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### Question about frequency mixer?

Posted: **Thu May 24, 2018 4:08 pm**

by **Github**

I am confused about how does frequency mixer actually work. As we know, if we mix a 5 Mhz and a 20 Mhz signal together, it generates 15 Mhz and 25 Mhz signal (ignore harmonic wave for simplicity). If we connect the signal to spectrum analyser, we'll see four signals, 5 15 20 and 25 Mhz. But here is the problem, what we put into the spectrum analyzer is 5 Mhz and 20 Mhz combined at time domain, and it can be split back into 5 and 20 Mhz by fourier transform, then how does 15 and 25 Mhz being formed?

### Re: Question about frequency mixer?

Posted: **Wed May 30, 2018 4:26 pm**

by **hotpaw2**

It's trigonometry. If you combine two frequency sinusoids by adding them, it won't mix them, you will end up with just 5 and 20. However, if you multiply two sinusoids, then this modulation will produce two side-bands. This is because of the trigonometric product-sum identity: sin(a) * sin(b) == 0.5 * ( cos(a-b) + cos(a+b) ). You get more then just the original two sinusoids.

See:

https://en.wikipedia.org/wiki/List_of_t ... identities for a list of trig identities. Lots of textbooks and web sites contain proofs of the above. Works with both real values and complex numbers (IQ data).