Munny
posted this
09 October 2020

- Last edited 12 October 2020
We have resonance and we have turns ratio. Seems to me we need a method to our madness...

Suppose we want one coil's resonant frequency to be 1/2 or 1/4th of the other coil's. How would we do this fairly accurate?

I use the A_{L} value of the core for my reference.

http://www.encyclopedia-magnetica.com/doku.php/al_value

Take note of the L over N^{2}

Next, it would be good to know approximately what frequency we are dealing with:

https://www.omnicalculator.com/physics/resonant-frequency-LC#how-to-calculate-resonant-frequency

See that little square root of L times C?

So let's try a little example...

I have a monster ferrite C-core that has an A_{L} value of roughly 5500 nH/t^{2}. So lets wrap 100 turns on there and see what sort of inductance we get. The little online calculator above says: 55mH. Okay good. So let's parallel a 100pF capacitor just for calculation purposes; we get resonance at 67.864 kHz.

Next, calculate the other coil for 1/4 wavelength or four times the frequency of 271.456 kHz. Now take that value and the same 100pF and recalculate the inductance. You should get 3.4375 mH. So how many turns do we need for that? I get 25 turns. Imagine that, exactly 1/4 the number of turns--see why I told you to look at the squares and square roots in those formulas. The value of capacitance for this doesn't matter because it is exactly the same for both coils, but to know the real resonant frequencies the device will run at, you have to know the capacitance.

The point I want to make in all this boils down to something pretty simple. **The turns ratio is the frequency/wavelength ratio.** So now you know and can experiment with all sorts of various ratios. I haven't got that far myself to prove anything, but I suspect there is a constant where things begin to happen. It could be ½, ¼, √2, golden ratio, bifurcation ratio, or something else where magic begins and this all becomes a done deal. If someone finds the magic number, please don't keep it to yourself. Holler out, "There's gold in them there hills!"

The other thing to consider is the Q-Factor.

https://en.wikipedia.org/wiki/Q_factor

For certain keep the resistance low and use a top-notch non-polarized, low ESR capacitor that can handle some amps. For this particular device, I'm not certain if having a large capacitor and small inductor is the way to go, or the other way around. I have a hunch the inductor should be larger but do use large wire to keep the resistance low. It could all come down to how you match the impedance to the load--you may actually want reflections to get it to work properly. Also remember this if you use filament lamps: The resistance goes up as the lamp illuminates, so your Q-Factor drops. What you may want to do is wrap a small length of nichrome wire around a thermal probe and use that instead of a lamp. Unless the wire starts to glow orange, its resistance will stay fairly constant.