Radios, how do they work?

This is an excellent article, thank you for submitting it! I love how effortlessly this article delivered an intuition for why an ideal antenna length would be half of the wavelength of the signal you want to receive. I was also delighted by the point about how all methods of modulating a wave can be recontextualized as frequency modulation!

I think this undersells the trick behind radio.

Say we have the technology to broadcast a signal from an antenna to receivers, with some bandwidth B. Without getting clever, we can only send or receive one signal, since any others would interfere with each other.

The trick is, can we do something to shift the bandwidth B to some other base frequency F such that B + F > B? Or B + (N - 1)F > B? And if we can do that, and then downshift from B + NF back to B, it means we can broadcast to multiple channels, and receivers can tune their antennas to F and downshift the decoded signal to 0 and receive it at the original bandwidth B.

A cheap way to do this is amplitude modulation, where multiplying a signal with bandwidth B by a carrier signal of frequency F shifts it up to the range F +/- B and we can space channels apart by 2B to get however many channels our antennas allow for.

The real question is, why is it 2B and not B? Well that lies in some Fourier analysis, where the bandwidth of a signal extends into negative frequency ranges. But neverless, there is another trick, called single-side-band modulation (SSB) where we can shift a signal into the range F + B instead of F +/- B, and demodulate it into -B, B to get the original.

And that gets us to the 1950s in terms of radio technology.

The trick behind FM is to understand we can get more bandwidth by shifting the frequency response not into a series of non-overlapping channels centered at carrier frequencies like AM, but to distribute most of the information across many non overlapping bands over the entire spectrum of the antennas. To do this we don't modulate the amplitude of the carrier, but its frequency. This makes it possible to distribute far more bandwidth across a wide range of frequencies, and it's how FM radio works today.

These concepts create the foundation for modern radio communication, We can modulate data signals to different bandwidths and receive them, provided we know where to tune to. And these bandwidths can either be continuous chunks of spectrum (AM), or interleaved (FM). The next step is to think in terms of time, which is to say that we can have receivers negotiate not only which ranges in frequency they care about, but which time frames they want to listen before waiting for their next time slot.

For those interested in the theory, the fundamental problem is that we can design antennas that can transmit or receive at some fixed maximum bandwidth, bounded by physics. The engineering problem is to find out how to share that bandwidth to maximize the number of receivers and/or senders by sharing the same bandwidth. Amplitude modulation is excellent, but it divides the bandwidth up into a fixed number of channels of maximum individual bandwidth. FM is a bit more efficient in how it can allow many broadcasters to even more receivers choose which channels they receive. But for modern communications, where we need high bandwidth for distinct transmitter/receiver connections, we need protocols to figure out how to share the bandwidth over the air and the two tricks are to divide that bandwidth by frequency (like AM and FM) or time (sharing the same frequency channels, but only picking the frames that we care about), or both.

And for those even deeper into the theory, one question you might ask is, if we can divide spectrum and time to get some bandwidth B per channel, how many bits can we send/receive over a distinct channel?

The answer is C = Blog2(1 + S/N) where B is the bandwidth and S/N is the signal to noise ratio determined by the environment (how much noise is present relative to the signal being transmitted). The crazy thing is this was proven in the 1940s and everyone interested should go read The Mathematical Theory of Communication by Claude Shannon. This is referred to as the Shannon-Hartley theorem, and it determines the channel capacity (C, in bits/second) of any communication channel in the presence of noise.

The math concepts might seem heady, but it's actually fairly approachable and available online. It's fascinating that the fundamentals were proven out in one work nearly 80 years ago by a handful of people, and the math is not that bad.

The thing that makes this nuts is that if an engineer picks some target bitrate for a device, say a cellphone watching video, they can work backwards to determine the channel capacity they need, do some experiments to figure out noise, and then determine what the target their modem protocol needs to reach to be suitable. And this is how we get 5G and fiber or whatever comes next.

Magnets

Yes, we did this in middle school. Was great fun :D