Data and Formulae

One of the greatest things about amateur radio is the ability to build your own things. Whether it be radios, test equipment or antennas, a basic understaning of electronics will be very useful. Therefore, it is always useful to have some of the necessary formulae and laws related to the subject to hand. Below is a handy reference for when the formula you require just escapes you..

Capacitance

The capacitiance of a parallel plate capacitor is: C = 0.224KA/d picofarads Where K is the dielectric constant (for example, the constant of air is 1), A is the area of dielectric (sq in)and d is the thickness of the dielectric (in).

If, however, you wish to express A in centimetres squared and d in cm then the formula becomes: C = 0.0885 KA/d picofarads.

Capacitors in series:

To find the value of a number of capacitors in series, the formula is: 1/C = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn

Capacitors in parallel:

To find the value of a number of capacitors in parallel, the formula is: C = C1 + C2 + C3 + ... + Cn

The Decibel:

The decibel is a logarithmic unit, commonly used to express the relationship between two power levels, voltages or currents. It is commonly used to express the gain of an antenna. It is one tenth of a bel (B) and is written dB. The number of decibels is used to represent the difference between two power levels - P1 and P2 - and is 10 times the common logarithm of the power ratio. Thus the expression is: N = 10log^10 P2/P1 decibels

Frequency, wavelength, velocity:

The velocity of propagation of a radio wave is: V = fλ centimetres per second Where f is the frequency in hertz and λ is the wavelength in cm. In free space the velocity of propogation is approximately
3*10^8 m/s.
If f is in kilohertz and λ in metres,
f = 300,000/λ kilohertz
λ = 300,000/f metres

Ohm's Law:

Ohm's Law is a fundamental principle in electronics that describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. It states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. The formula for Ohm's Law is: V = IR, I = V/R and R = V/I Where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms.

Power:

Power (P) in an electrical circuit is the rate at which energy is transferred or converted. It is calculated using the formula: P = VI Where P is the power in watts, V is the voltage in volts, and I is the current in amperes. Power can also be calculated using Ohm's Law as: P = I^2R or P = V^2/R depending on the known variables.

Resistors in series:

To find the value of a number of resistors in series, the formula is: R = R1 + R2 + R3 + ... + Rn

Resistors in parallel:

To find the value of a number of resistors in parallel, the formula is: 1/R = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn