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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.