S-72.244 Modulation and Coding Methods Linear Carrier Wave Modulation 1
Linear carrier wave (CW) modulation Bandpass systems and signals Lowpass (LP) equivalents Amplitude modulation (AM) Double-sideband modulation (DSB) Modulator techniques Suppressed-sideband amplitude modulation (LSB, USB) Detection techniques of linear modulation Coherent detection Noncoherent detection AM DSB LSB USB 2
Baseband and CW communications carrier Baseband communications is used in PSTN local loop baseband CW PCM communications for instance between exchanges (fiber-) optical communication Using carrier to shape and shift the frequency spectrum (eg CW techniques) enable modulation by which several advantages are obtained different radio bands can be used for communications wireless communications multiplexing techniques become applicable exchanging transmission bandwidth to received SNR 3
Defining bandpass signals The bandpass signal is band limited V ( f) = 0, f < f W f > f + W V bp c c bp ( f) 0,otherwise We assume also that (why?) W << In telecommunications bandpass signals are used to convey messages over medium In practice, transmitted messages are never strictly band limited due to their nature in frequency domain (Fourier series coefficients may extend over very large span of frequencies) non-ideal filtering f C 4
Example of a bandpass system Consider a simple bandpass system: a resonant (tank) circuit j L j C z = ω / ω p z = R + z V ( ω) H( ω) = V ( ω) i p in out jωl + 1/ jωc H( ω) = V ( ω)/ V ( ω) = z / z H( ω) = 1/[1 + jq( f / f0 + f0/ f)] out in p i Q= R C/ L f0 = (2 π LC ) 1 z p Tank circuit 5
Bandwidth and Q-factor The bandwidth is inversely proportional to Q-factor: B = f / Q 3dB 0 for the tank circuit ( : Q= R C/ L) System design is easier (next slide) if the fractional bandwidth 1/Q=B/f 0 is kept relatively small: 0. 01 < B / f < 0. 1 Some practical examples: 0 6
Why system design is easier for smaller fractional bandwidths (FB)? Antenna and bandpass amplifier design is difficult for large FB:s: one will have difficult to realize components or parameters in circuits as too high Q too small or large values for capacitors and inductors These structures have a bandpass nature because one of their important elements is the resonant circuit. Making them broadband means decreasing resistive losses that can be difficult 7
I-Q (in-phase-quadrature) description for bandpass signals In I-Q presentation bandpass signal carrier and modulation parts are separated into different terms v () t = At ()cos[ ω t+ φ()] t bp v () t = v () t cos( ω t) v () t sin( ω t) bp i C q C C v () t = At ()cos φ(), t v () t = At ()sin φ() t i q Bandpass signal in frequency domain Bandpass signal in time domain cos( α + β) = cos( α)cos( β) dashed line denotes envelope sin( α)sin( β) 8
The phasor description of bandpass signal Bandpass signal is conveniently represented by a phasor rotating at the angular carrier rate ω + φ ( t) : vbp() t = vi()cos( t ωct) vq()sin( t ωct) vi() t = At ()cos φ(), t vq() t = At ()sin φ() t v() t 0,arctan( v ()/ t v()) t A( t) = v 2 ( t) + v 2 i q i ( t) φ() t = i q v() t < 0, π + arctan( v ()/ t v()) t i q i C t 9
Lowpass (LP) signal vbp() t = vi()cos( t ωct) + vq()sin( t ωct) vi () t = At ()cos φ() t vq () t = At ()sin φ() t Lowpass signal is defined by yielding in time domain 1 Vlp( f) 2 Vi( f) + jvq( f) 1 1 vlp() t = F Vlp( f) = 2 vi() t + jvq() t Taking rectangular-polar conversion yields then [ φ φ ] v () t = At ()cos () t + jsin ()/2 t lp v () t = At ()/2, arg v () t = φ() t lp v () t = At ()exp jφ () t 1 lp 2 lp 10
Transforming lowpass signals and bandpass signals v () t = At ()cos[ ω t+ φ()] t bp { ω φ } v = Re At ()exp[ j t+ ()] t bp Physically this means that the lowpass signal is modulated to the carrier frequency ω when it is transformed to bandpass signal. Bandpass signal can be transformed into lowpass signal by (tutorials). What is the physical meaning of this? c At () vbp = 2Re exp[ jφ()]exp[ t jωct] 2 vlp () t v = 2Re v ()exp[ t jω t] { } bp lp c V ( f) = V ( f + f ) u( f + f ) lp bp C C c 11
Amplitude modulation (AM) We discuss three linear mod. methods: (1) AM (amplitude modulation), (2) DSB (double sideband modulation), (3) SSB (single sideband modulation) AM signal: x () t = A[1 + µ x ()]cos( t ω t+ φ()) t C c m c = Accos( ωct+ φ ()) t + Acµ xm()cos( t ωct+ φ()) t Carrier φ(t) is an arbitrary constant. Hence we note that no information is transmitted via the phase. Assume for instance that φ(t)=0, then the LP components are Also, the carrier component contains no information-> Waste of power to transmit the unmodulated carrier, but can still be useful (how?) Information carrying part v() t = At ()cos( φ ()) t = At () = A[1 + µ x ()] t i c m v () t = At ()sin( φ()) t = 0 q 0 µ 1 xm( t) 1 12
AM: waveforms and bandwidth AM in frequency domain: x () t = A[1 + µ x ()]cos( t ω t) c c m c = Accos( ω ct) + µ xm()cos( t ωct) Carrier Informationcarryingpart Xc( f) = Acδ ( f fc)/2 + µ AX c m( f fc)/2 Carrier Informationcarryingpart AM bandwidth is twice the message bandwidth W: f > 0( for brief notations) [ ] vt ()cos( ω t+ φ) V( f f )exp jφ + V( f + f )exp jφ 1 c 2 c c 13
AM waveforms (a): modulation (b): modulated carrier with µ<1 (c): modulated carrier with µ>1 Envelope distortion! ( AMsignal: x () t = A[1 +µ x ()]cos( t ω t)) c c m c 14
AM power efficiency AM wave total power consists of the idle carrier part and the 2 2 2 useful signal part: ( AMsignal: x () t = A[1 + µ x ()]cos( t ω t)) c m c c < xc() t >=< Ac cos ( ωct) > Carrier 2 2 2 2 +< µ Ac x ()cos ( ) m t ωct > Power: S 2 2 2 = A /2 /2 c + µ AS c X Assume A C =1, S X =1, then for µ=1 (the max value) the total power is P T max = 1 / 2 + 1 / 2 Carrier power P C 3 3 Modulation power 2P SB X Therefore at least half of the total power is wasted on carrier Detection of AM is simple by enveloped detector that is a reason why AM is still used. Also, sometimes AM makes system design easier, as in fiber optic communications 15
DSB signals and spectra In DSB the wasteful carrier is suppressed: x () t = Ax ()cos( t ω t) c c m c The spectra is otherwise identical to AM and the transmission BW equals again double the message BW X ( f) = AX ( f f )/2, f > 0 c c m c In time domain each modulation signal zero crossing produces phase reversals of the carrier. For DSB, the total power S T and the power/sideband P SB have the relationship 2 S AS /2 2P T c X SB 2 = = P = AS /4( DSB) Therefore AM transmitter requires twice the power of DSB transmitter to produce the same coverage assuming S X =1. However, in practice S X is usually smaller than 1/2, under which condition at least four times the DSB power is required for the AM transmitter for the same coverage SB c X AM: x () t = A[1 +µ x ()]cos( t ω t) c c m c 16
DSB and AM spectra AM in frequency domain with x ( t) = A cos( ω t) m m m Xc( f) = Acδ ( f fc)/2 + µ AX c m( f fc)/2, f > 0 (general expression) Carrier Informationcarryingpart X ( f) = Aδ ( f f )/2 + µ AA δ( f ± f )/2(tone modulation) c c c c m c m In summary, difference of AM and DSB at frequency domain is the missing carrier component. Other differences relate to power efficiency and detection techniques. (a) DSB spectra, (b) AM spectra 17
AM phasor analysis,tone modulation AM and DSB can be inspected also by trigonometric expansion yielding for instance for AM x ( t) = A A µ cos( ω t)cos( ω t) + A cos( ω t) C C m m C C C A A µ A A µ C m C m = cos( ω ω ) t + cos( ω + ω ) t C m C m 2 2 + A cos( ω t) C This has a nice phasor interpretation; take for instance µ=2/3, A m =1: C 2 At () = Ac 1+ cosωct 3 A mµ = 2 3 AMsignal: xc() t = Ac[1 +µ xm()]cos( t ωct) At () 18
Linear modulators Note that AM and DSB systems generate new frequency components that were not present at the carrier or at the message. Hence modulator must be a nonlinear system Both AM and DSB can be generated by analog or digital multipliers special nonlinear circuits based on semiconductor junctions (as diodes, FETs etc.) based on analog or digital nonlinear amplifiers as log-antilog amplifiers: p = logv + logv 10 p = v v 1 2 1 2 v 1 v 2 Log Log 10 p vv 1 2 19
(a) Product modulator (b) respective schematic diagram =multiplier+adder ( AMsignal: x () t = A[1 +µ x ()]cos( t ω t)) c c m c 20
Square-law modulator (for AM) Square-law modulators are based on nonlinear elements: (a) functional block diagram, (b) circuit realization 21
Balanced modulator (for DSB) By using balanced configuration non-idealities on square-law characteristics can be compensated resulting a high degree of carrier suppression: Note that if the modulating signal has a DC-component, it is not cancelled out and will appear at the carrier frequency of the modulator output 22
Synchronous detection All linear modulations can be detected by synchronous detector Regenerated, in-phase carrier replica required for signal regeneration that is used to multiple the received signal Consider an universal*, linearly modulated signal: x () t = [ K + K xt ()]cos( ω t) + K x ()sin( t ω t) c c µ c µ q c The multiplied signal y(t) is: ALO xc() t ALOcos( ωct) = [ Kc + Kµ xt ()][1+ cos(2 ωct) ] Kµ xq()sin(2 t ωct) 2 ALO = [ Kc + Kµ xt ()] 2 { } Synchronous detector *What are the parameters for example for AM or DSB? 23
The envelope detector Important motivation for using AM is the possibility to use the envelope detector that has a simple structure (also cheap) needs no synchronization (e.g. no auxiliary, unmodulated carrier input in receiver) no threshold effect ( SNR can be very small and receiver still works) 24
Envelope detector analyzed Assume diode half-wave rectifier used to rectify AM-signal. Therefore after the diode AM modulation is in effect multiplied with the half-wave rectified sinusoidal signal w(t) 1 2 1 v = [ A+ mt ()cos ] ω t cosω t cos3 ω t... R C + + C C 2 π 3 wt () 1 v = [ A+ mt () R ] + other higher order terms π The diode detector is then followed by a lowpass circuit to remove the higher order terms The resulting DC-term may also be blocked by a capacitor Note the close resembles of this principle to the synchronousdetector (why?) cos ( ) 1 cos(2 ) 2 2 1 x = [ + x ] 25