### Author Topic: Sinewave squared (multiplied by itself)  (Read 1683 times)

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#### Circlotron

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##### Sinewave squared (multiplied by itself)
« on: August 31, 2016, 10:57:48 am »
So we put a sinewave into both inputs of a four quadrant multiplier and out the other side comes another sinewave at twice the frequency, and offset so that it swings from zero to X volts, not equally either side of zero like the input waveform. Then we put the output through a cap to centre the waveform on zero, and (maybe) through a hi Q tuned circuit to reduce any slight amount of distortion. Then we put this double frequency sinewave through another multiplier so it is now 4X the original frequency, and so on and so on... What interesting property is there about a sinewave that allows us to do this?

#### dannyf

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##### Re: Sinewave squared (multiplied by itself)
« Reply #1 on: August 31, 2016, 11:01:10 am »
Trigonometry.
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#### DmitryL

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##### Re: Sinewave squared (multiplied by itself)
« Reply #2 on: August 31, 2016, 11:09:07 am »
What interesting property is there about a sinewave that allows us to do this?

All sinewave properties can be easily deducted from definition:
e^ix = cos(x) + i*sin(x)

#### rstofer

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##### Re: Sinewave squared (multiplied by itself)
« Reply #3 on: August 31, 2016, 04:37:36 pm »

#### SeanB

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##### Re: Sinewave squared (multiplied by itself)
« Reply #4 on: August 31, 2016, 07:25:47 pm »
The offset comes from the non zero constants in the multiplier, you can use an offset compensating DC current to get them to zero, but it will always be there as a temperature and time dependant drift. You tend to forget those constants in Math, but in any multiplication and such those are always there and implied, even if you rarely write them down. Whatever plus c........

#### Circlotron

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##### Re: Sinewave squared (multiplied by itself)
« Reply #5 on: August 31, 2016, 10:02:36 pm »
The offset comes from the non zero constants in the multiplier,
The idea was that both multiplier inputs received the same identical signal, the product of which is only positive or zero. If there was an instant where one input was pos and the other neg then that would make the output swing neg, but yeah, I see what you are saying.

#### dannyf

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##### Re: Sinewave squared (multiplied by itself)
« Reply #6 on: August 31, 2016, 10:15:35 pm »
Any signal will have a non negative average if it is squared.

That's by definition.
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