Introduction to Capacitors






Introduction to Capacitors
Capacitors are simple passive device that can store an electrical charge on
their plates when connected to a voltage source


In this introduction to capacitors tutorial, we will see that capacitors are
passive electronic components consisting of two or more pieces of conducting
material separated by an insulating material. The capacitor is a component
which has the ability or “capacity” to store energy in the form of an
electrical charge producing a potential difference (Static Voltage) across
its plates, much like a small rechargeable battery.

There are many different kinds of capacitors available from very small
capacitor beads used in resonance circuits to large power factor correction
capacitors, but they all do the same thing, they store charge.

In its basic form, a capacitor consists of two or more parallel conductive
(metal) plates which are not connected or touching each other, but are
electrically separated either by air or by some form of a good insulating
material. This insulating material could be waxed paper, mica, ceramic,
plastic or some form of a liquid gel as used in electrolytic capacitors.

As a good introduction to capacitors, it is worth noting that the insulating
layer between a capacitors plates is commonly called the Dielectric.






Due to this insulating layer, DC current can not flow through the capacitor
as it blocks it allowing instead a voltage to be present across the plates
in the form of an electrical charge.

The conductive metal plates of a capacitor can be either square, circular or
rectangular, or they can be of a cylindrical general shape, size and construction of a parallel plate capacitor depending on its application and voltage rating.
 

A Typical Capacitor
When used in a direct current or DC circuit, a capacitor charges up to its
supply voltage but blocks the flow of current through it because the
dielectric of a capacitor is non-conductive and basically an insulator.
However, when a capacitor is connected to an alternating current or AC
circuit, the flow of the current appears to pass straight through the
capacitor with little or no resistance.

There are two types of electrical charge, a positive charge in the form of
Protons and a negative charge in the form of Electrons. When a DC voltage is
placed across a capacitor, the positive (+ve) charge quickly accumulates on
one plate while a corresponding and opposite negative (-ve) charge
accumulates on the other plate. For every particle of +ve charge that
arrives at one plate a charge of the same sign will depart from the -ve
plate.

Then the plates remain charge neutral and a potential difference due to this
charge is established between the two plates. Once the capacitor reaches its
steady state condition an electrical current is unable to flow through the
capacitor itself and around the circuit due to the insulating properties of
the dielectric used to separate the plates.

The flow of electrons onto the plates is known as the capacitors Charging
Current which continues to flow until the voltage across both plates (and
hence the capacitor) is equal to the applied voltage Vc. At this point the
capacitor is said to be “fully charged” with electrons.

The strength or rate of this charging current is at its maximum value when
the plates are fully discharged (initial condition) and slowly reduces in
value to zero as the plates charge up to a potential difference across the
capacitors plates equal to the source voltage.

The amount of potential difference present across the capacitor depends upon
how much charge was deposited onto the plates by the work being done by the
source voltage and also by how much capacitance the capacitor has and this
is illustrated below.

	
	introduction to capacitors the symbol

The parallel plate capacitor is the simplest form of capacitor. It can be
constructed using two metal or metallised foil plates at a distance parallel
to each other, with its capacitance value in Farads, being fixed by the
surface area of the conductive plates and the distance of separation between
them. Altering any two of these values alters the the value of its
capacitance and this forms the basis of operation of the variable
capacitors.

Also, because capacitors store the energy of the electrons in the form of an
electrical charge on the plates the larger the plates and/or smaller their
separation the greater will be the charge that the capacitor holds for any
given voltage across its plates. In other words, larger plates, smaller
distance, more capacitance.

By applying a voltage to a capacitor and measuring the charge on the plates,
the ratio of the charge Q to the voltage V will give the capacitance value
of the capacitor and is therefore given as: C = Q/V this equation can also
be re-arranged to give the familiar formula for the quantity of charge on
the plates as: Q = C x V

Although we have said that the charge is stored on the plates of a
capacitor, it is more exact to say that the energy within the charge is
stored in an “electrostatic field” between the two plates. When an
electric current flows into the capacitor, it charges up, so the
electrostatic field becomes much stronger as it stores more energy between
the plates.

Likewise, as the current flowing out of the capacitor, discharging it, the
potential difference between the two plates decreases and the electrostatic
field decreases as the energy moves out of the plates.

The property of a capacitor to store charge on its plates in the form of an
electrostatic field is called the Capacitance of the capacitor. Not only
that, but capacitance is also the property of a capacitor which resists the
change of voltage across it.



The Capacitance of a Capacitor
Capacitance is the electrical property of a capacitor and is the measure of
a capacitors ability to store an electrical charge onto its two plates with
the unit of capacitance being the Farad (abbreviated to F) named after the
British physicist Michael Faraday.

Capacitance is defined as being that a capacitor has the capacitance of One
Farad when a charge of One Coulomb is stored on the plates by a voltage of
One volt. Note that capacitance, C is always positive in value and has no
negative units. However, the Farad is a very large unit of measurement to
use on its own so sub-multiples of the Farad are generally used such as
micro-farads, nano-farads and pico-farads, for example.



Standard Units of Capacitance



Microfarad
1(μF)
1μF = 1/1,000,000 = 0.000001 = 10-6 F
Nanofarad
(nF)
1nF = 1/1,000,000,000 = 0.000000001 = 10-9 F
Picofarad
(pF)
1pF = 1/1,000,000,000,000 = 0.000000000001 = 10-12 F


Then using the information above we can construct a simple table to help us
convert between pico-Farad (pF), to nano-Farad (nF), to micro-Farad (μF)
and to Farads (F) as shown.
1,000 10,000 


Pico-Farad (pF)
Nano-Farad (nF)
Micro-Farad (μF)
Farads (F)
1.0 
0.001 
 
10.0 
0.01 
 
1,000,000 
1,000 
1.0 
 
  
10,000 
10.0 
 
  
100,000 
100 
 
  
1,000,000 
1,000 
0.001
  
  
10,000 
0.01
  
  
100,000 
0.1
  
  
1,000,000 
1.0




Introduction to Capacitors – Capacitance
The capacitance of a parallel plate capacitor is proportional to the area, A
in metres2 of the smallest of the two plates and inversely proportional to
the distance or separation, d (i.e. the dielectric thickness) given in
metres between these two conductive plates.

The generalised equation for the capacitance of a parallel plate capacitor
is given as: C = ε(A/d) where ε represents the absolute permittivity of
the dielectric material being used. The dielectric constant, εo also known
as the “permittivity of free space” has the value of the constant 8.854
x 10-12 Farads per metre.

To make the maths a little easier, this dielectric constant of free space,
εo, which can be written as: 1/(4π x 9×109), may also have the units of
picofarads (pF) per metre as the constant giving: 8.85 for the value of free
space. Note though that the resulting capacitance value will be in
picofarads and not in farads.

Generally, the conductive plates of a capacitor are separated by some kind
of insulating material or gel rather than a perfect vacuum. When calculating
the capacitance of a capacitor, we can consider the permittivity of air, and
especially of dry air, as being the same value as a vacuum as they are very
close.

	



Introduction to Capacitors Example No1
A capacitor is constructed from two conductive metal plates 30cm x 50cm
which are spaced 6mm apart from each other, and uses dry air as its only
dielectric material. Calculate the capacitance of the capacitor.
	

the capacitance of a capacitor

Then the value of the capacitor consisting of two plates separated by air is
calculated as 0.221nF, or 221pF.



Introduction to Capacitors – The Dielectric
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
Constant, k 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
	
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 = (εo*εr x 1 x A)/d is exactly the same as saying: C = (εo*εr*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.



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:

	
	introduction to capacitors with 8 plates

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.




Introduction to Capacitors – Voltage Rating

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.



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.

We have seen in this introduction to capacitors tutorial that 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
capacitors, I shall limit them to the most commonly used types.


Introduction to Capacitors
Types of Capacitor
Capacitor Characteristics
Capacitance and Charge
Capacitor Colour Codes
Capacitors in Parallel
Capacitors in Series
Capacitance in AC Circuits
Capacitor Tutorial Summary
Capacitive Voltage Divider
Ultracapacitors