Analog Modulation Lab

Data Communication, Lecture 8. Put a message tone on a carrier with AM, FM and PM, see each spectrum, and plan a radio band. Works offline.

AM signal (orange) and its envelope (blue dashed)
Spectrum: carrier at fc, sidebands at fc ± fm

Amplitude modulation

Bandwidth 2 × fmTotal power Pc(1 + m²/2)Power in sidebands

Message (blue) and FM signal (orange): frequency follows the message
Spectrum: lines at fc ± n·fm with heights |Jn(β)|, shaded = Carson bandwidth

Frequency modulation

β = Δf / fmCarson 2(1 + β)fmLines above 1% of carrier

FM broadcast: audio up to 15 kHz with β about 4–5, so about 150–180 kHz, inside the 200 kHz channel each station gets.

Message
FM: frequency highest where the message is highest
PM: frequency highest where the message rises fastest

Same message, two methods

PM of a message is the same as FM of its slope (derivative). That is why a PM signal changes frequency where the message changes fastest, not where it is largest.

Stations packed into a broadcast band

How many stations fit?

Channel widthChannels in the band

AM needs 2 × 5 kHz = 10 kHz per station; FM needs 2(1 + 4) × 15 kHz = 150 kHz, allocated 200 kHz.