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Modulated Signal EE1: Introduction to Signals and Communications Professor Kin K. Leung EEE and Computing Departments Imperial College [email protected] Lecture Three Lecture Aims ● To examine modulation process ● Baseband and bandpass signals ● Double Sideband Suppressed Carrier (DSB-SC) - Modulation - Demodulation ● One of various modulators - Switching modulator 2 Modulation ● Modulation is a process that causes a shift in the range of frequencies in a signal. ● Two types of communication systems - Baseband communication: communication that does not use modulation - Carrier modulation: communication that uses modulation ● The baseband is used to designate the band of frequencies of the source signal. (e.g., audio signal 4kHz, video 4.3MHz) 3 Modulation (continued) In analog modulation the basic parameter such as amplitude, frequency or phase of a sinusoidal carrier is varied in proportion to the baseband signal m(t). This results in amplitude modulation (AM) or frequency modulation (FM) or phase modulation (PM). The baseband signal m(t) is the modulating signal. The sinusoid is the carrier or modulator. 4 Why modulation? ● To use a range of frequencies more suited to the medium ● To allow a number of signals to be transmitted simultaneously (frequency division multiplexing) ● To reduce the size of antennas in wireless links 5 Amplitude Modulation ● Carrier At cos(cc ) - Phase is constant c 0 - Frequency is constant ● Modulating signal m(t) ● With amplitude spectrum 6 Modulated signal ● Modulated signal: m(t)cosct 7 Modulated signal ● Modulated signal: m(t)cosct 8 Modulated signal ● Baseband spectrum: B Hz ● M() is shifted to M(+ c) and M(- c) 9 Demodulation of DSB signal ● Process modulated signal m(t)cosct ● Multiply modulated signal with cosct 1 et() mt ()cos2 t mt () mt ()cos2 t cc2 11 EM() () M ( 2 ) M ( 2 ) 24 cc 10 Demodulation of DSB signal ● Process modulated signal m(t)cosct 11 Example: AM of a cosine signal ● Modulating signal m(t)=cos mt ● Carrier cos ct ● Modulated signal ϕ(t) = m(t) cos ct =cos mt cos ct 12 Amplitude spectrum ● Baseband signal M () (mm ) ( ) 1 ()ttt cos( ) cos( ) DSB SC2 c m c m (c m ) 13 Demodulation of DSB signal ● Process modulated signal m(t)cosct 14 Modulators ● We need to implement multiplication m(t) cos ct ● Among various methods, we can use - Switching modulators ● Switching modulators can be implemented using diodes - (not included in your exam) 15 Switching modulator using square pulses ● Consider a square pulse train ● The Fourier series for this periodic waveform is 12 1 1 wt( ) cosccc t cos3 t cos5 t 235 ● The signal m(t)w(t) is 12 1 mtwt() () mt () mt ()coscc t mt ()cos3 t 23 16 Switching modulator 17 Double Sideband Suppressed Carrier ● A receiver must generate a carrier in frequency and phase synchronism with the carrier at the transmitter ● This calls for sophisticated receiver and could be quite costly ● An alternative is for the transmitter to transmit the carrier along with the modulated signal ● In this case the transmitter needs to transmit much larger power 18 Amplitude Modulation ● Carrier A cos(ct c ) - Phase is constant c 0 - Frequency is constant. ● Modulation signal m(t) ● With amplitude spectrum ● Full AM signal is AMcc()tA cos tmt ()cos t Amt( ) cosc t ● Spectrum of full AM signal 1 ()()()tM M A ()() AM2 c c c c 19 Full AM Modulated signal ● DSB Modulated signal: ● Full AM signal 20 Full AM Modulated signal ● Signal ● Modulating signal ● Modulated signal: A mt()cos c t 21 Envelope detection is not possible when ● Signal ● Modulating signal ● Modulated signal: A mt()cos c t 22 Envelope detection condition ● Detection condition A + m(t) ≥ 0 ● Let mp be the maximum negative value of m(t). This means that m(t) ≥ -mp ● When we have A ≥ mp, we can use envelope detector m ● The parameter p is called the modulation index A ● When 0 ≤ μ ≤ 1, we can use an envelope detector 23 Envelope detection example ● Modulating signal mt() B cosm t ● Modulating signal amplitude is mBp B ● Hence and B A A ● Modulating and modulated signals are mt() B cosmm t A cos t AMcmc(tAmttA ) ( ) cos 1 cos t cos t 24 Demodulation of DSB signal ● Consider modulation index to be 0.5 ● For modulation index 1 25 Sideband and Carrier power ● Consider full AM signal ()tA cos tmt ()cos t AMc c carrier sidebands ● Power Pc of the carrier A cos ct A2 2 ● Power Ps of the sideband signals 0.5mt2 ( ) ● Power efficiency useful powerP mt2 ( ) s 100% 22 total power PPcs Amt () 26 Maximum power efficiency of Full AM ● When we have mt() A cosm t () A 2 ● Signal power is mt2 () 2 ● When 0 ≤ μ ≤ 1 ● When modulation index is unity, the efficiency is max 33% ● When μ=0.3 the efficiency is 0.3 2 100% 4.3% 2 0.3 2 27 Generation of AM signals ● Full AM signals can be generated using DSB-SC modulators ● But we do not need to suppress the carrier at the output of the modulator, hence we do not need a balanced modulators ● Use a simple diode 28 Simple diode modulator design ● Input signal ctmtcosc ( ) ● Consider the case c >> m(t) ● Switching action of the diode is controlled by ctcosc ● A switching waveform is generated. The diode open and shorts periodically with w(t) ● The signal is generated vtbb' () c cos c tmtwt () () 29 Diode Modulator ● Diode acts as a multiplier vtbbn () c cos c tmtwt () () 12 1 1 ctmtcoscccc ( ) cos t cos3 t cos5 t 235 c 2 costmtt ( )cos other terms 2 cc suppressed by AM bandpass filter 30 Demodulation of AM signals ● Rectifier detector 31 Demodulation of AM signals ● Half-wave rectified signal R is given by Rc A mt()cos t wt () where w(t) 12 1 1 vAmttRcccc( ) cos cos t cos3 t cos5 t 235 1 Amt( ) other terms of higher frequencies 32 Demodulation of AM signals using an envelope detector ● Simple detector ● Detector operation 33 Envelope detector example ● For the single tone ● Design envelope detector 34 Double vs Upper/Lower Side Band (USB/LSB) Modulated Signal 35 EE1: Introduction to Signals and Communications Professor Kin K. Leung EEE and Computing Departments Imperial College [email protected] Lecture Four Lecture Aims ● Angle Modulation - Phase and Frequency modulation - Concept of instantaneous frequency - Examples of phase and frequency modulation - Power of angle-modulated signals 37 Angle modulation Consider a modulating signal m(t) and a carrier vc(t) = A cos(ωct + θc). The carrier has three parameters that could be modulated: the amplitude A (AM) the frequency ωc (FM) and the phase θc (PM). The latter two methods are closely related since both modulate the argument of the cosine. 38 Instantaneous frequency ● By definition a sinusoidal signal has a constant frequency and phase: Acos(ct c ) ● Consider a generalized sinusoid with phase θ(t):(t) Acos(t) ● We define the instantaneous frequency ωi as: d ()t i dt ● Hence, the phase is t ()td ( ) . i 39 Phase modulation We can transmit the information of m(t) by varying the angle θ of the carrier. In phase modulation (PM) the angle θ(t) is varied linearly with m(t) : ()ttkmtcp () where kp is a constant and ωc is the carrier frequency. Therefore, the resulting PM wave is PM()tA cos c tkmt p () The instantaneous frequency in this case is given by d ()tkmt () icpdt 40 Frequency modulation In PM the instantaneous frequency ωi varies linearly with the derivative of m(t). In frequency modulation (FM), ωi is varied linearly with m(t). Thus icf()tkmt (). where kf is a constant. The angle θ(t) is now tt ()tkmdtkmd () () . cf c f The resulting FM wave is t FM()tA cos c tkmd f ( ) 41 Example Sketch FM and PM signals if the modulating signal is the one above (on the left). 5 The constants kf and kp are 2π×10 and 10π, respectively, and the carrier frequency fc =100MHz. 42 FM example ● Instantaneous angular frequency icf kmt() k ● Instantaneous frequency fff mt() 1085 10 mt () ic2 (f ) 1085 10mt ( ) 99.9 MHz i min min (f ) 1085 10mt ( ) 100.1 MHz i max max 43 PM example k ● Instantaneous frequency f f p m (t) 108 5m (t) i c 2 ( f ) 108 5m (t) 108 105 99.9MHz i min min ( f ) 108 5m (t) 108 105 100.1MHz i max max 44 Bandwidth of angle modulated waves In order to study bandwidth of FM waves, define t at() m ( ) d and jtkat () jk a() t ˆ cf f jct FM ()tAe Aee The frequency modulated signal is ˆ FM()tt Re FM () 45 Bandwidth of angle modulated waves jk a(t ) Expanding the exponential e f in power series yields 2 n kkff ˆ 2 nn jct FM()tA 1 jkatat f () () j at () e 2!n ! and ˆ FM()tt Re FM () 23 kkff23 Atkattattattcoscf ( )sin c ( )cos c ( )sin c 2! 3! 46 Narrow-Band Angle Modulation The signal a(t) is the integral of m(t). It can be shown that if M(ω) is band limited to B, A(ω) is also band limited to B. If |kf a(t)| ≪ 1 then all but the first term are negligible and FM()~tA cos c tkat f ()sin c t This case is called narrow-band FM. Similarly, the narrow-band PM is given by PM (t)~Acosct k pm(t)sinct 47 Narrow-Band Angle Modulation Comparison of narrow band FM with Full AM. Narrow band FM FM()~tA cos c tkat f ()sin c t Full AM A mt()coscc t A cos t mt ()cos c t Narrow band FM and full AM require a transmission bandwidth equal to 2B Hz.
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