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Basic equations for tesla coil builders

Théorie pour débutants en bobines de Tesla

Last update
2010-11-05

Foreword   

Tesla coil experimenting is more efficient and rewarding if you know at any time where you are and where you go. So some calculus is not a useless thing, before or after you bild your basic components.

Some measuring instruments are also a good thing. I use a Wawetek LCR55 LCR bridge. Warning ! Before measuring any capacitor be carefull of discharging it first.

The following equations, derived from the theories of electricity and magnetism, are ready to use and will make easier your life of TC builder. If hand and pencil are not your favorite tools, a pocket calculator will do the job in a few seconds.

Avant propos   

L'expérimentation dans le domaine des bobines de Tesla est plus efficace et vous apporte plus de satisfactions si vous savez à tout moment où vous en êtes et où vous allez. Ainsi quelques calculs, avant ou après la réalisations de vos composants de base, ne sont pas chose inutile.

Un minimum de moyens de mesure est aussi une bonne chose. J'utilise un pont RLC Wawetek LCR55. Attention ! Avant toute mesure sur des condensateurs prenez bien soin de les décharger préalablement.

Les équations ci-après, dérivées et adaptées de la théorie de l'électricité et du magnétisme, sont prêtes à l'emploi et vous simplifierons le travail. Si vous n'êtes pas adepte du calcul manuel, une calculatrice de poche fera le travail en quelques secondes.

1.a - RESISTANCE OF A CONDUCTOR
                                      l
The basic formula is R(ohms) = Rho x ---
                                      S
where   Rho : resistivity in ohms/meter
        l   : length in meters
        S   : section in m²
        x   : multiply by

It may be convenient in calculus to use
units more adapted to wires.

                      8
Let       r = Rho x 10
                       -8    8
Example   r = 1.72 x 10  x 10  = 1.72
coper
                                l(m)
then      R(ohms) = 0.01 x r x ------
                               S(mm²)
                                   l(m)
and       R(milliohms) = 10 x r x ------
                                  S(mm²)

Example of my TC#1 secondary

l = 215m  S = 0.1256mm²

                    215
R = 0.01 x 1.72 x ------ = 29.442 ohms
                  0.1256

The value measured (±1%) is 29.7 ohms.
Good !
1.b - RESISTIVITY OF SOME METALS AND ALLOYS
                      -8
Coper        1.72 x 10
                      -8
Aluminium    2.82 x 10
                      -8
Silver       1.63 x 10
                      -8
brass        6.71 x 10
                     -8
Chromium     2.6 x 10
                      -8
Nickel       8.69 x 10
                      -7
Platinum     1.06 x 10
                     -8
Tungsten     5.6 x 10

1.c - AWG GAUGE METRIC EQUIVALENCE
AWG     Ø(mm)     S(mm²)
------- --------- ---------
32      0.20       0.031
30      0.25       0.06
28      0.32       0.08
26      0.404      0.128
24      0.51       0.205
22      0.64       0.326
20      0.812      0.519
18      1.02       0.79
16      1.29       1.31
15      1.5        1.76
14      1.63       2.08
12      2.05       3.31
10      2.588      5.262
 9      2.906      6.632
 8      3.268      8.387
 7      3.665     10.511 
2.a - CAPACITANCES
Capacitance of a sphere of radius r
in free space
         r(m)
C(F) = -------  or C(pF) = 1.111 x r(cm)
             9
       9 x 10
Example
r being the radius of the sphere in cm
if r = 10 cm , then  C = 11.11 pF
Capacitance of a plane
or layered capacitor
                     S
C(pF) =  0.0885 x K ---
                     d
K : dielectric constant
S : surface of one of the facing
    plates in cm²
d : distance between plates in cm
For multilayers capacitors,
multiply by the number of
pairs of facing layers.
2.b - DIELECTRIC CONSTANTS
Material        Dielectic  Puncture
                constant   voltage
                           (kV/cm)
--------------- ---------- ---------
Air             1.00576    30
Bakelite        4.4 - 5.8  120
Epoxy(PC Board) 5.2        280
Formica         4.6 - 4.9  180
Glass           4 - 10     75 - 300
Mica            5.45       600 750
Mylar           3.0 - 3.1  3000
Nylon           3.2        160
Oil (mineral)   2.1 - 2.7  30 - 80
Paper           2 - 4      80 - 100
Plexiglass      2.7        40 - 100
Polycarbonate   2.96       160
Polyethylene    2.25       400
Polystyrene     2.55       200 - 300
Porcelain       6.1        16 - 110
PTFE (Teflon)   2.1        400 - 800
PVC             2.95       290
Quartz          3.9        400
Silicone RTV    3.6        220 
3.a - INDUCTANCES

Pancake winding (flat spiral)
Typical use: TC primary

                       1
L(µH) = n² x d x --------------
                             w
                 40.8 + 112 ---
                             d

           ------------------
          /               a
         / L (40.8 + 112 ---)
        /                 d
n = \  /   ------------------
     \/            d


where      n : number of turns
           w : width of the winding
           d : average diameter
           x : multiply by

Can apply also for conical winding,
                          h
more accurate results if --- < 0.3
                          w

Solenoid
Typical use: TC secondary


               0.2 x n² x d
L(µH) =  -----------------
                          l
                  9 + 20 ---
                          d

           --------------
          /           l
         / L (9 + 20 ---)
        /             d
n = \  /   --------------
     \/       0.2 x d

where    n : number of turns
         l : length of the winding
         d : diameter of the coil form
         x : multiply by
Winding on a toroidal core

Typical use:
protection chokes for transformer

L = n² x Al

where n : number of turns
      Al: specific inductance parameter
          usualy expressed in nH/turn²
3.b - EXAMPLES OF WINDINGS
Flat spiral winding
cross sectional view

                 center axis
|     w     |    |
|<--------->|    |
|           |    |
o o o o o o o    |    o o o o o o o
      |          |          |
      |                     |
      |          d          |
      |<------------------->|

Inverted conical spiral winding
cross sectional view

                   center axis
      w            |
|<--------->|      |
|           |      |
o           |      |               o--/-
   o        |      |            o     |
      o     |      |         o        |h
      |  o  |      |      o  |        |
      |     o      |   o     |      --/-
      |                      |
      |            d         |
      |<-------------------->|

Example of my TC#1 primary 
n = 12 , d = 20cm , w = 10cm , h = 3.5cm

L (calculated) 29.75 µH
L (measured ±3%) 30.1 µH


Solenoid

   ooooooooooooooooooooooooooooooo----/-
                                      |
axis                                  |
------------------------------------  |d
                                      |
                                      |
   ooooooooooooooooooooooooooooooo----/-
   |                             |
   |               l             |
   |<--------------------------->|

Example of my TC#1 secondary-->
n = 855 , d = 8 cm , l = 38 cm

L (calculated) 11.24 mH
L (measured ±3%) 11.6 mH
Toroidal
Example: Al = 1500, you wind 40 turns
L = 40² x 1500 = 2400000 nH = 2.4 mH
4.a - RESONANCE OF AN LC CIRCUIT

         1
F = -----------------
               ------
    2 x Pi x \/ L x C

For usual values in TC experimenting,
one can use the following equation.
L expressed in µH  AND  C in nF
OR
L expressed in mH  AND  C in pF

              5032.96
F(kHz) = ----------------
           --------------
         \/ L(µH) x C(nF)
4.b -
Example

my 30 µH primary coil
paralleled with 6 nF

L = 30 µH , C = 6 nF

            5032.96
F(kHz) = -------------  = 375 kHz
           -----------
         \/ 30 x 6
Nikola Tesla Theory Measurements My first TC The Tesla Magnifier Magnifier project Links Homepage

    
File: equations.html - Robert L.E. Billon, 2000-10-18 - Last update: 2010-11-05