# What does 'rotating vector addition' mean in this context, and how does it generate AM and FM?

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:

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

• 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
Commented Jul 3, 2021 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
Commented Jul 3, 2021 at 16:29
• Hi @jonk, I think you might have it right. See here museatex.com/phase.htm I'm trying to develop a clear conceptual connection between "rotating vector" and AM and FM. Commented Jul 3, 2021 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. It's not about your subject, directly. But it shows you, visually. You can see the rotating vector addition IN SPADES! Just watch.
– jonk
Commented Jul 3, 2021 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 en.wikipedia.org/wiki/Phasor upload.wikimedia.org/wikipedia/commons/8/89/Unfasor.gif Am I understanding this correctly? Commented Jul 3, 2021 at 16:41

## 1 Answer

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:

And this slide on page 19:

• Wow, that's actually really helpful! Thanks! Commented Jul 4, 2021 at 6:07