Table Of Content

frequency is greater than the modulating trea fof modulation is known as modulated signal, ‘Modulation may be claveified as continuous wave mi . smovtilation and " cain. waveform is continuous in nature then the modulation proces i eld ae ante tuodulation, The examples ofthis ‘ype of modulation are amplitude modulation and angle modloaig Gn the other hand, ifthe carrier waveform isa p map b ile type ber ‘ fee eapulés modulation. The examples of thi trrechaok ime oa Lhe ty f i -Amplit Modulation (PAM), Pulse-Width Modulation (PWM), Pulae Code Melcluee oi coe families of continuous-wave (CW) Amplitude Modulation and Angle Modulation are the twe modulation systems. In amplitude modulation, the amplitude of a sinusoidal, cartier wave is varied in accordance with the baseband (modulating) signal. On the ather hand, lation, the angle ‘ofthe sinusoidal carvier wave is varied in accordance with bassband pe ee 7 Amplitude modulation is discussed in this chapter, whereas the angle modulation will be discussed innext chapter. (2) Multiplexing ‘Multiplexing is a technique in which several message signals are combined into a composite ‘signal for transmission over a common channel, In order to transmit a number of these signals ‘over the same channel, the signals must be kept apart so that they do not interfere with ech other, and hence they can be separated easily at the receiver end. Basically, multiplexing is of two types as under: @ frequency division multiplexing (FDM) (id) time-division multiplexing (TDM) equency Division Multiplexing (FDM) (impo ‘The FDM scheme is illustrated in figure 3.1 with the simultaneous transinission ‘message or baseband signals. The spectra of the message signals and the sum ‘carriers are indicated in the figure. DSB modulation is used in illustrating the sf 3.1, Any type of modulation can be used in FDM as long as theTarrier spacing avcid spectral overlapping. However, the most widely used method of modulation is ‘At the receiving end of the channel the three modulated signals are separated by b (BPFs) and then demodulated. channel bandwidth is allotted iy ‘then every user ean be given by each user for one second :ime ls. Because digital signals ure f wherens Intersymbol Interference ‘suecinl cares. jum amplitude of the carrier of the modulating or baseband (1) the carrier frequency, For ‘zero in equation (3.1). to amplitude modulation onal Lo the instantaneots ‘and modulated signe! time-domain behavio" signal avis onor intelligen® signal or si iv) Inthe process of amplitude modulation, the frequency and phase of the carrier qwhereas the maximum amplitude varies according to the instantaneous value of information signal. 3 (¢) Equation (3.2) represents an amplitude modulated wave. This wave has a ide A +x(1). This implies that the amplitude of the wave i ‘with the value of the modulating signal x(t). The frequency of ap mo de Pigs Mustration of amplitude modulation. ¥ (i) The resulting signal from the process of amlitude-modulation i called amplitude modulated a t point P, the modulating ide modulation occurs. This means | ccordance with the ite want to know the ra - find its spectrum oy fyectt®™ sthe Fourier transform of 4 sthe Fourier transform of 0) and. bbe as shown in figure 3,9(q) dtothe interval —co,, << inot have any frequency corn ignal frequency ranges ext, yt. Practically there is no meaning mathematical convenience only , a5 Ponte, from 0 to w,, or simply th of a conine signal c+! a? AB lB = AMPLITUDE | (NEAR MODULATION = To find the spectrum af AM wave, wo take ‘The Fourier transform of s(t) may be found of separately as follow: To find the Fourier transform of x(¢ transform as Ko a X(w) then 6 x(t) + Xw-0) ‘This property states that if a signal x(¢) is multi ied by ol ‘time-domain, then 4 (o) in frequency-domain is shifted by an amount Similarly, x) Xo+o) But, since e™ is not a real function and cannot be gencrated shifting in practice is uchieved by multiplying x0 by a sinusoid such aa cos ay ) eos. we first nate the iv ty] (ett « grin ao be . } x40) c08 oy Excel +fanem Henee, using equations (9.10) and (8.11), we get Qemed +1 [X@-0.)4 Xora] 18) This means that the multipliention ofa signal 10) by a sinusoid of rsquency shifts the spectrom X(@) by +o, ; The Fourier transform of the second factor A cos wt will be as in equation (3.8) Acos wt + nA[B(o + w,) + Ko ~0,)) ‘This means that Fourier transform of A cos ot consists of two impulses att @. ‘Therefore, the Fourier transform of AM wave given by equation (3.6) will be the sum of (@.14) and (9.15), ¢ Thus, Sw) J Xto-0,)+X(o+o,)] afore.) +B ~a,)] Above equation for Amplitude Modulated Wave alee ys ‘V2 [X(w— @) + X(o + @)) representa the spectrum of original ate Fike isaive dlvcticn ty tp lara, Si ae TA[5(m + tw.) + 8(c9 - «,] represents the presence of carrier wignil Le, egrctoce ‘Thus the spectrum of modulated signal contains shifted wpectrusm of “Spectrum of carrier signal as shown in figure 3.96) ur only the positive frequene fs BP the positive frequency, positive side. = Thiy ‘component present nent is 0, ~ 0, inthy 3.17) ting signal and A represents the ‘of modulation or modulation Percentage modulation. 18) ‘of AM signal only if the per ‘than 100, the baseband baseband signal distortion and the AM mn in figure 3.4(a) and n the amplitude of the = AMPLITUDE (LINEAR) MODULATION. (i) Amplitude Modulation with m, > 1 In this ease, the waveform of the AM signal is as shown in figure 8.4(@). Here: ‘a baseband signal exceeds ore ie ie Vat ar PA Tn thie case, the modulation index mis more than 1 or 100% JIB! Single Tone Amplitude Modulation (AM) Till now, we discussed amplitude modulation in which we assumed that bi signal is a random signal which coatains a large number of frequency ‘component a arjer signal (fixed frequency signal) is modulated by a lange mumber of itude modulation in which the m In this section, we shall diseuss amplitude d odulation is dane by @ single f signal consists of only one (single) frequency ie. m ‘This type of amplitude modulation is known as: single tone amplitude madulation: ‘Let us consider a single tone modulating sigma as Let the carrier signal be €() = Aeos od ‘We know that the general expression for AM signal in att) = [A +a] cos and s(t) = A con of + a) 208 OF Putting the value of x(t), we set sii) = Acos af + Vy, cas @,t 609 tf 140) = A.con p+ Vg O86 60" Sal sh of in equation (3.23) we wet an deosas mcf] oe modulating signal. simplified observe the frequency componeny, reson in AM signal ss, 0 = Acs oft +m, o04 2!) Ao TAeews+Am,cHosesey! = all =awnay+ ABE tee, st = Aoaigi-4 2s aniadeo,) 40006, ¥] a) = Arn AP y+ A colo, 0) tes ea erent tl te egy ‘components as follow: (0 Uppersideband (a, +g.) having ampli aA (i) ower ibn, With the help oft a mods AM) wave, ‘wean plat the frequency. a spectrum of single-tont — Eoite ont-sited frequency spectrum of single one AM wave. uses a 50 pill coil and frequencies upto § ki | a ee 1" AMPUTUDE tunear MooUUATION SolutHon: The oscillator in AM transmitter Besueney of eve osllator wil he the sesr ‘Therefor, ior rt to generate high carries frequency. Mensa, ier frequency. Carrive frequency, Here given that 50 * 10- and C= Ink =1x190¢R ‘Thus, =e i 1 Sny0%10% x1%x10" anfexie SRM aM f= 712 «10° = 712 ee Now, itis given that the highest modulating frequency is 8 kHz, Therefore, the frequency range occupied by the sidebands wilt range from 8 hE above to 8 kite below the carrier frequency, extending from Tto 4 kHz to 720kH:. Ans, J86" Power Content in AM Wave Tt may be observed from Ute expression of AM wave that the carrier component of the amplitude modulated wave has the same amplitude as unmodulated carrier. In addition to cartier companent, the modulated wave cunsists of twa sideband components. It means that the modulated wavecontains more power than the unmodulated carrier. However, since the amplitudes af two sidebands depend upon the modulation index, it may be anticipated that the total power of the amplitude modulated ‘wave would depend upon the modulation index also, In this section, we shall find the pawer contents ofthe carrier and the sidebands, ‘We know that the general expression of AM wave is given as 840) = A.cos @,t + x(l) 008 (8.25) ‘The total power P of the AM wave is the sum of the carrier power P, and sideband power P.. Carrier Power ‘The carrier power P, is equal to the mean-square (ms) value of the carrier term A cos Gt ie, P, = mean square value af A vos @,f a7 a Pp tacos alt= 3, [A*emtas ais 26) Sideband Power - J ‘The sideband power P, is equal to the mean square value ofthe sideband term x0) aos ab te: P, = mean square value of x() 08 0 f e P, = Lx cos i= ge [Aetna 7 * : Jee od] tena Ps a s 161 264) deeb [x*pens2aydt Lfjrowgl * Since period of the signal A.cos @,t is 2x. tuned to Currier frequen. Fi : 8.26 [contributions of the upper ang Lover ver sidebands will be . 48.29, ‘of the carrier power P_ and sidchang A331) is the power carried by the nsimission point of view because x P. is transmitted alongwith ,P, is the only useful message be expressed by n term known as as the per centage of total power Power of a Single-Tone article 9.6, we have found the power pais: Peodom signal ond may consist of several equonts eye (fsingle-tone Amplitude Modulated (AM) signal : “useansider that a carrier signal A ji spall =Vy,co8 0. ed Rene ieee ‘Then the Unmochilated or carrier power P, = mean square (ms value) 2, = emoge = ‘The sideband power P_ We know that the total modulated power P, is the sum of P. and P. ‘Therefore _ ample 8.4. The antenna current of wn AM Anodia bee rnc on me gi na antenna current If the per cent of {008 ( (UP. Tech, Sem, Exams oe of power Ifmocutation py Slutan: (0 evrront elation ia angocone amphiade mala seep fontaye modulation, Also find ot] or modulatod exirrent carrier or unmodulated current in, = modulation index Using equation (i, we get yA transmitter eurrent than the power ix or he values of unmodulated and modulated ate. Putting all the given values, we have and J, be the r.m.s value ofthe antenna resistance through which es Acey a | : ffano? = ition is expressed ai m, = (20.246 ~1) = YOasa = 0.701 701% T,28A and m,=08 wie Bate nen [loOE «ofl (aha Jy g/RGD SSX LMOR SIVA §S10y) Power Content in Multiple-Tone Amplitud “iy (ay, (ay) of the corresponding frequin, ‘be expanded as yA co 0, 608 yt + mA COS ©,t 08 wy (B40) (349) ‘Now putting the value of P_ and P, in equation (8 41), we get P,=P,+Pj= 4+) atm om Pet Pee + atom mt) 2 1 a ; a P, [bgimtemtemi] <n seaman) a o. : = Pl ‘ ee aa ‘This expression may be extenided upto to n-modulating terms ie. a gatoae = lieth ym mt P, f Be EO, 3.10.1. Total or Net Modulation Index for Multiple-Tone Mod ‘Let us consider that m, is the total or net modulation indexes for a multiy ‘We know that for a multiple-tone modulation, the total power is expressed a8 2 a 2 ay P,=P, hh Pe et ie 2) ae 2 where my, Mma... are the modulation indexes for different, ‘The power for AM wave is also expressed as fae P, =n[um] ‘Comparing equations (3.46) and (3.47), we get m2 = m2 + my + mg + mS or m= ‘This is the desired expression for the total or net modulation inde. ‘transmitter radiates 9K watts of power whe the carrier is sinusoidally mo a evi iad erste apd mulated (ASD) wave is known as Amplitude ‘The methde of AM Generation may be broadly classified as follow: low power level. At low arrier signal and | cig power levels, hated men nemslsting gal, Becmuse of this modulation 2s done a Sm Vek eer ed to boost the amplitude « : be you. fer he ie ant indigure 9.5(0), iis clear ha sand po peeiiated signal (ce. a sigma dehonds of the amplifier. A wideband pore motillated signal. Amplitude movtulatet ‘Malo called low-level amplitude modulation V7 Antenne |= AMPLITUDE (LINEAR) MODULATION. a 41.2. High Level Amplitude Modulation rr ore 3.5(8) shows the block diagram of a high lev ladle eno Petalation system, the rodulation is Be Nigh power level Meer mmesiulation at these high power levels, the baschand signal and the earr a te wer vets. Tn block dagram of ie 3.0) the lang Tova el eter wer amplified and then applied to AM high-level mo Sepiripi cs Fe a ameldarinequred uf. te prises ths eoaenseee a wiynal_On the other hand, for carrier signal, the nacrow band power amplifier i pees diene eequency signal. The collector modulatin method ia the example of high val Baseband or modulting ‘Signal source | Wideband > Power amplifier <7 Antenna WARING! (+) Block diagram for high level AM Modulation. afore we discuss low level and high level modulation methods in detail, we shall esablish she fact that a nan-linear resistance ofa non-linear device can be made ta produce ‘Amplitude Modulation when two different frequencies are passed together through it. 3.11.8. Non-linear resistance or Non-linear Circuits ‘We know that the relationsbip between voltage and current in a linear resistance is expressed . i oo i=bo voltage across the linear resistance surrent through linear resistance any constant of proportionality {equation (3.48) is applied toa resistor, then constant bi clearly its conductance. ‘Also, ifequation (2.49) is applied to the linear portion of the eransieiet ca eee hon iis the eolleetor current and va the voltage applied the base. ‘As more general, equation (3.49). may be isatbhy where a is the d.c. component of Now, let us consider @ non-linear resistance the current-voltage characteristics written a8 f the current. ‘ yesistance, For a non-linear j, ‘will be non-linear as shows: in figure 3.7. ‘The non-linear relationship between voltage and current may be expressed 8 eathveatedit. 50) ‘This means that non-linear resistance, the current In a practical modulation circuit, the fee frequencies are rejected vith the help ofa tunel circuits tan ne oa ‘be treated as a non-lineay chibit non-linear eharcty, ‘ si iste = 3.11.4. Square Law Diode Modulation juare law diode modulation eireu btn the input woltaze ofa nop, afusrlinent current-voltage characieratien tan Ine, ‘This method ia suited at low voltage levels because characteristics of a Fp 4, gf tho fact that current-voltage chara-cloriste of a * then Giode is highly nonlinear particularly in the low giitaye region as shown in figure 3.8, Figure 3.9 shows the cireuit of square law diode modulation a (a Tt may be observed from the figure 3.9, having different frequencies, tye Pie edisodilating siguk aco sotarerees : the diode, Ade battery V's connect arcs the diode to get a fixed operating point on the oi char ios of di e may be explained by considering -acheriatics of dinde, The: Wea 6 Si Gea the fact when two different % frequencies are passed through a nonlinear device, the process of 1. earier amplitude modulation takes place ‘signal (iodulating Hence, when carrier and signal) modulating frequencies are applied at the input of diode, then different frequency terms appear at the output of diode. These different frequency terms are applied across a tuned circuit which is tuned to the carrier frequeney and has just to pass two sidebands alongwith the carrier and reject other irequencies. of tuned circuit, carrier and two sidebands axe obtained ic, Amplitude M produced. ‘Mathematical Analysis Let us consider that carrier voltage is expressed as v, = V, cos where @, is the carrier frequency. Let the modulating volinge be expressed as Up, = Vig £08 Ot where wip is the modulating frequency. “The total! a.c, voltage across the diode is given 25