10.1 Formulas

Ohm's law

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E = I * R

I = E / R

R = E / I

E = voltage (volts)

I = current (amperes)

R = resistance (ohms)

Finding a transformer's impedance

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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

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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 substitute your cycle rate.

Watt's law

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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

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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

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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

C = capacitance in farads (divide by 1,000,000 to convert microfarads to Farads)

Frequecy of LC circuit

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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)

C = capacitance in farads (divide by 1,000,000 to convert microfarads to farads)

Q (quality) of an inductor

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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

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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

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where:

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:

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

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E=0.5*C*V*V

E= energy in joules (watt-seconds)

C= capacitqnce in farads

V= voltage

1uf= .000001 farad