# How harmonics happens when you mix two signals?

Doing a search in quora about Why does Amplitude Modulation have sideband frequencies? i found an answer and within it, a user answered with the following statement:

"When you try mixing two signals, there will be something know as harmonics that will occur. This means that frqncy X (+) Frqncy Y will not just form frequency Z but some more frequencies that will be embedded into the system."

Can someone clarify and or exemplify the statement?

• The statement can’t be clarified because it is ambiguous (does not specify the type of mixing, linear or non-linear, AM or other, nor the frequencies), and thus is very likely outright wrong. Sep 16, 2020 at 5:53

Amplitude modulation is a linear operation (excluding the carrier in the classical AM) and does not introduce harmonics due to the modulated signal. Sidebands are not harmonics. They are created as the message signal spectrum is shifted up to carrier frequency.

Frequency mixing of a message signal with a sinusoidal carrier, another definition of AM, does not introduce harmonics.

In a practical setting if there are some nonlinearities in the implementation (a deviation from the ideal case) you may have harmonics. Otherwise No.

• There is one case I can think of where harmonics appear in mixing: when a sinusoid of frequency $\omega_1$ modulates another sinusoid also of frequency $\omega_1$. Then, the resulting frequencies are $0$ and $2\omega_1$.
– Peter K.
Sep 14, 2020 at 21:31
• with analog mixing harmonics are inevitable due to the non-linearities so the harmonics will always be there (they just may be low enough to not care). Spur charts such as this one are used to determine where each of those harmonics will land and at what level: microwaves101.com/encyclopedias/mixer-spur-chart Sep 14, 2020 at 21:53
• @PeterK. Yes in that case the harmonic and the side lobe coincide :-)... just as 2 + 2 = 2*2 coincide :-) Sep 15, 2020 at 9:12
• @Fat32 yes agreed rereading the post, the harmonics associated with the non linearities are the reason other frequencies beyond $f_c+ f_m$ and $f_c-f_m$ appear but they have nothing to do with why AM has sidelobes which are those two components alone - so that other user’s comment she quoted is somewhat misplaced. I see why you made that point and why that comment would cause her confusion. Sep 15, 2020 at 12:04
• @DanBoschen yes! sometimes (increasingly more frequent nowadays) it's quite hard to understand what the actual problem is. The question titles and question bodies can be quite inconsistent if not totally exclusive. And here as you said the first sentence speaks about AM side lobes, but the paraphrase talks about mixing harmonics (due possible nonlinearities). All i could assume was that OP is doing a new research on AM; hence is more interested in side-lobes than mixing nonlinearity harmonics at this early stage.. Sep 15, 2020 at 12:32