6. Capacitors and Capacitance

Real capacitors

Capacitors are the electronic components that provide the capacitance required in electrical and electronic circuits.

Capacitors come in a wide variety of forms, each with its own properties. The physical capacitors may be either surface mount or the traditional leaded varieties as well as having different form factors and electrical performance properties.

Note on the Types of Capacitor:

There are many different types of capacitor that are available. Although capacitance is a universal measure, different capacitors have different characteristics in terms of elements like maximum current capability, frequency response, size, voltage, stability, tolerance and the like. To accommodate these parameters some capacitor types are better than others in some applications,

Read more about Capacitor Types.

Selection of leaded & SMD types of capacitor.

Selecting the right capacitor is not only a matter of choosing the right level of capacitance, but also many other aspects including the dielectric, size, levels of equivalent series resistance and many more items.

In view of all these requirements, there is a very wide selection of these electronic components available for use in electrical and electronic circuit designs, etc.

Capacitance is one of the main parameters associated with electrical and electronic science. Capacitance equations and calculations are used everyday in electronic circuit design and many other areas, and capacitance is not a measure that is only associated with capacitors, there can be levels of capacitance in many other electronic components including resistors, inductors, wires, printed circuit boards and many other items.

6. Capacitors and Capacitance

Application of alternating waveform to a capacitor

So far the case when a battery has been connected to charge the capacitor and disconnected and a resistor applied to charge it up have been considered. If an alternating waveform, which by its nature is continually changing is applied to the capacitor, then it will be in a continual state of charging and discharging.

For this to happen a current must be flowing in the circuit. In this way a capacitor will allow an alternating current to flow, but it will block a direct current. As such capacitors are used for coupling an AC signal between two circuits which are at different steady state potentials.

Current and voltage waveforms for a perfect capacitor - note the current leads the voltage waveform by 90°.
Current and voltage waveforms for a perfect capacitor
Note: the current leads the voltage waveform by 90°.

It is found that when the sine-wave is first applied first applied, the rate of change of the voltage is at its greatest and this means that the charge is increasing at its fastest rate and hence the current flowing into the capacitor will be at its greatest. In other words the current is at its maximum.

As the voltage on the capacitor increases, the rate of change of voltage decreases and as a result the increase in charge and hence the current falls. Eventually the peak of the voltage sine-eave is reached where there is no change in voltage and accordingly the current at this point is zero.

After the voltage peak, the voltage starts to decreases, and accordingly the level of charge falls and this means that current flows out of the capacitor from this point.

The remainder of the waveform follows in a similar fashion. As a result it can be seen that the voltage and current are not in phase with each other. The current lags the voltage by a quarter of a cycle, i.e. 90°.

It is possible to express the current and voltage relationship for a perfect capacitor as:

Vt = sin(ωt)

It = sin(ωt+90)

6. Capacitors and Capacitance

Capacitor charging and discharging

It is also possible to look at the voltage across the capacitor as well as looking at the charge. After all it is easier to measure the voltage on it using a simple meter. When the capacitor is discharged there is no voltage across it. Similarly, one it is fully charged no current is flowing from the voltage source and therefore it has the same voltage across it as the source.

In an ideal circuit with no stray resistance or inductance, when a voltage is applied to a capacitor, it would instantly charge up and the voltage across it would be the same as that of the source of the electric potential.

In reality there will always be some resistance in the circuit, and therefore the capacitor will be connected to the voltage source through a resistor. This means that it will take a finite time for the capacitor to charge up, and the rise in voltage does not take place instantly.

It is found that the rate at which the voltage rises is much faster at first than after it has been charging for some while. Eventually it reaches a point when it is virtually fully charged and almost no current flows.

In theory the capacitor never becomes fully charged as the curve is asymptotic. However in reality it reaches a point where it can be considered to be fully charged or discharged and no current flows.

Voltage of capacitor as it charges and discharges.
Voltage of capacitor as it charges and discharges

Similarly the capacitor will always discharge through a resistance. As the charge on the capacitor falls, so the voltage across the plates is reduced. This means that the current will be reduced, and in turn the rate at which the charge is reduced falls.

This means that the voltage across the capacitor falls in an exponential fashion, gradually approaching zero.

The rate at which the voltage rises or decays is dependent upon the resistance in the circuit. The greater the resistance the smaller the amount of charge which is transferred and the longer it takes for the capacitor to charge or discharge.

6. Capacitors and Capacitance

Electric fields and dielectrics

As there is a potential across the plates of a capacitor, there is an associate electric field present. With parallel plates, the electric field lines are generally parallel to each other and at right angles to the plates.

Capacitor plates showing electricfield lines between them. The field lines are parallel to each other and at right angles to the plates, but bulge out a little at the edge.
Capacitor plates showing electric field lines

Capacitors require some form of insulator between the two plates, otherwise the charge could not remain on the plates, it would dissipate through the medium between the two plates.

Whilst air is a good insulator, often the capacitor plates need to be kept apart by some form of rigid insulator.

 Diagrammatic view of a capacitor showing the parallel plates with the dielectric insulator between them
Simplified view of construction of capacitor showing the plates and insulating dielectric

The material between the two plates is called the dielectric. This not only acts as an insulator, but it also determines many of the other properties. A measure known as the dielectric constant affects the level of capacitance achievable for a given capacitor plate size and spacing.

High levels of relative permittivity / dielectric constant can increase the capacitance many times.

The topic of relative permittivity and dielectric constant, etc, is a topic in its own right, and although easy to comprehend, possibly needs to be looked at separately.

6. Capacitors and Capacitance

Units or capacitance

It is necessary to be able to define the “size” of a capacitor. The capacitance of a capacitor is a measure of its ability to store charge, and the basic unit of capacitance is the Farad, named after Michael Faraday.

It is worth defining the Farad which is the basic unit of capacitance.

Capacitance: Farad definition:

A capacitor has a capacitance of one Farad when a potential difference of one volt will charge it with one coulomb of electricity (i.e. one Amp for one second).

A capacitor with a capacitance of one Farad is too large for most electronics applications, and components with much smaller values of capacitance are normally used. Three prefixes (multipliers) are used, µ (micro), n (nano) and p (pico):

µ10-6 (millionth)1000000µF = 1F
n10-9 (thousand-millionth)1000nF = 1µF
p10-12 (million-millionth)1000pF = 1nF
6. Capacitors and Capacitance

What is capacitance

When looking at capacitance, it is first necessary to look at exactly what it is. Capacitance is effectively the ability to store charge. In its simplest form a capacitor consists of two parallel plates. It is found that when a battery or any other voltage source is connected to the two plates as shown a current flows for a short time and one plate receives an excess of electrons, while the other has too few.

In this way one plate, the one with the excess of electrons becomes negatively charge, while the other becomes positively charged.

Charge stored between two plates on a capacitor
Charge stored on two plates of a capacitor

If the battery is removed the capacitor will retain its charge. However if a resistor is placed across the plates, a current will flow until the capacitor becomes discharged.

Accordingly it is possible to define what capacitance is:

Capacitance definition:

Capacitance is the ability of a component or circuit to collect and store energy in the form of an electrical charge. It is the amount of electric charge stored on a conductor for a stated difference in electric potential.

The larger the plates, the more charge can be stored, and also the closer they are together, the more charge they store. The charge storage is also dependent upon the material between the two plates as well.

6. Capacitors and Capacitance

Introduction to Capacitors Summary

We have seen in this tutorial that the job of a capacitor is to store electrical charge onto its plates. The amount of electrical charge that a capacitor can store on its plates is known as its Capacitance value and depends upon three main factors.

  • Surface Area – the surface area, A of the two conductive plates which make up the capacitor, the larger the area the greater the capacitance.
  • Distance – the distance, d between the two plates, the smaller the distance the greater the capacitance.
  • Dielectric Material – the type of material which separates the two plates called the “dielectric”, the higher the permittivity of the dielectric the greater the capacitance.

We have also seen that a capacitor consists of metal plates that do not touch each other but are separated by a material called a dielectric. The dielectric of a capacitor can be air, or even a vacuum but is generally a non-conducting insulating material, such as waxed paper, glass, mica different types of plastics etc. The dielectric provides the following advantages:

  • The dielectric constant is the property of the dielectric material and varies from one material to another increasing the capacitance by a factor of k.
  • The dielectric provides mechanical support between the two plates allowing the plates to be closer together without touching.
  • Permittivity of the dielectric increases the capacitance.
  • The dielectric increases the maximum operating voltage compared to air.

Capacitors can be used in many different applications and circuits such as blocking DC current while passing audio signals, pulses, or alternating current, or other time varying wave forms. This ability to block DC currents enables capacitors to be used to smooth the output voltages of power supplies, to remove unwanted spikes from signals that would otherwise tend to cause damage or false triggering of semiconductors or digital components.

Capacitors can also be used to adjust the frequency response of an audio circuit, or to couple together separate amplifier stages that must be protected from the transmission of DC current.

When used on DC supplies a capacitor has infinite impedance (open-circuit), at very high frequencies a capacitor has zero impedance (short-circuit). All capacitors have a maximum working DC voltage rating, (WVDC) so it is advisable to select a capacitor with a voltage rating at least 50% more than the supply voltage.

There are a large variety of capacitor styles and types, each one having its own particular advantage, disadvantage and characteristics. To include all types would make this tutorial section very large so in the next tutorial about The Introduction to Capacitors I shall limit them to the most commonly used types.

6. Capacitors and Capacitance

Voltage Rating of a Capacitor

All capacitors have a maximum voltage rating and when selecting a capacitor consideration must be given to the amount of voltage to be applied across the capacitor. The maximum amount of voltage that can be applied to the capacitor without damage to its dielectric material is generally given in the data sheets as: WV, (working voltage) or as WV DC, (DC working voltage).

If the voltage applied across the capacitor becomes too great, the dielectric will break down (known as electrical breakdown) and arcing will occur between the capacitor plates resulting in a short-circuit. The working voltage of the capacitor depends on the type of dielectric material being used and its thickness.

The DC working voltage of a capacitor is just that, the maximum DC voltage and NOT the maximum AC voltage as a capacitor with a DC voltage rating of 100 volts DC cannot be safely subjected to an alternating voltage of 100 volts. Since an alternating voltage that has an RMS value of 100 volts will have a peak value of over 141 volts! (√2 x 100).

Then a capacitor which is required to operate at 100 volts AC should have a working voltage of at least 200 volts. In practice, a capacitor should be selected so that its working voltage either DC or AC should be at least 50 percent greater than the highest effective voltage to be applied to it.

Another factor which affects the operation of a capacitor is Dielectric Leakage. Dielectric leakage occurs in a capacitor as the result of an unwanted leakage current which flows through the dielectric material.

Generally, it is assumed that the resistance of the dielectric is extremely high and a good insulator blocking the flow of DC current through the capacitor (as in a perfect capacitor) from one plate to the other.

However, if the dielectric material becomes damaged due excessive voltage or over temperature, the leakage current through the dielectric will become extremely high resulting in a rapid loss of charge on the plates and an overheating of the capacitor eventually resulting in premature failure of the capacitor. Then never use a capacitor in a circuit with higher voltages than the capacitor is rated for otherwise it may become hot and explode.

6. Capacitors and Capacitance

Multi-plate Capacitor

capacitor construction

Now we have five plates connected to one lead (A) and four plates to the other lead (B). Then BOTH sides of the four plates connected to lead B are in contact with the dielectric, whereas only one side of each of the outer plates connected to A is in contact with the dielectric. Then as above, the useful surface area of each set of plates is only eight and its capacitance is therefore given as:

eight plate capacitor

Modern capacitors can be classified according to the characteristics and properties of their insulating dielectric:

  • Low Loss, High Stability such as Mica, Low-K Ceramic, Polystyrene.
  • Medium Loss, Medium Stability such as Paper, Plastic Film, High-K Ceramic.
  • Polarized Capacitors such as Electrolytic’s, Tantalum’s.
6. Capacitors and Capacitance

The Dielectric of a Capacitor

As well as the overall size of the conductive plates and their distance or spacing apart from each other, another factor which affects the overall capacitance of the device is the type of dielectric material being used. In other words the “Permittivity” (ε) of the dielectric.

The conductive plates of a capacitor are generally made of a metal foil or a metal film allowing for the flow of electrons and charge, but the dielectric material used is always an insulator. The various insulating materials used as the dielectric in a capacitor differ in their ability to block or pass an electrical charge.

This dielectric material can be made from a number of insulating materials or combinations of these materials with the most common types used being: air, paper, polyester, polypropylene, Mylar, ceramic, glass, oil, or a variety of other materials.

The factor by which the dielectric material, or insulator, increases the capacitance of the capacitor compared to air is known as the Dielectric Constantk and a dielectric material with a high dielectric constant is a better insulator than a dielectric material with a lower dielectric constant. Dielectric constant is a dimensionless quantity since it is relative to free space.

The actual permittivity or “complex permittivity” of the dielectric material between the plates is then the product of the permittivity of free space (εo) and the relative permittivity (εr) of the material being used as the dielectric and is given as:

Complex Permittivity

capacitor permittivity

In other words, if we take the permittivity of free space, εo as our base level and make it equal to one, when the vacuum of free space is replaced by some other type of insulating material, their permittivity of its dielectric is referenced to the base dielectric of free space giving a multiplication factor known as “relative permittivity”, εr. So the value of the complex permittivity, ε will always be equal to the relative permittivity times one.

Typical units of dielectric permittivity, ε or dielectric constant for common materials are: Pure Vacuum = 1.0000, Air = 1.0006, Paper = 2.5 to 3.5, Glass = 3 to 10, Mica = 5 to 7, Wood = 3 to 8 and Metal Oxide Powders = 6 to 20 etc. This then gives us a final equation for the capacitance of a capacitor as:

capacitance of a capacitor

One method used to increase the overall capacitance of a capacitor while keeping its size small is to “interleave” more plates together within a single capacitor body. Instead of just one set of parallel plates, a capacitor can have many individual plates connected together thereby increasing the surface area, A of the plates.

For a standard parallel plate capacitor as shown above, the capacitor has two plates, labelled A and B. Therefore as the number of capacitor plates is two, we can say that n = 2, where “n” represents the number of plates.

Then our equation above for a single parallel plate capacitor should really be:

actual capacitance of a capacitor

However, the capacitor may have two parallel plates but only one side of each plate is in contact with the dielectric in the middle as the other side of each plate forms the outside of the capacitor. If we take the two halves of the plates and join them together we effectively only have “one” whole plate in contact with the dielectric.

As for a single parallel plate capacitor, n – 1 = 2 – 1 which equals 1 as C = (εor x 1 x A)/d is exactly the same as saying: C = (εor*A)/d which is the standard equation above.

Now suppose we have a capacitor made up of 9 interleaved plates, then n = 9 as shown.