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

    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
          substitute your cycle rate.

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.
        X(c) = --------------
             2 * pi * f * C

X(c) = AC impedance (reactance) in ohms
pi = 3.1415
f = frequency in hertz
C = capacitance in farads (divide by 1,000,000 to convert microfarads to Farads)

Frequecy of LC circuit
This formula determines the resonant frequency of an LC tank circuit.
        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)
C = capacitance in farads (divide by 1,000,000 to convert microfarads to farads)

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)


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

C = capacitance in picofarads
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:
   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:
    29.85 x (H/D)
F = -------------------
     N x D


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= energy in joules (watt-seconds)
C= capacitqnce in farads
V= voltage
1uf= .000001 farad