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ForewordTesla 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 proposL'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. |
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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 |
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2.a - CAPACITANCES
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. |
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 |
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3.a - INDUCTANCESPancake 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 |
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4.a - RESONANCE OF AN LC CIRCUIT1 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 |
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File: equations.html - Robert L.E. Billon, 2000-10-18 - Last update: 2010-11-05 |