Chapter 2: ContinuousWave Modulation

1 Chapter 2 ContinuousWave Modulation 2.1 Introduction2 2.2 Amplitude Modulation The output of the modulator Where m(t) is the baseband signal , ka is the amplitude sensitivity. : carrier frequency : carrier amplitude ( ) cos(2 ) (2.1) c c c c A f c t  A f t s(t)  Ac1 kam(t)cos(2fct) (2.2) where is the hightest freqency of ( ) 2. (2.4) 1. ( ) 1, for all t (2.3) W m t f W k m t a c   X 1+k am(t) S(t) A ccos(2fct)3 Recall 1.Negative frequency component of m(t) becomes visible. 2.fcW  M(f)  fc lower sideband fc  M(f)  fc+W upper sideband 3.Transmission bandwidth B T=2W s(t)  Accos(2fct)  Ackam(t)cos(2fct) (2.2)         where ( ) is the Fourier Transform of ( ) ( ) ( ) (2.5) 2 ( ) ( ) 2 ( ) ( ) ( ) 1 2 ( )cos(2 ) ( ) ( ) 1 2 cos(2 ) M f m t s f A f f f f k A M f f M f f m t f t M f f M f f f t f f f f c c a c c c c c c c c c c                      4 Virtues and Limitations of Amplitude Modulation Transmitter Receiver Major limitations 1.AM is wasteful of power. 2.AM is wasteful of bandwidth.5 2.3 Linear Modulation Schemes Linear modulation is defined by Three types of linear modulation: 1.Double sidebandsuppressed carrier (DSBSC) modulation 2.Single sideband (SSB) modulation 3.Vestigial sideband (VSB) modulation ( ) Quadrature component ( ) In phasecomponent ( ) ( )cos(2 ) ( )sin(2 ) (2.7)     s t s t s t s t f t s t f t I Q I  c Q  c6 Notes: 1.s I(t) is solely dependent on m(t) 2.s Q(t)is a filtered version of m(t). The spectral modification of s(t) is solely due to sQ(t).7 Double SidebandSuppressed Carrier (DSBSC) Modulation The Fourier transform of S(t) is s(t)  Acm(t)cos(2fct) (2.8) ( ) ( ) (2.9) 1 2 s( f )  Ac  M f  fc  M f  fc   8 Coherent Detection (Synchronous Detection) The product modulator output is Let V(f) be the Fourier transform of v(t) cos( ) ( ) (2.10) 1 2 cos(4 ) ( ) 1 2 cos(2 )cos(2 ) ( ) ( ) cos(2 ) ( ) A A f t m t A A m t A A f t f t m t v t A f t s t c c c c c c c c c c c                cos ( ) (2.11) 1 2 v0(t)  AcAc  m t filtered out (Low pass filtered)9 Costas Receiver Ichannel and Qchannel are coupled together to form a negative feedback system to maintain synchronization The phase control signal ceases with modulation. 1 4 2 2 2 2 2 2 0 1 1 cos sin ( ) ( )sin(2 ) 4 8 ( ) (sin2 2 ) c c c A m t A m t A m t            (multiplier + very narrow band LF)10 QuadratureCarrier Multiplexing (or QAM) Two DSBSC signals occupy the same channel bandwidth, where pilot signal (tone ) may be needed. s(t)  Acm1(t)cos(2fct)  Acm2(t)sin(2fct)11 SingleSideband Modulation (SSB) The lower sideband and upper sideband of AM signal contain same information . The frequencydiscrimination method consists of a product modulator (DSBSC) and a bandpass filter. The filter must meet the following requirements: a.The desired sideband lies inside the passband. b.The unwanted sideband lies inside the stopband. c.The transition band is twice the lowest frequency of the message. To recover the signal at the receiver, a pilot carrier or a stable oscillator is needed (Donald Duck effect ).12 Vestigial Sideband Modulation (VSB) When the message contains near DC component The transition must satisfy (2.14) ( ) ( ) 1 for (2.13) b.The phaseresponseis linear : a. ( ) ( ) 1 B W f H f f H f f W f W H f f H f f T ν c c c c             Consider the negative frequency response: H f     f W c   f f c v  fc   f f c v f f c v  fc f f c v  f W c  Here, the shift response │H(ffc)│ is H f f   c  2 W  fv 0 fv f f c v  2 fc 2 f f c v  2 f W c  13and │H(f+fc)│ is H f f   c    2 f W c   2 f f c v 2 fc   2 f f c v  fv 0 fv W 14So, we get │H(ffc)│ +│ H(f+fc)│ is H f f   c  2 W  fv 0 fv f f c v  2 fc 2 f f c v  H f f   c    2 f f c v 2 fc   2 f f c v  fv 0 fv W 15Consider –W fm =w pre de FM o T c o T c N B A N B A 2 2 2 2   BT For the purpose of comparing different CW modulation systems, we define The average power of the modulated signal (SNR)c= The average power of channel noise in the message band Message signal with LP filter the same power as output modulated wave noise n(t) The equivalent baseband transmission model. with bandwidth wSupplements More precisely, we may express the DSBSC as m(t) S‘(t) cos(2πfc t+θ) θ is uniformly distributed over ﹝ 0, 2π﹞ S(t)=Ac m(t) cos(2πfc t+θ) At the receiver we may write S(t)=C Ac m(t) cos(2πfc t+θ)                         w w m m c m c c c c c x s s R P S f df C A R C A P C A E f t E m t E CA m t f t S f df P E S t R (0) ( ) (0) 2 2 cos (2 ) ( ) ( ( )cos(2 )) ( ) ( ) (0) 2 2 2 2 2 2 2 2 2 2     The average noise power in –w (t) increases or decreases 2 The discriminator output is equal to 1 ( ) ) ( ) 2 c P r t A t     nQ(t) r(t) x(t) A c P 1 0  P2 n I(t) 74Figure 2.44 Illustrating impulselike components in  (t)  d (t)dt produced by changes of 2 in  (t); (a) and (b) are graphs of (t) and  (t), respectively. 75A positivegoing click occurs , when , , 0 A negativegoing click occurs when , , 0 The carrierto noise ratio is defin ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) c c d t r t A t t d t dt d t r t A t t d t dt                      ed by (2.154) The output signaltonoise ratio is calculated as 1. The average output signal power is calculated assuming a sinusoidal modulation which produces . (noise free) 2. 2 0 2 c T T A B N B f     The average output noise power is calculated when no signal is present (The carrier is unmodulated). 76 2threshold effects may be avoided 20 (2.155), 2 20 or 2 When 0 2 0 2 A B N B N A T c c T     Figure 2.45 Dependence of output signaltonoise ratio on input carriertonoise ratio for FM receiver. In curve I, the average output noise power is calculated assuming an unmodulated carrier. In curve II, the average output noise power is calculated assuming a sinusoidally modulated carrier. Both curves I and II are calculated from theory. 77The procedure to calculate minimum 1. Given and W, determine (using Figure 2.26 or Carsons rule) 2. Given , we have 20 Capture Effect: The receiv 2 0 0 ( 20) 2 c T c T A B A N B N     er locks onto the stronger signal and suppresses the weaker one. 78FM Threshold Reduction (tracking filter) • FM demodulator with negative feedback (FMFB) • Phase locked loop Figure 2.46 FM threshold extension. Figure 2.47 FM demodulator with negative feedback. 79Preemphasis and Deemphasis on FM Figure 2.48 (a) Power spectral density of noise at FM receiver o (b) Power spectral density of a typical message signal. Figure 2.49 Use of preemphasis and deemphasis in an FM system. 80(2.162) 3 ( ) 2 The improvement factor is ( ) (2.158) power withde emphsis Average outputnoise (2.157) 2 ( ) ( ) ( ) , (2.146) 2 ( ) , The PSD at thediscriminator outputis , (2.156) ( ) 1 ( ) w w 2 2 3 2 de 2 0 2 2 2 de 2 2 0 de 2 2 0 pe de                      f H f df W I I f H f df N A B H f f A N f H f S f B f A N f S f W f W H f H f de W W c T c N T c N d d 81(2.161) 3 ( ) tan ( ) ( ) 1 ( ) 3 1 2 1 ( ) A de emphsis filter responseis ( ) 1 A simple pre emphsis filter responseis 0 1 0 3 0 2 0 2 3 0 de 0 pe             W f W f f W f f f df W I f H f j f f j f H f W W Example 2.6 Figure 2.50 (a) Preemphasis filter. (b) Deemphasis filter. 82 The main difference between FM and PM is in the relationship between frequency and phase. f = (12).ddt.  A PM detector has a flat noise power (and voltage) output versus frequency (power spectral density). This is illustrated in Figure 938a.  However, an FM detector has a parabolic noise power spectrum, as shown in Figure 938b. The output noise voltage increases linearly with frequency.  If no compensation is used for FM, the higher audio signals would suffer a greater SN degradation than the lower frequencies. For this reason compensation, called emphasis, is used for broadcast FM. Preemphasis for FM 83Figure 938. Detector noise output spectra for (a). PM and (b). FM. Preemphasis for FM 84 A preemphasis network at the modulator input provides a constant increase of modulation index mf for highfrequency audio signals.  Such a network and its frequency response are illustrated in Figure 939. Preemphasis for FM Fig. 939. (a)Premphasis network, and (b) Frequency response. 85 With the RC network chosen to give  = R1C = 75s in North America (150s in Europe), a constant input audio signal will result in a nearly constant rise in the VCO input voltage for frequencies above 2.12 kHz. The largerthannormal carrier deviations and mf will preemphasize highaudio frequencies.  At the receiver demodulator output, a lowpass RC network with  = RC = 75s will not only decrease noise at higher audio frequencies but also deemphasize the highfrequency information signals and return them to normal amplitudes relative to the low frequencies.  The overall result will be nearly constant SN across the 15 kHz audio baseband and a noise performance improvement of about 12dB over no preemphasis. Phase modulation systems do not require emphasis. Preemphasis for FM 86Preemphasis and deemphasis: (a) schematic diagrams; (b) attenuation curves Preemphasis and Deemphasis on FM 87Example of SN without preemphasis and deemphasis. Preemphasis and Deemphasis on FM 88Example of SN with preemphasis and deemphasis. Preemphasis and Deemphasis on FM 89Dolby dynamic preemphasis 90Figure 2.55 Comparison of the noise performance of various CW modulation systems. Curve I: Full AM,  = 1. Curve II: DSBSC, SSB. Curve III: FM,  = 2. Curve IV: FM,  = 5. (Curves III and IV include 13dB preemphasis, deemphasis improvement.) 91In making the comparison, it is informative to keep in mind the transmission bandwidth requirement of the modulation systems in question. Therefore, we define normalized transmission bandwidth as B W B T n  Table 2.4 Values of B n for various CW modulation schemes FM AM, DSBSC SSB B n   2   5 2 1 8 16 92李家同教授我的恩師

Chapter Continuous-Wave Modulation 2.1 Introduction 2.2 Amplitude Modulation c(t )  Ac cos(2fct ) Ac : carrier amplitude fc : carrier frequency 1+kam(t) (2.1) S(t) X Accos(2fct) The output of the modulator s(t )  Ac1  kam(t )cos(2fct ) (2.2) Where m(t) is the baseband signal , ka is the amplitude sensitivity kam(t )  1, for all t f c  W where W is the hightest freqency of m(t ) (2.3) (2.4) s(t )  Ac cos(2fct )  Ackam(t ) cos(2fct ) (2.2) Recall  ( f  fc)   ( f  fc) m(t ) cos(2fct )  M ( f  fc )  M ( f  fc ) Ac kaAc M ( f  fc)  M ( f  fc) s( f )   ( f  fc )   ( f  fc )  2 where M ( f ) is the Fourier Transform of m(t ) cos(2fct )  (2.5) 1.Negative frequency component of m(t) becomes visible 2.fc-W  M(f)  fc lower sideband fc  M(f)  fc+W upper sideband 3.Transmission bandwidth BT=2W Virtues and Limitations of Amplitude Modulation Transmitter Receiver Major limitations 1.AM is wasteful of power 2.AM is wasteful of bandwidth 2.3 Linear Modulation Schemes Linear modulation is defined by s(t )  sI (t ) cos(2fct )  sQ (t ) sin(2fct ) (2.7) sI (t )  In - phase component sQ (t )  Quadrature component Three types of linear modulation: 1.Double sideband-suppressed carrier (DSB-SC) modulation 2.Single sideband (SSB) modulation 3.Vestigial sideband (VSB) modulation Notes: 1.sI(t) is solely dependent on m(t) 2.sQ(t)is a filtered version of m(t) The spectral modification of s(t) is solely due to sQ(t) Double Sideband-Suppressed Carrier (DSB-SC) Modulation s(t )  Acm(t ) cos(2fct ) (2.8) The Fourier transform of S(t) is  s( f )  Ac  M ( f  fc )  M ( f  fc ) (2.9) Coherent Detection (Synchronous Detection) The product modulator output is v (t )  Ac' cos(2fct   ) s(t )  Ac' Ac cos(2fct ) cos(2fct   )m(t ) 1  AcAc' cos(4fct   )m(t )  AcAc' cos( )m(t ) filtered out Let V(f) be the Fourier transform of v(t) v 0(t )  AcAc' cos  m(t ) (Low pass filtered) (2.10) (2.11) Costas Receiver I-channel and Q-channel are coupled together to form a negative feedback system to maintain synchronization  0 2 2 Ac cos  sin  m (t )  Ac m (t )sin(2 ) 2  Ac m (t )  (sin2  2 ) The phase control signal ceases with modulation (multiplier + very narrow band LF) Quadrature-Carrier Multiplexing (or QAM) Two DSB-SC signals occupy the same channel bandwidth, where pilot signal (tone ) may be needed s(t )  Acm1(t ) cos(2fct )  Acm2(t ) sin(2fct ) 10 Pre-emphasis and De-emphasis on FM Example of S/N with preemphasis and deemphasis 89 Dolby dynamic preemphasis 90 Figure 2.55 Comparison of the noise performance of various CW modulation systems Curve I: Full AM,  = Curve II: DSB-SC, SSB Curve III: FM,  = Curve IV: FM,  = (Curves III and IV include 13-dB pre-emphasis, de91 emphasis improvement.) In making the comparison, it is informative to keep in mind the transmission bandwidth requirement of the modulation systems in question Therefore, we define normalized transmission bandwidth as Bn  BT W Table 2.4 Values of Bn for various CW modulation schemes FM Bn AM, DSB-SC SSB 2 5 16 92 李家同教授-我的恩師