Principles of Communications Meixia Tao Dept. of Electronic Engineering Shanghai Jiao Tong University Chapter 3: Analog Modulation Selected from Ch 3, Ch 4.1-4.4, Ch 6.1-6.2 of of Fundamentals of Communications Systems, Pearson Prentice Hall 2005, by Proakis & Salehi Meixia Tao @ SJTU Topics to be Covered AM/FM radio FM radio TV broadcast Source Modulator Channel Demodulator Output Amplitude modulation Angle modulation (phase/frequency) Effect of noise on amplitude modulation Effect of noise on frequency modulation Meixia Tao @ SJTU 2 Modulation What is modulation? Transform a message into another signal to facilitate transmission over a communication channel Generate a carrier signal at the transmitter Modify some characteristics of the carrier with the information to be transmitted Detect the modifications at the receiver Why modulation? Frequency translation Frequency-division multiplexing Noise performance improvement Meixia Tao @ SJTU 3 Analog Modulation Characteristics that be modified in sin carrier Amplitude → Amplitude modulation Frequency → Angle modulation Phase Meixia Tao @ SJTU 4 Amplitude Modulation Double-sideband suppressed-carrier AM (DSB-SC) Baseband signal (modulating wave): mt() Carrier wave Modulated wave st()= ctmt () () = Amtcc ()cos(ωθ t+ 0 ) Meixia Tao @ SJTU 5 Spectrum of DSB-SC Signals Spectrum of M(f) message M(0) -W 0 W f Spectrum of DSB-SC S(f) (1/2)AcM(0) USB LSB LSB USB -f -W -f -f +W f -W f f c c c 0 c c fc+W 1 S( f ) = A [M ( f − f ) + M ( f + f )] 2 c c c Translation of the original message spectrum to Meixia Tao @ SJTU 6 Bandwidth and Power Efficiency S(f) (1/2)AcM(0) -f -W -f -f +W f -W f f c c c 0 c c fc+W Required channel bandwidth BWc = 2 Required transmit power TT/2 /2 112 22 2 Ps= lims ( t ) dt = lim Acc m( t ) cos (ωθ t+ 0 ) dt TT→∞ TT∫∫−−TT/2 →∞ /2 22 T /2 AAcc1 2 =limm ( t )[ 1+ cos(2ωθcmt += 20 )] dt P 22T →∞ T ∫−T /2 Meixia Tao @ SJTU 7 Demodulation of DSB-SC Signals Phase-coherent demodulation s(t) Product v(t) Low-pass vo(t) modulator filter cos( 2πfct) Local PLL oscillator (phase-locked loop) If there is a phase error φ, then Scaled version of message signal Unwanted Meixia Tao @ SJTU 8 Demodulation of DSB-SC Signals Pilot-tone assisted demodulation Add a pilot-tone into the transmitted signal Filter out the pilot using a narrowband filter Meixia Tao @ SJTU 9 Conventional AM Modulating wave Carrier wave: Baseband signal (normalized): Modulated wave a ≤1 Modulation index: a Modulated wave a >1 overmodulated Meixia Tao @ SJTU 10 Spectrum of Conventional AM Spectrum of M(f) M(0) message signal -W 0 W f (Ac/2)δ(f+fc) (Ac/2)δ(f-fc) S(f) (1/2)aAcM(0) 0 -fc-W -fc -fc+W fc-W fc fc+W f AccAa Sf()=δδ( f −+ fcc) ( f + f) + Mf( −+ fc) Mf( + f c) 22 Meixia Tao @ SJTU 11 Bandwidth and Power Efficiency Required channel bandwidth BWc = 2 Required transmit power carrier power message power Modulation efficiency 2 a 2 AP 2 power in sideband cm aP E = = 2 = m total power A2 a2 1+ aP2 c + AP2 m 22cm Meixia Tao @ SJTU 12 Example Message signal: mt ( ) = 3cos(200 ππ t ) + sin(600 t ) −5 Carrier: ct( )= cos(2 × 10t ) Modulation index: a=0.85 Determine the power in the carrier component and in the sideband components of the modulated signal Meixia Tao @ SJTU 13 Demodulation of AM signals Envelop Detector The simplicity of envelop detector has made Conventional AM a practical choice for AM-radio broadcasting Meixia Tao @ SJTU 14 Single Sideband (SSB) AM Common problem in AM and DSBSC: Bandwidth wastage SSB is very bandwidth efficient H(ω) ω Meixia Tao @ SJTU 15 Expression of SSB signals The baseband signal can be written as the sum of finite sinusoid signals n mt( )=∑ xi cos(2πθ ft i +≤ i ) , f ic f i=1 Then its USB component is n Ac mtc( )=∑ xi cos[ 2πθ ( f ci++ ft ) i )] 2 i=1 After manipulation nn Ac mc() t=∑∑ xicos(2πθ ft ii +− ) cos 2 πft c x isin(2 πθ ft ii + ) sin 2 πft c 2 ii=11 = AAcc = mt()cos2ππ ftcc− mt ()sin2 ft 22Hilbert transform of m(t) Meixia Tao @ SJTU 16 About Hilbert Transform 1∞ x ()τ 1 xt()⇔ xt () xt()= dτ = xt() ∗ πτ∫−∞ tt− π −>jf,0 Hf()= j , f < 0 0,f = 0 H (ω) 相移 1 90° ω ω -90° Meixia Tao @ SJTU 17 Generation of SSB-AM Signal • The spectral efficiency of SSB makes it suitable for voice communication over telephone lines (0.3~3.4 kHz) • Not suitable for signals with significant low frequency components Meixia Tao @ SJTU 18 Vestigial Sideband: VSB VSB is a compromise between SSB and DSBSC M(f) . VSB signal bandwidth is B = W+fv . VSB is used in TV -W 0 W f broadcasting and similar signals where low frequency components are significant S(f) -f c 0 fc f W fv fv W Meixia Tao @ SJTU 19 Comparison of AM Techniques DSB-SC: more power efficient. Seldom used Conventional AM: simple envelop detector. AM radio broadcast SSB: requires minimum transmitter power and bandwidth. Suitable for point-to-point and over long distances VSB: bandwidth requirement between SSB and DSBSC. TV transmission Meixia Tao @ SJTU 20 Signal Multiplexing Multiplexing is a technique where a number of independent signals are combined and transmitted in a common channel These signal are de-multiplexed at the receiver Two common methods for signal multiplexing TDM (time-division multiplexing) FDM (frequency-division multiplexing) Meixia Tao @ SJTU 21 FDM LPF: ensure signal bandwidth limited to W MOD (modulator): shift message frequency range to mutually exclusive high frequency bands BPF: restrict the band of each modulated wave to its prescribed range Meixia Tao @ SJTU 22 FDM application in telephone comm. Voice signal: 300～3400Hz Message is SSB modulated. In 1st-level FDM, 12 signal are stacked in frequency, with a freq. separation of 4 kHz between adjacent carriers A composite 48 kHz channel, called a group channel, transmits 12 voice-band signals simultaneously In the next level of FDM, a number of group channel (typically 5 or 6) are stacked to form a supergroup channel Higher-order FDM is obtained by combining several supergroup channels => FDM hierarchy in telephone comm. systems Meixia Tao @ SJTU 23 Quadrature-Carrier Multiplexing Transmit two messages on the same carrier as st()= Amc12 ()cos2 t( ππ ftcc) + Am ()sin2 t( ftc) cos() and sin() are two quadrature carriers Each message signal is modulated by DSB-SC Bandwidth-efficiency comparable to SSB-AM Synchronous demodulation of m1(t): 2 st( )cos( 2π ftc) = Am c12( t )cos( 2 π ftcc) + Am( t )sin( 2 ππ ftc) cos( 2 ft c) AA A =++ccm() t m ()cos4 t( ππ ft) c m()sin4 t( ft) 2211 cc 22 LPF Meixia Tao @ SJTU 24 Application: AM Radio Broadcasting Commercial AM radio uses conventional AM Superheterodyne receiver: from variable carrier freq of the incoming RF to fixed IF Meixia Tao @ SJTU 25 Topics to be Covered Source Modulator Channel Demodulator Output Amplitude modulation Angle modulation (phase/frequency) Effect of noise on amplitude modulation Effect of noise on frequency modulation Meixia Tao @ SJTU 26 Angle Modulation . Either phase or frequency of the carrier is varied according to the message signal . The general form: θ(t): the time-varying phase instantaneous frequency of s(t): 1dtθ () ft()= f + ic2π dt Meixia Tao @ SJTU 27 Representation of FM and PM signals Phase modulation (PM) θ ()t= kmtp () where kp = phase deviation constant Frequency modulation (FM) 1 d where kf = frequency fi() t−= f cf k mt () = θ () t deviation constant/frequency 2π dt sensitivity t The phase of FM is θ()t= 2 π k md ( ττ ) f ∫0 Meixia Tao @ SJTU 28 Distinguishing Features of PM and FM No perfect regularity in spacing of zero crossing Constant envelop, i.e. amplitude of s(t) is constant Relationship between PM and FM ∫ m(t)dt FM wave m(t) Phase integrator modulator π + AC cos[2 f ct k p ∫ m(t)dt] AC cos(2πf ct) d m(t) m(t) dt Frequency PM wave differentiator modulator AC cos[2πf ct + 2πk f m(t)] AC cos(2πf ct) Will discuss the properties of FM only Meixia Tao @ SJTU 29 Example: Sinusoidal Modulation Sinusoid modulating wave m(t) FM wave d m(t) dt PM wave Meixia Tao @ SJTU 30 Example: Square Modulation Square modulating wave m(t) FM wave PM wave Meixia Tao @ SJTU 31 FM by a Sinusoidal Signal Message Instantaneous frequency of resulting FM wave Frequency deviation: Carrier phase t ∆f θ(t )= 2 πτ( f ( ) −= f) d τsin(2 πft ) ∫0 ic m fm = βπsin(2ftm ) Modulation index: Meixia Tao @ SJTU 32 Example Problem: a sinusoidal modulating wave of amplitude 5V and frequency 1kHz is applied to a frequency modulator. The frequency sensitivity is 40Hz/V. The carrier frequency is 100kHz. Calculate (a) the frequency deviation (b) the modulation index Solution: Frequency deviation ∆f = k f Am = 40×5 = 200Hz ∆f 200 Modulation index β = = = 0.2 fm 1000 Meixia Tao @ SJTU 33 Spectrum Analysis of Sinusoidal FM Wave Rewrite the FM wave as In-phase component Quadrature-phase component Define the complex envelop of FM wave ~ jβ sin(2πfmt) s (t) = sI (t) + jsQ (t) = Ace ~ s (t) retains complete information about s(t) j[2πfct+β sin(2πfmt)] ~ j2πfct s(t) = Re{Ace }= Re[s (t)e ] Meixia Tao @ SJTU 34 ~ jβ sin(2πfmt) s (t) = Ace is periodic, expanded in Fourier series as ∞ ~ j2πnfmt s (t) = ∑cne n=−∞ where n-th order Bessel function of the first kind 1 π Jn (ββ )= expj( sin x− nx) dx 2π ∫−π Hence, cn = Ac J n (β ) Meixia Tao @ SJTU 35 ~ Substituting into s (t) ∞ ~ s (t) = Ac ∑ J n (β )exp( j2πnfmt) n=−∞ FM wave in time domain FM wave in frequency-domain ∞ Ac S( f ) = ∑ J n (β )[δ ( f − fc − nfm ) +δ ( f + fc + nfm )] 2 c n=−∞ Meixia Tao @ SJTU 36 Properties of Bessel Function Property 1: for small β ≤0.3