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RISC-division Aalborg University, Department of Communication Technology Niels Jernes Vej 12 – A6, DK-9220 Aalborg East RISC8-1-TCMT-mm9/05 1/2 050330/OKJ rev. 060306/OKJ Transceiver Components and Measuring Techniques, mm9 Suggested solutions 1. A receiver is required to pass a blocking test with a –39 dBm CW-blocker at an offset of 600 kHz from the desired channel. The reference (desired) signal level is –99 dBm, the detection SNR is 9 dB and the channel bandwidth is 200 kHz. What is the required phase noise spectral density of the local oscillator signal at 600 kHz offset? Approximation: Assume that the LO phase noise spectrum is flat from 500 kHz to 700 kHz offset. = = = Reference signal level Required S/N-ratio Allowed disturbance level (in 200 kHz bandwidth) Bandwidth = 200 kHz (Approximation: Flat spectrum over 200 kHz band) Allowed disturbance level in 1 Hz bandwidth Blocker (=carrier) level L(600 kHz) = Allowed noise spectral density relative to carrier or another way around: Reference signal level - Required S/N-ratio = Allowed disturbance level (in 200 kHz bandwidth) - Blocker level = Disturbance level relative to blocker level = Allowed oscillator noise relative to carrier (in 200 kHz bandwidth) - Bandwidth = 200 kHz (Approximation: Flat spectrum over 200 kHz band) = L(600 kHz) = Allowed noise spectral density relative to carrier -99 9 -108 53 -161 -39 -122 -99 9 -108 -39 -69 dBm dB dBm dBHz dBm/Hz dBm dBc/Hz dBm dB dBm dBm dBc 53 dBHz -122 dBc/Hz Note: This calculation does not include other noise and distortion products which may degrade the BER. 2. A single loop PLL has an offset in the loop filter corresponding to a phase offset, Δθ, of 0.01 rad (0.57Ε). The loop parameters are: N = 1000 Loop division ratio. fref = 100 kHz Reference frequency (at phase detector). Loop natural frequency. fn = 1 kHz ϕ = 53o Loop phase margin. a. Calculate the relative level of the spurious signal at 1st and 2nd harmonic of the reference frequency. Use (the reformulated) results from “Brennan” for a 3rd order loop with a phase-frequency detector for relative levels of the sidebands at ω0 ± nωref : Ole Kiel Jensen, [email protected], Telephone +45 9635 8663 RISC-division Aalborg University, Department of Communication Technology Niels Jernes Vej 12 – A6, DK-9220 Aalborg East SideBand relative, voltage ( n ⋅ ω ref ) = ( 2/2 2 ⎛ Δθ ⎞ sin⎜ n ⎟ ⋅ H closedloop ( n ⋅ ω ref ) n ⎝ 2 ⎠ N ⋅ ω n2 (tg (ϕ ) + 1 / cos(ϕ )) s + ω n3 ) H closedloop ( s ) = 3 s + ω n ( tg (ϕ ) + 1 / cos(ϕ )) s 2 + ω n2 ( tg (ϕ ) + 1 / cos(ϕ )) s + ω n3 H closedloop ( nω ref >> ω n ) ≈ N ⋅ ω n2 (tg (ϕ ) + 1 / cos(ϕ )) 2 n 2ω ref b. Calculate the settling time to 2% frequency error for a frequency step using “Brennan” fig. 7.6 or (7.22): ω Error (t ) = Δω [1 + ω nt − (ω nt )2 ]e−ω nt a. Approximation: fref >> fn H closedloop ( nω ref >> ω n ) ≈ n=1 n=2 0.299 0.0747 2.99Α10-3 ~ -50.5 dB 747Α10-6 ~ -62.5 dB N ⋅ ω n2 (tg (ϕ ) + 1 / cos(ϕ )) 2 n 2ω ref SideBand relative, voltage ( n ⋅ ω ref ) = 2 ⎛ Δθ ⎞ sin⎜ n ⎟ ⋅ H closedloop ( n ⋅ ω ref ) n ⎝ 2 ⎠ b. Reading from Figure 7.6: ωnt . 9 Solving: ω Error (t ) = Δω [1 + ω nt − (ω nt )2 ]e−ω t n gives by iteration ωnt ∼= 7.9 tSettling = 7.9/ωn = 1.26 ms Ole Kiel Jensen, [email protected], Telephone +45 9635 8663