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# Tutorial4_solution - 1 Tutorial 4 Frequency Modulation(FM...

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Principles of Communications 1 Tutorial 4 Frequency Modulation (FM)

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Principles of Communications 2 Problem 1 Consider the following FM signal: where f c = 100 kHz and f m =1 kHz. Determine: (i) Instantaneous phase; (ii) Instantaneous frequency; (iii) Peak frequency deviation. s FM ( t ) = 100cos(2 π ( f c t + sin( f m t ) + 2sin(2 f m t )))
Principles of Communications 3 Solution Ψ ( t ) = 2 π ( f c t + sin( f m t ) + 2sin(2 f m t )) f ( t ) = 1 2 π d Ψ ( t ) dt = f c + f m cos( f m t ) + 4 f m cos(2 f m t ) Δ f = max | f ( t ) f c | = max f m cos( f m t ) + 4 f m cos(2 f m t ) (i) Instantaneous phase (ii) Instantaneous frequency (iii) Peak frequency deviation 4 5 5 Hz m m m f f f k = + = =

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Principles of Communications 4 Problem 2 A 1-GHz carrier is frequency-modulated by a 10-kHz sinusoid so that the peak frequency deviation is 100 Hz. Determine (i) the modulation index β ; (ii) the modulation index if the modulating signal amplitude was doubled; (iii) the modulation index if the modulating signal frequency was doubled; (iv) the modulation index if both the amplitude and the frequency of the modulating signal were doubled.
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