Resonator for a non-sine wave ... ?

[john1]

Hi,

I'm trying to find out if a resonant circuit could be made,
which will resonate at a non-sinusoidal wave form.

I believe that most wave forms can be reproduced by adding
together sine waves of different amplitudes, and multiples
or sub-multiples of the desired frequency.

But can a circuit be made which would resonate to a non-sine
wave ... ?

John

this is not a school project,
i've been pondering it on and off for months

 

[bloki]

It is not clear what do you mean by resonant circuit and what dou you mean by resonate.

 

[zachtheterrible]

He wants a resonant circuit that will produce something other than a sinewave I think?

Just guessing here but I think that you have to modify the output of the resonant circuit in order to get a squarewave, triangle wave, sawtooth, etc.

 

[bloki]

I think he is trying to discover hot water.

 

[Optikon]

Hi,

I'm trying to find out if a resonant circuit could be made,
which will resonate at a non-sinusoidal wave form.

I believe that most wave forms can be reproduced by adding
together sine waves of different amplitudes, and multiples
or sub-multiples of the desired frequency.

But can a circuit be made which would resonate to a non-sine
wave ... ?

John

this is not a school project,
i've been pondering it on and off for months

You have to be more clear? What about several resonators(sine wave) at different frequencies & magnitudes, then add them up.. that's sorta a non sinewave resonator.. LOL..

I think you need to study the mathematics to further understand the nature of resonance. Generally, resonance results from a solution to a differential equation for which there is only a sinusoidal solution. I suppose one could prove that under the conditions & assumptions of resonance, it is impossible for a resonant solution that is non-sinusoidal..

In say the electrical LC resonant tank case, the circuit can be described by a differential equation for which there is only a sinusoid solution. I believe resonance in general (mechanical, chemical & otherwise) all follow the same restrictions. Also keep in mind, there is no closed form expressions for poorly behaving waveforms (with discontinuities like quare waves etc..)

 

[Optikon]

I believe that most wave forms can be reproduced by adding
together sine waves of different amplitudes, and multiples
or sub-multiples of the desired frequency.

Most? how about All of them (that are physically possible and well behaved Dirchlet condition-wise)

Well its refreshing that you believe what Joseph Fourier proved to be true long ago.. all is good and well.

 

[john1]

Hi,

Well i had heard something to that effect a long time ago.
That judicious adding of harmonics could produce almost any shape of wave-form.
Although i don't recall those people you mentioned, well behaved or not.

As you can probably tell from my earlier post, i was thinking about multiple
RC tanks, to give me a resonance for a particular wave shape.

However this is proving extremely difficult to accomplish.
So i am now considering trying to make a mechanical unit which will respond
to this awkward wave-shape, which is a very low frequency (below audio)

I am sort of thinking along these lines:
(1) maybe i could make a mechanical gently vibrating contraption of the wave-shape
i want,
(2) then i could amplify the signal from the sensor which is waiting for
the appearance of this wave-shape to come along,
(3) If the wave shape is present, it will be faint, and below audio frequencies,
but maybe a centre-zero meter might respond by comparison to the locally
generated signal ... maybe it would sway from side to side ...

I dunno, any ideas welcome at this point.

Regards, John

 

[bloki]

Ordinary church bell has multiple resonances. Bell sound is not a sinus.
For example a violin has multiple resonator. String excited by fiddle in front of resonator produces a nonsinusoidal sound.

 

[Roff]

I don't know if you could make this work in near-real-time, (or if you even need to), but you could sample the waveform at a relatively high frequency (>10*fundamental), digitize it,store it, analyze to determine the period, read one cycle from memory repeatedly, and convert the digital signal back to analog with a D/A converter. You might be able to use a DSP.

 

[john1]

Hi, zach, bloki, Optikon, Ron H,

Thank you Ron H, and if i understand you correctly, you describe converting
this wave-form into digital form, in order to use it in some way.

Well after some considerable thought, that is pretty much the same lines as
i was thinking.

For this purpose the shape of the Very Low Frequency wave is known, and yes
it could easily be sampled many times, and an average produced, which could
then be 'looped' as you describe.

This would produce a locally generated wave-shape, which could then be used
against the input from the sensor, which would be highly amplified.

I was thinking carefully about what i said about the centre-zero meter going
from side to side slowly.
Took me a while to realise i was thinking about BFO, then i realised that the
meter wouldn't really act like that, because the frequency difference wouldn't
show up unless it was rectified. Then it would show as slow forward surges.

That would probably be acceptable.
I feel that such an arrangement would have a very very high 'rejection' co-ef
or 'Q' as they used to call it. This application has to differentiate signal
from a lot of background vibrations.

I think that will do the job, i will start getting things together to make
this project.

Cheers, John

 

[Roff]

Wait a minute! If you want high Q, it sounds like you are wanting to extract the fundamental frequency (a sine wave) from a complex waveform. A high-Q resonant circuit does just that. Maybe you should be a little more forthcoming if you really want help. There is a lot of experience here that you can tap if you are not too paranoid.

 

[john1]

Hi ...

Maybe 'Q' was an incorrect descriptive choice.
It is not a sine wave that is being sought.
It is a particular shape of wave-form of a very low frequency.

Earlier i was thinking it might be possible to cobble up a
resonant circuit that would respond to this odd wave-shape,
but that is either extremely difficult, or totally impractical.

And yes, you are i think quite right, i am rather paranoid.

However i think that comparisons with a locally produced
wave, of the desired shape, would do the job.
Especially if the comparisons were somehow 'cumulative' this
would need the operator to synchronise the local generator by
manual adjustment, in order that a 'cumulative' effect could
build, and show clearly on a monitor or meter, against a
background of noise and vibrations.

I must thank you all for your help, and i feel i can move
forward on this now.

Best regards, John