Why does an AM radio channel require any bandwidth at all? Why can’t it just transmit on a single, precise frequency?
In: 95
The transmission of AM is actually on quite narrow band. Technically, it can’t be exactly a single frequency because the modulation of the carrier — even if it only varies the amplitude — can also be understood as linear combination of frequencies around the carrier waveform, even if the bandwidth is quite narrow relative to the carrier frequency.
It comes from trigonometric identities such as this: sin(a + b) = sin(a)*cos(b) + cos(a)*sin(b). If a is the carrier and b is the signal waveform, and you can interpret modulation as sin(a + b) + sin(a – b) = sin(a) * cos(b). The right hand side of the equation is actually the modulation of carrier waveform a with signal b, and it looks indistinguishable from linear combination of two frequencies, a+b and a-b. Thus to carry 10 kHz signal you’d need 20 kHz bandwidth to do it around the carrier frequency — can’t escape the math.
Also, nobody is going to place radio stations 20 kHz apart even if they only had to carry up to 10 kHz sounds. In order to receive one station, you’d require incredibly good filter that hears exactly the very narrow bandwidth around the center frequency and that is practically hard. It might be doable digitally using modern technology, I guess, but not analog crap equipment of yore.
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