《信号与系统 Signals and Systems》课程教学资料（英文版）lecture15 The Concept of modulation

Signals and Systems Fall 2003 Lecture #15 28 October 2003 Complex exponential amplitude modulation 2. Sinusoidal am 3. Demodulation of Sinusoidal AM 4. Single-Sideband(SSB)AM 5. Frequency-Division Multiplexing 6. Superheterodyne receivers

Signals and Systems Fall 2003 Lecture #15 28 October 2003 1. Complex Exponential Amplitude Modulation 2. Sinusoidal AM 3. Demodulation of Sinusoidal AM 4. Single-Sideband (SSB) AM 5. Frequency-Division Multiplexing 6. Superheterodyne Receivers

The Concept of modulation Transmitted Signal Carrier Signal Why? More efficient to transmit E&M signals at higher frequencies Transmitting multiple signals through the same medium using different carriers Transmitting through "channels, with limited passbands Others How? Many metho Focus here for the most part on Amplitude Modulation(AM) X(1) y(t=X(tc(t) c()

The Concept of Modulation Why? • More efficient to transmit E&M signals at higher frequencies • Transmitting multiple signals through the same medium using different carriers • Transmitting through “channels” with limited passbands • O t h e r s... • Many methods • Focus here for the most part on A mplitude Modulation (AM ) How? x(t) Transmitted Signal Carrier Signal

Amplitude Modulation(AM)of a Complex exponential carrier c(t) Wc-carrier frequency jEct X(w)*clw) cga) 2丌 X u)* 2d(w-wc) 2TU X((-c) (Oc-OM)Oc(oc+OM)(

Amplitude Modulation (AM) of a Complex Exponential Carrier

Demodulation of Complex Exponential AM x(t) y() x(t) nwct cos wct+] sin wct Corresponds to two separate modulation channels( quadratures) with carriers 90 out of phase cOS (ct lmt

Demodulation of Complex Exponential AM Corresponds to two separate modu l ation channels (quadratures) with carriers 90 o out of phase

Sinusoidal am x(t) cOS O t X(j)米丌{6(u-uc)+6(u+c)} oXOw-wc))+eXo(w+wc) Drawn assuming (uc-oMωl(oc+uM (c)

Sinusoidal AM Drawn assuming ωc > ωM

Synchronous Demodulation of Sinusoidal AM Hojo) 2 y(t) w(t) cos(ot+θ) Lowpass filter Local oscillator Y(o) Suppose 0=0 for now → Local oscillator is in phase with the carrier (c-oM) Wc(ac+OM Co (20c-aM2a

Synchronous Demodulation of Sinusoidal AM Suppose θ = 0 for now, ⇒ Local oscillator is in phase with the carrier

Synchronous demodulation in the Time domain w(t)=y(t)cos wct=a(t) cos wct=o(t)+ o(t)cos 2wct High-frequency signals Then t)= filtered out by the LPF Now suppose there is a phase difference, i.e. 0#0, then w(t)= y(t) cos(wct+0)=(t)cos wct cos(wct+8 a(t)cos 8+o(t)(cos(2wct+0)) OW (t)=a(t)cos g HF signal Two special cases 0=T/2, the local oscillator is 90o out of phase with the carrier or(o=0, signal unrecoverable 2)0=0(0)-slowly varying with time, =r(t=cos[0(o).x(o) → time-varying gain

Synchronous Demodulation in the Time Domain Two special cases: 1) θ = π/2, the local oscillator is 90 o out of phase with the carrier, ⇒ r ( t) = 0, signal unrecoverable. Now suppose there is a phase difference, i.e. θ ≠ 0, then 2) θ = θ ( t) — slowly varying with time, ⇒ r ( t) ≅ cos[ θ ( t)] • x ( t), ⇒ time-varying “gain

Synchronous Demodulation (with phase error) in the Frequency domain Demodulating signal has phase difference 0w.r. the modulating signal COS ( wct+0)=eect +e 3e 3at j6 丌e( )+丌e-06(u+ W(jo) -je 20 M (20OM)20 Again, the low-frequency signal(o<Om)=0 when 0=T/2

Synchronous Demodulation (with phase error) in the Frequency Domain Again, the low-frequency signal ( ω < ω M) = 0 when θ = π/2. Demodulating signal – has phase difference θ w.r.t. the modulating signal

Alternative: Asynchronous Demodulation Assume @c >> OM, so signal envelope looks like x(t) Add same carrier with amplitude a to signal x(t) y(t)=(A+X(t))cosOct elope=A+x(t) cos (,t Y(jo) Envel Time domain Frequency Domain a=0= DSB/SC (Double Side Band, Suppressed Carrier) A>0+DSB/WC Double Side Band, With Carrier)

Alternative: Asynchronous Demodulation • Assume ωc >> ωM, so signal envelope looks like x(t) • Add same carrier with amplitude A to signal A = 0 ⇒ DSB/SC (Double Side Band, Suppressed Carrier) A > 0 ⇒ DSB/WC (Double Side Band, With Carrier) Time Domain Frequency Domain

Asynchronous Demodulation(continued) Envelope Detector r(t) w(t) Y(t) c R W(t) In order for it to function properly, the envelope function must be positive for all time, i.e. A+x(o)>0 for all t Demo: Envelope detection for asynchronous demodulation Advantages of asynchronous demodulation Simpler in design and implementation Disadvantages of asynchronous demodulation Requires extra transmitting power [Acoso t]2 to make sure A+x(t)>0=Maximum power efficiency=1/3(P8.27)

Asynchronous Demodulation (continued) Envelope Detector Disadvantages of asynchronous demodulation: — Requires extra transmitting power [Acos ω c t]2 to make sure A + x ( t) > 0 ⇒ Maximum power efficiency = 1/3 (P8.27) In order for it to function properly, the envelope function must be positive for all time, i.e. A + x ( t) > 0 for all t. Demo: Envelope detection for asynchronous demodulation. Advantages of asynchronous demodulation: — Simpler in design and implementation