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Back to the simple things; Multiply a sine wave by 3
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Back to the simple things; Multiply a sine wave by 3
*** Check out my last post, I added 10 sine`s ,1f to 10f !
Hello gang,
We all know we can easily multiply a sine wave to get double the frequency, but have you ever tried multiplying a sine wave by 3 to get 3 times the frequency ? Well here is a simple circuit I came up with. It works across the entire audio frequency range and as you can see by the frequency analysis we get a perfect sine wave out. It does also work with a triangle wave for 3 times the frequency, but you do NOT get a triangle wave out, so it's like a wave shaper at 3 times the frequency. Hope someone can make use of this, and please do make comments and suggestions.
Later then, BobF.....
P.S., Yes, you can of course remove the frequency readout if you wish!
Hello gang,
We all know we can easily multiply a sine wave to get double the frequency, but have you ever tried multiplying a sine wave by 3 to get 3 times the frequency ? Well here is a simple circuit I came up with. It works across the entire audio frequency range and as you can see by the frequency analysis we get a perfect sine wave out. It does also work with a triangle wave for 3 times the frequency, but you do NOT get a triangle wave out, so it's like a wave shaper at 3 times the frequency. Hope someone can make use of this, and please do make comments and suggestions.
Later then, BobF.....
P.S., Yes, you can of course remove the frequency readout if you wish!
Last edited by BobF on Thu Mar 26, 2020 2:52 pm, edited 1 time in total.
 BobF
 Posts: 592
 Joined: Mon Apr 20, 2015 9:54 pm
Re: Back to the simple things; Multiply a sine wave by 3
BobF wrote:
Hello gang,
We all know we can easily multiply a sine wave to get double the frequency, but have you ever tried multiplying a sine wave by 3 to get 3 times the frequency ? Well here is a simple circuit I came up with. It works across the entire audio frequency range and as you can see by the frequency analysis we get a perfect sine wave out. It does also work with a triangle wave for 3 times the frequency, but you do NOT get a triangle wave out, so it's like a wave shaper at 3 times the frequency. Hope someone can make use of this, and please do make comments and suggestions.
Later then, BobF.....
P.S., Yes, you can of course remove the frequency readout if you wish!
One word "Brilliant" idea and I love the way you presented this on the graph while changing the settings. Thanks for sharing this. I found it addicting while playing with it.

pshannon  Posts: 144
 Joined: Fri Jan 02, 2015 3:08 am
Re: Back to the simple things; Multiply a sine wave by 3
Very nice BobF
thanks !
thanks !
 RJHollins
 Posts: 1456
 Joined: Thu Mar 08, 2012 7:58 pm
Re: Back to the simple things; Multiply a sine wave by 3
That’s amazing Bob! I had no idea such a thing was possible.
I’m not a maths guy so I wonder if you or someone else could explain how it works.
Thanks for sharing this. Into my toolbox it goes!
Cheers
Spogg
I’m not a maths guy so I wonder if you or someone else could explain how it works.
Thanks for sharing this. Into my toolbox it goes!
Cheers
Spogg

Spogg  Posts: 2689
 Joined: Thu Nov 20, 2014 4:24 pm
 Location: Birmingham, England
Re: Back to the simple things; Multiply a sine wave by 3
Nice, Bob!
The product of two waves with frequencies f1 and f2 yields two waves with new frequencies f1 + f2 and f1  f2. Hence the product of a wave with itself yields a wave at double frequency plus a DC offset. If you multiply again, you get a mix of waves with frequencies 3f, f, and f. By carefully subtracting the original wave, you can isolate the wave with triple frequency 3f.
The product of two waves with frequencies f1 and f2 yields two waves with new frequencies f1 + f2 and f1  f2. Hence the product of a wave with itself yields a wave at double frequency plus a DC offset. If you multiply again, you get a mix of waves with frequencies 3f, f, and f. By carefully subtracting the original wave, you can isolate the wave with triple frequency 3f.

martinvicanek  Posts: 1122
 Joined: Sat Jun 22, 2013 8:28 pm
Re: Back to the simple things; Multiply a sine wave by 3
martinvicanek wrote:Nice, Bob!
The product of two waves with frequencies f1 and f2 yields two waves with new frequencies f1 + f2 and f1  f2. Hence the product of a wave with itself yields a wave at double frequency plus a DC offset. If you multiply again, you get a mix of waves with frequencies 3f, f, and f. By carefully subtracting the original wave, you can isolate the wave with triple frequency 3f.
Martin, thanks for your great explanation, I like the "carefully subtract" part. To be honest, my thoughts before I tested this, I was concerned that I might hear a lot of distortion or a loud pop/boom sound which I did not. I am curious and I put some questions below.
1. Does anyone know if this is practiced with actual analog sound equipment?
2. Is this all Digital and math?
3. Is there a keyboard synth that actually does this?

pshannon  Posts: 144
 Joined: Fri Jan 02, 2015 3:08 am
Re: Back to the simple things; Multiply a sine wave by 3
Great explanation Martin, thank you!
@pshannon: The trickiest thing in the analogue world would be to produce a pure and accurate sinewave over the whole audio range. Any deviation from ideal would introduce unwanted sum and difference partials. The old method of using diode shapers acting on a triangle wave would be inadequate.
Digital synths make use of waveform tables that can be read out at different speeds to produce the desired pitches. One example is the DX7. So there would be no need for such a thing in the digital synth world.
The big advantage of Bob’s system is that you only need one oscillator in FlowStone to create the first 3 partials, so it’s cheaper on CPU.
Now I’m wondering about using the system to make F5. F4 is easy of course…
Cheers
Spogg
@pshannon: The trickiest thing in the analogue world would be to produce a pure and accurate sinewave over the whole audio range. Any deviation from ideal would introduce unwanted sum and difference partials. The old method of using diode shapers acting on a triangle wave would be inadequate.
Digital synths make use of waveform tables that can be read out at different speeds to produce the desired pitches. One example is the DX7. So there would be no need for such a thing in the digital synth world.
The big advantage of Bob’s system is that you only need one oscillator in FlowStone to create the first 3 partials, so it’s cheaper on CPU.
Now I’m wondering about using the system to make F5. F4 is easy of course…
Cheers
Spogg

Spogg  Posts: 2689
 Joined: Thu Nov 20, 2014 4:24 pm
 Location: Birmingham, England
Re: Back to the simple things; Multiply a sine wave by 3
Thanks for the nice comments gang.
@Martin, thanks so much for the math explanation, I should have thought to add that.
@pshannon, I do not know of any analog Synth's that incorporate this but I do believe this can be done in hardware. Of course you would need very precise sine oscillators and multipliers that do not introduce any distortion and the subtraction has to have just the right amplitude. Any modular synth owners out there that would like to try this and confirm for us?
@Spoog, 5x , good question, is it possible!
Later then, Bob.....
@Martin, thanks so much for the math explanation, I should have thought to add that.
@pshannon, I do not know of any analog Synth's that incorporate this but I do believe this can be done in hardware. Of course you would need very precise sine oscillators and multipliers that do not introduce any distortion and the subtraction has to have just the right amplitude. Any modular synth owners out there that would like to try this and confirm for us?
@Spoog, 5x , good question, is it possible!
Later then, Bob.....
 BobF
 Posts: 592
 Joined: Mon Apr 20, 2015 9:54 pm
Re: Back to the simple things; Multiply a sine wave by 3
pshannon wrote:Does anyone know if this is practiced with actual analog sound equipment?
Yes, but with the caveats that Spogg mentioned about accuracy  the multiplication of two audio signals, respecting their polarity, is a ring modulator.
All schematics/modules I post are free for all to use  but a credit is always polite!
Don't stagnate, mutate to create!
Don't stagnate, mutate to create!

trogluddite  Posts: 1615
 Joined: Fri Oct 22, 2010 12:46 am
 Location: Yorkshire, UK
Re: Back to the simple things; Multiply a sine wave by 3
For some arbitrarily low value of "easy": 2F is easy, so 4F is easy, and 4F mixed with F gives you 5F+3F. So one oscillator plus three mixing operations gives you the first 4 harmonics.BobF wrote:@Spoog, 5x , good question, is it possible!
The details are left as an exercise for the reader.
I keep a pair of oven mitts next to my computer so I don't get a concussion from slapping my forehead while I'm reading the responses to my questions.
 deraudrl
 Posts: 165
 Joined: Thu Nov 28, 2019 9:12 pm
 Location: SoCal
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