Tele3113 tut3
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This document contains two questions about FM signals and phase-locked loops (PLL). Question 1 asks about the instantaneous frequency, modulation index, effective bandwidth using Carson's rule and universal rule, and Fourier transform of an FM signal. Question 2 provides a block diagram of a PLL and asks the student to show equations for the voltage controlled oscillator output, input to the VCO, and how the PLL locks into the input signal's phase. It also asks how the input to the VCO would be related to the message signal for an FM input.
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TELE3113 Analogue and Digital Communications
Tutorial 3
Question 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 70
Question 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.](https://image.slidesharecdn.com/tele3113tut3-110609223301-phpapp02/85/Tele3113-tut3-1-320.jpg)
Tele3113 tut3
- 1. 1 TELE3113 Analogue and Digital Communications Tutorial 3 Question 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 70 Question 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.