Uhich each component ofthe modulate signal) is uniquely de- ‘ecmined by mi)? Mpy Figure P3.8 3.9 Figure P3.9 shows the circuit diagram ofa balanced mod lator: The input applied to the top AM modulator s mi), whereas {hat applied tothe lower AM modulator is mt: these two meter letors have the same amplitude sensitivity. Show thatthe oot s() ofthe balanced modulator consists of a DSB-SC medulend signal Aco ap onctaer 0 Ae ay) Figure P3.9 3.10 Figure 3.10 shows the circuit details of the’ ring. modu- lator. Assume thatthe diodes are identical and the tanaformes are perfectly balanced. Let R denote the terminating resistance rt the input end and ouput end of the modulator (asuming ideal 1:1 transformers). Determine the ouput voltage of the mosilaace for each of the two conditions described in Figures 3.100 and 3.106. Hence, show that these two output voliages are equal ma magnitude and opposite in polarity ‘114 DSB-SC modulated signal is demodulated by applying 10 a coherent detector. (a) Evaluate the effect ofa frequency error AY inthe local car- rier frequency of the detector, measured with respect tothe ‘air frequency of the incoming DSB-SC signal (b) For te case ofa sinusoidal modulating wave, show that be- cause ofthis frequency error, the demodulated signal exh. bits beats atthe enor frequency. hsrate your answer with «sketch of this demodulated signal S(t) =A, cos(2afn(s) 3.16 The sit wee 4, cos(2/t) isthe camer wave and mt) i the mesiage Be oe Signal This modolated signal is applied to a squarclaw dante, characterized by $0) ~ abe ag where a isa co [Re cumput v0 is next applied to-a narrow-band fer with a pase of the upper sid band amplitude response of one, mid 2s and rin Af Assume that As small enough ro reat the spec (8) IF we sep ‘rum of vr) as essentially constant inside the passband ofthe flee ‘muitiptex (a) Determine the spectrum ofthe square-aw device ouput) ate (©) Show thatthe Filter output x) is approximately sinuses What isn ziven by () The vs i through ar ott) = Lear costar) duced by ¢ i Wha is where Eis the energy ofthe message signal mt, Bea Seem e acu camer multiplex system AMET Using 9 xed signal produced atthe transmit - ‘usput in Figure 3.160 is applied to a communication channel transfer fonction HP), The owpat of this channel isin tur apd ‘othe receiver input in Figure 3.16b, Prove thatthe condition Mk+N=WUL-N. o=sew is necessary fr recovery of the message signals mi) and me) the receiver outputs; f isthe carrier frequency. and Wis the Sage bandwidth. Hint: Evaluate the spectra of the two rece outputs. Amplitude Double id 3.14 Suppose that in the receiver of the quadature-ca ‘multiplex system of Figure 3.16 the local carrer available for & ‘modulation has a phase eror with respect to the carey cy used in the transmiter. Assuming a distorionless communica channel between transmitter and receive, err will cause crass-ta t arise between the two demodita Signals atthe receiver outputs. By cross-talk we meen thas a tion of one message signal appears atthe receiver output bela ‘ng to the other message signal, and vice versa 3.15 A particular version of AM stereo uses quadrature mul plexing. Specifically the cartier A. cos(29f is used to modhll the sum sign 1m (0) = Va + me) + mete) where Vo is de offset included forthe purpose of transmit the carrier component, my i the lfi-hand audio signal, and isthe right-hand audio signa. The quadrature carrer A, sin(2y 's used to moxilat the difference signal m(t) = mit) ~ me) (4) Show that an envelope detector may be used to recover sum (+ m(2) from the quadrature-multipleed. sg How would you minimize the signal distortion produced bf the envelope detector? Show that a coherent detecior can recover the difee md0)— m0) How are the desired mi?) and m)fnally obtained? o3.16 The single tne modulating signal mi) = Ay cos(2afyt is tse to generate the VSB signal 1 1) = AWA, cos!2n(f + fat) + 4Away(t ere « is «constant, les than unity, representing the attenuation the upperside frequency. (a) Hf we represent this VSB signal as a quadrature ‘muluplex (0) = Ag (oos(2aft) + Acma(e)sin( 22/0) What is mstty? ‘The VSB signal, plus the carrier A, cos(2n/t, i passed through an envelope detector. Determine the distortion pro duced by the quadrature component. n-) What is the value of constant « For which this distortion reaches its worst posible condition? 3.17 Using the message signal m= 7 termine and sketch the mdulated waves nethods of modulation: for the following {) Amplitude modolation with 50 percent modulation, (0) Double sideband.suppressed carrier modulation 3.48 The local oscillator used forthe demodulation of an SSB Signal 0) has a frequency error AY measured with respect to the tae frequency used to generates). Otherwise, there is per fet synchronism between this oscillator in the receiver and the ‘xcillatoe supplying the carrier wave inthe transmiter. Evaluate the demodulated signal for the following two situations: a) The SSB signal s) consists of the upper sideband only. (b) The SSB-signal sr) consists ofthe lower sideband only, 4.19 Figure P3.19 shows the block diagram of Weaver's method Arfenerating SSB modulated waves. The message (modulating) signal mi) i limited to the frequency band f, = if| =f. The snilary carries applied to the first pair of product modulators has fequency fo, which ies a the centr ofthis band, as shown by bth hi ‘The low-pas filters inthe upper and lower branches are identi tach with auto frequency equal to (fy faV2. The carrier ap led ro the second pair of product mexduators has a frequency at is greater than (f, ~ V2. Sketch the spectra at the various ‘ints inthe modulator of Figure P3.19, and hence show that. For the lower sideband, the contributions of the upper and lower branches are of opposite polarity, and by addin them a the modulator output, the lower sideband is suppressed For the upper sideband, the contributions of the upper and lower branches are of the same polanty and by adding them, the upper sideband is transmitted eon|2n(f.~ ft] How would you modify the modulator of Figure P3.19, xo ‘that only the lower sideband is transmited? Figure P3.19 3.20 (4) Consider a message signal m() containing frequency com- Ponents at 100,200, and 400 He. This signal is applied to an ‘SSB modulator together with a cartier at 100 kHz, with only the upper sideband retained. In the coherent detector used to recover mi), the local oscillator supplies & sine wave of fe quency 100.02 kHz. Determine the frequency components ‘ofthe detector output Repeat your analysis, assuming that only the lower sidebana is wansonted 3.21. The spectrum ofa voice signal mis ero ouside the in terval fo 5 |f| = fa. In order to ensure communication privacy. this signal is aplied to a scrambler that consists ofthe following cay. cade of components: a product modulator, «high-pass fer ‘second product modulator, anda low-pass filter. The carer wave ‘spplied tothe first product modulator has a frequency eaual to whereas that applied to the second product modulator has a fe quency equal to f, +f: both of them have unit amplitude. The high-pass and lowpass filters have the same cutoff frequency a Assume that > jy (a) Derive an expression for the scrambler output ff), and sketch its spectrum (b) Show thatthe orignal voice signal mit) may be recovered from st) by using an wascrambler that is identical to the unit described abo 3.22 A method that is used for carer recovery in SSB modu- lation systems involves transmitting two pilot frequencies that are appropriately positioned with respect to the transmitted sideband This is illustrated in Figure P3.22u for the case when only the lower sideband is traosmitted, In this case, the pilot frequencies and fz are defined by ere and re