III. Amplitude Modulation
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1 III. Amplitude Modulation AM schemes Double sideband suppressed carrier (DSB-SC) Double sideband transmitted carrier (DSB-WC) Modulation eiciency & index Single sideband (SSB) Vestigial sideband (VSB) Amplitude shit keying (ASK) Modulators Gated modulator Square law modulator SSB modulator Vestigial modulator Demodulators Coherent demodulation gated demodulation requency mismatch eects quadrature receiver SSB demodulation VSB demodulation ASK demodulation Incoherent demodulation rectiier detector envelope detector SSB incoherent demodulation ASK incoherent demodulation AM Broadcast 10/25/03 EC2500.MPF/Fall-FY04 1
2 III. Amplitude Modulation 1) Double Sideband Suppressed Carrier s(t) s m (t) cos (2 c t) S() S m () = m m S m () 10/25/03 EC2500.MPF/Fall-FY04 2
3 Multiple Signal Transmission s 1 (t) s 1 (t) cos 2 c 1 t cos 2 c 2 t sm 1 sm 2 t t s m (t) S 1 () S 2 () S m () Transmission constraints? 10/25/03 EC2500.MPF/Fall-FY04 3
4 Receiver S m () 10/25/03 EC2500.MPF/Fall-FY04 4
5 Example: inormation signal s t sin 2 t t s(t) s m (t) cos (2 c t) c = 10 Hz 1) Plot s m (t) 2) Compute and plot S m () 3) Design the receiver needed to recover s(t) rom s m (t) 10/25/03 EC2500.MPF/Fall-FY04 5
6 10/25/03 EC2500.MPF/Fall-FY04 6
7 2) Double Sideband Transmitted Carrier s 1 (t) A s m (t) s m (t) = S m () = cos 2 t c s(t) t s(t) + A t s m (t) t 10/25/03 EC2500.MPF/Fall-FY04 7
8 Modulation Eiciency eiciency signal power total power Modulation Index m max s t A s m (t) m = t cos2 t s t A? 0 10/25/03 EC2500.MPF/Fall-FY04 8
9 3) Single Sideband Recall double sideband AM S m () c c Are both sides really needed? S USB () c c S LSB () c c 10/25/03 EC2500.MPF/Fall-FY04 9
10 4) Vestigial Sideband (VSB) SSB needs less requency bandwidth than DSB SSB transmitter and receivers are complicated (expensive) VSB is a trade-o between DSB and SSB 10/25/03 EC2500.MPF/Fall-FY04 10
11 5) Amplitude Shit Keying (ASK) s(t) s m (t) cos (2 c t) s(t) T 2T 3T t s m (t) t 10/25/03 EC2500.MPF/Fall-FY04 11
12 ASK Spectrum S m () - Typical s(t) not periodic, due to random 0 & 1 bits 1) Periodic s(t) case 2) Extension to non periodic s(t) case 1) Periodic s(t): s(t) T b =T/2 T b S( ) a ( k ) k Recall Delta s are located at k 0 =k/2t b =kr b /2 k t 0 10/25/03 EC2500.MPF/Fall-FY04 12
13 2) Extension to non periodic s(t) case Recall the Power Spectrum o random NRZ was deined as (section II.A): De: The power spectral density (PSD) or a non periodic signal s(t) is deined as: 2 1 T G /2 2 ( T j t ) lim s ( t ) e dt T T /2 10/25/03 EC2500.MPF/Fall-FY04 13
14 ASK Spectrum or random bits signal 10/25/03 EC2500.MPF/Fall-FY04 14
15 7) Modulators a) Gated modulator Introduction y s(t) 1 (t) BPF y 2 (t) S() A p(t) m m y 1 (t) = Y 1 ()= 10/25/03 EC2500.MPF/Fall-FY04 15
16 Implementation Note: we need to implement s(t).p(t) with pt () 0 1 s(t) + ~ - e 2 (t) Process corresponds to a switch operating at a rate o c times/sec Too ast or a mechanical switch, must be electric. 10/25/03 EC2500.MPF/Fall-FY04 16
17 C D 1 & D 2 are a matched pair D 3 & D 4 + s(t) + ~ - A D 1 D 3 B e 2 (t) D 2 - D + ~ D 4 Acos(2 c t) - 1) Acos(2 c t)>0 => 1) Acos(2 c t)<0 => 10/25/03 EC2500.MPF/Fall-FY04 17
18 b) Square law modulator + y s(t) 1 (t) y y ( ) 2 2 (t) 3 (t) BPF S() A s c (t) m m y 2 (t) = Y 2 ()= 10/25/03 EC2500.MPF/Fall-FY04 18
19 S() A m m Y 2 () Y 3 () 10/25/03 EC2500.MPF/Fall-FY04 19
20 b) SSB modulator s(t) s m (t) H 1 () y USB (t) cos (2 c t) S() A c c S m () H 1 () 0 0 s(t) H 1 () - + s LSB (t) cos (2 c t) H 2 () S m () H 2 () /25/03 EC2500.MPF/Fall-FY04 20
21 Potential problem with above SSB modulator 10/25/03 EC2500.MPF/Fall-FY04 21
22 Phase shit SSB modulator y 1 (t) s(t) 90 ~ cos (2 c t) 90 H p () y 4 (t) y 3 (t) y 2 (t) y(t) H p () S() j j A m m H p () = j sgn () Y 1 () 10/25/03 EC2500.MPF/Fall-FY04 22
23 Y 3 () Y 4 () Y 2 () 10/25/03 EC2500.MPF/Fall-FY04 23
24 Y 1 () + Y 2 () Y 1 () Y 2 () 10/25/03 EC2500.MPF/Fall-FY04 24
25 SSB time domain expression y 1 (t) s(t) 90 ~ cos (2 c t) 90 H p () y 4 (t) y 3 (t) y 2 (t) y(t) j H p () j SSB requency domain expression 10/25/03 EC2500.MPF/Fall-FY04 25
26 10/25/03 EC2500.MPF/Fall-FY04 26
27 Vestigial Sideband (VSB) modulator s(t) H() s m (t) cos (2 c t) 10/25/03 EC2500.MPF/Fall-FY04 27
28 8) Demodulators Two dierent types: coherent: requires synchronization incoherent: simple to implement a) Coherent demodulation S() S m () A A/2 m m m c s m (t)? y(t) y 2 (t) c(t) = cos (2 c t) Y 1 () 10/25/03 EC2500.MPF/Fall-FY04 28
29 y 2 (t) = 10/25/03 EC2500.MPF/Fall-FY04 29
30 Gated Demodulator Do we have to use a cos (2 c t) to recover s(t)? Assume c(t) deined as c(t) T/2 T 2T t 10/25/03 EC2500.MPF/Fall-FY04 30
31 10/25/03 EC2500.MPF/Fall-FY04 31
32 Square Law Demodulator s m (t) (. ) 2 y(t) 2 y() t s () t Acos(2 t) m c DBB-WC modulation case s m (t)= y(t)= 10/25/03 EC2500.MPF/Fall-FY04 32
33 Frequency & Phase Mismatch Eects s m (t) y 1 (t) LPF y(t) cos 2 c t c c y1 t s t cos 2 t cos 2 t 10/25/03 EC2500.MPF/Fall-FY04 33
34 10/25/03 EC2500.MPF/Fall-FY04 34
35 Quadrature Receiver s () t 1 s 1 (t) LPF ( ) 2 s m (t) cos 2 t c s () t 2 s 2 (t) LPF ( ) 2 s o (t) cos 2 t c 10/25/03 EC2500.MPF/Fall-FY04 35
36 10/25/03 EC2500.MPF/Fall-FY04 36
37 Single Sideband Demodulation S() S USB () m m y 1 (t) s USB (t)? y(t) cos (2 c t) Y 1 () 10/25/03 EC2500.MPF/Fall-FY04 37
38 y1 t 10/25/03 EC2500.MPF/Fall-FY04 38
39 Vestigal Sideband Demodulation V S S H m 10/25/03 EC2500.MPF/Fall-FY04 39
40 ASK Demodulation s m (t) T b A t We know which signal shape is sent originally take advantage o it Matched ilter detector Recall: binary matched ilter detector T b 0 dt s m (t) s 1 (t) T b compare to threshold T b 0 dt s 0 (t) 10/25/03 EC2500.MPF/Fall-FY04 40
41 s m (t) t T b s m (t) T b 0 dt Y compare to threshold T h Acos 2 t c Y How to compute the threshold T h? T 0 0 b Y As t cos 2 t dt when s t A cos 2 t Y T b A 2 2 T 2 b c A 0 2 ATb m c m c 2 c cos 2 t dt 1 cos 4 t when sm t Acos 2 ct 2 0 when s 0 Threshold = m t dt 10/25/03 EC2500.MPF/Fall-FY04 41
42 Carrier requency recovery in AMTC when c is transmitted narrowband BP ilter phase lock loop cos2 s t A ct LPF y(t) = BPF ~cos 2 t c 10/25/03 EC2500.MPF/Fall-FY04 42
43 b) Incoherent (asynchronous) Demodulation t Square Law Detector s m (t) ( ) 2 LPF y 1 (t) y 2 (t) ( ) y y 1 2 t t LPF cuto requency: Constraint needed on signal amplitude: 10/25/03 EC2500.MPF/Fall-FY04 43
44 Rectiier Detector H() s m (t) Rect y 1 (t) LPF m m s m (t) 0 t m cos2 c s t A s t t y 1 (t) y1 t 0 t Expand cos 2 t c Fundamental period or cos2 t cos 2 t c in a Fourier series expansion c cos 2 t c 10/25/03 EC2500.MPF/Fall-FY04 44 t
45 Envelope Detector t Need to ollow envelope only! e i (t) A B e 0 (t) (1) e i (t) < e 0 (t) V A < V B diode shuts o capacitor discharges in R (2) e i (t) e 0 (t) V A V B diode transmits capacitor loads s m (t) e 0 (t) t 10/25/03 EC2500.MPF/Fall-FY04 45
46 Envelope Detector Constraints ilter RC detector time constraint must be small enough to be able to track changes in s m (t) peak values Problem when RC time constraint is too large! Demodulated signal doesn t ollow envelope. s m (t) t ilter RC detector time constraint must be large enough to ollow the envelope trend only. High requency components are generated when RC time constraint is too small (capacitor discharges too ast). s m (t) t What is the maximum charge in prior values in s m (t)? 10/25/03 EC2500.MPF/Fall-FY04 46
47 Single Sideband (non-coherent) Demodulator (1) Add carrier to make demodulation easier. S() m m S m () LSB cos2 c s t A t s t cos 2 ˆ ct s t sin 2 ct Acos2 2 s t 1 A cos 2 ct s ˆ t sin 2 ct 2 2 t c 10/25/03 EC2500.MPF/Fall-FY04 47
48 (2) Use envelope detector to recover inormation signal. envelope o s t A cos 2 t c s t sin 2 t c ˆ 2 2 s t 1 E A s ˆ t 2 2 s t 2 A when As t 10/25/03 EC2500.MPF/Fall-FY04 48
49 ASK Incoherent Demodulator s m (t) BPF Envelope Detector y(t) T compare to threshold T k s m (t) A How to select T h? t A y(t) 0 t 10/25/03 EC2500.MPF/Fall-FY04 49
50 9) Applications to the AM superheterodyne receiver Application o modulation property p t s t cos 2 t P 0 Applications: communication systems; Amplitude modulation (AM) systems. Speech exist in the range 300Hz~5KHz Atmosphere attenuates signals rapidly in the range 10Hz-->20KHz, and propagates much better at high requencies shit speech to higher requency range 10/25/03 EC2500.MPF/Fall-FY04 50
51 Recall what the AM signal looks like Example: cos40 cos400 x t t t x(t) envelope Time t (msec) 1 xt cos 440 t cos 360 t 2 1 e e e e 4 j440t j440t j360t j360t 10/25/03 EC2500.MPF/Fall-FY04 51
52 10/25/03 EC2500.MPF/Fall-FY04 52
53 Spectrum o x(t) or generic requencies: cos2 cos2 y t t t cos cos t t 1 exp j 2 1 2t exp j 2 1 2t 4 exp j2 texp j2 t Y() 2 ( ) ( 2 1 ) called carrier requency Note: Change 2 you change where the requency s components are or a constant 1 10/25/03 EC2500.MPF/Fall-FY04 53
54 How to recover the original speech signal? Demodulate. 10/25/03 EC2500.MPF/Fall-FY04 54
55 Several basic operations are needed in a broadcast receiver: 1. Station separation: must be able to pick out a speciic signal and reject others 2. Ampliication: needed when the signal picked up by the radio antenna is too weak to drive the loudspeakers 3. Demodulation: The received signal is centered around the carrier requency and must be demodulated beore it is ed into the speakers In standard AM: - The maximum audio signal requency is around 5kHz - Each station is assigned 10kHz by the FCC (i.e., each adjacent carriers are separated by 10kHz) - The AM requency band assignment is 540kHz --> 1600kHz 10/25/03 EC2500.MPF/Fall-FY04 55
56 Filter constraints: We need tuneable ilters with sharp cuto requencies to select the station we want impossible to realize! What is done instead: We build a ixed bandpass ilter and shit the input requencies so that the requencies o interest alls within the ixed passband o the ilter Such a shiting process is called heterodyning The receiver doing this operation is called a superheterodyne receiver Basic AM superheterodyne receiver diagram Radio requency (RF) ampliier Intermediate requency (IF) ampliier Detector Baseband Ampliier Speaker LO Receiver Components: - RF ampliier: ampliies a portion o the spectrum (tuneable) - Local oscillator (Mixer): shits the signal to a speciic requency range - IF ampliier: ilters and ampliies around a ixed reqency (or AM systems around 455kHz) - Detector: demodulates (i.e., extracts) the audio signal - Baseband ampliier: ampliies the audio signal 10/25/03 EC2500.MPF/Fall-FY04 56
57 Example: - Assume no RF ampliier (will be added and discussed later) - Consider the case o a 1kHz AM wave modulated by a carrier at 1MHz (i.e., the station center requency is at 1MHz) The generated AM signal has requencies at: Mixer requencies at: AM signal (IF) ampliier LO requency at: Note: only components around 455kHz are accepted by the IF ampliier What is the IF ampliier required bandwidth? 10/25/03 EC2500.MPF/Fall-FY04 57
58 What happens i we want to accept a station located at 1600kHz? Assume the IF ampliier is centered around 455KHz. Mixer requencies at: AM signal (IF) ampliier LO requency at: Note: only components around 455kHz are accepted by the IF ampliier 10/25/03 EC2500.MPF/Fall-FY04 58
59 Summary: - The key is to make the LO track the incoming signal so hat the dierence between the incoming signal and the LO requency is a constant requency (called the IF requency) equal to 455KHz. - By convention the LO has to be at a requency 455KHz above the incoming carrier requency. - Once we have the IF ampliier output, we can demodulate. 10/25/03 EC2500.MPF/Fall-FY04 59
60 The Potential Image Frequency problem: Sometimes we can get a signal other than that desired at the IF ampliier Example: Assume we have a desired signal o requency 1KHz modulated at 620KHz and an undesired signal o requency 1 KHz modulated at 1530KHz AM modulated requencies located at: Mixer requencies at: AM signal (IF) ampliier LO requency at: Note: only components around 455kHz are accepted by the IF ampliier 10/25/03 EC2500.MPF/Fall-FY04 60
61 Desired signal 620K Undesired signal 1530K Y() 2K -1530K -620K 620K 1530K Shit to the right Shit to the let 10/25/03 EC2500.MPF/Fall-FY04 61
62 Notes: 1. Both desired and undesired modulated signals have identical components ater the mixer. These components won t be separated. 2. Such undesired modulated components are called image requencies (they are the requencies which appear in the correct range to the IF ampliier, while they are undesirable to start with. Question: how to determine the image requency which will be a problem to a speciic AM signal? 10/25/03 EC2500.MPF/Fall-FY04 62
63 10/25/03 EC2500.MPF/Fall-FY04 63
64 How to use the RF ampliier to remove the image requency problem Mixer requencies at: (IF) ampliier RF AM signal LO requency at: Note: only components around 455kHz are accepted by the IF ampliier 10/25/03 EC2500.MPF/Fall-FY04 64
65 10/25/03 EC2500.MPF/Fall-FY04 65
66 Application to Frequency Division Multiplexing x 1 (t) cos2p a t) x 2 (t) cos2 b t) y(t) x 3 (t) cos2 c t) Y() 10/25/03 EC2500.MPF/Fall-FY04 66
67 Demodulation 10/25/03 EC2500.MPF/Fall-FY04 67
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