Introduction to Resonance

[pese]

Here is an excellent tool for preliminary calculations, if you are wanting to play around a bit.

http://www.pronine.ca/lcf.htm

If you start playing with series LC circuits the ressonant point will be the same, but the impedance function on this calc will not give an acurate awnser.

With your "inductance-problem" i ca help you
(any "radio-amateur" know this (that have constructed his old tube equipments)

Capacicit Inductance frequency , all with "one view"  print it out (wallpaper)


http://www.beis.de/Elektronik/Nomograms/RF-WP/RF-Wallpaper.html

The RF-Wallpaper

(Impedance Chart)

an R - L - C - f Nomogram as a PDF-File

This nomogram provides a quick graphical way to evaluate relations between R, L, C and f according to the corresponding formulas.

Its use should be obvious: Just look where the lines of the two given values (components or frequency) cross each other and follow the line of the value you're looking for.

I provided two nomograms: One is for the overview of several decades and with a second one with only one decade results of higher precision may be evaluated.

Should you often have to deal with the evaluation of passive components I recommend to hang these nomograms on the wall, just like I've done since my first steps in electronics. You will very soon get used to use them over and over and won't want to miss them. They are really convenient.

Gustav Pese

[armagdn03]

Pese

Love ya man, thanks for the great input. I plan on going through all of the relationships with respect to band width, quality factor etc in design and evaluation of such tank circuits when the time comes to start optimising things. This will undoubtedly be a great tool for people to use.

To all who have not been privy to this info:
I  want to emphisize that what needs to grasped is the concept, dont worry about perfecting things and small details till you see the big picture.
Im not gonna out inductances, or capacitances, or part numbers or wire guages ha ha ha, im sure you all have plenty of stuff laying around if you want to tinker. I just think its way better to learn by doing things yourself and figuring it out with out precise in structions, then all that you see are details. I still contend though that you dont have to build to larn. Build once you know every aspect of the thing will work. Otherwise just build little tests to test concepts such as I am doing here. The next installment will be up tomorow when Erfinder can put it up.

Thanks again Pese, that will be very useful.

[Charlie_V]

The power Tesla is referring to in almost all of those quotes on "http://www.forgotten-genius.com/" is referring to what I call Oscillation power (or Reactive power).  Here is an example of what he means:

You have a capacitor of 0.2 micro farads and a resistor of 20,000 ohms.  Lets assume we use a 10,000V source that can supply 1amps.  We have a spark gap so that when the capacitor reaches 10kV the spark gap discharges into a 4 micro henry inductor of very low resistance (i.e. large wires).  So, the capacitor and inductor make a tank circuit when the spark gap discharges.

The time it requires to charge the capacitor up to 10,000V is roughly 0.004 seconds.  Since the capacitor is discharged so rapidly when the gap fires, we can neglect the fall time of the capacitor.  This means that we can fire the gap at about 250 times in one second (250Hz).  How much energy is in the capacitor when it dumps into the inductor? 
E=0.5*C*V^2
So the there are 10 Joules in the capacitor when it fires.  We are inputting P=10/0.004, about 2500 Watts of power into the tank circuit.  HOWEVER! What is the power in the tank circuit - it is NOT 2500 Watts!  The resonant circuit oscillates at 177,940 Hz [ f = 1/(2*PI*sqrt(LC)) ].  The time constant of the tank circuit is 5.6 micro seconds!!!  The energy in the capacitor is still 10 Joules, so the power of the oscillation is 10/5.6micro which is equal to about 1.779 Mega Watts (1,779,406 Watts). 

Do we have over unity?  No we don't, that is because that 1.8 mega watts of power is all reactive.  This means that the 10 Joules of energy is only tossed back and forth between the capacitor and inductor 177,940 times in one second but the amount of energy in the system does not change (just 10 Watts and decreasing due to resistance).

How does this apply to anything useful?  Well, it allows us to take an oscillation and passively intensify it.  We can then use a resonant cavity (which is a device that increases the amplitude of a wave by bouncing smaller waves of the same frequency back and forth within it self many times, each small wave adds to the others before it dies giving you an over all wave of the same frequency but large amplitude) to amplify the oscillations and distribute them over greater distances. 

That's what a Tesla coil is suppose to do - not make sparks.  You transfer a slow vibration (DC or low frequency AC) to a very intense high frequency oscillation with a tank circuit.  The field of the primary inductor magnetically couples to the secondary (so the energy - 10 Joules using our last example - is input through the magnetic field).  The secondary acts as a resonant cavity for those waves (hence the quarter wavelength - just like a guitar or flute, all it does is amplify the vigorous oscillations of the tank circuit).  Whatever you connect to the ground terminal of the secondary, it will also begin to oscillate at whatever frequency the primary tank circuit is at.  Those vibrations can go for a very long distances assuming the ground plane will accept those frequencies.  The earth for example likes low frequencies, harmonics of 7.5Hz.  Telsa said not to use below 30kHz when using the earth.  You can definitely use higher than 30kHz but the oscillations will not traverse the planet, they will drop off as you get away from the transmitter. 

Those oscillations I'm talking about travel through the ground plane (whether its the earth or a wire), they do not travel in the air.  You can collect them using another Tesla coil whose secondary matches the same frequency as the oscillations. Basically you can transmit that 10 Joules of energy from one Tesla coil to the other using the ground connection - disconnect the ground and you stop transmission like cutting a wire.  However, if the two coils are close enough they can magnetically couple like transformers, which can go pretty far but not nearly the distance that the ground oscillations will cover. 

Unfortunately Tesla tried to tell people this, and no one understood it and they ignored him.  They still ignore it when he has patents and papers which tell you EXACTLY how to do it.  Read his Colorado spring notes - it even gives the capacitance, inductance, and voltages he used, shows pictures of lighting up bulbs in a field 100s of feet away (well past the magnetic field coupling range) and still no one uses this technique. 

Whats best is that they (Tesla coils) can pick up outside oscillation very well.  Mine is 15 feet tall and in the building its in it produces 15Volts at 60 Hertz and its resonance is 240kHz!  That would make it the 4000 Harmonic but 15 Volts for the 4000 Harmonic is amazing, just think if it was tuned to 60 Hertz haha!  I could draw all the power I wanted from the Grid!!!  But this opens the door to new ways of energy harvesting that a solar panel could never do. 

Once I can get a source that has enough UHMF, I plan to power a 25W light bulb from hopefully greater than 30 Meters, which should beat MIT's pathetic 3 foot display.  I think it can go farther than 30 meters but it really depends on the frequency and how much voltage my setup can withstand - distance for a ground oscillation at 250kHz is very dependent on the voltage and it should die off pretty quick because 250kHz is way too high for the earth - time will tell I suppose.

[armagdn03]

The energy in the capacitor is still 10 Joules, so the power of the oscillation is 10/5.6micro which is equal to about 1.779 Mega Watts (1,779,406 Watts). 

Do we have over unity?  No we don't, that is because that 1.8 mega watts of power is all reactive.  This means that the 10 Joules of energy is only tossed back and forth between the capacitor and inductor 177,940 times in one second but the amount of energy in the system does not change (just 10 Watts and decreasing due to resistance).

Thank you for sharing your example. I would however like to comment specifically on this statement. This is the very problem that people have suposedly been trying to solve for quite some time.

The problem is this. That 10 joules is indeed just tossed back and forth over and over, decaying with time due to system losses. If you try and tap that circuit. i.e inductively, directly, however, you will just use that 10 joules, and you will have just that 10 joules or less due to decay. but...

What if that 10 joules of work can be used to do work, over and over while not being depleated???
That right there is the entire point of the inductive transfer into a working circuit of resonant quality.

For example, a person could create a motor that is based on an LC, the rotoverter is a good example, terribly constructed for its perpose, but thats because they are taking existing equipment built for one thing, and using it for another application. They are tuning the load, to the source. If you have a room full of tuning forks, you are multiplying your power through transfer from one system of resonance to another. Do you think that the adition 100 forks makes the origional die 100 times quicker? this doesnt match what you would intuitively think, or what you would find experimentally. The tuning forks can take on different forms, as long as they are tuned to one another.

Someone asked a while back on a thread here if turning on a huge ammountof radios would depleat the antenas power, great question, it applies.
one example:
http://www.altenergy-pro.com/device02.htm
I do not know this man, but I know this concept would work, if you consider each of the 3 receiving coils as tuned loads, you will not deplete the source.

ah....now we walk into the world of transducers and how to sever ties to the source.
that 10 joules can indirectly do work over and over each time it is transfered back and forth, as long as the source doesnt depleat the oscillations. What do you think our friend Doc Stiffler is trying to do, again it could be done better but the concepts are the same, and this will be shown.....

The question has never been how much energy does an LC have....it has been, What do we do with its oscillations.

[gotoluc]

Hi armagdn03,

thank you for starting this very important Introduction to Resonance topic.

I have known for a while now that this is an area I need to better understand to further circuit effect quality. So you have my full interest and support to your topic.

I applaud your effort and am very grateful for you to take time to share your knowledge.

Luc