Angle modulation - Angle Modulation(Exponential modulation...

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Unformatted text preview: Angle Modulation (Exponential modulation ¡ • In angle modulation, the amplitude of the modulated signal remains constant while the phase Ф(t¡ fluctuates proportional to the modulating signal. • The information is conveyed in the zero crossings of the carrier and not in its envelope. • So any amplitude distortion would seriously corrupt an envelope modulated wave but has no effect on the detection of angle modulated wave. This is why it is widely employed for high quality links when bandwidth is not important Angle Modulation • The general modulation equation • s(t¡ = A(t¡ cos θ(t¡ = A(t¡ cos ( 2Π f c t + Ф(t¡ ¡ θ(t¡ = 2Π f c t + Ф(t¡ = instantaneous phase. θ ’ (t¡ = 2Π f c + Ф ’ (t¡ = instantaneous freq. - If Ф(t¡ is proportional to m(t¡ phase mod.- If Ф’(t¡ is proportional to m(t¡ freq. mod. Angle Modulation • Phase Modulation Ф(t) = k p m(t) k p = phase modulation constant in radians /volt The phase modulated wave will be: s PM (t) = A c cos (ω c t + k p m(t)) Angle Modulation • Frequency Modulation dФ = k f m(t¡ dt k f = frequency deviation constant in radians/sec.volt ( or Hertz/volt¡ Ф(t¡ = k f ∫ m(λ¡ d λ s FM (t¡ = A c cos (ω c t +k f a(t¡ ¡ a(t ¡ F.M . P.M . Angle Modulation • In case of a sinusoidal signal Angle Modulation • m(t¡ = A m cos ω m t • The instantaneous phase deviation of the modulated signal is Ф(t¡ = k p A m cos ω m t → for phase mod. = k f A m sin ω m t → for frequency ω m mod. Angle Modulation • In general the modulated signal can be written as:- s(t¡ = A c cos ( ω c t + β sin ω m t ¡ where :- β = modulation index = ∆f f m = k f A m → FM ω m = k p A m → PM max frequency deviation = ∆f Angle Modulation FM PM f i = f c + ∆f θ i =ω c t + k p A m cos ω m t =f c + k f A m cos ω m t ∆θ = β = k p A m ∆f = k f A m ∆ω = k p A m ω m ∆θ = k f A m f m β = ∆f = ∆ω Bandwidth of Angle Modulated Waves S FM (t¡= Re- Modulated = unmodulated + various AM terms- B.W of: a(t¡ : W, a 2 (t¡: 2W, …. a n (t¡: nW- Infinite B.W S FM (t¡=Re S FM (t ¡ • If | K f a(t¡ | << 1 ( or β << 1¡ N.B. F.M. S FM = Note the similarity between N.B.F.M and AM- carrier + side bands- B.W. = 2W- side band spectrum of FM has a phase shift of π/2 with respect to the carrier • Similarly N.B.P.M S PM = The possibility to use DSB-SC modulators in the generation of NBFM and NBPM Wide Band F.M • s FM (t¡ = A c cos ( ω c t + β sin ω m t ¡ = Re ( A c exp (j ω c t¡ exp (j β sin ω m t ¡ ¡ Is a periodic function of time with a fundamental frequency f m . It can be expanded in Fourier series as:- W.B.F.M ∫ ∑- ∞-∞ = = = T/2 T/2 t jnω- t sinω j n t jnω n n t sinω j dt e e T 1 F e F e m m m m β β W.B.F.MW....
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Angle modulation - Angle Modulation(Exponential modulation...

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