Introduction to Resonance

[barbosi]

There is something I'm missing. While all this stuff meets all common knowledge and I'm not going to argue about that, there are few formulas thought in schools that do not make any sense to me.

An example is here http://www.pronine.ca/lcf.htm and for your convenience I attach a screenshot.

So my trouble is to understand where is the impedance formula coming from?
And I'm sure it is pretty familiar to many.
Does anyone realises that the infinite impedance (at resonance) has the value of 31.6227... ohms? (see screenshot)

Maybe is just me sweeping under the rocks...

[AbbaRue]

If I wanted to get 2 coils to resonate at alternated times and use the back emf of one to help energize the other.
How would I go about doing this?
Sort of a teeter toter effect.
I want to make a 2 cylinder electromagnetic piston engine.

[armagdn03]

To awnser Barbosi

In a perfect world, there would be no losses in the components. Perfect inductors, and perfect capacitors would give infinite impedance in parallel configuration, and zero impedance in series. The calculation given for impedance is a closer aproximation to real life where we do not have perfect loss-less systems. You can see from the equation which components to use to get higher or lower impedances.

To awnser AbbaRue

Sorry, im not here to speculate on how to make certain devices, if you think about why whats happening is happening, you will find that that is not directly possible.

[barbosi]

The calculation given for impedance is a closer aproximation to real life where we do not have perfect loss-less systems.

Well this is a darn sloppy approximation. And the formula for impedance is flat out wrong if you pay attention to the parameters. While you may have for different values the same resonant frequency, the impedance varies like hell.

From the values on my screenshot you get frequency about 50kHz and Z abut 31 ohms/.
If you change to C=100uF and L=100nH you'll have the same frequency but Z=0.031 ohms  (which in no way approximates infinite).

That was all my point and I see almost nowhere that familiar formula, which was also kind of useless.
And I'm pretty sure was at the base of transmission lines theory, matching impedance stuff, etc.
But is OK, I'm not going to hog the thread with a pervert formula. 

[armagdn03]

HA HA HA 
that rant cracked me up a bit,

I didnt actually check the acuracy of that formula, I cannot vouch for it. The one for finding resonant freq is correct though. But its true, you may have the same resonant freq with diferent sized caps and inductors, which will have different impedances. Impedance matching is important when optimising, for now though, this information is just meant to give the bigger picture, dont get bogged down with details. Find other calculators, find books, find articles, check formulas, go and learn!

And hey........dont just take one source and believe it! fact check! be a detective! I just like that calc because you could enter any 2 of 3 variables, didnt ever really use the impedance part, notice I didnt talk about calculating impedance....were not there yet.