Intermediate Frequency (IF) Image frequency ERG2310A-II p. II-33 Amplitude Modulation: SSB DSB modulation: ω By mixing with a sinusoidal carrier at c rad/sec, half of this spectral ω density is translated up in frequency and centered about c and half is ω translated down to (- c ). Î Doubling of the bandwidth of a given signal Since each half contains all the information about the signal, the original signal can be recovered again from either the upper or lower pair of sidebands by an appropriate frequency translation. So only the upper or the lower pair of sidebands is required to transmit. Such kind of modulation is called single-sideband (SSB) modulation. It is efficient because it requires no more bandwidth than that of the original signal and only half of the corresponding DSB signal. ERG2310A-II p. II-34 Amplitude Modulation: SSB SSB: SSB: ERG2310A-II p. II-35 Amplitude Modulation: SSB Generation of SSB Signals -first generate a DSB signal, then suppress one of the sidebands by filtering. ERG2310A-II p. II-36 Amplitude Modulation: SSB ω Generation of SSB: Phase-Shift Method ℑ{e j mt } ω Consider the modulating signal x(t) is x(t) = e j mt ω j ct 0 ω ω and let the carrier signal be m e . ω ℑ j ct ω ω ω {e } Multiplying, we get x(t)e j ct = e j mt e j ct ω ω 0 c Taking the real part, we have ω ω ℑ{e j ct e j mt } ω ω ω ω ω ω Re{e j mt e j ct } = Re{e j mt }Re{e j ct } − Im{e j mt }Im{e j ct } ω ω ω ω = ω ω − ω ω 0 c c+ m cos mt cos ct sin mt sin ct ω ω ℑ{Re[e j ct e j mt ]} Because this represents the upper sideband, we write = ω ω − ω ω sSSB+ (t) cos mt cos ct sin mt sin ct ω −ω -ω 0 ω ω +ω − ω c m c c m Similarly, by using x ( t ) = e j m t , the lower sideband is = ω ω + ω ω sSSB− (t) cos mt cos ct sin mt sin ct In general, we can write s (t) = x(t)cosω t ± xˆ(t)sinω t SSBm c c where xˆ(t) is that signal obtained by shifting the phase of x(t) by 90° at each frequency. ERG2310A-II p. II-37 Amplitude Modulation: SSB Generation of SSB Signals : Phase-Shift Method ERG2310A-II p. II-38 Amplitude Modulation: SSB Demodulation of SSB Signals The synchronous detector will properly demodulate SSB-SC signals ERG2310A-II p. II-39 Amplitude Modulation: SSB s (t) = x(t)cosω t ± xˆ(t)sinω t Given that the incoming SSB-SC signal is SSBm c c = ω + ∆ω +θ Let the locally generated carrier signal be c(t) cos[( c )t ], where (∆ω) is the frequency error and θ is the phase error. s (t)c(t) = [x(t)cosω t ± xˆ(t)sinω t]cos[(ω + ∆ω)t +θ ] SSBm c c c = 1 ∆ω +θ + ω + ∆ω +θ 2 x(t){cos[( )t ] cos[(2 c )t ]} 1 ∆ω +θ − ω + ∆ω +θ m 2 xˆ(t){sin[( )t ] sin[(2 c )t ]} After passing through a low-pass filter, the output xo(t) becomes = 1 ∆ω +θ 1 ∆ω +θ Distorted ! xo (t) 2 x(t)cos[( )t ] m 2 xˆ(t)sin[( )t ] = 1 If ∆ω=0 and θ =0, then xo (t) 2 x(t) ERG2310A-II p. II-40 Amplitude Modulation: SSB Example: When an SSB (upper/lower-sideband) is received and fed into the following demodulator: sSSB±(t)IF Amp LPF xo(t) (SSB-SC at 20 MHz) (10.000-10.003 MHz) π π cos(2 fct) cos(2 fdt) -f -f +f +f c d d 3kHz c fc=30.003MHz Upper sideband f =10.003MHz SSB-SC d -20 MHz 0 20 MHz Freq. 10.003 MHz 10 MHz -f -f +f +f c d d 3kHz c fc=30.000MHz Lower sideband f =10.000MHz SSB-SC d -20 MHz 0 20 MHz Freq. 10.003 MHz 10 MHz ERG2310A-II p. II-41 Amplitude Modulation: SSB Single Sideband-Large Carrier (SSB-LC) Signals An expression for an SSB-LC signal is = ω + ω ω s(t) Ac cos ct x(t)cos ct m xˆ(t)sin ct The original signal x(t) can always be recovered from s(t) using synchronous detection. If the carrier is large, however, envelope detection can also be used. The envelope can be written as 2x(t) x 2 (t) xˆ 2 (t) = + 2 + ˆ 2 = + + + r(t) [Ac x(t)] [x(t)] Ac 1 2 2 Ac Ac Ac If the carrier is much larger than the SSB-SC envelope, we have ≈ + 2x(t) ≈ + x(t) = + r(t) Ac 1 Ac 1 Ac x(t). Ac Ac Thus after discarding the dc term introduced by carrier, the SSB-LC signal can then be demodulated correctly using an envelope detector. ERG2310A-II p. II-42 Amplitude Modulation: VSB Vestigial sideband (VSB) modulation is a compromise between DSB and SSB. In VSB modulation, one passband is passed almost completely whereas only a residual portion of the other sideband is retained in such a way that the demodulation process can still reproduce the original signal. ω SDSB( ) −ω 0ωω c ω c SVSB( ) −ω 0ωω c c The partial suppression of one sideband reduces the required bandwidth from that required for DSB but does not match the spectrum efficiency of SSB. If a large carrier is also transmitted, the desired signal can be recovered using an envelope detector. If no carrier is sent, the signal can be recovered using a synchronous detector or the injected carrier method. ERG2310A-II p. II-43 Amplitude Modulation: VSB Generation of VSB Signals ω = 1 ω −ω + 1 ω +ω ω SVSB( ) [2 X( c ) 2 X( c )]H( ) The filtering operation can be represented by a filter H (f) that passes some of the lower (or upper) sideband and most of the upper (or lower) sideband. ERG2310A-II p. II-44 Amplitude Modulation: VSB Demodulation of VSB Signals sVSB(t) LPF xo(t) ω Synchronous Demodulation cos ct The spectral density of the received vestigial-sideband signal is ω = 1 ω −ω + 1 ω + ω ω SVSB ( ) [ 2 X ( c ) 2 X ( c )]H ( ) The output of the synchronous detector is = ω xo (t) [sVSB (t)cos ct]LP ω = 1 ω []ω + ω + 1 ω []ω −ω X o ( ) 4 X ( ) H ( c ) LP 4 X ( ) H ( c ) LP = 1 ω []ω + ω + ω −ω 4 X ( ) H ( c ) H ( c ) LP For faithful reproduction of x(t), we require that ω − ω + ω + ω = ω ≤ ω [H ( c ) H ( c )]LP constant, m . ERG2310A-II p. II-45 Amplitude Modulation: VSB ω − ω + ω + ω = ω ≤ ω [H ( c ) H ( c )]LP constant, m . ω By letting the constant be 2H( c) : ω − ω + ω + ω = ω ω ≤ ω [H ( c ) H ( c )]LP 2H ( c ), m ω ω Thus, H( ) exhibits odd symmetry around the carrier frequency c. The sum of the values of H(ω) at any two frequencies equally ω displaced above and below c is unity. ERG2310A-II p. II-46 Amplitude Modulation: VSB Synchronous Demodulation of VSB Signals Received ω VSB signal SVSB( ) −ω 0 ω ω c c ω After mixer Xd( ) −2ω −ω 0 ω 2ω ω c c c c ω After LPF Xo( ) −ω 0 ω ω c c ERG2310A-II p. II-47 Amplitude Modulation: VSB Example of VSB Signals: Television signal Television picture signal has nominal bandwidth of 4.5MHz If DSB modulation is used, it requires at least 9MHz for each TV channel. So, VSB modulation is used so that the whole TV signal is confined to about 6MHz. ERG2310A-II p. II-48 Angle Modulation A continuous-wave (CW) sinusoidal signal can be varied by changing its amplitude and its phase angle. = ω + φ s(t) A(t)cos[ ct (t)] To carry a message signal x(t): Amplitude modulation: Keep θ(t) constant and varies A(t) proportionally to x(t). = []ω + φ ∝ s(t) A(t)cos ct o where A(t) x(t) Angle modulation: ω φ Keep A(t) constant and varies [ ct+ (t)] proportionally to x(t). = [][]ω + φ ω + φ ∝ s(t) Acos ct (t) where ct (t) x(t) ERG2310A-II p. II-49 Angle Modulation Phasor Representation The phasor representation of a constant-amplitude sinusoid is shown as follows ω A: magnitude of the phasor i(t) θ(t): phase angle θ (t) = ω t + φ(t) +θ θ(t) c o ω i(t) : instantaneous angular rate dθ (t) dφ(t) ω (t) = = ω + i dt c dt θ = t ω τ τ +θ (t) i ( )d 0 ∫0 ERG2310A-II p. II-50 Angle Modulation If the phase φ(t) is varied linearly with the input signal x(t) , we have θ = ω + +θ φ ∝ (t) ct k p x(t) 0 i.e. (t) x(t) ω θ where c , kp , 0 are constants. As the phase is linearly related to x(t), this type of angle modulation is called phase modulation (PM) with = ω + +θ sPM (t) Ac cos[ ct k p x(t) o ] and , φ(t) is called instantaneous phase deviation. dθ (t) dφ(t) dx(t) ω (t) = = ω + ⇒ ω = ω + k i dt c dt i(PM) c p dt ERG2310A-II p.