Mixing Frequencies: Summing vs Multiplication - Jason O

[Jdo300]

Hello All,

I have two questions regarding mixing of frequencies. I heard that there is a difference between two waves that simply ‘add’ mathematically, and two waves that are ‘multiplied’ mathematically. If I have two frequencies, say 10Hz and 11Hz and I add the waves together so that they produce a beat frequency. I attached a graph showing the difference between the two frequencies being summed and multiplied below. If this process were to occur inside an antenna. What kind of setups would be used to produce the two waveforms in the antenna?

My second question relates to resonant coupling. If the antenna were setup so that it produced the multiplied waveform, if there were an outside signal that was equal to the frequency of the beat wave in the antenna, would they couple to each other? (In this case, the outside wave would have a frequency of 1Hz). I know these frequencies are ridiculously low but just using them as examples to prove my point here (and match up with the graph I made). Any comments and suggestions welcome.

Thanks,
Jason O

P.S. NOTE: Blue graph is waves added and Red graph is waves multiplied.

 

[Averagesupernova]

Don't have a lot of time to post right now, but your graph is wrong. Blue wave is the multiplied one. Do a search on this forum. I think it would be worth your time. There has been at least one thread with rather heated discussion as to what mixing and modulation actually are.

 

[Jdo300]

Hello,

Yeah, I probably got the terminology backwards but the point I want to make is that I don't want to use a carrier frequency and ride another signal on top of it. The red graph was produced by the function Sin(10x)*Sin(11x). So the two input frequencies are almost the same but just slightly detuned from each other to make the LF waveform. The function Sin(10x) + Sin(11x) is what produced the blue graph.

How would one make thi red waveform using the two input waves that I mentioned?

Thanks,
Jason O

 

[berkeman]

You need to have a non-linear effect in order to mix. Addition is a linear effect, and mixing results from non-linear (multiplication) processes. An antenna is a linear device, so you won't get any mixing or modulation in just the antenna or feed coax.

The simplest and most typical mixer circuit is a Gilbert cell.

http://members.tripod.com/michaelgellis/gilbert.html

 

[AlephZero]

You need to have a non-linear effect in order to mix. Addition is a linear effect, and mixing results from non-linear (multiplication) processes.

True. Maybe it's worth pointing out that analogies with HEARING beats when two audio sine waves are played from separate loudspeakers, etc, can be misleading, because the human hearing system is intrinsically nonlinear. That's why you can hear artefacts like difference tones clearly (especially after a bit of ear training!) but they won't show up on signal analyzer.

 

[Averagesupernova]

...That's why you can hear artefacts like difference tones clearly (especially after a bit of ear training!) but they won't show up on signal analyzer.

Care to explain this a bit farther?

 

[AlephZero]

It's a well documented pcychoaoustic and musical effect. Suppose you have two musical instruments like flutes that play fairly pure tones. If they play two different notes like C and E (approx. frequences 512Hz and 640Hz) you hear those two notes and also a strong tone at 640-512 = 128 Hz which is a C two octaves below. In some cases the difference tone can sound as loud as the actual tones. You can also do it with two signal generators sending sine waves to two different loudspeakers of course.

Clearly the only "demodulation" is inside your hearing system, since there is no phyiscal coupling between the two sound sources. If you record the sound with a microphone and an FFT analyser, you see two peaks at 512 and 640 (plus some higher frequency harmonics) but nothing at 128.

Some musicians also claim to be able to hear "sum tones" (i.e. a note at 512+640 = 1152 Hz) but that is less common than hearing difference tones.

See "difference tones" in a text of psychoacoustics for more info - and probably also speculation on how humans percieve pitch, which AFAIK is not yet well understood.

Difference tones are used intentionally in some types of music. For example in barber-shop quartet singing, the notes in the chords are deliberately arranged to produce the effect of a phantom "fifth singer". They are also used in some pipe-organs to produce the impression of very low pitched sounds without the expense of very large pipes.