| MadSci Network: Physics |
Hi Sharon,
That is a very good question, and fortunately, one for which a good answer exists. Let's start with your last question. You mentioned that you could not find a resonance equation for DC. The reason for that is that a pure DC signal cannot cause resonance. Resonance is something associated with oscillations, and hence requires some time dependence of the current.
The trick here is that you are applying pulsed DC, or, in other words, some sort of a block wave. Now, the "flat" parts of the current indeed do not cause a resonance. However, the leading and falling edges, in other words, the "switching on and off" of the current do.
I will attempt to explain this to you. Imagine you draw a a block wave on a piece of paper, and draw a "normal" wave. If you want to do this really nicely, you should draw a sine [1] wave, but any normal, wavy shape will illustrate the principle. It is easiest if you draw both waves on the same axis, with the same period. With this, I mean that the zeros of both waves line up, and that the block wave is positive when the sine wave is, and that it is negative when the sine wave is. You can see that the block wave and the sine wave both are, well, waves in a sense, and as such, are in a way AC signals.
But there is more. If you look more closely, you can see that the sine and the block wave are not the same. The block wave "switches on" immediately, whereas the sine wave changes lazily. If you were to draw the difference, you would see "humps" before and after the zero points. Now, the funny thing is, depending on how you drew it, more humps in the difference between the wave, than in the original wave. If you drew them such that the heights are the same, there are four humps for every two humps of the block or sine wave, whereas if you gave both waves the same area, there are six. What this basically means is that the DC block wave consists of two AC waves: one with the same frequency, and one with a higher frequency.
Now, if you look in even more detail, subtracting a higher frequency sine wave from the difference produces even more smaller humps. In fact, you can keep doing this as long as you want, finding components with an ever higher frequency. Mathematicians call this Fourier Analysis. You can find a graphical example in [2].
Okay, so your DC block wave consists of many different AC signals. Why is this handy for finding resonance? Well, imagine that you don't know your resonance frequency precisely. If you use AC, you might not hit it. If you use a DC block wave, you have such a wealth of different AC frequencies, one is bound to hit the resonance frequency.
I dug a little bit deeper and found [3], which is a site on using a DC charger for a Tesla coil. Essentially, it uses pulsed DC. While the details are quite a bit more complicated than the simple explanation I just gave about the basic theory, the key here again is the pulsing, which in his case is done by a spark gap. The same goes for using a capacitor bank, which has the advantage that it could supply a higher power.
Thanks again for your interesting question. Analysis of circuits such as Tesla coils is in principle quite doable, although it requires some somewhat advanced (undergrad university level) mathematical tools. Good luck with you project, and please, keep it safe!
Regards,
Bart Broks
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