Vakkursus EMS310/311 Course EMS310/311 - Electrical, Electronic ...

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5 Herlei uitdrukkings vir die ontvanger intree S/R (na die ontvanger-BDF) en die ontvanger uitgang S/R, (SNR) i and (SNR) 0 repektiewelik, in die geval van AM-DSB-OD met moduleersein m(t) en Tx en Rx draers van %2cos(ωct) en %2cos(ωct+θ), onderskeidelik, met θ=π/4 [rad]. Aanvaar `n perfekte BDF by die ontvanger en `n SWG- kanaal met tweesydige DDS N/2 [W/Hz]. Beskryf die volledige demodulasieproses analities. Hoe vergelyk die S/R-werkverrigting van hierdie AM-DSB-OD stelsel met die ideale basisband-verwysingstelsel in 4 hierbo? Verklaar enige verskille. Derive expressions for the receiver input (after the Rx BPF) and the receiver output SNRs, (SNR) i and (SNR) 0, respectively, in the case of AM-DSB-SC with modulating signal m(t) and Tx and Rx carriers of %2cos(ωct) and %2cos(ωct+θ), respectively, with θ=π/4 [rad]. Assume a perfect BPF at the receiver and an AWGN channel with two-sided PSD N/2 [W/Hz]. Show the complete demodulation process analytically. How does the SNR performance of this AM-DSB-SC system compare with the ideal reference baseband system in 4 above? Explain any differences. EINDE END <strong>EMS310</strong>_Klastoets2_07.wpd LPL/04/07 6 / 7 [6]
T F ω n ξ = APPENDIX A PLL IDENTITIES The following formulas are relevant to a second order PLL with passive loop filter, F(ω), with components (R 1, R 2, C). The natural angular frequency of the PLL is described by: K′ = K N ⎡ K′ ⎤ = ⎢ ⎥ ⎣τ T ⎦ 1 ⎡ K ′ ⎤ ⎢ ⎥ 2 ⎣ τ T ⎦ 1 2 ( ∆ ω ) = 3 2ξωn [sec] 2 4( ∆ f ) = 3 ; B ξ = 1 = 0707 . 2 L 2 1 2 [ rad / s] (1) where is the total loop gain, with N the loop division factor. The total loop filter constant is given by τT = ( R1 + R2) C . The damping constant of the PLL is given by: The -3dB bandwidth of the closed-loop transfer function, H(ω), is: [ τ + 1 2 ] <strong>EMS310</strong>_Klastoets2_07.wpd LPL/04/07 7 / 7 K ′ 2 2 2 [ 2 1 2 1 1] ω− 3 = ω ξ + + ξ + + The closed-loop noise bandwidth, BL, of the PLL is given by: ∞ 2 dB n ( ) [ rad / s ] ω n ⎡ 1 ⎤ BL= ∫ H( ω ) . df = ⎢ξ + ⎥ [ Hz ] 0 2 ⎣ 4ξ ⎦ If the input signal frequency and phase falls within the bandwidth of the loop filter, locking will occur without cycle slipping, for a angular frequency difference of: ∆ω K′ . τ 2 = τ + τ L n 1 2 ≈ 2ξω [ rad/s] if K′ >> The maximum angular frequency difference which the PLL will be able to Pull-In (with or without cycle slipping) is approximately equal to: [ K ] 1 2 2 ∆ ω = 2 2ξω ′ − ω 1 2 . [rad/s] (6) PI n n The maximum frequency-offset, ∆ωHI [rad/s], from the nominal VCO-frequency of ωo [rad/s], which the PLL will be able to track without cycle slipping, after it has already locked onto the input signal, is given by: ∆ω HI = K′ [rad / s] (7) The time it takes for a PLL to lock onto a frequency component ∆ω [rad/s] away from the nominal VCO frequency, is: (2) (3) (4) (5) (8)
Page 1 and 2: Departement Elektriese, Elektronies
Page 3 and 4: 2 Identifiseer en skets die boublok
Page 5: 4 Herlei ‘n noubandmodel (tyd-uit

Vakkursus EMS310/311 Course EMS310/311 - Electrical, Electronic ...

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