# Building a DRSSTC Pt. 3 - Primary Circuit Design

Blog entry posted in 'Building a Dual-Resonant Solid State Tesla Coil', July 26, 2014.

Hello everyone, and welcome back to my blog!

In this entry I will describe the process involved in designing a tank circuit to operate at the same resonant frequency as the secondary.

Once again I will be using JavaTC to do most of the work, though there are some things I'll need to do myself first. JavaTC is really just a way to check your math.

Let's start by deciding what capacitance will be convenient. I know this sounds a little careless and non-scientific, but I have found it to be the best first step. Since finding a suitable capacitor is so difficult, it's really best to find one and tailor the primary coil to match.

When picking out a capacitor for your DRSSTC, there are several things you need to watch out for:

1. Make sure they have a high pulse current. The tank capacitor can see several hundred amps, or more if you're running CW, so if the ones you pick out can't handle it, you might have a small bomb on your hands.
2. Make sure they are rated for a voltage MUCH higher than your bus voltage (that is, the voltage you are applying to the bridge). Some experienced DRSSTC builders have recommended choosing a capacitor voltage that is roughly 30x higher than your supplied voltage. This is because the voltage on the primary can ramp up significantly during operation.
3. The capacitors should have a very low dissipation factor. Otherwise you will lose a lot of your energy and you will get a poor output from the Tesla coil.
4. They must have a low ESR. If the capacitors have a high ESR, it will lead to excessive internal heating which will cause the cap to degrade, and possibly even explode. Likewise, their equivalent series inductance should be low.
5. The best choices are polypropylene film/foil capacitors as they work best at high frequencies and have a low dissipation factor.

The first thing I had to do before looking for capacitors was determine the voltage rating I'd need. I plan to supply 170VDC to the bridge (rectified 120VAC mains), so that means my capacitors should be rated for Vc = 170 * 30 = 5100 volts.

After searching for a while I found two 10nF 5kv capacitors on e-bay that, for the most part, fit the above criteria. Paralleling them will give me 20nF at 5kV. I know I said the capacitors should be rated for 5.1kV, and not 5kV, but since the "30x the bus voltage" was a rough generalization, I figured I'd risk the extra 100V.

So now that I have a capacitor, I can design my primary coil based on that value. To get a general value for the primary inductance required to match the resonance of the secondary, I'm going to use the same formula that I mentioned in the previous section:

$f=\frac{1}{2*\pi *\sqrt{L*C}}$

Since I know the frequency of the secondary is 218.02 kHz, and I know the capacitance of the tank capacitor, all I need to do is solve for L:

$L=\frac{1}{4*C*\pi ^{2}*f^{2}}$

Plug in 20nF for C and 218.02 kHz for f and I get about 26.65uH. Therefore, in order for the primary to resonate at the same frequency as the secondary, my primary coil will have to have an inductance of about 26.65 microhenrys.

I'm not going to worry about this value too much at this point, as it, along with the secondary coil specs, will probably change slightly throughout the remainder of the design process. JavaTC will take care of any adjustments that need to be made.

Now that we have a rough estimate of the primary circuit, we can plug it in to JavaTC and see what we get. The values for the secondary will be the same as what I plugged in earlier. However, we now have the value for the primary capacitor and a value for primary coil inductance. Notice that the primary capacitor is in uF, so I will have to enter 0.02uF instead of 20nF.

Now, the primary is a bit tricky here--instead of asking for the primary coil inductance, it asks for the dimensions. Therefore, we'll have to do a little math. Now, I plan to use insulated #12 AWG wire for my primary, which I know has a diameter of 0.0808" (Yes, I know--America should have gone Metric a LONG time ago :D ). I also know that I would like a cylindrical primary, and that I will want to minimize the height of my primary as much as possible to help prevent the topload from arcing to it. Therefore, the turns will be wound as close together as possible. Now, once again this is just a general plan and will likely change--The insulation should be enough to prevent shorting, but in case it doesn't I can spread each winding out a bit. I don't anticipate needing to do this though, so I will plan on 0" spacing between turns. I'm ignoring the thickness of the insulation.

So the question now is, how many turns should the primary be? Now, just like with a SGTC I will want to have a tap to make the coil length adjustable, but we need a rough idea of the number of turns, so that we can give it to JavaTC. Knowing that I want to allow about half an inch between the primary and the secondary (to help prevent arcing), my primary must have a diameter of 5.5", which means a radius of 2.75".

Now the fun part: Calculating the number of turns. I'll begin with the following formula:

$L=\frac{D^2*n^2}{18D+40l}$

where L is the inductance, D is the overall diameter of the primary, n is the number of turns, and l is the length of the coil. Now, we have the inductance and the diameter, but we're missing both l and n. Therefore, we need to get one in terms of the other. If we know the number of turns, the spacing between each one, and the diameter of the wire, then we know the overall length. Therefore, I'm going to re-write the formula as follows:

$L=\frac{D^2*n^2}{18D+40n(d+s)}$

where L, D, and n are the same as before, d is the diameter of the wire, and s is the spacing between each turn. Notice that we replaced l with n(d+s)--the number of turns times the wire diameter, plus the number of turns times the spacing between the turns. This isn't precise, but it should work for our purposes.

The question is then to solve for n. I won't go through the entire process, but we eventually end up with the following:

$n=\frac{\sqrt{2}\sqrt{L(200L(d+s)^2+9D^3)}+20dL+20Ls}{D^2}$

Whew! Wasn't that fun?

I think I'm going to end this entry here as it has already gone on for longer than intended. We've done a fair amount of the required math so far, so in the next entry we'll figure out the required dimensions of the primary coil, as well as the remainder of the JavaTC calculations.

I hope you've enjoyed this post, and as always, feel free to comment or PM me with questions and/or feedback!

'Til next time!