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Basic equations for tesla coil buildersThéorie pour débutants en bobines de Tesla |
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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.
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 !
-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
Capacitance of a sphere of radius r in free spacer(m) C(F) = ------- or C(pF) = 1.111 x r(cm) 9 9 x 10Example r being the radius of the sphere in cm if r = 10 cm , then C = 11.11 pFCapacitance of a plane or layered capacitor S C(pF) = 0.0885 x K --- dK : dielectric constant S : surface of one of the facing plates in cm² d : distance between plates in cmFor multilayers capacitors, multiply by the number of pairs of facing layers.
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
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
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
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)
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
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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