1

I am currently learning about wave modulation. In communication theory, it is said that 'rotating vector addition' generates AM (amplitude modulation) and FM (frequency modulation). What does 'rotating vector addition' mean in this context, and how does it generate AM and FM?

EDIT

Chapter 2.6 Phasors and the Addition of Waves of Optics, fifth edition, by Hecht:

enter image description here

Chapter 2.11 Twisted Light of Optics, fifth edition, by Hecht:

enter image description here enter image description here

The Pointer
  • 1,241
  • 1
  • 11
  • 24
  • 1
    Not one of those links mentions the word, *"rotating"*. Would you mind providing a link to a site from which you are able to say, *"it is said that..."*? (Of course, I have something in my mind about it. But I want to see the source of your question and not your interpretations from it.) – jonk Jul 03 '21 at 16:16
  • \$\textbf{z}_t=A\, e^{j\,\left(\omega\,t+\theta\right)}=A\,e^{j\,\left(2\pi\,f_0\,t+\theta\right)}\$ is just a rotating vector on the complex plane. You can see this by noting the role of \$t\$ in Euler's, and then \$x_t=\mathscr{R}\left\{A\, e^{j\,\left(2\pi\,f_0\,t+\theta\right)}\right\}\$ is just the projection of it onto the real-number axis. It's a helpful tool in visualizing. It's likely that this is at least part of what you are referring to. But without your source, there's no way to tell for sure. – jonk Jul 03 '21 at 16:29
  • Hi @jonk, I think you might have it right. See here http://www.museatex.com/phase.htm I'm trying to develop a clear conceptual connection between "rotating vector" and AM and FM. – The Pointer Jul 03 '21 at 16:32
  • Do you follow the first two paragraphs, completely? Or not? Oh, crap. I think I know of a video you need to see. Just a sec.... Take a look [here](https://youtu.be/-qgreAUpPwM). It's not about your subject, directly. But it shows you, visually. You can see the rotating vector addition IN SPADES! Just watch. – jonk Jul 03 '21 at 16:34
  • @jonk The first paragraph is clear to me – it seems to me that it's basically describing frequency (cycles over time). The second paragraph is a bit more difficult for me to follow, but, based on my knowledge of (harmonic) waves from physics, it seems to be describing something like a phasor https://en.wikipedia.org/wiki/Phasor https://upload.wikimedia.org/wikipedia/commons/8/89/Unfasor.gif Am I understanding this correctly? – The Pointer Jul 03 '21 at 16:41
  • Did you get the *spiral* (I would have said *helix*) that the author mentions in the 2nd paragraph, too? This whole area is perhaps one of the things in EE that relates directly to something truly beautiful in mathematics. It's just... awesome to behold. It is a big part of why I even care, at all, about EE, today. If EE was just a bunch of memorization of EE collections of rules, I'd stay far away from it. It is *because* EE relies upon some of these key concepts in math that it attracts me more to it. – jonk Jul 03 '21 at 16:43
  • @jonk This reminded me of some sections of my textbook *Optics*, fifth edition, by Hecht. I have edited my post with the relevant images. Is this effectively the phenomena? – The Pointer Jul 03 '21 at 16:48
  • I actually have, and have read Hecht!. It's my absolute favorite book on optics!! It's what I used when contracting with the team that developed the first successful re-writable CD-ROM!! It helped me a lot. And there is a relationship. For AM and FM, though, it's simpler to follow. (I have to juggle fewer things in mind.) – jonk Jul 03 '21 at 16:49
  • @jonk Yes, it seems to be well-regarded. I've been studying it slowly, since it is quite dense for a beginner such as myself. – The Pointer Jul 03 '21 at 16:52
  • My copy may be older than yours, it's by Hecht & Zajac. I haven't checked to see if Zajac has been dropped from the author list in more recent editions. – jonk Jul 03 '21 at 16:54
  • @jonk So the second paragraph of http://www.museatex.com/phase.htm is effectively describing so-called "twisted light"? The rotating vector creates a spiral/helix that is moving along some time line (through the middle of the spiral/helix, as seen in figure 2.33)? The problem is that I'm still confused how this generates AM and FM (say, using a laser beam). – The Pointer Jul 03 '21 at 16:56
  • I don't think so. The twisted light is more complex to imagine in mind. I'd avoid getting stuck on that. Go simpler. The video I linked is something to just sit back and watch and let it seep into you. You will see a non-rotating vector at the start. This is the DC vector. Then you will see, attached to it, a rotating vector. This will be the modulating frequency vector. Note that it rotates at a constant angular velocity. Then, attached to that, is yet another vector (added) that is rotating at a *different* but constant angular velocity. This might be a single 'audio tone', for example. – jonk Jul 03 '21 at 16:59
  • This is why it was possible for the *ancients* to reasonably find that the Earth was the center of the universe, using a complex Platonic set of "circles on circles" to approximate the motion of the planets and the sun around the Earth. A Fourier can map pretty much *anything* with circles moving at constant angular rates, given enough of them to do it. *"Give me enough vectors rotating at constant angular velocity and the ability to add them and I'll approximate anything and everything!"* – jonk Jul 03 '21 at 17:12

1 Answers1

0

This 152 page reference may have relevant information concerning AM:

https://web.sonoma.edu/esee/courses/ee442/archives/sp2019/lectures/lecture06_am_modulation.pdf

Shows this slide on page 16:

enter image description here

And this slide on page 19:

enter image description here

SystemTheory
  • 821
  • 4
  • 8