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chapter3_fm

# chapter3_fm - ANALOG MODULATION PART II ANGLE MODULATION...

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ANALOG MODULATION PART II: ANGLE MODULATION

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2 What is Angle Modulation? In angle modulation, information is embedded in the angle of the carrier. We define the angle of a modulated carrier by the argument of... s t ( 29 = A c cos θ t ( 29 ( 29
3 Phasor Form In the complex plane we have t=1 t=0 t=3 Phasor rotates with nonuniform speed

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4 Angular Velocity Since phase changes nonuniformly vs. time, we can define a rate of change This is what we know as frequency ϖ i = d θ i ( t ) dt s t ( 29 = A c cos 2 π f c t + φ c θ i t ( 29 1 2 4 3 4 d θ i dt = 2 π f c
5 Instantaneous Frequency We are used to signals with constant carrier frequency. There are cases where carrier frequency itself changes with time. We can therefore talk about instantaneous frequency defined as f i t ( 29 = 1 2 π d θ i t ( 29 dt

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6 Examples of Inst. Freq. Consider an AM signal Here, the instantaneous frequency is the frequency itself, which is constant s t ( 29 = 1 + km ( t ) [ ] cos 2 π f c t + φ c θ i t ( 29 1 2 4 3 4 d θ i dt = 2 π f c
7 Impressing a message on the angle of carrier There are two ways to form a an angle modulated signal. Embed it in the phase of the carrier Phase Modulation(PM) Embed it in the frequency of the carrier Frequency Modulation(FM)

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8 Phase Modulation(PM) In PM, carrier angle changes linearly with the message Where 2πf c =angle of unmodulated carrier k p =phase sensitivity in radians/volt s t ( 29 = A c cos θ i t ( 29 ( 29 = A c cos 2 π f c t + k p m t ( 29 ( 29
9 Frequency Modulation In FM, it is the instantaneous frequency that varies linearly with message amplitude, i.e. f i (t)=f c +k f m(t)

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10 FM Signal We saw that I.F. is the derivative of the phase Therefore, f i t ( 29 = 1 2 π d θ i t ( 29 dt θ i t ( 29 = 2 π f c t + 2 π k f m t ( 29 0 t s t ( 29 = A c cos 2 π f c t + 2 π k f m ( t ) dt 0 t
11 FM for Tone Signals Consider a sinusoidal message The instantaneous frequency corresponding to its FM version is m ( t ) = A m cos 2 π f m t ( 29 f i t ( 29 = f c + k f m ( t ) = f c resting frequency { + k f A m cos 2 π f m t ( 29

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12 Illustrating FM 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 FM message Inst.frequency Moves with the Message amplitude
13 Frequency Deviation Inst. frequency has upper and lower bounds given by f i t ( 29 = f c + f cos 2 π f m t ( 29 where f = frequency deviation = k f A m then f i max = f c + f f i min = f c - ∆ f

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14 FM Modulation index The equivalent of AM modulation index is β which is also called deviation ratio . It quantifies how much carrier frequency swings relative to message bandwidth β = f W baseband { or f f m tone {
15 Example:carrier swing A 100 MHz FM carrier is modulated by an audio tone causing 20 KHz frequency deviation. Determine the carrier swing and highest and lowest carrier frequencies f = 20 KHz frequency swing = 2 f = 40 KHz frequency range : f high = 100 MHz + 20 KHz = 100.02 MHz f low = 100 MHz - 20 KHz = 99.98 MHz

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16 Example: deviation ratio What is the modulation index (or deviation ratio) of an FM signal with carrier swing of 150 KHz when the modulating signal is 15 KHz?
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