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- 1. 1 TELE3113 Analogue and Digital Communications Tutorial 3Question 1 (FM signal)Consider the FM signal s(t) = 10 cos[4π103 t + 0.1 sin(2π10t)] volts.a) What is the instantaneous frequency fi (t) of the signal s(t)? (1 mark)b) What is the modulation index β of the signal s(t)? (1 mark)c) What is the effective bandwidth using Carson’s rule? (1 mark)d) What is the effective bandwidth using universal rule? Table 1 may be used. (1 mark)e) Show the Fourier transform of the signal s(t) and sketch the amplitude spectra. (2 marks) TABLE I β 0.1 0.3 0.5 1 2 5 10 20 30 2nmax 2 4 4 6 8 16 28 50 70Question 2 (PLL)Phase-locked loop (PLL) can be used to demodulate FM signal and lock in phase.1) Show a block diagram of the PLL.2) The voltage controlled oscillator (VCO) is operating at a center frequency of f c . Let the input to the VCO be v(t). Show the VCO output.3) Let the input to the PLL be s(t) = Ac sin[2πfc t + φ1 (t)] and the loop ﬁlter be the ﬁrst order with a gain KL . If the output of the VCO is r(t) = Av cos[2πfc t + φ2 (t)]. Show that the input of the VCO can be approximated as v(t) = K[φ1 (t) − φ2 (t)].4) Explain how the PLL is able to lock into the phase of the input signal.5) If the input signal was an FM signal, show that when in lock the input of the VCO should be proportional to the message signal.

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