is β. ss(tt) = AA cc cos [2ππff cc tt + ββ sin(2ππff mm tt)] ββ = ff ff mm We assume that the carrier frequency f c is large enough compared to the bandwidth of FM signal. s(t) FM = Re[Ac exp (j2πf c t + jβ sin(2πf m t )] = Re[s(t) exp(j2πf c t)] where s(t) is the complex envelope of the FM signal s(t) FM ss(tt) = cccc eeeeee(jj2ππff mm tt) where the complex Fourier coefficient cn is defined by cccc = ff mm AA cc 1 2 ff mm 1 2 ff mm exp [jjjj sin(2ππff mm tt) jj2ππππff mm tt]dddd 33

34 Assume xx = 2ππff mm tt cccc = AA cc 2ππ 1 2 ff mm 1 2 ff mm ππ JJ nn (ββ) = 1 2ππ cn=a c J n (β) ππ TT = 2ππ ωωωω exp [jjjj sin xx nnnn]dddd exp [jjjj sin xx nnnn]dddd ss(tt) FFFF = AA cc. RRRR[ JJ nn (ββ) eeeeee(jj2ππ(ff cc + nnnn mm ) tt) nn= This is the desired form for the Fourier series representation of the single-tone FM signal s(t) for an arbitrary value of β. The discrete spectrum of s(t) is obtained by taking the Fourier transforms of both sides. Plots of Bessel functions JJ nn (ββ )of the first kind for varying d 34

35 ss(ff) FFFF = AA cc 2 JJ nn(ββ)[δδ(ff ff cc nnnn mm ) + δδ((ff + ff cc + nnnn mm )] nn= JJ nn (ββ ) properties : 1-JJ nn (ββ) = ( 1) nn JJ nn (ββ) for all n, both positive and negative 2-for small values of the modulation index ββ : Example 7: JJ 0 (ββ) 1 JJ 1 (ββ) ββ 2 JJ nn (ββ) 0, nn > 2 nn= JJ 2 nn (ββ) = 1 The investigate variations in the amplitude and frequency of a sinusoidal modulating signal affect the spectrum of the FM signal. Discrete amplitude spectra of an PM signal, normalized with respect to the carrier amplitude, for the case of sinusoidal modulation of fixed frequency and varying amplitude. Only the spectra for positive frequencies are shown. 35

36 Discrete amplitude spectra of an FM signal, normalized with respect to the carrier amplitude, for the case of sinusoidal modulation of varying frequency and fixed amplitude. Only the spectra for positive frequencies are shown. 36

37 Example 8: Compare AM to FM for x(t)= cos (ωmt). The advantages of FM: 1-constant power 2-no need to transmit carrier ( unless DC important) 3-bandwidth 37

38 Generation of FM signals There are two distinct methods of generating WBFM signals: a) Direct FM b) Indirect FM. Details on their generation are as follows. a) Indirect FM (Armstrong s method). In this method - attributed to Armstrong - first a narrowband FM signal is generated. This is then converted to WBFM by using frequency multiplication. This is shown schematically in Fig Generation of WBFM (Armstrong method) The generation of NBFM has already been described. A frequency multiplier is a nonlinear device followed by a BPF. A nonlinearity of order n can give rise to frequency multiplication by a factor of n. consider a square law device with output y (t ) = x2 (t ) where x (t ) is the input. Let x (t ) be the FM signal. xx(tt) = cos[θθ(tt)], wwheeeeee θθ(tt) = ωω cc tt + 2ππkk tt yy(tt) = cos 2 [θθ(tt)] = 1 2 [1 + cos[2θθ(tt)] yy(tt) = cos[2ωω cctt] + 4ππkk tt The DC term can be filtered out to give an FM output. Carrier frequency:2f c Frequency deviation of NBFM: f tt tt mm(αα)dddd mm(αα)dddd 38

39 Frequency deviations: f,2: f, n: f The multiplication scheme used in FM transmitter Frequency f 64 convertor f 48 fc1=200 khz fc1=200 khz f1=25 Hz f1=25 Hz fc2=12.8 MHz f2=1.6 Hz fc3=200 khz f3=25 Hz fc4=200 khz f4=25 Hz Crystal oscillator 10.9 MHz The carrier frequency of the NBFM signal fc1, is 200 khz with the corresponding Δf1 = 25 Hz. Desired FM output is to have the frequency deviation Δf4 = 75 khz and a carrier (fc 4 ) of 91.2 MHz. To obtain Δf4 = 75 khz starting from Δf1 = 25 Hz, we require a total frequency multiplication of ( )/25=3000 f c 1=200kHz total multiplication factor =64 48=3072 carrier frequency (f c 4) = =614.4 MHz the final required carrier frequency is 91.2 MHz Δf2 = Δf3 = 1.6 khz 39

40 Example 10 ; Armstrong s method is to be used to generate a WBFM signal. The NBFM signal has the carrier frequency fc1 = 20 khz. The WBFM signal that is required must have the parameters fc = 6 MHz and Δf = 10 khz. Only frequency triples are available. Draw the schematic block diagram of this example. Total frequency multiplication required = / =300 Frequency triples=3 5 = =729 these six cannot be used as a single cascade because, that would result in a carrier frequency equal to = 14.58MHz. Generation of WBFM from NBFM of example the final frequency deviation required is 10 khz NBFM f 1 = /729=13.71Hz After the frequency conversion stage, we have one more stage multiplication by 3. the carrier frequency at the mixer output fc3 fc3 3=6MHz fc3=2 MHz f LO =6,86 MHz 40

41 Exercise In the indirect FM scheme shown in Fig. 5.17, find the values of fc,i and Δfi for i = 1, 2 and 3. What should be the centre frequency, f 0, of the BPF. Assume that f LO > f c,2. Direct FM Method (1) A common method used for generating FM directly is to vary the inductance or capacitance of a tuned electronic oscillator. If L and C are the inductance and capacitance, of a simple tuned circuit. The oscillation frequency f 0 of a parallel tuned circuit with inductance L and capacitance C is given by: ff oo = 1 2ππ LLLL ωω oo = 1 LLLL Let C be varied by the modulating signal m(t ), as given by cc(tt) = cc oo kkkk(tt) 41

42 k:constant ωω ii (tt) = 1 kkkk (tt) [1 + ] LLCC oo 2cc oo ωω cc = 1 LLcc oo ωω ii (tt) = ωω cc + cc ff mm(tt) kkkk (tt) 2cc oo 1 c(t ) of the oscillator circuit is: cc ff = kkωω cc 2cc oo cc dd = cc oo kkkk(tt) cc(tt) = (cc 1 + cc oo ) kkkk(tt) = cc oo kkkk(tt) Where cc oo = cc 1 + cc oo Example 11: cc dd = vv dd pppp Consider the circuit of Fig for the direct generation of FM. The diode a pacitance Cd, is related to the reverse bias as, v d : the voltage across the varactor v B =4v m(t)=0.054 sin [( 10 π 10 3 )t] c 1 =250 pf the circuit resonates at 2 MHz when m(t)=0 cc dd = sin [(10ππ 10 3 )tt] 3 ff ii (tt) = sin [(10ππ 10 3 )tt] 42

43 Method ( 2) The electronic switch is designed such that it is in position 1 when y (t ) = V0 and goes to position 2 when y ( t) =- V0 For 0 < t t1 xx(tt) = EE RRRR vv 0dddd 0 When t=t 1,let x(t) become E 0.then y(t) = -vv 0 and the electronic switch assume positio2. EE 0 = EE tt 1 RRRR vv 0dddd tt 1 = 2RRRREE 0 vv 0 The output x (t ) decreasing to t=t 2 when x(t)=- EE

44 tt 2 tt 1 = 2RRRREE 0 vv 0 The x(t) and y(t) are periodic with period 4RRRREE 0 vv 0 The fundamental frequency of these waveforms When v 0 =E 0 ff 0 = 2RRRREE 0 vv 0 ff 0 = 1 4RRRR Direct and Indirect FM Transmitter. How to transmit a signal with frequency ranging in (-5KHz,5KHz) using a channel operating in (100KHz,110KHz)? What should be the carrier frequency? Draw the block diagrams for the modulator and demodulator, and sketch the spectrum of the modulation and demodulation 1 44

45 45

46 FDM Receiver Block diagram of FDM system. 46

47 Modulation steps in an FDM system Application of modulation and FDM 1-AM Radio (535KHz--1715KHz): Each radio station is assigned 10 KHz, to transmit a mono-channel audio (band limited to 5KHz) Using Amplitude modulation to shift the baseband signal 2- FM Radio (88MHz--108 MHz): Each radio station is assigned 200 KHz, to transmit a stereo audio. The left and right channels (each limited to 15KHz) are multiplexed into a single baseband signal using amplitude modulation Using frequency modulation to shift the baseband signals 3- TV broadcast (VHF: 54-88, MHz, UHF: MHz) Each station is assigned 6 MHz The three color components and the audio signal are multiplexed into a single baseband signal Using vestigial sideband AM to shift the baseband signals. 47

48 Angle modulation spectrum assume that θθ(tt) = ββ sin(2ππff mm tt) ββ: modulation index and is the maximum value of phase deviation for both FM and PM. The signal: ss(tt) = AA cc cos [2ππff cc tt + ββ sin(2ππff mm tt)] ββ = ff ff mm We assume that the carrier frequency f c is large enough compared to the bandwidth of FM signal. x c (t) = A c cos[( 2πf c t + jβ sin(2πf m t )] = Re[A c exp (jβsin(2πf m t ))exp(j2πf c t)] The signal can be expressed as: xx cc (tt) = RRRR[xx cc (tt)ee jj 2ππff cctt ] the complex envelope of the modulated carrier signal xx cc (tt) = AA cc ee jjjj sin (2ππff mm tt) The complex envelope is periodic with frequency fm and can therefore be expanded in a Fourier series. The Fourier coefficients are given by ffff 1/2ffff ee jjjj sin (2ππff mm tt) 1/2ffff ee jj 2ππππ ff mm tt dddd = 1 2ππ ππ ββsin (xx) ee [jjjjjj ππ The integral is a function of n and b and is known as the Bessel Function of the first kind of order n and argument ββ the Fourier series for the complex envelope can be written as: dddd 48

49 eeeeeeeeeesin (2ππff mm tt) = JJ nn (ββ) eeeeee(jj2ππff mm tt) nn= xx cc (tt) = RRRR[(AAAA JJ nn (ββ) eeeeee(jj2ππππππππππ) eeeeee(jj2ππππππππππ)) nn= xx cc (tt) = AAAA JJ nn (ββ) cccccc(2ππ(ffff + nnnnnn) tt nn= JJ nn (ββ) = JJ nn (ββ) nn eeeeeeee JJ nn (ββ) = JJ nn (ββ) nn oooooo relationship between values of Jn(ββ )for various values of n is the recursion formula JJ nn+1 (ββ) = 2nn ββ JJ nn(ββ) + JJ nn 1 (ββ) Spectra of an angle-modulated signal. (a) Single-sided amplitude spectrum. (b) Single-sided phase 49

50 Amplitude spectrum of an FM complex envelope signal for increasing b and decreasing 50

51 Item 4 : detectors and Receivers Principle of AM Detector. Envelope Detectors. assume the circuit as shown : The envelope detector circuit the diode D to be ideal. When it is forward biased, it acts as a short circuit and thereby, making the capacitor C charge through the source resistance Rs. When D is reverse biased, it acts as an open circuit and C discharges through the load resistance RL. As the operation of the detector circuit depends on the charge and discharge of the capacitor C V 1 (t) before DC block V out (t) after DC block Envelope detector waveforms 51

52 Synchronous Detectors. RR ss CC 1 ff cc 1 ff cc RR LL CC 1 WW Coherent detector for demodulating DSB-SC modulated Illustrating the spectrum of a product modulator output with a vv(tt) = 1 2 AA ccaa cc cos(4ππff cc tt + φφ) mm(tt) AA ccaa cc cos(φφ)mm(tt) vv 0 (tt) = 1 2 AA ccaa cc cos(φφ) mm(tt) 52

53 Costas PLLs systems utilizing feedback can be used to demodulate angle-modulated carriers. A feedback system also can be used to generate the coherent demodulation carrier necessary for the demodulation of DSB signals. One system that accomplishes this is the Costas PLL illustrated in Figure The input to the loop is the assumed DSB signal x(t)=m(t)cos(2πf c t ) The lowpass filter preceding the VCO is assumed sufficiently narrow so that the output is K sinð2uþ, essentially the DC value of the input. This signal drives the VCO such that u is reduced. For sufficiently small u, the output of the top lowpass filter is the demodulated output. 53

54 Low pass filter m(t)cos (θ) Demodulated output xx(tt) = mm(tt) cos ωω cc tt 2 cos( ωω cc tt + θθ) VCO KKsin(2θθ) 1 2 mm2 (tt)sin(2θθ) Low pass filter 90 o phase shift 2 sin( ωω cc tt + θθ) Low pass filter m(t)sin(θθ) 54

55 Demodulation of FM Signals. Balanced Slope Detector. There are three tuned circuits: two on the secondary side of the input transformer and one on the primary. The resonant circuit on the primary is tuned to fc whereas the two resonant circuits on the secondary side are tuned to two different frequencies, one above fc and the other, below fc. The outputs of the tuned circuits on the secondary are envelope detected separately; the difference of the two envelope detected outputs would be proportional to m(t ). 55

56 VV PPPPPP = II PPPPPP XX PPPPPP = II PPPPPP jjjjll PPPPPP 1 ωω ωω 0 2 the width of linear frequency response is about 3B, where 2B is the width of the 3- db bandwidth of the individual tuned circuits) and does not require any DC bock (The two resonant frequencies of the secondary are appropriately selected so that output of the discriminator is zero for f = fc ), it suffers from the disadvantage that the three tuned circuits are to be maintained at three different frequencies Foster Seely Discriminator The voltage applied to D1: vv 2222 = ii ss ( jjxx cccc ) = jjjj LL 1 vv iiii xx cc2 RR 2 + jjxx 2 The voltage applied to D2: vv 6666 = vv iiii vv

57 vv 6666 = vv iiii 1 2 vv 2222 Reponses curve of the Foster- Seely discriminator 57

58 Ratio Detector. Comparing the ratio detector circuit with that of the Foster-Seely discriminator, we find the following differences: direction of D2 is reversed, a parallel RC combination consisting of (R5 + R6 ) and C5 has been added and the output Vout is taken across a different pair of points. We shall now briefly explain the operation of the circuit. vv oooooo = vv 64 + vv 47 = vv 64 vv 74 vv oooooo = vv vv 54 = kk[ vv 62 vv 63 ] the Foster-Seely discriminator and the ratio detector have been the work horses of the FM industry. Companies such as Motorola have built high quality FM receivers using the Foster-Seely discriminator and the ratio detector FM Pre emphasis and De emphasis concept: 58

59 Ultimately recovery of m(t) from an FM signal involves differentiation always worries signals engineers because it is a high frequency boost out to all frequencies TROOBLE : that boosts the noise from the channel in the receiver, but only just restore the signal. The receiver FM signal: tt φφ FFFF (tt) = AAAAAAAA [ωω cc (tt) + kk FF mm(ττ)dddd + φφ 0 nnnnnnnnnn (tt)] The derivate of the phase of φφ FFFF (tt): = kk ff mm(tt) + dd dddd φφ nnnnnnnnnn (tt) iiii ffffffffffffffffff dddddddddddd kk ff MM(ωω) + jjjj. NN(ωω) nnnnnnnnnn uuuuuuuuuuuuuuuuuu Desired boost to the noise Preemphasis and Deemphasis filters. this system has been used in commercial broadcasting as shown in figure below : the pre emphasis ( before modulation ) and de emphasis ( after modulation ) filter H p (ω) and H d (ω) the frequency f 1 is 2.1 khz and f 2 is typically 30 khz or more. these filter can be realized by simple RC circuits. the pre emphasis transfer function is : K: the gain = ωω2 ωω1 HH pp (ωω) = KK jjjj + ωω1 jjjj + ωω2 HH pp (ωω) = ωω2 jjjj + ωω1 ωω1 jjjj + ωω2 59

60 For ω «ω1, For ω1 «ω «ω2 HH pp (ωω) 1 HH pp (ωω) jjjj ωω1 Preemphasis filter The preemphasizer acts as a differentiator at intermediate frequency kHz, which effectively makes the scheme PM over these frequencies. this mean that FM with PDE is FM over the modulating signal frequency range of khz and is nearly PM over the range of khz as desired. The deemphasis filter H d (ω) is : For ω «ω2, deemphasis filter HH dd (ωω) = HH pp (ωω) ωω1 jjjj + ωω1 jjjj + ωω1 ωω1 HH pp (ωω)hh dd (ωω) 1 oooooooo tthee bbbbbbbbbbbbbb 0 15kkkkkk 60

61 a) FM stereo transmitter,b) spectrum of a baseband signal, c) FM stereo receiver 61

62 Receivers. Radio receiver is an electronic equipment which pick ups the desired signal, reject the unwanted signal and demodulate the carrier signal to get back the original modulating signal. Function of Radio Receivers. 1-Intercept the incoming modulated signal 2-Select desired signal and reject unwanted signals 3-Amplify selected R.F signal 4-Detect modulated signal to get back original modulating signal 5-Amplify modulating frequency signal Design of Receiver: Requirements: Has to work according to application as for AM or FM signals Tune to and amplify desired radio station Filter out all other stations Demodulator has to work with all radio stations regardless of carrier frequency Classification of Radio Receivers. 1-Depending upon application a) AM Receivers - receive broadcast of speech or music from AM transmitters which operate on long wave, medium wave or short wave bands. b) FM Receivers receive broadcast programs from FM transmitters which operate in VHF or UHF bands. c) Communication Receivers - used for reception of telegraph and short wave telephone signals. 62

63 d) Television Receivers - used to receive television broadcast in VHF or UHF bands. e) Radar Receivers used to receive radio detection and ranging signals. 2-Depending upon fundamental aspects a) Tuned Radio Frequency (TRF)Receivers b) Super-heterodyne Receivers Typical receiver circuits include: RF amplifiers, IF amplifiers, AGC,AFC and Special circuits TRF (Tuned Radio frequency) RECEIVER. Advantages of TRF: TRF receivers are simple to design and allow the broadcast frequency 535 KHz to 1640 KHz. High sensitivity. 63

64 Disadvantages of TRF: 1-At the higher frequency, it produces difficulty in design. 2-It has poor audio quality. 3-Instability:1- reactance of stray capacitances decreases at higher frequencies resulting in increased feedback. 2-Due to high frequency, multi stage amplifiers are susceptible to breaking into oscillation. 3-gain of RF amplifier is very high,a small feedback from output to input with correct phase can lead to oscillations. 4-Variation in BW: 1-The bandwidth is inconsistent and varies with the center frequency when tuned over a wide range of input frequencies. 2-As frequency increases, the bandwidth ( f/q) increases. Thus, the selectivity of the input filter changes over any appreciable range of input frequencies. 5-Poor Selectivity: 1-The gains are not uniform over a very wide frequency range. 2-Due to higher frequencies ability to select desired signal is affected. Superheterodyne Receiver The shortcomings of the TRF receiver are overcome by the super heterodyne or superhet receiver. Basically, the receiver consists of a radio-frequency (RF) section, a mixer and local oscillator, an intermediate-frequency (IF) section, demodulator, and power amplifier. Typical frequency parameters of commercial AM and FM radio receivers are listed in Table Low side f LO =f RF f IF High side= f LO =f RF +f IF 64

65 Typical frequency parameter of AM and FM radio receivers AM Radio FM Radio RF carrier range MHz MHz Midband frequency of IF section MHz 10.7 MHz IF bandwidth 10 khz 200 khz The Figure shows the block diagram of a superheterodyne receiver for amplitude modulation using an envelope detector for demodulation. Antenna Loud speaker RF section Mixer IF section Envelop detector Audio amplifier Tuning Local oscillator Superheterodyne Receiver 65

66 Disadvantages : 1-Stability as high frequency is down converted to IF the reactance of stray capacitances will not decrease as it was at higher frequencies resulting in increased feedback. 2- No variation in BW- as IF range is 438 to 465 KHz (in case of AM receivers) mostly 455KHz,appropriate for Q limit (120). 3-Better selectivity- as no adjacent channels are picked due to variation in BW. Typical spectrum at the input to the RF stage of a superhet Spectrum at the input of the IF stage of a stage of a superhet 66

67 67

68 Item 5 : Pulse Modulation 68

69 Sampling Theorem Let g(t) is analog signal Let gg δδ (tt) denote the ideal sampled signal Where TT ss : sampling period gg δδ (tt) = gg(nntt ss )δδ(tt nntt ss ) nn= ff ss = 1 TTss sampling rate GG ss (ff) = The Fourier transform of gg δδ (tt): 1-GG(ff) = 0 ffffff ff WW gg nn jjjjjjjj exp ( 2WW WW ) nn= GG ss (ff) = ff ss GG(ff) GG(ff mmff ss ) mm = 69

70 2- ff ss = 2WW NNNNNNNNNNNNNN rrrrrrrr TT ss = 1 GG(ff) = 1 2WW 2WW GG(ff) = 1 2WW GG ss(ff), WW < ff < WW NNNNNNNNNNNNNN iiiiiiiiiiiiiiii nn jjjjjjjj gg exp, WW < ff < WW 2WW WW nn= The inverse Fourier transform: gg(tt) = The integral term : GG(ff) exp(jj2ππππππ) dddd gg(tt) = gg(tt) = gg nn 2WW 1 2WW WW WW nn exp jj2ππππ tt dddd 2WW gg nn sin (2πWt nπ) 2WW 2πWt nπ nn= = gg nn nn= sinc( (2πWt nπ) < tt < 2WW 70

71 Spectrum of signal Spectrum of an under sampled version of the signal exhibiting the aliasing phenomenon To combat the effects of aliasing in practice, we may use two corrective measures: 1-Prior. to sampling, a low-pass anti-aliasing filter is used to attenuate those high frequency components of the signal that are not essential to the information being conveyed by the signal. 2-The filtered signal is sampled at a rate slightly higher than the Nyquist rate. Anti- alias filtered spectrum of an information signal Magnitude response of reconstruction filter 71

72 Example12 : The time function f(t)= 5 cos 2π (1000)t cos 2π(300)t is sampled at 2100 cycle rate, somewhat higher than required minimum sampling rate for unique reconstruction. it samples for t second. reconstruction takes place by passing the sample signal through a 1600Hz low pass filter having a unity gain. determine its sampled and filtered spectrum. Solution: ssssssssssssss ssssssssssss = ssssss ωω tt 0 2 tt ωω ff(ff) = 5 [mm ( )tt + mm( )tt] 2 = 5 [mm (1300)tt + mm(700)tt] 2 2- ff(ff) = 5 [mm ( )tt + mm( )tt + mm( )tt + 4 mm tt = 5 [mm (3400)tt + mm(800)tt + mm(2800)tt + mm(1400)tt] 4 X(f) (T/ t) 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/ f Sampled spectrum 72

73 y(f) (T/ t) 5/4 5/4 5/4 5/4 5/4 5/4 5/4 5/ f filter spectrum yy(tt) = 55 tt cccccc 2222( )tt cccccc 2222(333333)tt TT + 55 tt cccccc 2222( )tt cccccc 2222(333333)tt TT Exercise 73

74 Type of Pulse Modulation. Pulse Amplitude Modulation PAM. A PAM waveform consists of a sequence of flat-topped pulses designating sample values. The amplitude of each pulse corresponds to the value of the message signal m(t) at the leading edge of the pulse. The essential difference between PAM and the sampling operation discussed in the previous chapter is that in PAM we allow the sampling pulse to have finite width. The finite width pulse can be generated from the impulse-train sampling function by passing the impulse train samples through a holding circuit. The impulse response of the ideal holding circuit is given by: Holding network Impulse response of holding network Generation of PAM Amplitude response of holding network Phase response of holding network 74

75 Op-amp 2 :is a high input-impedance voltage follower capable of driving lowimpedance loads. The resistor R: is used to limit the output current of op-amp 1 when the FET is on and provides a voltage division with r d of the FET. (r d, the drain-to-source resistance, is low but not zero) h(tt) = tt 1 2 ττ ττ The holding circuit transforms the impulse function samples: mm δδ (tt) = mm(nntt ss )δδ(tt nntt ss ) mm cc (tt) = nn= mm(nntt ss ) ( tt (nntt ss ττ ) ττ nn= h(ff) = ττττττττττ (ffff)ee jjjjjjjj the holding network does not have a constant amplitude response over the bandwidth of m(t), amplitude distortion results. This amplitude distortion, which can be significant unless the pulse width t is very small, can be removed by passing the samples, prior to reconstruction of m(t), through a filter having an amplitude response equal to 1/H(f) over the band width of m(t). Pulse Width Modulation PWM 1-In pulse width modulation (PWM), the width of each pulse is made directly proportional to the amplitude of the information signal. 2-In pulse position modulation, constant-width pulses are used, and the position or time of occurrence of each pulse from some reference time is made directly proportional to the amplitude of the information signal. 3-PWM and PPM are compared and contrasted to PAM as shown in the Figure. 75

76 a PWM modulator circuit is show below. This circuit is simply a high-gain comparator that is switched on and off by the saw tooth waveform derived from a very stable-frequency oscillator. 76

77 1-Notice that the output will go to +V cc the instant the analog signal exceeds the saw tooth voltage. 2-The output will go to -V cc the instant the analog signal is less than the saw tooth voltage. With this circuit the average value of both inputs should be nearly the same. 3-This is easily achieved with equal value resistors to ground. Also the +V and V values should not exceed V cc. Pulse Position Modulation PPM APPM signal consists of a sequence of pulses in which the pulse displacement from a specified time reference is proportional to the sample values of the information-bearing signal. xx(tt) = gg(tt tt nn ) nn= 77

78 where g(t)represents the shape of the individual pulses, and the occurrence timestt nn are related to the values of the message signal m (t) at the sampling instants nts. The spectrum of a PPM signal is very similar to the spectrum of a PWM signal. PPM demodulator. Example 13:Draw the PAM, PWM and PPM of the analog signal ( sin wave ). 78

79 Exercise Draw the PMA pulse triangle, PWM and PPM that generated from this circuit. 79

80 Exercise Draw the PMA pulse triangle, PWM and PPM that generated from this circuit. 80

81 Multiplexing. Time- Division Multiplexing Multiplexing is a modulation method which improves channel bandwidth utilisation. TDM is another form of multiplexing based on sampling which is a modulation technique. In TDM, samples of several analogue message symbols, each one sampled in turn, are transmitted in a sequence (time slots). 81

82 Time division multiplexing of two signal the total number of baseband samples in a T-s interval is nn ss = NN ii=1 2WW ii TT Assuming that the baseband is a low pass signal of bandwidth B, the required sampling rate is 2B. In a T-s interval, we then have 2BT total samples. NN nn ss = 2BBBB = 2WW ii TT ii=1 NN BB = WW ii ii=1 82

83 Item 6 : Noise in Communication Systems Electrical noise may be said to be the introduction of any unwanted energy, which tend to interfere with the proper reception and reproduction of transmitted signals. 1- Unwanted Signals that tend to disturb the Transmission and Processing of Signals in Communication System and over which we have incomplete control. 2-Noise is a general term which is used to describe an unwanted signal which affects a wanted signal. 3-These unwanted signals arise from a variety of sources. The Noise Parameters: 1-Signal to noise ratio 2-Noise factor 3-Noise equivalent band width 4-Effective noise temperature Sources of noise :External and Internal External : 1-Atmosphere disturbance (e.g. electric storms, lighting, ionospheric effect etc), so called Sky Noise 2-Cosmic noise which includes noise from galaxy, solar noise 3- Hot spot due to oxygen and water vapour resonance in the earth s atmosphere. Internal : 1-Electronic communication systems are made up of circuit elements such 83