# Calculating Tesla coil Primary

I am working on a tesla coil, but I did not use any equations until now, and I am trying to get it to work without redoing the whole thing.

All of my formulas are from the teslacoildesign.com site.

The secondary coil is what we do not want to re-do. This took hours and hours of winding. Here are the values that we calculated. We used fishing line with 24awg wire to space out the coil:

Secondary Coil

Height= 46.5 inches

Diameter = 12 inches

Wire = 24 AWG = .0201 inch Dia.

Fishing line (for spacing) diameter = .56mm =.02204 inch

$$Turns = \frac{1}{(Fishing\,line\,Diameter + Wire\,Diameter + .000001)} \times 46.5 \times .97$$

$$=\frac{1}{.0201+.02204+.000001}\times 46.5 \times .97 = 1070.335 \,turns$$

That is very close to our estimate of 1062.9 turns by measuring a small portion of the coil, and multiplying. Will use average.

Secondary Turns = 1066.6

Secondary Capacitance (pF) =

$$= 0.29 \times Winding\,Height + 0.41 \times \frac{Secondary\,Form\,diameter}{2} +$$ $$+ 1.94 \times \frac{\sqrt{\bigg(\dfrac{Secondary\,Form\,Diameter}{2}\bigg)^3}} {Secondary\,Wire\,Winding\,Height}$$

$$= 0.29 \times 46.5 + 0.41 \times \frac{12}{2} + 1.94 \times \sqrt{\Big(\frac{12}{2}\Big)^3}/46.5 = 20.126pF$$

Secondary Coil Capacitance = 20.126 picoFarads

Secondary Height to Width Ratio = 46.5:12 = 3.875:1

$$Secondary\,Coil\,wire\,length =$$ $$= \frac{secondary\,coil\,turns \times secondary\,form\,diameter \times \pi}{12}$$

$$=\frac{ 1066.6 \times 12 \pi}{12} = 3350.82\, feet$$

Secondary Coil wire length = 3350.82 feet

All Above Looks good, but here is where I start running into problems

$$Secondary\,wire\,weight\,(lb) =$$ $$= \pi \times \Big(\frac{Secondary\,bare\,wire\,diameter}{2}\Big)^2 \times Secondary\,coil\,wire\,length \times 3.86$$

So, I enter the values $\pi \big(\dfrac{0.0201}{2}\big)^2 \times 46.5 \times 3.866$

And I get .05704 Pounds, which is obviously not the weight of my wire.

Then, I get very confused here, where they state:

Secondary Inductance = ((((Secondary Coil Turns 2) × ((Secondary Form Diameter ∕ 2) 2)) ∕ ((9 × (Secondary Form Diameter ∕ 2)) + (10 × Secondary Wire Winding Height))))

What Value is the inductance? when I calculated it with my values, I got 78822.3815

" Secondary Coil Inductance " = 78822.3815

After this, I am confused with all of the values, because they do not state the units.

For starters, I have a 6 inch ring diameter by 19 inch overall diameter Toroid for the top load.

Here is an image of my current setup. I have a primary coil already setup, but I am assuming it is not correct.

I have a primary capacitor of 10-15 NanoFarads, calculated for a good Larger Than Resonant cap. I am designing it for a 30ma 15k NST although all I have is Microwave transformers, I plan to get an NST.

So, how can I figure out how to design the primary for resonance, and am I on the right track?

And no, we do not want to rewind the whole coil!, so if anything to change, it will be everything but the secondary

• One small thing, in your calculation for weight, where at the end you multiplied by 46.5 x 3.86, that should be 3350.82 x 3.86 (you used the Secondary height instead of the Secondary coil wire length). – tcrosley May 16 '14 at 0:55
• I was editing your question to improve formatting of the equations but had to stop because the last equation doesn't look right. There seems to be a few math operators missing at (Secondary Coil Turns 2) and ∕ 2) 2)). If you can fix that, I'll finish formatting them. Also, please take a look at the other equations I formatted and check if they are correct. They are a bit complex to format, so I may have added errors. Thanks! – Ricardo May 16 '14 at 12:41

of course you don't want to to remake the secundary coil.

I've made a tesla coil my self three actually before one worked.

What you need is "THE SPREADSHEET"

you can download that file at the bottom of this site: http://home.wtal.de/herbs_teslapage/design.html

then fill everything in what you know and what you have and then just play around with some values of the things you want to change to make it all come out accordingly to your secondary.

Then you can proceed to the most important step where "the magic comes".

## Tuning:

-you've to get the primary's oscillation frequency the same as the secondary's resonance frequency -you can achieve this by searching for an ideal point on your primary For this you'l need an oscilloscope and a waveform-generator more information about tuning here: http://www.hvtesla.com/tuning.html

good luck with building your coil!

• I got the fancy equipment out (scope, Freq. Gen & Counter ), and measured the resonant frequency of 88Khz for the sec. and we just bought a hundred feet of copper tubing for the primary so we can get it to resonate at the same frequency. Does it sound good so far? – skyler Jun 24 '14 at 13:38
• If you fill in the capacitor value and a little specs of your primary then you can adjust the values and you'll see at which frequency the primary will resonate I made the primary a little to large so I had some tolerance to adjust the tap point with the function generator and the scope – Bruce Jun 25 '14 at 9:50