# Capacitors

## Definition of Capacitance.

The capacitance of an object is defined as being equal to the charge required to raise the potential of that object by one Volt.

C = Q/V

where,

C is the capacitance in Farads,

Q is the charge in Coulombs,

V is the potential in Volts.

## Capacitance Of A Parallel Plate Capacitor.

The capacitance of a parallel plate capacitor with plates of area A and separation between the plates d is given by:

MathML formulaFormula ImageStraight text formula
$C = K e ε 0 A d$ C = Keε0 A / d

Where:

C = capacitance, Farads

Ke = Dielectric coefficient, no units (dimensionless)

ε0 = Permittivity of free space, Coulombs2/Newton-meter2

A = Surface area of each capacitor plate, meters squared

d = Separation of capacitor plates, meters

## Capacitance of an Isolated Spherical Conductor.

A conducting sphere which is at an infinite distance from any other conductor has capacitance. It is, however, impossible to place a conducting sphere at an infinite distance from other conductors. In practice, the following equation applies when a spherical conductor is placed far away from other conductors:

MathML formulaFormula ImageStraight text formula
$C = 4 π ε a$ C = 4πεa

Where:

C = capacitance, Farads

ε0 = Permittivity of surrounding medium, Farads per meter

a = radius of sphere, meters

It is also intersting to note that the earth itself may be thought of as an isolated sphere. Calculation reveals that it has a capacitance of 700µF.

## Capacitors in Series.

The reciprocal of the total capacitance CT of several capacitors C1, C2, C3, ..., Cn connected in series is given by the sum of the reciprocal of each capacitance.

1/CT = (1/C1) + (1/C2) + (1/C3) + ... + (1/Cn)

## Capacitors in Parallel.

The total capacitance of capacitors in parallel, CT, is simply the sum of the individual capacitances C1, C2, C3, ..., Cn.

CT = C1 + C2 + C3 + ... + Cn

## Types of Capacitor.

### Mica Capacitors

Mica is a naturally occuring mineral made up of complex aluminium-potassium silicates that have a monoclinic structure - i.e. the mineral splits easily into plates. Mica capacitors are general purpose capacitors that are highly stable and have low dissipation. They are not produced in high capacitance values, however, as the Mica is rather costly.

### Polycarbonate Capacitors

Polycarbonate capacitors are frequently manufactured in a miniature laminate fashion for PCB mounting. They typically have a tolerance of 5% or 10%, and a temperature coefficient of 65ppm deg. C ^-1. They are often self healing i.e. an overvoltage will cause a discharge between the plates that will evaporate the metal so leaving them intact. In fact they can be manufactured so that an overvoltage is deliberately applied during manufacture to guarantee a design voltage.

### Polystyrene Capacitors

Polystyrene capacitors have very low losses (i.e. very high insulation resistance) and are therefore suitable for charge storage and filter applications. They are suitable for high frequencies, and can be manufactured to very close tolerances, typically +\- 1%. A typical temperature coefficient is -160 +\- 80ppm deg C^-1. They are suitable for timing applications or radio frequency circuits. One lead is often marked with a band to indicate that it is connected internally to a shield (for R.F. purposes):

### Ceramic Capacitors

Ceramic capacitors are general purpose capacitors frequently used in decoupling applications. They have tolerances of typically +80% \ -20%. They usually have metallised conducting plates and are encased in a type of cement. Modern PCB mounting ceramics have a coloured band on top which indicates the following:

Capacitor ValueTemperature CoefficientColoured Band
1.8pF to 18pF zero Black
22pF to 150pF -150ppm deg. C ^-1 Orange
180pF to 330pF -750ppm deg. C ^-1 Violet
390pF to 4700pFmedium permittivity Yellow
10nF to 22nF high permittivity Green

Ceramic Capacitors are available in three main types:

#### High Permittivity Ceramic Capacitors

These ceramic capacitors have a permittivity of around 1200, and so are compact. Their value , however, is quite sensitive to temperature.

#### Medium Permittivity Ceramic Capacitors

These ceramics have a negative temperature coefficient and so are used with other capacitors to correct sensitivity to temperature.

#### Low Permittivity Ceramic Capacitors

Low permittivity ceramic capacitors have a good frequency response but a low working voltage.

### Paper Capacitors

Paper capacitors were once used routinely but have been largely superseded by capacitors employing plastic dielectrics. The paper capacitor was cheap and had a reasonable capacitance to size ratio. It consisted of a paper dielectric impregnated with wax or oil, and conductors which were either thin aluminium foils or sputtered-on metallised aluminum. The capacitor was enclosed in a plastic case, or in older types a wax coating. Typical tolerances were of the order +/- 20%.

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