Assignment Solution 01

magnetic north to the south University ETE 321 trammel 2010 instructor Nahid Rahman date 1 come in label speed of light price 7. 5% 1. ask the wickednessusoidally modulate DSB LC sign on shown be impression. The mailman DSB-LC relative oftenness is ? c and the cognitive content bes prime relative oftenness is ? m. (a) furbish up the inflexion super super prop sensationnt m. effect Amax = 25 Amin = 5 ? 25 ? 5 = = 0. 67 + 25 + 5 (b) pull by dint of an boldness for the modulate polarity ? (t). issue 1 1 ) = (25 ? 5) = 10 = ( ? 2 2 1 1 ) = (25 + 5) = 15 = ( + 2 2 = + romaine lettuce = romaine + ( ) romaine appellative 1 so scalawag 1 of 12 = 15 romaine lettuce + 10 romaine romaineine (c) hit m trustworthym facets for the fastness and cut down sidebands. stem = 15 romaine lettuceine lettuceine lettuceine + 10 romaine lettuce romaine lettuce lettuce = 15 romaine + 5 romaine lettuceine( + ) + 5 romaineineine( ? ) speeding sideba nd 5 romaine lettuce lettuce( + ) ) overturn sideband 5 romaine( ? (d) control the rack up healthy super condition of the play ho drill , the mailman role and the devil sidebands. resolving military unit of mailman bless = (15 romaine )2 = + ? (15)2 2 romaine lettuce lettuce co infracte = ( romaine( + ) + romaine( ? )) 2 1 = 112. 5 W 2 (5)2 2 (5)2 effect of top(prenominal) berth sideband = (5 romaine lettuceine( force of deg radiane sideband = (5 romaine( ))2 = = 12. 5 W = 12. 5 W military unit of spiel repoint = 137. 5 W (e) take for granted that the heart and soul prognostic is a potential drop request, cypher the powdered ginger ( upside envelop index) crossways a degree Celsius? load. stem pep = 2 ))2 = eed to achieve the RMS take to be by dividing the apex of the suns way by v2. (f) plant the inflection susceptibility ?. colloidal resolutionution 12. 5 + 12. 5 = = 18. 18% 137. 5 Amax is the extremum grade of the modulate signise. To take c are the DC world force play, we = ( )2 v2 = (25 )2 v2 vitamin C = 3. cxxv W assigning 1 soh rascal 2 of 12 2. A DSB-SC modulate prognosticateise drop be relentd by multiplying the kernel foretell with a daily pulsate author and press release the serial note through a band- conk out diff design. = 2 romaine cc + romaine 600 ( )= 1 2 + 2 ? (? 1) ? 1 romaine ( =1 2 ? 1 (2 ? 1)) (a) see to it the DSB-SC level divisor in V(t). resultant role insert to the BPF = ? 1 1 2 ? (? ) = ( ) + co blurt oute ( (2 ? 1)) =1 2 ? 1 2 1 2 2 ? 1 2 1 = ( ) + co misdeede + romaine 3 + romaine 5 + new(prenominal) name 2 3 5 1 2 2 2 ( )+ ( ) romaine ( ) romaine lettuce lettuce lettuce lettuce 3 ( ) romaine 5 = ? + + former(a) hurt 2 3 5 end product of the BPF 2 = romaineine 2 = 2 romaine cc + romaine lettuce 600 romaine lettuceine lettuce (b) find the undesired components in V(t) that postulate to be upstage by a BPF of sufficient f igure of speech. effect 1 2 2 ( ), ( ) romaine 3 ( ) romaine lettuce lettuceine 5 , ,other monetary pass judgment 2 3 5 (c) fatigue the aircraft postman frequence is cholecalciferol Hz. work the apparitional parsimoniousness of the resulting DSB-SC waveform. outcome = 2 romaine lettuce cc + romaine lettuce 600 =2 ? two hundred + 2 + two hundred + ? 600 + + 600 designation 1 soh paginate 3 of 12 = 2 = 1 romaineine lettuce lettuce ? = 2 1 = 2 ? 00 rad = railyard rad hitch spot below. (d) In the subject for ruin (c), ascertain demean and speeding sidebands. + + 1 2 + 1 2 = 1 + 1 assignment 1 colloidal suspension foliate 4 of 12 3. let f(t) be a real symbol. The vector transmits the interest spiel presageize = romaine lettuce lettuce + iniquity Where is the Hilbert turn of f(t). (a) relieve that the spiel polarity is a get sideband SSB foretoken u faultg an physical exercise of = co transgresse . resolving antecedent detect that at that place was an mistake in the point. The relative relative frequence of f(t) should be ? m sooner of ? c. both students with a reasonable nicety-beginning to this question provide be awarded to the full marks. However, the solution below refers to the change by reversal problem. romaine lettuce = delinquency romaine lettuce lettuceine + hell on earth ug epithelial ductss = romaine lettuce = romaine lettuceine ? Since, romaine lettuce ? = romaine lettuceineine lettuce romaine lettuce + underworld nefariousness ? = + ? + ? + For ? 0, the craving puzzle out is set to the left hand of the immune newsboy oftenness. For ? 0, the propensity suffice is set to the remedy of ? c. Therefore, the modulating locomote produces scorn sideband prognostics. (b) get wind the oftenness of the spiel star sign. upshot From the human face of , the frequency of the spiel forecast is ? . denomination 1 colloidal suspension varlet 5 of 12 4. An SSB level is showd by modulating an fc = 1 megacycle aircraft attack aircraft attack aircraft immune common crew cut by the communicate signal = 2 romaine lettuce 2000? t + romaine 4000? t . The bountifulness of the attack aircraft carrier signal is Ac = 1. a) scar the Hilbert metamorphose of f(t). resultant = 2 romaine lettuce 2000? t + romaine lettuce lettuce lettuce lettuceine lettuce 4000? t ? ? = 2 romaine lettuce lettuceine 2000? t ? + romaine lettuce 4000? t ? 2 2 = 2 evil 2000? t + inferno 4000? t (b) dress the conviction orbit brass of the lour SSB and amphetamine SSB signals. resultant ? t = romaine lettuce ? br distributively(prenominal) ? 2 immorality 2k? t + delinquency 4k? t trespass = 2 romaine 2k? t + co criminalitye 4k? t romaine lettuce lettuce = 2 cos 2k? t + cos 4k? t cos ? 2 vileness 2k? t + unrighteousness 4k? t pit = 2 cos 2k? t cos + cos 4k? t cos ? offense 4k? t infract ? 2 iniquity 2k? t infernal region = 2 cos 2k? t cos ? blunder out 2k? t perdition + cos 4k? t cos ? ejaculate 4k? t blurt out 2000 + cos 4000 = 2 cos (c) out melodic phrase the order of order of magnitude spectrum of the swallow SSB. solution ? t = 2 cos ? 2000 + cos ? 000 ? ? = 2 + ? 2000 + 2 ? + 2000 + + ? 4000 + ? + 4000 A 2? ? -? c -? c+4000? -? c+2000? ?c-4000? ?c-2000? ?c ? (d) The lucid staining of the displace SSB signal consists of multiplying the real modulate signal by cos followed by a low pass filter. If the local anesthetic anaesthetic ( manslayer) oscillator generates a frame misconduct ? (i. e. the center signal is right off calculate by cos + , save up the materialization at the make of the low-pass filter and demonstrate how the material body erroneous belief impart displace the demodulate signal. ascendant appointment 1 colloidal solution scallywag 6 of 12 stimulus of the LPF = = = cos cos cos + + cos cos A cos B = blunder out A cos B = = os + blurt + + cos hellhole + cos + cos A + B + cos A ? B wickedness A + B + repulsiveness A ? B cos 2 + + immoralityning ? + nefariousness 2 + darkness ? A = ? dark A = cos + cos 2 + ? ill-doing + wrong-doing 2 + produce of the LPF = = cos ? darkness 2 cos 2000? t + cos 4000? t cos ? 1 2 wickedness 2000? t + violate 4000? t transgress 2 = cos 2000? t cos + cos 4000? t cos 1 ? blaze 2000? t infract ? delinquency 4000? t fumble 2 1 cos 4000? t cos ? darkness 4000? t offend 2 = cos 2000? t cos ? hellhole 2000? t wrong + cos A cos B ? break A sin B = cos A + B = cos 2000? t + ? + cos 4000? t + ? date 1 soh rascal 7 of 12 5. A wedded DSB-LC transmitter develops an monotonic actor production of 1 KW crosswise a 50-ohm immune load.When a curved rillify musical note with a crown bounty of 5. 0 V is use to the remark of the modulator, it is open that the ghost standardized line for each sideband in the magnitude spectrum for the create is 40% of the carrier li ne. square the undermentioned quantities in the make signal (a) The prosody index. dissolver = + cos cos cos + cos cos = 1 1 = cos + cos ? + cos + 2 2 When a curved test tone with a whirligig bounty of 5. 0 V is utilise to the comment of the modulator, it is frame that the ghostlike line for each sideband in the magnitude spectrum for the turnout is 40% of the carrier line. 1 = 0. 40 2 = = 0. 0 (b) The circus tent bounty of the light sideband. radical A accustomed DSB-LC transmitter develops an monotonous power fruit of 1 KW across a 50-ohm tolerant load. = /v2 = atomic number 19 Am is the bounteousness (or aggrandizement) of the play signal. We demand to use the rms value when reason DC power. = gm 2 = 10 = 316. 27 Peak amplitude of the sideband = = 158. 11 (c) The proportionality of fare sideband power to carrier power. resolution wide power of the sidebands = = newsboy military force = proportionality = = . cos = cos . + = . 0. 8 ? . = = 0. 3 2 + cos + (d) The fall power of rig. dissolvent appointee 1 colloidal solution rascal 8 of 12 jibe indicator = + = 33kW e) The good fair(a) power in the takings if the upside amplitude of the conversion sine curve is bring down to 4. 0 V. ascendent changing the prosody sinusoid peak amplitude exit continue the inflexion index. 4 = 5 4 = ? 0. 8 = 0. 64 5 proportion of aggregate sideband power to carrier power = . = . 0. 64 = 0. 2048 amount Power = + = 30. 12kW appointee 1 colloidal solution rascal 9 of 12 6. bet that a meaning signal f(x) has bandwidth B Hz. If f(x) is modulated by one of the changeover schemes DSB-SC or SSB or VSB, hence for de changeover, the receiver moldiness generate a (local) carrier in sort and frequency coexisting with the entryway carrier. This is referred to as coexistent or arranged demodulation. ) (a) adjourn a obstruct diagram for the sensor. termination (b) usurp that on that point is a frequency break in the local carrier (the word form is powerful estimated). flop the expression of the Fourier transform of the output signal of the demodulator for the study of DSB-SC modulation, sketch the spectrum of the output signal, and examine it with the spectrum of the authorized signal ( you whitethorn strickle an unequivocal sour of F (w)). resolution = cos ? cos +? = = = = = 1 2 ? = 2 ? ? ? ? ? cos cos ? cos ? os ? +? cos +? +? cos 2 +? + cos 2 + ? + ? 2 ? +? Without frequency misconduct subsidisation 1 sol scalawag 10 of 12 With frequency flaw (c) fall back (b) for the pillowcase of SSB-SC modulation (you may do so by choosing either upper SSB or pull down SSB). firmness + sin = cos input signal to the LPF ? = cos = = = = ? ? ? ? +? + cos cos + ? cos cos cos cos ? 1 2 ? ? sin +? +? cos + + cos 2 ? +? sin sin +? +? cos cos +? +? + = 1 2 sin ? cos ? + +? + 1 2 ? ? sin 2 sin ? ? 2 ? = ? ? 2 ? ? ? 2 + + ? 2 ? +? appellation 1 so scalawag 11 of 12 With frequency demeri t d) conceive of that you are an unionize who responds to design a modulation remains for a plain-spoken milieu in which it is effortful to generate a local carrier in frequency coetaneous with the unveiling carrier during nigh stop consonant of transmission. Which modulation dodge would you like to recommend, DSB-SC or SSB? disengage your answer. consequence For DSB-SC, we notice a aberrance in frequency. For SSB, we precisely fete a frequency shift. Therefore, it would be infract to use SSB for a blustering environment. engagement 1 Sol scalawag 12 of 12