chapter3_am

# chapter3_am - ANALOG MODULATION PART I AMPLITUDE MODULATION...

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ANALOG MODULATION PART I: AMPLITUDE MODULATION

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03/10/10 Copyright 1999 by B.Mobasseri 2 WHAT IS ANALOG MODULATION? Analog modulation consists of two parts Analog message Carrier Analog message is then impressed upon the amplitude, frequency or phase of the carrier We then say carrier is “modulated” by the message
03/10/10 Copyright 1999 by B.Mobasseri 3 Amplitude Modulation Define the message by a baseband signal m(t). Define the “carrier” by a sinusoidal signal c(t) with amplitude A c and frequency f c The AM signal is then given by s t ( 29 = A c 1 + k a m t ( 29 [ ] cos 2 π f c t ( 29

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03/10/10 Copyright 1999 by B.Mobasseri 4 AM Envelope The “envelope” of an AM signal is the factor in front of the carrier, Envelope is a baseband signal and contains all the information an AM signal carries 1 + k a m t ( 29 [ ]
03/10/10 Copyright 1999 by B.Mobasseri 5 AM Example 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -3 -2 -1 0 1 2 3 AM BASEBAND carrier message

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03/10/10 Copyright 1999 by B.Mobasseri 6 Requirements on the Envelope To prevent “overmodulation”, the envelope must always be positive, 1 + k a m ( t ) 0 2200 t or k a m ( t ) 1 1 + k a m ( t ) 0 1 + k a m ( t ) < 0 overmodulation
03/10/10 Copyright 1999 by B.Mobasseri 7 Finding AM Spectrum Fourier transform modulation property says Taking Fourier transform s t ( 29 = A c 1 + k a m t ( 29 [ ] cos 2 π f c t ( 29 = A c cos 2 f c t ( 29 + A c k a m t ( 29 cos 2 f c t ( 29 S f ( 29 = A c δ f - f c ( 29 + f + f c ( 29 [ ] + A c k a 2 M f - f c ( 29 + M f + f c ( 29 [ ]

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03/10/10 Copyright 1999 by B.Mobasseri 8 Showing AM Spectrum Baseband AM M(f) upper sideband lower sideband f c W f c +W f c -W -f c AM bandwidth=2W
03/10/10 Copyright 1999 by B.Mobasseri 9 Tone Modulation Tone modulation is when the message is a simple sinusoid The corresponding AM signal is m t ( 29 = A m cos 2 π f m t ( 29 s t ( 29 = A c 1 + μ cos 2 f m t ( 29 [ ] cos 2 f c t ( 29 with μ= k a A m

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03/10/10 Copyright 1999 by B.Mobasseri 10 Modulation Index The quantity μ is called modulation index or modulation factor . Modulation index must be less or equal to 1
03/10/10 Copyright 1999 by B.Mobasseri 11 Finding Modulation Index A max A min A max = A c 1 + μ [ ] A min = A c 1 - μ [ ] A c 1 + cos 2 π f m t ( 29 [ ] cos 2 f c t ( 29 μ= modulation index= A max - A A max + A

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03/10/10 12 What is μ Here? 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -3 -2 -1 0 1 2 3 AM BASEBAND
03/10/10 Copyright 1999 by B.Mobasseri 13 AM Power The power of AM signal is split between carrier and message A c 1 + μ cos 2 π f m t ( 29 [ ] cos 2 f c t ( 29 = A c cos 2 f c t ( 29 + A c cos 2 f m t ( 29 cos 2 f c t ( 29 = A c cos 2 f c t ( 29 carrier 1 2 4 3 4 + A c 2 cos f c + f m ( 29 t + A c 2 cos f c - f m ( 29 t message 1 2 4 4 4 4 4 4 3 4 4 4 4 4 4

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03/10/10 Copyright 1999 by B.Mobasseri 14 Components of AM Power Carrier power= Upper sideband power= Lower sideband= Carrier power= Total message power= 1 2 A c 2 1 8 μ 2 A c 2 1 8 2 A c 2 1 2 A c 2 1 4 2 A c 2
03/10/10 Copyright 1999 by B.Mobasseri 15 Total AM Power Total AM power is the sum of carrier and message power P T = P carrier + P sideband = 1 2 1 + μ 2 2 A c 2

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03/10/10 Copyright 1999 by B.Mobasseri 16 Distribution of AM Power
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chapter3_am - ANALOG MODULATION PART I AMPLITUDE MODULATION...

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