Tutorial8_ans - 1. =ct + sinmt + 2sin2mt EE 3008. FM...

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EE 3008. FM Tutorial Solutions 1. θ = ω c t + sin ω m t + 2sin2 ω m t t t dt d m m m m c ω θ 2 cos 4 cos + + = Therefore ∆ω = ω m cos ω m t+4 ω m cos2 ω m t At t=0, ∆ω max = ω m +4 ω m = 5 ω m or f max =5f m = 5kHz 2.(i) β = ∆ω / ω m =100/(10 × 10 3 ) = 0.01 (NBFM), B 2f m =20kHz. (ii) NBFM, B 2f m =20kHz. (iii) NBFM, B 2f m =40kHz. (iv) NBFM, B 2f m =40kHz. 3.(i) f=4 × 1000=4kHz (ii) W 100 50 2 100 ) ( 2 2 = × = Φ = R t P t (iii) f m =1kHz, β = f/f m =4, f c =10 7 Hz=10MHz (i.e., n=0) Therefore at 10 MHz, the average power is W 16 ) 4 . 0 ( 100 ) 4 ( 2 2 0 0 = = × = J P P t (iv) Using Carson’s rule: B 2( f + f
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