# Re: Coil dimensions

Original poster: Mddeming@xxxxxxx In a message dated 5/27/06 3:12:37 P.M. Eastern Daylight Time, tesla@xxxxxxxxxx writes:
```Original poster: "Andrew Bonnell" <andrewbonnell@xxxxxxxxx>

What determines the coil dimensions for the primary and secondary
coils (ex. secondary height, number of coils on primary and
secondary, shape of primary, diameter of primary and secondary,
etc.)?  What equations are used?  Thanks.

Andrew

Hi Andrew,

```
There are several different factors that come into play in TC design. Every TC is a balancing act between conflicting parameters. For example, short, fat secondary coils have a higher X/R ratio but are more likely to arc to ground or to the primary and the inter-turn voltage difference can really cause insulation punctures. On the other hand, a very tall skinny coil is mechanically unstable, has higher resistance and poorer coupling as well as much lower operating frequency and (IMO) look rather tacky. Resonance requires that L(pri) X C(pri) = L(sec) X C(sec) and that frequency is given by:
```
f = sqrt[1/LC - (R/2L)^2] / 2pi

If the resistance is very small compared to the impedance this simplifies to

f = 1/[2pisqrt(LC)]

The maximum voltage gain is given by V(sec) ~ V(pri)*sqrt(L(sec)/L(pri)

```
This would seem to imply that L(pri) should be as small as possible and L(sec) as large as possible. However, the smaller the L(pri) the greater the peak primary current and the larger the C(pri) must be fpr a fixed frequency (f). The secondary coil has a certain amount of internal capacitance between the turns which limits the resonant frequency. The more turns, the larger this C value will be. It is the energy stored in the topload that produces the discharges, so you want the C(top) to be the larger part of total C(sec).
```So what we want is :

```
A secondary coil with lots of turns (high L) but not too many (low C, low R) and tall enough to allow long streamers, but not too tall due to mechanical instability and poor coupling.
```A primary with a small L, but not too small (low surge)
```
A topload thsat is large enough to store a good portion of the energy, but not too large lest the frequency be too low and the primary cap need to be too large.
```
The simplest "close enough" formula for inductance of a secondary coil is

L = (rN)^2 / (9r-10h)     where

L is in microhenries
N is number of turns
r is radius of coil (inches)
h is height of winding (inches)

For a flat spiral primary,:

L=(rN)^2 / (8r+11B)
L is in microhenries
N is number of turns
r is AVERAGE radius of coil (inches) = r(inner) r(outer) / 2
B is width of coil (inches) = r(outer)-r(inner)

```
A good balance for a beginning secondary coil is to plan on a h/d ratio between 4:1 and 7:1 with about 1200-1800 turns of wire. Consulting a wire table will give you the wire thickness,(t) so
```N = 0.95h/t  The 95% is because no one winds a perfectly tight coil.

The wire length will be 2pi rN in inches.
```
Plan on your primary coil having twice the needed inductance for the unloaded frequency, so that when a topload is added, you will still be able to tune.
```
```
These formulas will get you in the ballpark. The programs listed in the archives can calculate L, C, f, etc.down to the "nose hair of a gnat" using much more sophisticated formulas, but then you lose all the learning that comes with using stone axes, flint knives, and simple arithmetic.
```
```
Many people start with a specific transformer and use Terry's tables to find a suitable capacitance. Then they figure the secondary size and back-calculate into the required L(pri).
```
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A good beginning toroid has minor diameter = coil diameter and major diameter = 3 or 4 times coil diameter. Again, check archives for toroid capacitance calculations. etc.
```
Hope this is some help,

Matt D.

```