10.1 Formulas

Ohm's law
-------------------------

E = I * R
I = E / R
R = E / I

E = voltage (volts)
I = current (amperes)
R = resistance (ohms)

Finding a transformer's impedance
-------------------------

This formula is useful for finding the input transformer's impedance so a capacitor can be matched with it.

Z = E / I
Z = impedance in ohms
E = secondary voltage output
I = secondary current ouput in amps (divide milliamps by 1000 to get amps)

Matching capacitor size to transformer
--------------------------

1
C =   -------------------
2 x pi x Z x .00006

C = capacitance in microfarads needed for primary capacitor.
Z = Transformer Impedence
pi = 3.141592654
Note: The .00006 is the 60 Hz AC, if you live outside the US then

Watt's law
-------------------------
This formula is useful to find a transformer's power output based on it's output voltage and current or to find other values such as current or voltage output based on it's power rating.

P = E * I
E = P / I
I = P / E

P = power in watts or volt-amperes (VA)
E = voltage in volts
I = current in amps

Inductive reactance
-------------------------
This formula finds the reactance (AC impedance) of a given inductor at a given frequency.

X(l) = 2 * pi * f * L

X(l) = AC impedance (reactance) in ohms
pi = 3.1415
f = frequency in hertz
L = inductance in henries (divide by 1,000,000 to convert microhenries t0 henries)

Capacitive reactance
-------------------------
This formula is the same as the inductive reactance formula except for one point, the value is inverted. It determines the reactance (AC impedance) of a capacitor at a given frequency.
1
X(c) = --------------
2 * pi * f * C

X(c) = AC impedance (reactance) in ohms
pi = 3.1415
f = frequency in hertz

Frequecy of LC circuit
-------------------------
This formula determines the resonant frequency of an LC tank circuit.
1
--------------
______________
f = \/2 * pi * L * C

f = frequency in hertz
pi = 3.1415
L = inductance in henries (divide by 1,000,000 to convert microhenries to henries)

Q (quality) of an inductor
-------------------------
This finds the quality (how good it is) of an inductor. It's based on it's resistance and it's reactance.

Q = X(l) / R

Q = quality (there is no unit for quality)
X(l) = inductor's reactance in ohms
R = the inductor's resistance in ohms

Wheeler's Formula for Inductance
-------------------------
L(uH) = (r^2) * (N^2) / (9*r + 10*h)

where:

r = coil RADIUS in inches
N = number of turns
h = coil height in inches

Another useful formula is Medhurst's formula for self capacitance of a coil.

Medhurst's formula: C = K x D
-------------------------
where:

K = constant which depends on the ratio of the coil height to diameter
x = means multiply K times D
D = solenoidal coil diameter in centimeters
H = coil height in centimeters

H/D       K
5.0     0.81
4.5     0.77
4.0     0.72
3.5     0.67
3.0     0.61
2.5     0.56
2.0     0.50
1.5     0.47
1.0     0.46

Now that you know the inductance and self capacitance of your secondary coil you can determine the resonant frequency by applying the resonant frequency formula:
1
f =  --------------------
__________
2 pi   / L C

f = frequency in cycles per second
L = circuit inductance in henries
C = circuit capacitance in farads
pi = 3.141592654

This is remarkably accurate for most secondary coils. You can also determine your resonant frequency after adding a toroid by adding the toroid's capacitance to the Medhurst value.

If you are just interested in computing self-resonant frequencies there is another formulad which I have found useful and generally accurate. Its not quite as accurate as the above method.

The formula is:
(1/5)
29.85 x (H/D)
F = -------------------
N x D

where:

F= self resonant frequency in Mhz of an isolated coil
H= coil height in meters
D= coil diameter in meters
N= total number of turns
Make sure the top line reads " (H/D) to the 1/5 power"

Calculating joules
-------------------------
E=0.5*C*V*V

E= energy in joules (watt-seconds)