Special thanks for all the formulas provided by Bob Schumann

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Formula Collection

FORMULA NAME: Single Layer Coil Formula
FORMULA USAGE: To calculate inductance in single layer coils.
APPLICATION: Use to ballpark Tesla coil secondary inductance.
FORMULA DEFINTIONS
L is the inductance in microhenrys. N is the number of turns.
A is the mean radius in inches. B is the length of the coil in inches.
(N * A)^2
L = --------------------------
(9 * A) + (10 * B)
SQR(L * ((9 * A) + (10 * B)))
N = -----------------------------------------------
A
9L + SQR(81 * L^2 + 40 * B * N^2* L)
A = ------------------------------------------------------
2 * (N^2)
(((N * A)^2) / L) - (9 * A)
B = -----------------------------------------------
10
EXAMPLE APPLICATION
Secondary diameter is 4 inches. (Let's call this SD)
Length of coil windings is 15 inches.
Wire diameter is .03 inches.(Let's call this WD)
Turns per inch = 1 / wd = 33.3333 (Let's call this TPI)
With this prior information we can now determine N, A, and B.

B = 15
N = B * TPI = 15 * 33.33333 = 500
A = (SD + WD) / 2 = (4 + .03) / 2 = 2.015

Now plugging into to the above formula to solve for L

(500 * 2.015)^2
L = ----------------------------------
(9 * 2.015) + (10 * 15)

1015056.25
L = ----------------------------------
168.135

L = 6037.150207 microhenrys (Multiply by 10^-6 for henrys)
L = .0063715 henrys



FORMULA NAME: Resonance Formula
FORMULA USAGE: To find resonant frequency
APPLICATION: Guess!
FORMULA DEFINITIONS
RF is the resonant frequency in hertz. L is the inductance in henrys.
C is the capacitance in farads. pi = 3.141592654
1
RF = ------------------------------------
2 * pi * SQR(L * C)
L = (1 / (2 * pi * RF * SQR(C)) ^ 2) C = (1 / (2 * pi * RF * SQR(L)) ^ 2)
EXAMPLE APPLICATION
Let's use the inductance calculated from single layer example.
L = .0063715 henrys
Lets say that the seondary and torroid capacitance = 10pf
C = .00000000001

Now plugging into to the above formula to solve for RF

1
RF = ----------------------------------------------------------------------------------
2 * 3.141592654 * SQR(.0063715 * .00000000001)

RF = 630520.6113 hertz


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