# Modulation Sideband Questions (Specific Questions)

#### sjgallagher2

Joined Feb 6, 2013
131
This is a very common question I've found by looking around, I've read many answers but they all say the same thing about sidebands: they carry the information. Or at least, in AM they do. That's what I'm actually learning about right now. Apparently the sidebands are generated around the carrier, for example a modulating signal with a frequency f1 and a carrier with f0 generate sidebands f0+/f1. As to why there's any energy at all why all you're doing is modulating the amplitude, people throw some trigonometry around, saying things like the frequencies are generated from multiplying the two cosine waves and stuff like that. Well here's the issue: when I multiply x and y, I get z, not z and x+/-y side answers. So I look up what happens when you multiply two sin functions. I found a page on here about multiplying sine waves, but the answer ended up being frequency +/- frequency again, "just because" it seems like. Maybe I need to delve deeper into the maths or something, because that isn't a very good reason. Long story short, despite all this knowledge of sidebands, I have exactly zero understanding.

My Questions:
1. Why +/-? What's significant about the sum and difference?
2. Why are two identical sidebands generated above and below? (Similar to above question)
3. Can you graph the sidebands in the way most books show AM? (A low frequency sine wave, a high frequency sine wave, and then an overlay of the two combined, with an envelope detailed around the carrier in the shape of the low frequency sine wave. You know, that old diagram).

In this picture:

4. Can you see the sidebands?
5. Are they left out?
6. Does that even make sense?

If you have to throw around maths that look like this: http://physics.stackexchange.com/qu...he-cause-of-sidebands-in-amplitude-modulation
Just tell me to "Check the maths" and save yourself some trouble, then I'll redouble my efforts to understanding what's going on there.

7. Can you analogize the sidebands? (Is analogize a word? Make me an analogy I'm trying to say).

Okay I'm done. Proper help is so appreciated, I can't articulate. Thanks.

#### crutschow

Joined Mar 14, 2008
31,097
All of you questions basically boil down to understanding the trig involved. The multiplication of two sine waves generates the sum and difference of the two frequencies. So if you don't understand the math, I'm not sure there's a simpler way to describe the process. The world of engineering is the world of applied math.

1. There is no particular significance to the sum and difference, that's just what the process of modulation generates.

2. Again, that's what the math predicts and that's what is generated.

3. I can't graph it any better than the books.

4. If you use a spectrum analyzer in the frequency domain you can indeed see the sidebands. But you can't see them in the time domain as shown in the diagram.

5. No. They just aren't visible in the time domain.

6. Yes.

7. I don't think so. (At least I can't think of a good analogy).

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#### t_n_k

Joined Mar 6, 2009
5,455
Simply multiplying two sinusoids or co-sinusoids of different frequency doesn't produce the AM signal. You just get the sum and difference terms as you indicate. With zero modulation signal, the carrier is still transmitted in AM and you may deduce that the simple multiplication does not allow that outcome.

#### crutschow

Joined Mar 14, 2008
31,097
Simply multiplying two sinusoids or co-sinusoids of different frequency doesn't produce the AM signal. You just get the sum and difference terms as you indicate. With zero modulation signal, the carrier is still transmitted in AM and you may deduce that the simple multiplication does not allow that outcome.
Yes, simply multiplying the two signals together does not give a standard broadcast band AM signal with a carrier. But it does produce a suppressed carrier double-sideband AM signal. This can be filtered to generate a single-sideband AM signal, commonly used for HAM radio transmissions. This has the advantage of concentrating all the signal power into the one sideband, for relatively efficient transmission of the signal (high signal-to-noise ratio relative to the signal power).