Communications. AM, DSBSC, VSB, SSB, FM, PM, Narrow band FM, PLL Demodulators, and FLL Loops Sampling Systems

Transcription

1 Couniations Contents Introdution to Couniation Systes Analogue Modulation AM, DSBSC, SB, SSB, FM, PM, Narrow band FM, PLL Deodulators, and FLL Loops Sapling Systes Tie and Frequeny Division ultiplexing systes, Nyquist Priniple, PAM, PPM, and PWM. Priniples of Noise Rando variables, White Noise, Shot, Theral and Fliker Noise, Noise in asade aplifiers Pulse Code Modulation PCM and its derivatives, Quantising Noise, and Exaples Digital Couniation Tehniques ASK, FSK, PSK, QPSK, QAM, and M-ary QAM. Case Studies Spread Spetru Systes, Mobile radio onepts, GSM and Multiple Aess Shees Mobile radio

2 Introdution to Modulation and Deodulation The purpose of a ouniation syste is to transfer inforation fro a soure to a destination. In pratie, probles arise in baseband transissions, the ajor ases being: Noise in the syste external noise and iruit noise redues the signal-to-noise (S/N) ratio at the reeiver (Rx) input and hene redues the quality of the output. Suh a syste is not able to fully utilise the available bandwidth, for exaple telephone quality speeh has a bandwidth 3kHz, a o-axial able has a bandwidth of 100's of Mhz. Radio systes operating at baseband frequenies are very diffiult. Not easy to network.

3 Multiplexing Multiplexing is a odulation ethod whih iproves hannel bandwidth utilisation. For exaple, a o-axial able has a bandwidth of 100's of Mhz. Baseband speeh is a o

4 1) Frequeny Division Multiplexing FDM This allows several 'essages' to be translated fro baseband, where they are all in the sae frequeny band, to adjaent but non overlapping parts of the spetru. An exaple of FDM is broadast radio (long wave LW, ediu wave MW, et.)

5 ) Tie Division Multiplexing TDM TDM is another for of ultiplexing based on sapling whih is a odulation tehnique. In TDM, saples of several analogue essage sybols, eah one sapled in turn, are transitted in a sequene, i.e. the saples oupy adjaent tie slots.

6 Radio Transission Aerial diensions are of the sae order as the wavelength,, of the signal (e.g. quarter wave /4, / dipoles). is related to frequeny by For baseband speeh, with a signal at 3kHz, (3x10 3 Hz) λ = where is the veloity of an eletroagneti wave, and = f 3x10 8 /se in free spae. λ = 3x10 3x = 10 5 etres or 100k. Aerials of this size are ipratial although soe transissions at ery Low Frequeny (LF) for speialist appliations are ade. A odulation proess desribed as 'up-onversion' (siilar to FDM) allows the baseband signal to be translated to higher 'radio' frequenies. Generally 'low' radio frequenies 'boune' off the ionosphere and travel long distanes around the earth, high radio frequenies penetrate the ionosphere and ake spae ouniations possible. The ability to 'up onvert' baseband signals has ipliations on aerial diensions and design, long distane terrestrial ouniations, spae ouniations and satellite ouniations. Bakground 'radio' noise is also an iportant fator to be onsidered. In a siilar ontent, optial (fibre opti) ouniations is ade possible by a odulation proess in whih an optial light soure is odulated by an inforation soure.

7 Networks A baseband syste whih is essentially point-to-point ould be operated in a network. Soe fors of aess ontrol (ultiplexing) would be desirable otherwise the perforane would be liited. Analogue ouniations networks have been in existene for a long tie, for exaple speeh radio networks for abulane, fire brigade, polie authorities et. For exaple, 'digital speeh' ouniations, in whih the analogue speeh signal is onverted to a digital signal via an analogue-to-digital onverter give a for ore onvenient for transission and proessing.

8 What is Modulation? In odulation, a essage signal, whih ontains the inforation is used to ontrol the paraeters of a arrier signal, so as to ipress the inforation onto the arrier. The Messages The essage or odulating signal ay be either: analogue denoted by (t) digital denoted by d(t) i.e. sequenes of 1's and 0's The essage signal ould also be a ultilevel signal, rather than binary; this is not onsidered further at this stage. The Carrier The arrier ould be a 'sine wave' or a 'pulse train'. Consider a 'sine wave' arrier: v t = osω t+ φ If the essage signal (t) ontrols aplitude gives AMPLITUDE MODULATION AM If the essage signal (t) ontrols frequeny gives FREQUENCY MODULATION FM If the essage signal (t) ontrols phase- gives PHASE MODULATION PM or M

9 Considering now a digital essage d(t): If the essage d(t) ontrols aplitude gives AMPLITUDE SHIFT KEYING ASK. As a speial ase it also gives a for of Phase Shift Keying (PSK) alled PHASE REERSAL KEYING PRK. If the essage d(t) ontrols frequeny gives FREQUENCY SHIFT KEYING FSK. If the essage d(t) ontrols phase gives PHASE SHIFT KEYING PSK. In this disussion, d(t) is a binary or level signal representing 1's and 0's The types of odulation produed, i.e. ASK, FSK and PSK are soeties desribed as binary or level, e.g. Binary FSK, BFSK, BPSK, et. or level FSK, FSK, PSK et. Thus there are 3 ain types of Digital Modulation: ASK, FSK, PSK.

10 Multi-Level Message Signals As has been noted, the essage signal need not be either analogue (ontinuous) or binary, level. A essage signal ould be ulti-level or levels where eah level would represent a disrete pattern of 'inforation' bits. For exaple, = 4 levels

11 What is Deodulation? Deodulation is the reverse proess (to odulation) to reover the essage signal (t) or d(t) at the reeiver.

12 Suary of Modulation Tehniques 1

13 Suary of Modulation Tehniques

14 Modulation Types AM, FM, PAM

15 Modulation Types AM, FM, PAM

16 Modulation Types (Binary ASK, FSK, PSK)

17 Modulation Types (Binary ASK, FSK, PSK)

18 Modulation Types 4 Level ASK, FSK, PSK

19 Modulation Types 4 Level ASK, FSK, PSK

20 Analogue Modulation Aplitude Modulation Consider a 'sine wave' arrier. v (t) = os( t), peak aplitude =, arrier frequeny radians per seond. Sine = f, frequeny = f Hz where f = 1/T. Aplitude Modulation AM In AM, the odulating signal (the essage signal) (t) is 'ipressed' on to the aplitude of the arrier.

21 Message Signal (t) In general (t) will be a band of signals, for exaple speeh or video signals. A notation or onvention to show baseband signals for (t) is shown below

22 Message Signal (t) In general (t) will be band liited. Consider for exaple, speeh via a irophone. The envelope of the spetru would be like:

23 Message Signal (t) In order to ake the analysis and indeed the testing of AM systes easier, it is oon to ake (t) a test signal, i.e. a signal with a onstant aplitude and frequeny given by t os t

24 Sheati Diagra for Aplitude Modulation DC is a variable voltage, whih an be set between 0 olts and + olts. This sheati diagra is very useful; fro this all the iportant properties of AM and various fors of AM ay be derived.

25 Equations for AM Fro the diagra vs t = DC + t os ωt where DC is the DC voltage that an be varied. The equation is in the for Ap os t and we ay 'see' that the aplitude is a funtion of (t) and DC. Expanding the equation we get: v s t = osω t+t os ω t DC

26 Equations for AM Now let (t) = os t, i.e. a 'test' signal, v t = osω t+ osω tos ω t 1 + os Using the trig identity osaos B = os A+ B+ osa B we have v s s t = osω t ω +ω t + osω ω t DC Coponents: Carrier upper sideband USB lower sideband LSB Aplitude: DC / / DC Frequeny: + f f + f f + f This equation represents Double Aplitude Modulation DSBAM

27 The following diagras represent the spetru of the input signals, naely ( DC + (t)), with (t) = os t, and the arrier os t and orresponding wavefors. Spetru and Wavefors

28 Spetru and Wavefors The above are input signals. The diagra below shows the spetru and orresponding wavefor of the output signal, given by v s t DC os t os t os t

29 Double Sideband AM, DSBAM The oponent at the output at the arrier frequeny f is shown as a broken line with aplitude DC to show that the aplitude depends on DC. The struture of the wavefor will now be onsidered in a little ore detail. Wavefors Consider again the diagra DC is a variable DC offset added to the essage; (t) = os t

30 Double Sideband AM, DSBAM This is ultiplied by a arrier, os t. We effetively ultiply ( DC + (t)) wavefor by +1, -1, +1, -1,... The produt gives the output signal v s t DC t os t

31 Double Sideband AM, DSBAM

32 Modulation Depth Consider again the equation v t = + os ω tos ω t The ratio is DC v s s DC t = 1+ osω tosω t DC DC, whih ay be written as defined as the odulation depth,, i.e. Modulation Depth Fro an osillosope display the odulation depth for Double Sideband AM ay be deterined as follows: = DC DC E ax E in

33 Modulation Depth E ax = axiu peak-to-peak of wavefor E in = iniu peak-to-peak of wavefor Modulation Depth This ay be shown to equal DC Eax E = E + E ax as follows: in in E ax DC E in DC = DC DC DC DC = = DC DC

34 Double Sideband Modulation 'Types' There are 3 ain types of DSB Double Sideband Aplitude Modulation, DSBAM with arrier Double Sideband Diinished (Pilot) Carrier, DSB Di C Double Sideband Suppressed Carrier, DSBSC The type of odulation is deterined by the odulation depth, whih for a fixed (t) depends on the DC offset, DC. Note, when a odulator is set up, DC is fixed at a partiular value. In the following illustrations we will have a fixed essage, os t and vary DC to obtain different types of Double Sideband odulation.

35 Graphial Representation of Modulation Depth and Modulation Types.

36 Graphial Representation of Modulation Depth and Modulation Types.

37 Graphial Representation of Modulation Depth and Modulation Types 3 Note then that DC ay be set to give the odulation depth and odulation type. DSBAM DC >>, 1 DSB Di C 0 < DC <, > 1 (1 < < ) DSBSC DC = 0, = The spetru for the 3 ain types of aplitude odulation are suarised

38 Bandwidth Requireent for DSBAM In general, the essage signal (t) will not be a single 'sine' wave, but a band of frequenies extending up to B Hz as shown Reeber the 'shape' is used for onveniene to distinguish low frequenies fro high frequenies in the baseband signal.

39 Bandwidth Requireent for DSBAM Aplitude Modulation is a linear proess, hene the priniple of superposition applies. The output spetru ay be found by onsidering eah oponent osine wave in (t) separately and suing at the output. Note: Frequeny inversion of the LSB the odulation proess has effetively shifted or frequeny translated the baseband (t) essage signal to USB and LSB signals entred on the arrier frequeny f the USB is a frequeny shifted replia of (t) the LSB is a frequeny inverted/shifted replia of (t) both sidebands eah ontain the sae essage inforation, hene either the LSB or USB ould be reoved (beause they both ontain the sae inforation) the bandwidth of the DSB signal is B Hz, i.e. twie the highest frequeny in the baseband signal, (t) The proess of ultiplying (or ixing) to give frequeny translation (or up-onversion) fors the basis of radio transitters and frequeny division ultiplexing whih will be disussed later.

40 Power Considerations in DSBAM Reebering that Noralised Average Power = ( RMS ) pk = we ay tabulate for AM oponents as follows: v s t = osω t+ osω +ω t + osω ω t DC Coponent Carrier USB LSB Aplitude pk DC Power Power DC DC = DC 8 8 = DC 8 8 Total Power P T = Carrier Power P + P USB + P LSB

41 Fro this we ay write two equivalent equations for the total power P T, in a DSBAM signal DC DC T + = + + = P The arrier power DC = P P + P = P P T 1 + = P P T and 8 8 DC DC DC T + + = P or i.e. Either of these fors ay be useful. Sine both USB and LSB ontain the sae inforation a useful ratio whih shows the proportion of 'useful' power to total power is = + P P = P P T USB Power Considerations in DSBAM

42 Power Considerations in DSBAM For DSBAM ( 1), allowing for (t) with a dynai range, the average value of ay be assued to be = 0.3 Hene, 4+ = = Hene, on average only about.15% of the total power transitted ay be regarded as 'useful' power. ( 95.7% of the total power is in the arrier!) Even for a axiu odulation depth of = 1 for DSBAM the ratio 4+ = 1 6 i.e. only 1/6th of the total power is 'useful' power (with /3 of the total power in the arrier).

43 Exaple Suppose you have a portable (for exaple you arry it in your ' bak pak') DSBAM transitter whih needs to transit an average power of 10 Watts in eah sideband when odulation depth = 0.3. Assue that the transitter is powered by a 1 olt battery. The total power will be where P 4 = 10 Watts, i.e. P T P = P + P + P = = = Watts Hene, total power P T = = Watts. Hene, battery urrent (assuing ideal transitter) = Power / olts = i.e. a large and heavy 1 olt battery aps! Suppose we ould reove one sideband and the arrier, power transitted would be 10 Watts, i.e aps fro a 1 olt battery, whih is ore reasonable for a portable radio transitter.

44 Single Sideband Aplitude Modulation One ethod to produe signal sideband (SSB) aplitude odulation is to produe DSBAM, and pass the DSBAM signal through a band pass filter, usually alled a single sideband filter, whih passes one of the sidebands as illustrated in the diagra below. The type of SSB ay be SSBAM (with a 'large' arrier oponent), SSBDiC or SSBSC depending on DC at the input. A sequene of spetral diagras are shown on the next page.

45 Single Sideband Aplitude Modulation

46 Single Sideband Aplitude Modulation Note that the bandwidth of the SSB signal B Hz is half of the DSB signal bandwidth. Note also that an ideal SSB filter response is shown. In pratie the filter will not be ideal as illustrated. As shown, with pratial filters soe part of the rejeted sideband (the LSB in this ase) will be present in the SSB signal. A ethod whih eases the proble is to produe SSBSC fro DSBSC and then add the arrier to the SSB signal.

47 Single Sideband Aplitude Modulation

48 Single Sideband Aplitude Modulation with (t) = os t, we ay write: v s t = osω t+ osω +ω t + osω ω t DC The SSB filter reoves the LSB (say) and the output is v s t = osω t+ osω +ω t DC Again, note that the output ay be SSBAM, DC large SSBDiC, DC sall SSBSC, DC = 0 For SSBSC, output signal = v s t = osω +ω t

49 Power in SSB Fro previous disussion, the total power in the DSB signal is P T = P 1+ = PT = P + P + P for DSBAM. 4 4 Hene, if P and are known, the arrier power and power in one sideband ay be deterined. Alternatively, sine SSB signal = v s t = osω t+ osω +ω t DC then the power in SSB signal (Noralised Average Power) is P SSB DC = + DC = + 8 Power in SSB signal = DC + 8

50 Deodulation of Aplitude Modulated Signals There are ain ethods of AM Deodulation: Envelope or non-oherent Detetion/Deodulation. Synhronised or oherent Deodulation.

51 Envelope or Non-Coherent Detetion An envelope detetor for AM is shown below: This is obviously siple, low ost. But the AM input ust be DSBAM with << 1, i.e. it does not deodulate DSBDiC, DSBSC or SSBxx.

52 Large Signal Operation For large signal inputs, ( olts) the diode is swithed i.e. forward biased ON, reverse biased OFF, and ats as a half wave retifier. The 'RC' obination ats as a 'soothing iruit' and the output is (t) plus 'distortion'. If the odulation depth is > 1, the distortion below ours

53 Sall Signal Operation Square Law Detetor For sall AM signals (~ illivolts) deodulation depends on the diode square law harateristi. The diode harateristi is of the for i(t) = av + bv + v3 +..., where v = +t ω t DC os i.e. DSBAM signal.

54 Sall Signal Operation Square Law Detetor i.e. a +t os ω t+b +t os ω t +... DC DC = a DC +a t os ω t +... os ω t+b + t +t DC DC = = a a +a t os ω t os ω t+ b + b t +bt DC DC DC DC +a t os ω t 'LPF' reoves oponents. b + DC bdc t + b t + DC +b os ω t +... Signal out = a DC b + DC +b DC t i.e. the output ontains (t)

55 Synhronous or Coherent Deodulation A synhronous deodulator is shown below This is relatively ore oplex and ore expensive. The Loal Osillator (LO) ust be synhronised or oherent, i.e. at the sae frequeny and in phase with the arrier in the AM input signal. This additional requireent adds to the oplexity and the ost. However, the AM input ay be any for of AM, i.e. DSBAM, DSBDiC, DSBSC or SSBAM, SSBDiC, SSBSC. (Note this is a 'universal' AM deodulator and the proess is siilar to orrelation the LPF is siilar to an integrator).

56 Synhronous or Coherent Deodulation If the AM input ontains a sall or large oponent at the arrier frequeny, the LO ay be derived fro the AM input as shown below.

57 Synhronous (Coherent) Loal Osillator If we assue zero path delay between the odulator and deodulator, then the ideal LO signal is os( t). Note in general the will be a path delay, say, and the LO would then be os( (t ), i.e. the LO is synhronous with the arrier ipliit in the reeived signal. Hene for an ideal syste with zero path delay Analysing this for a DSBAM input = +t os ω t DC

58 Synhronous (Coherent) Loal Osillator X = AM input x LO = = +t os ω t DC +t os ω tosω t DC = 1 1 +t + os ω t DC DC DC t t x = + osω t+ + osω t We will now exaine the signal spetra fro 'odulator to x'

59 Synhronous (Coherent) Loal Osillator (ontinued on next page)

60 Synhronous (Coherent) Loal Osillator and Note the AM input has been 'split into two' 'half' has oved or shifted up to t f osω t+dcosω t and half shifted down to baseband, DC and t

61 Synhronous (Coherent) Loal Osillator The LPF with a ut-off frequeny f will pass only the baseband signal i.e. out = DC t + In general the LO ay have a frequeny offset,, and/or a phase offset,, i.e. The AM input is essentially either: DSB SSB (DSBAM, DSBDiC, DSBSC) (SSBAM, SSBDiC, SSBSC)

62 1. Double Sideband (DSB) AM Inputs The equation for DSB is +t os ω t diinished arrier or suppressed arrier to be set. Hene, x = AM Input x LO 1 DC Sine osaos B = os A+ B+ osa B x x = DC = DC + t t + DC x = os t + osω os os x = where DC allows full arrier (DSBAM), +t os ω t. osω DC ω +ω + Δωt + Δφ+ osω ω + Δωt + Δφ+ osδωt + Δφ DC ω + Δωt + Δφ+ osδωt + Δφ + Δω t + Δφ t + os Δωt + Δφ + Δω t + Δφ + Δω t + Δφ ω t

63 1. Double Sideband (DSB) AM Inputs The LPF with a ut-off frequeny f Hz will reove the oponents at (i.e. oponents above ) and hene out = DC t os( t + φ) + os ωt + φ DC t Obviously, if Δω= 0 and Δφ 0 we have, as previously out = + Consider now if is equivalent to a few Hz offset fro the ideal LO. We ay then say out = DC os Δωt t + The output, if speeh and proessed by the huan brain ay be intelligible, but would inlude a low frequeny 'buzz' at, and the essage aplitude would flutuate. The requireent = 0 is neessary for DSBAM. os Δωt

64 1. Double Sideband (DSB) AM Inputs Consider now if is equivalent to a few Hz offset fro the ideal LO. We ay then say DC t out = os Δωt + osδωt The output, if speeh and proessed by the huan brain ay be intelligible, but would inlude a low frequeny 'buzz' at, and the essage aplitude would flutuate. The requireent = 0 is neessary for DSBAM. Consider now that = 0 but 0, i.e. the frequeny is orret at but there is a phase offset. Now we have out = DC Δφ t + 'os()' auses fading (i.e. aplitude redution) of the output. os os Δφ

65 1. Double Sideband (DSB) AM Inputs The ' DC ' oponent is not iportant, but onsider for (t), if if π π Δφ= (90 0 ), os = 0 i.e. Δφ= π (180 0 ), osπ = 1 i.e. out out t = t = π os = 0 os π = t The phase inversion if = ay not be a proble for speeh or usi, but it ay be a proble if this type of odulator is used to deodulate PRK However, the ajor proble is that as inreases towards π the signal strength output gets weaker (fades) and at π the output is zero

66 1. Double Sideband (DSB) AM Inputs If the phase offset varies with tie, then the signal fades in and out. The variation of aplitude of the output, with phase offset is illustrated below Thus the requireent for = 0 and = 0 is a 'strong' requireent for DSB aplitude odulation.

67 . Single Sideband (SSB) AM Input The equation for SSB with a arrier depending on DC is DC os i.e. assuing t = ω t os ω t+ osω +ω t Hene = osω t+ osω +ω t osω + x DC t + Δφ = + 4 DC os os DC ω + Δωt + Δφ+ osδωt + Δφ ω +ω + Δωt + Δφ+ osω 4 Δω t Δφ

68 . Single Sideband (SSB) AM Input The LPF reoves the oponents and hene DC os 4 Δωt + Δφ+ osω Note, if = 0 and = 0, DC + osω t reovered. 4,i.e. Δω t Δφ t = ω t os has been Consider first that 0, e.g. an offset of say 50Hz. Then out = DC os Δωt + osω Δωt 4 If (t) is a signal at say 1kHz, the output ontains a signal a 50Hz, depending on DC and the 1kHz signal is shifted to 1000Hz - 50Hz = 950Hz.

69 . Single Sideband (SSB) AM Input The spetru for out with offset is shown Hene, the effet of the offset is to shift the baseband output, up or down, by. For speeh, this shift is not serious (for exaple if we reeive a 'whistle' at 1kHz and the offset is 50Hz, you hear the whistle at 950Hz ( = +ve) whih is not very notieable. Hene, sall frequeny offsets in SSB for speeh ay be tolerated. Consider now that = 0, = 0, then out = DC os Δφ+ osω t Δφ 4

70 . Single Sideband (SSB) AM Input This indiates a fading DC and a phase shift in the output. If the variation in with tie is relatively slow, thus phase shift variation of the output is not serious for speeh. Hene, for SSB sall frequeny and phase variations in the LO are tolerable. The requireent for a oherent LO is not as a stringent as for DSB. For this reason, SSBSC (suppressed arrier) is widely used sine the reeiver is relatively ore siple than for DSB and power and bandwidth requireents are redued.

71 Coents In ters of 'evolution', early radio shees and radio on long wave (LW) and ediu wave (MW) to this day use DSBAM with < 1. The reason for this was the redued oplexity and ost of 'illions' of reeivers opared to the extra ost and power requireents of a few large LW/MW transitters for broadast radio, i.e. siple envelope detetors only are required. Nowadays, with odern integrated iruits, the ost and oplexity of synhronous deodulators is uh redued espeially opared to the additional features suh as synthesised LO, display, FM et. available in odern reeivers. Aplitude Modulation fors the basis for: Digital Modulation Aplitude Shift Keying ASK Digital Modulation Phase Reversal Keying PRK Multiplexing Frequeny Division Multiplexing FDM Up onversion Radio transitters Down onversion Radio reeivers

72 Chapter Three: Aplitude Modulation

73 Introdution Aplitude Modulation is the siplest and earliest for of transitters AM appliations inlude broadasting in ediu- and high-frequeny appliations, CB radio, and airraft ouniations

74 Basi Aplitude Modulation The inforation signal varies the instantaneous aplitude of the arrier

75 AM Charateristis AM is a nonlinear proess Su and differene frequenies are reated that arry the inforation

76 Full-Carrier AM: Tie Doain Modulation Index - The ratio between the aplitudes between the aplitudes of the odulating signal and arrier, expressed by the equation: = E E

77 Overodulation When the odulation index is greater than 1, overodulation is present

78 Modulation Index for Multiple Modulating Frequenies Two or ore sine waves of different, unorrelated frequenies odulating a single arrier is alulated by the equation: 1

79 Measureent of Modulation Index

80 Full-Carrier AM: Frequeny Doain Tie doain inforation an be obtained using an osillosope Frequeny doain inforation an be alulated using Fourier ethods, but trigonoetri ethods are sipler and valid Sidebands are alulated using the forulas at the right f usb f f f lsb f f E lsb E usb E

81 Bandwidth Signal bandwidth is an iportant harateristi of any odulation shee In general, a narrow bandwidth is desirable Bandwidth is alulated by: B F

82 Power Relationships Power in a transitter is iportant, but the ost iportant power easureent is that of the portion that transits the inforation AM arriers reain unhanged with odulation and therefore are wasteful Power in an AM transitter is alulated aording to the forula at the right Pt P 1

83 Quadrature AM and AM Stereo Two arriers generated at the sae frequeny but 90º out of phase with eah other allow transission of two separate signals This approah is known as Quadrature AM (QUAM or QAM) Reovery of the two signals is aoplished by synhronous detetion by two balaned odulators

84 Quadrature Operation

85 Suppressed-Carrier AM Full-arrier AM is siple but not effiient Reoving the arrier before power aplifiation allows full transitter power to be applied to the sidebands Reoving the arrier fro a fully odulated AM systes results in a double-sideband suppressed-arrier transission

86 Suppressed-Carrier Signal

87 Single-Sideband AM The two sidebands of an AM signal are irror iages of one another As a result, one of the sidebands is redundant Using single-sideband suppressed-arrier transission results in redued bandwidth and therefore twie as any signals ay be transitted in the sae spetru allotent Typially, a 3dB iproveent in signal-to-noise ratio is ahieved as a result of SSBSC

88 DSBSC and SSB Transission

89 Power in Suppressed-Carrier Signals Carrier power is useless as a easure of power in a DSBSC or SSBSC signal Instead, the peak envelope power is used The peak power envelope is siply the power at odulation peaks, alulated thus: PEP p RL

90 ANGLE MODULATION

91 ANGLE MODULATION Part 1 Introdution

92 Introdution Angle odulation is the proess by whih the angle (frequeny or phase) of the arrier signal is hanged in aordane with the instantaneous aplitude of odulating or essage signal.

93 Cont d lassified into two types suh as Frequeny odulation (FM) Phase odulation (PM) Used for : Coerial radio broadasting Television sound transission Two way obile radio Cellular radio Mirowave and satellite ouniation syste

94 Cont d Advantages over AM: Freedo fro interferene: all natural and external noise onsist of aplitude variations, thus reeiver usually annot distinguish between aplitude of noise or desired signal. AM is noisy than FM. Operate in very high frequeny band (HF): 88MHz-108MHz Can transit usial progras with higher degree of fidelity.

95 FREQUENCY MODULATION PRINCIPLES In FM the arrier aplitude reains onstant, the arrier frequeny varies with the aplitude of odulating signal. The aount of hange in arrier frequeny produed by the odulating signal is known as frequeny deviation.

96 Resting f Inreasing f Dereasing f Carrier Modulating signal FM Inreasing f Resting f

97 PHASE MODULATION(PM) The proess by whih hanging the phase of arrier signal in aordane with the instantaneous of essage signal. The aplitude reains onstant after the odulation proess. Matheatial analysis: Let essage signal: t And arrier signal: os t os[ t ] t

98 PM (ont d) Where = phase angle of arrier signal. It is hanged in aordane with the aplitude of the essage signal; i.e. K ( t) K os t After phase odulation the instantaneous voltage will be v (t) os( t K os t) or v p p (t) C C os( Where p = Modulation index of phase odulation C C K is a onstant and alled deviation sensitivities of the phase t p os t)

99 FREQUENCY MODULATION (FM) A proess where the frequeny of the arrier wave varies with the agnitude variations of the odulating or audio signal. The aplitude of the arrier wave is kept onstant.

100 FM(ont d) Matheatial analysis: Let essage signal: t And arrier signal: os t os[ t ] t

101 FM (ont d) During the proess of frequeny odulations the frequeny of arrier signal is hanged in aordane with the instantaneous aplitude of essage signal.therefore the frequeny of arrier after odulation is written as i K 1 v t K os To find the instantaneous phase angle of odulated signal, integrate equation above w.r.t. t i dt i C 1 K os t dt t sin t C 1 1 C t K

102 FM(ont d) Thus, we get the FM wave as: v FM (t) os 1 C os( C t K1 sin t) v FM ( t) os( t sin t) C C f Where odulation index for FM is given by f K1

103 FM(ont d) Frequeny deviation: f is the relative plaeent of arrier frequeny (Hz) w.r.t its unodulated value. Given as: d ax ax in C C C K K C 1 1 in K 1 f d K1

104 FM(ont d) Therefore: f f K1 f f ;

105 Equations for Phase- and Frequeny-Modulated Carriers Toasi Eletroni Couniations Systes, 5e Copyright 004 by Pearson Eduation, In. Upper Saddle River, New Jersey All rights reserved.

106 Exaple (FM) Deterine the peak frequeny deviation ( f) and odulation index () for an FM odulator with a deviation sensitivity K 1 = 5 khz/ and a odulating signal, v (t) os(000t)

107 Exaple (PM) Deterine the peak phase deviation () for a PM odulator with a deviation sensitivity K =.5 rad/ and a odulating signal, (t) os(000t) v

108 FM&PM (Bessel funtion) Thus, for general equation: v FM ( t) os( t os t) C C f os( os ) n () os n Jn n (t) C n J n () os t n t n

109 Bessel funtion v t FM {J C 0 ( f )os C t J 1 ( f )os ( C )t J 1 ( f )os ( C )t J ( )os ( )t J ( )os( )t...j ( )...} f C f C n f

110 B.F. (ont d) It is seen that eah pair of side band is preeded by J oeffiients. The order of the oeffiient is denoted by subsript. The Bessel funtion an be written as N = nuber of the side frequeny M f = odulation index...!! / 1! 1! / 1 4 n n n J f f n f f n

111 B.F. (ont d)

112 Bessel Funtions of the First Kind, J n () for soe value of odulation index

113 Representation of frequeny spetru

114 Exaple For an FM odulator with a odulation index = 1, a odulating signal v (t) = sin(π1000t), and an unodulated arrier v (t) = 10sin(π500kt). Deterine the nuber of sets of signifiant side frequenies and their aplitudes. Then, draw the frequeny spetru showing their relative aplitudes.

115 Angle Modulation Part FM Bandwidth Power distribution of FM Generation & Detetion of FM Appliation of FM

116 FM Bandwidth Theoretially, the generation and transission of FM requires infinite bandwidth. Pratially, FM syste have finite bandwidth and they perfor well. The value of odulation index deterine the nuber of sidebands that have the signifiant relative aplitudes If n is the nuber of sideband pairs, and line of frequeny spetru are spaed by f, thus, the bandwidth is: For n 1 Bf nf

117 FM Bandwidth (ont d) Estiation of transission b/w; Assue f is large and n is approxiate f + ; thus B f =( f + )f B = f f ( ) f f ( f f)...(1) (1) is alled Carson s rule

118 Exaple For an FM odulator with a peak frequeny deviation, Δf = 10 khz, a odulating-signal frequeny f = 10 khz, = 10 and a 500 khz arrier, deterine Atual iniu bandwidth fro the Bessel funtion table. Approxiate iniu bandwidth using Carson s rule. Then Plot the output frequeny spetru for the Bessel approxiation.

119 Deviation Ratio (DR) The worse ase odulation index whih produes the widest output frequeny spetru. Where DR f (ax) f (ax) f (ax) = ax. peak frequeny deviation f (ax) = ax. odulating signal frequeny

120 Exaple Deterine the deviation ratio and bandwidth for the worst-ase (widest-bandwidth) odulation index for an FM broadast-band transitter with a axiu frequeny deviation of 75 khz and a axiu odulating-signal frequeny of 15 khz. Deterine the deviation ratio and axiu bandwidth for an equal odulation index with only half the peak frequeny deviation and odulating-signal frequeny.

121 FM Power Distribution As seen in Bessel funtion table, it shows that as the sideband relative aplitude inreases, the arrier aplitude,j 0 dereases. This is beause, in FM, the total transitted power is always onstant and the total average power is equal to the unodulated arrier power, that is the aplitude of the FM reains onstant whether or not it is odulated.

122 FM Power Distribution (ont d) In effet, in FM, the total power that is originally in the arrier is redistributed between all oponents of the spetru, in an aount deterined by the odulation index, f, and the orresponding Bessel funtions. At ertain value of odulation index, the arrier oponent goes to zero, where in this ondition, the power is arried by the sidebands only.

123 Average Power The average power in unodulated arrier The total instantaneous power in the angle odulated arrier. The total odulated power R P R (t)] t os[ 1 1 R P (t)] t [ os R R (t) P t t R R R R P P P P P n n t ) (.. ) ( ) (

124 Exaple For an FM odulator with a odulation index = 1, a odulating signal v (t) = sin(π1000t), and an unodulated arrier v (t) = 10sin(π500kt). Deterine the unodulated arrier power for the FM odulator given with a load resistane, R L = 50Ω. Deterine also the total power in the angle-odulated wave.

125 Quiz For an FM odulator with odulation index, =, odulating signal, v (t) = os(π000t), and an unodulated arrier, v (t) = 10 os(π800kt). a) Deterine the nuber of sets of signifiant sidebands. b) Deterine their aplitudes. ) Draw the frequeny spetru showing the relative aplitudes of the side frequenies. d) Deterine the bandwidth. e) Deterine the total power of the odulated wave.

126 Generation of FM Two ajor FM generation: i) Diret ethod: i) straight forward, requires a CO whose osillation frequeny has linear dependene on applied voltage. ii) iii) iv) Advantage: large frequeny deviation Disadvantage: the arrier frequeny tends to drift and ust be stabilized. Coon ethods: i) FM Reatane odulators ii) arator diode odulators

127 Generation of FM (ont d) 1) Reatane odulator

128 Generation of FM (ont d) ) arator diode odulator

129 Generation of FM (ont d) ii) Indiret ethod: i. Frequeny-up onversion. ii. iii. Two ways: a. Heterodyne ethod b. Multipliation ethod One ost popular indiret ethod is the Arstrong odulator

130 Wideband Arstrong Modulator

131 Arstrong Modulator A oplete Arstrong odulator is supposed to provide a 75kHz frequeny deviation. It uses a balaned odulator and 90 o phase shifter to phaseodulate a rystal osillator. Required deviation is obtained by obination of ultipliers and ixing, raise the signal fro 400kHz 14.47Hz to 90.MHz suitable for broadasting. 75kHz

132 FM Detetion/Deodulation FM deodulation is a proess of getting bak or regenerate the original odulating signal fro the odulated FM signal. It an be ahieved by onverting the frequeny deviation of FM signal to the variation of equivalent voltage. The deodulator will produe an output where its instantaneous aplitude is proportional to the instantaneous frequeny of the input FM signal.

133 FM detetion (ont d) To detet an FM signal, it is neessary to have a iruit whose output voltage varies linearly with the frequeny of the input signal. The ost oonly used deodulator is the PLL deodulator. Can be use to detet either NBFM or WBFM.

134 PLL Deodulator 0 (t) f i FM input Phase detetor Low pass filter Aplifier f vo CO (t)

135 PLL Deodulator The phase detetor produes an average output voltage that is linear funtion of the phase differene between the two input signals. Then low frequeny oponent is pass through the LPF to get a sall d average voltage to the aplifier. After aplifiation, part of the signal is fed bak through CO where it results in frequeny odulation of the CO frequeny. When the loop is in lok, the CO frequeny follows or traks the inoing frequeny.

136 PLL Deodulator Let instantaneous freq of FM Input, f i (t)=f +k 1 v (t), and the CO output frequeny, f CO(t)=f 0 + k (t); f 0 is the free running frequeny. For the CO frequeny to trak the instantaneous inoing frequeny, f vo = f i ; or

137 PLL Deodulator f 0 + k (t)= f +k 1 v (t), so, ( t) f f k v ( t) 0 1 If CO an be tuned so that f =f 0, then Where (t) is also taken as the output voltage, whih therefore is the deodulated output ( t) k v ( t) 1

138 Coparison AM and FM Its the SNR an be inreased without inreasing transitted power about 5dB higher than in AM Certain fors of interferene at the reeiver are ore easily to suppressed, as FM reeiver has a liiter whih eliinates the aplitude variations and flutuations. The odulation proess an take plae at a low level power stage in the transitter, thus a low odulating power is needed. Power ontent is onstant and fixed, and there is no waste of power transitted There are guard bands in FM systes alloated by the standardization body, whih an redue interferene between the adjaent hannels.

139 Appliation of FM FM is oonly used at HF radio frequenies for high-fidelity broadasts of usi and speeh (FM broadasting). Noral (analog) T sound is also broadast using FM. The type of FM used in broadast is generally alled wide-fm, or W-FM A narrowband for is used for voie ouniations in oerial and aateur radio settings. In two-way radio, narrowband narrow-f (N-FM) is used to onserve bandwidth. In addition, it is used to send signals into spae.

140 Suary of angle odulation -what you need to be failiar with

141 Suary (ont d)

142 Suary (ont d) Bandwidth: a) Atual iniu bandwidth fro Bessel table: B ( n f ) b) Approxiate iniu bandwidth using Carson s rule: B ( )

143 Suary (ont d) Multitone odulation (equation in general): Kv i Kv 1 i f 1 os 1t f os t... i C t f f 1 f sin 1t sin f 1 t...

144 Suary (ont d) ]... sin sin os[ ] sin sin os[ os t t t t f f t f f t t v t v f f C C C C f i C f

145 Suary (ont d)- Coparison NBFM&WBFM

146 ANGLE MODULATION Part 3 Advantages Disadvantages

147 Advantages Wideband FM gives signifiant iproveent in the SNR at the output of the RX whih proportional to the square of odulation index. Angle odulation is resistant to propagation-indued seletive fading sine aplitude variations are uniportant and are reoved at the reeiver using a liiting iruit. Angle odulation is very effetive in rejeting interferene. (iniizes the effet of noise). Angle odulation allows the use of ore effiient transitter power in inforation. Angle odulation is apable of handing a greater dynai range of odulating signal without distortion than AM.

148 Disadvantages Angle odulation requires a transission bandwidth uh larger than the essage signal bandwidth. Angle odulation requires ore oplex and expensive iruits than AM.

149 END OF ANGLE MODULATION

150 Exerise Deterine the deviation ratio and worst-ase bandwidth for an FM signal with a axiu frequeny deviation 5 khz and axiu odulating signal 1.5 khz.

151 Exerise For an FM odulator with 40-kHz frequeny deviation and a odulatingsignal frequeny 10 khz, deterine the bandwidth using both Carson s rule and Bessel table.

152 Exerise 3 For an FM odulator with an unodulated arrier aplitude 0, a odulation index, = 1, and a load resistane of 10-oh, deterine the power in the odulated arrier and eah side frequeny, and sketh the power spetru for the odulated wave.

153 Exerise 4 A frequeny odulated signal (FM) has the following expression: v f ( t) 38os( t f sin t) The frequeny deviation allowed in this syste is 75 khz. Calulate the: Modulation index Bandwidth required, using Carson s rule