Excuse me I am a complete beginner. If LF radio waves are sent with let’s say frequencies of 100 kHz, how can data be modulated to that signal considering the signal is so long? For example, how can let’s say a 40-bit code be transmitted on that LF radio wave over a short distance like 10 feet using modulation?

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    $\begingroup$ Pick your favorite modulation (say Morse code) and go for it on allowed wavelengths... $\endgroup$ – Jon Custer Jan 28 at 0:52
  • $\begingroup$ use ASK or FSK but at 100kHz only 10 feet away you do not have "wave propagation", that is direct coupling probably magnetic between two coils. $\endgroup$ – hyportnex Jan 28 at 1:21

Any form of modulation requires a non-zero bandwidth. If I send only a simple sine wave with no modulation, the receiver can't get any information out of that signal because I didn't put any into it. Its like a pendulum continuing to swing at the same frequency and amplitude, so you can't tell anything else about it (it contains no other information). But if I start pushing on the pendulum at different times and with different forces, its amplitude will vary and also the frequency energy will not always be at exactly the free-swinging frequency. So any modulation will always produce energy at other frequencies. So someone else observing the pendulum can get information from it (specifically, the information about how I varied my pushing of the pendulum).

Now let's say I amplitude modulate a signal such that there are 10000 different amplitude levels, and each level means something different. If there is no noise in the system, and the receiver can measure those levels, then obviously I can send a lot of data. Even if its a 1Hz carrier, that's still 10000 different levels per second. However, in practice all signals have a bit of noise (undesirable energy) in them. The noise can come from a variety of sources. We've found that the theoretical maximum data rate that can be sent through a channel (assuming ideal modulation) depends on the maximum allowed power, maximum allowed frequency bandwidth, and the noise (see Shannon-Hartley theorem).

Also note that ideal modulation means that the entire allowed band is filled with otherwise unpredictable data (consider that any predictability in the data is not "new" information, and therefore wastes bandwidth). So for ideal modulation, this means you won't even see the carrier frequency any more than any other frequency.

  • $\begingroup$ Wait so let’s say it’s at like 50khz meaning that maybe the sin carrier wave we can say only goes through one full iteration before reaching the receiver-are u still able modulate that signal considering there is only one iteration you can change/ modulate? $\endgroup$ – Andy Lebowitz Jan 28 at 11:52
  • $\begingroup$ By "iteration" do you mean a single state of amplitude? If so, that is called a "symbol". If that's what you mean... $\endgroup$ – Digiproc Jan 28 at 16:17
  • $\begingroup$ ... then you are correct in assuming a single symbol (without any others) won't convey much, if any, information, because in practice a receiver typically can't know an isolated amplitude symbol because signals inadvertently vary in intensity because of multipath (i.e. reflectors, etc.). So, for amplitude, anyway, a receiver can't demodulate until it knows the true amplitude of at least one symbol. The same goes for a an isolated phase symbol. Of course, a single isolated frequency modulation symbol can be known, though. $\endgroup$ – Digiproc Jan 28 at 16:17

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