Amplitude Modulation (Large Carrier)
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1 Department of Electrical, Computer, and Biomedical Engineering Ryerson University ELE 635: Lecture Four Handout Condensed from Lathi Amplitude Modulation (Large Carrier) Amplitude Modulation ϕ AM (t)= A c cos ω c t + m(t) cos ω c t =[A c + m(t)] cos ω c t If m(t) ←→ M (ω), then we have: ϕ AM ←→ (1/2)[M (ω + ω c )+ M (ω - ω c )] + πA c [δ (ω + ω c )+ δ (ω - ω c )] For envelope detection: A c + m(t) ≥ 0 for all t. Which is the same as: A c ≥ m p
Transcript of Amplitude Modulation (Large Carrier)
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Department of Electrical, Computer, and Biomedical EngineeringRyerson University
ELE 635: Lecture Four HandoutCondensed from Lathi
Amplitude Modulation (Large Carrier)
Amplitude Modulation
ϕAM(t) = Ac cosωct+m(t) cosωct = [Ac +m(t)] cosωct
If m(t)←→M(ω), then we have:
ϕAM ←→ (1/2)[M(ω + ωc) +M(ω − ωc)] + πAc[δ(ω + ωc) + δ(ω − ωc)]
For envelope detection:
Ac +m(t) ≥ 0 for all t. Which is the same as:Ac ≥ mp
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Modulation Index
µ = mp
Ac
For envelope detection:0 ≤ µ ≤ 1
Whenµ > 1 only synchronous detection is possible.
Tone Modulation
Modulating signal is a sinusoid:m(t) = B cosωmt. Find the spectrum.
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Generation of AM Signals
vbb′ = [c cosωct+m(t)]w(t) (1)
= [c cosωct+m(t)]
[
1
2+
2
π
(
cosωct−1
3cos 3ωct+
1
5cos 5ωct− ...
)]
(2)
=c
2cosωct+
2
πm(t) cosωct+ terms suppressed by bandpass filter. (3)
Demodulation of AM Signals
Rectifier Detector
vbb′ = [A+m(t)](cosωct)w(t) (4)
= [A+m(t)] cosωct
[
1
2+
2
π
(
cosωct−1
3cos 3ωct+
1
5cos 5ωct− ...
)]
(5)
(6)
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Envelope Detector
More on Modulation Index
Ex2. Find all modulation indexes in terms ofAc.
