The capacitor is an essential component in many electronic circuits, functioning as a reservoir
temporary electricity supply. A capacitor's ability to store charge is measured in farads, a unit
which quantifies how much electrical charge can be stored by a potential difference of one volt. In addition to
store energy, capacitors have the ability to filter and smooth voltage variations in power sources.
power, acting as important elements in filtering circuits and in audio systems to separate
frequency components. They are also used in timing circuits, where the time constant
of the circuit determines the speed at which the circuit responds to voltage changes.
Basically, the capacitor consists of two metal plates parallel to each other.
One of the plates assumes positive charge and the other negative charge. Usually who provides
these charges to the capacitor is a source of voltage or current. This distribution of
charges generates a uniform electric field between the plates, oriented of the plate with charge
positive for the negatively charged plate. Is due to this electric field
generated by the accumulation of charges between its plates that the capacitor has the property
of storing energy between its terminals. The unit of measurement of the capacitance is the
farad or coulomb / volt . In practice this unit is very large. That's why we use your
submultiples, such as microfarad, nanofarad or picofarad .
Figure 03-01
In the Figure 03-01 we can see, schematically, what a capacitor is like. The capacitance of a
capacitor depends basically on its geometry as the distance between
plates (D in the figure) and the area, A, of the plates.
There is also a constant of proportionality,
called electrical permissiveness of the medium. This constant depends on the material that is placed
between the plates. In vacuum its value is 8.85 x 10 -12F / m or C2 / N
The capacitance of a capacitor with a given geometry and dielectric
between its plates can be calculated through the eq. 03-01:
eq. 03-01
Where the variables are:
C - Capacitance whose unit of measure is farad.
εr- Relative permissivity of the dielectric is dimensionless.
εo - Permissivity of vaccum whose unit of measure is farad/metro.
D - Distance between the plates, whose unit of measure is meter.
A - Area whose unit of measure is m2.
Thus, for each material used as dielectric we have a constant with numerical values
which will imply different capacitance values. It should be noted that for
the vacuum the electrical permissiveness is
εo = 8.85 x 10 -12 F / m .
The ratio between the permissivity of the dielectric used between the capacitor plates
and that of the vacuum is called
of relative permissivity , εr.
Some books represent the relative permissivity by the letter K. In the Table 03-01
we present some materials used in the manufacture of capacitors and their respective
permissiveness.
Table 03-01
Material of Dieletric
Perm. Relative (εr ou K)
Vaccum
1.00000
Air
1.00059
Water 20°C
80.40
Water 25°C
78.50
Ethanol
25
Germanium
16
Silicon
12
Aluminium
8.10 a 9.50
Soapstone (MgO - SiO2)
5.50 a 7.20
Mica
5,400 a 8,700
Oil
4.6000
Paper
4.00 a 6.00
Waxer Paper
2.50
Plastic
3.00
Polystyrene
2.50
Porcelain
6.00
Pyrex
5.10
Titanates
50 a 10,000
In practice, there are several types of capacitors that depend on which material is
used as dielectric . Thus, we have the capacitors of tantalum, paper, mica, ceramics, polyester, oil,
electrolytic, adjustable etc ... each with its own characteristics.
The value of the capacitance can be written on the body of the
capacitor or in the form of color coding. It should be noted that each capacitor
has a maximum working voltage, which must not be exceeded at the risk of the same
be broken.
From the year 2 000, another type of capacitor called Supercapacitor appeared on the market.
We have prepared a special chapter about this type of capacitor. Access here!.
Dielectric strength is a fundamental property of insulating materials, measured in volts per meter (V/m).
It indicates the ability of a dielectric material to resist electric fields without ionization and consequent
loss of its insulating properties. When the voltage applied to a dielectric exceeds its dielectric strength, voltage occurs.
electrical breakdown, leading to the phenomenon known as breakdown, which results in the formation of a conductive path through
of the material and, often, in the destruction of its molecular structure. The breakdown voltage is, therefore, the voltage limit that the dielectric
can withstand before failing, and exceeding it implies the material's inability to continue functioning as an effective insulator.
There are several types of capacitors, varying according to the type of dielectric used in their construction.
There is a huge range of possibilities regarding the dielectric. Which dielectric to use depends on some factors, such as:
The desired value of capacitance;
Working voltage;
Capacitor size;
Sensitivity of capacitor capacitance varies depending on temperature.
Let's analyze some types of capacitors on the market.
Mica Capacitors
Figura 03-02
As the name suggests, the dielectric is mica. These capacitors are used in precision circuits and,
mainly in high frequency circuits. In general, the capacitance of these capacitors varies from a few
pF up to a few thousand pF. The working voltage can range from a few tens of volts to around 18 kV.
As can be seen in Figure 03-02 the capacitance value is printed on the side of the capacitor. Its value is 4,700 pF
or 4.7 nF and this value has a tolerance of
± 5%.
Ceramic Capacitors
Figura 03-03
In this case, the dielectric used is ceramics that have an excellent working voltage, reaching values such as 10 kV.
Its capacitance varies from 10 pF to 0.05 uF. Figure 03-03 shows some ceramic capacitors with different sizes.
Its use depends on the type of assembly, whether printed circuit (the two side capacitors), SMD (the central capacitors), etc ...
Capacitors of Film, Foil, Polyester
Polypropylene, Teflon
Figura 03-04
In this case, the name of the capacitor is associated with the type of dielectric used in its construction. In general, the manufacturing process
is by stacking or rolling, and can take on a rounded or flat shape. Its insulation voltage can reach 2.5 kV.
The capacitance varies between 100 pF and 50 uF.
Electrolytic Capacitors
The types of capacitors studied above are the types that do not have polarity, that is, any terminal can be connected
in any polarity of the voltage source. The next two types of capacitors we will see are of the polarized type, that is,
each terminal of the capacitor must be connected in the correct polarity, otherwise the capacitor will be damaged. That's why these types
of capacitors come with the polarity printed on their casing. See Figure 03-05, the polarity printed on the body of the
capacitor, as well as its capacitance and maximum working voltage.
Figura 03-05
In this type of capacitor, the anode or positive plate is made of a metal that forms a layer of insulating oxide
through anodization. This layer acts as the dielectric of the capacitor. A solid, liquid or gel electrolyte covers the
surface of this oxide layer, serving as the cathode or negative plate of the capacitor.
Due to their very thin dielectric oxide layer and increased anode surface, electrolytic capacitors have a
much higher capacitance-voltage per unit volume compared to ceramic capacitors or film capacitors and thus
can have large capacitance values.
The electrolytic capacitor is internally composed of two aluminum sheets separated by a layer of aluminum oxide, rolled up
and soaked in a liquid electrolyte (composed predominantly of boric acid or sodium borate). As it is composed of rolled leaves,
has a cylindrical shape. Its dimensions vary according to the capacitance and maximum working voltage.
Tantalum Capacitors
The tantalum capacitors are another type of electrolytic capacitor. The material used for the electrodes is tantalum.
Figura 03-06
This type of capacitor is superior in performance to the aluminum electrolytic capacitor in terms of temperature and operating frequency.
Its cost is higher than aluminum ones. Tantalum capacitors have numerous applications due to their long-term stability, high capacity,
reliability and low leakage currents. Due to these characteristics they are widely used in the telecommunications, aerospace and military industries.
The anode is made from a porous tantalum metal pellet covered by a layer of insulating oxide that forms the dielectric,
surrounded by liquid or solid electrolyte as a cathode. Capacitors can also include silver, carbon or polymer.
In this topic we show the main types of capacitors used in electronic equipment in our modern world.
There are other types of capacitors that can be found in more specific literature.
Additional Considerations
Currently, a special type of capacitor called Supercapacitor, also known as Ultracapacitor or Hypercapacitor,
has appeared on the market.
This type of capacitor represents a significant advance in storage technology
power. Since the early 2000s, they have stood out for their ability to reach hundreds or even thousands of farads,
a great evolution compared to traditional capacitors. Although initially limited by a low insulation voltage
of about 2.7 V, recent research has made remarkable progress. For example, oxygen vacancy engineering techniques
have significantly improved the electrochemical performance of metal oxides used as electrodes, resulting in an increase
substantial in conductivity and capacitance. Furthermore, the development of new materials and processes is driving
the application of supercapacitors in various areas, from renewable energy to environmental conservation, contributing to
cleaner transport systems and to reduce carbon emissions. With these advances, supercapacitors are
increasingly closer to overcoming current limitations and becoming crucial components for efficient energy storage in the future,
including the prospect of replacing batteries, as we know that batteries, in addition to having a very short useful life, cause
serious environmental problems in their disposal.
They are able to accept and deliver charge much faster than conventional
batteries and support many more charge and discharge cycles. Unlike ordinary capacitors, supercapacitors
do not use a conventional solid dielectric, but rather electrostatic double layer capacitance and pseudocapacitance
electrochemistry, both contributing to the total energy storage capacity of the device. These characteristics
make supercapacitors ideal for applications that require many rapid charge and discharge cycles, such as in vehicles
automobiles, buses, trains, cranes and elevators, where they are used for regenerative braking, energy storage
short-term or super-fast energy delivery. Additionally, smaller drives are used as backup
power for static random access memory (SRAM). With the advancement of technologies and the growing need for
efficient and fast energy storage solutions, supercapacitors are becoming an essential part
of new technologies, offering a promising alternative for storing electrical energy.
If the reader is interested in knowing more about supercapacitor, they can access the
special chapter that we prepared with a lot of information, including presenting practical examples already incorporated
to our daily lives. Access here!.
As with the resistors, we have three types of capacitor associations that we can find
in electrical circuits. The series,parallel and mixed.
To study capacitor associations, we must not forget the relationship that existy between
load, voltage and capacitance value. The relationship between these variables is given by:
What characterizes an association series is the charge in each
capacitor that should be the same on any capacitor that is part of the series association.
Hence, the voltage across each capacitor will depend only on the value of its capacitance.
Figure 03-02
In the Figure 03-02, we see a series association fed by a voltage source V.
The sum of the voltage drops in the capacitors shall be equal to the voltage V of the source,
(V = V1 + V2 + V3). To calculate the equivalent capacitance of a series association,
for any number of capacitors, we must use the equation given below.
What characterizes a parallel association is that all
the capacitors are subject to the same potential difference. Therefore, the charge on each
depends on the value of its capacitance.
Figure 03-03
In the Figure 03-03, we see a parallel association fed by a voltage source V.
Note that the voltage V is the same for all capacitors. Then, the sum of the charge
each capacitor will equal the total charge supplied by the voltage source.
In this case, we will have
that the value of total capacitance of the association will be given by the sum of all
capacitances that are part of the circuit. Then, to calculate the total capacitance of a parallel association,
for any number of capacitors, we use the eq. 03-04 given below:
In the mixed association, as the name is saying,
we will have a circuit that contains both parallel and serial association. The Figure 03-04
show this kind of circuit.
Figure 03-04
To calculate the total capacitance of a mixed association, we must calculate the capacitance
capacitors that are associated in parallel and
calculate the capacitance in series associations until you reach the final result.
With this calculated value, we can calculate the total charge supplied by the voltage source.
To calculate the partial charge of each capacitor in the circuit, we must go back
capacitor to capacitor, not forgetting that capacitors that are in a series circuit
will have the same charge regardless of the value of their capacitance. Therefore, the value of the voltage between the
each capacitor in a series circuit will depend only on its capacitance.
Since the capacitor generates an electric field between the plates, then it is able to
store energy. Remember that the unit of measure of energy is joule.
We can determine the energy stored in a capacitor by
any of the three equations below, where the variables involved are:
W - Energy stored in the capacitor whose unit of measure is joule.
C - Capacitance whose unit of measure is farad.
q - Electric charge of capacitor whose unit of measure is coulomb.
V - Eletric voltage in the terminals of capacitor whose unit of measure is volts
eq. 03-05
eq. 03-06
eq. 03-07
Observation
1 - A capacitor can absorb power from a circuit storing energy in its
electric field.
2 - In a circuit the capacitor can return in the form of power the energy
accumulated in its electric field.
6. Continuous Current Capacitor BehaviorTransients
We must always keep in mind that a capacitor maintains a direct relation between
charge, capacitance and voltage to which it is subjected. Let's repeat the eq. 03-02
so that it does not fall into oblivion.
eq. 03-02
In this item we will study the behavior of a capacitor in relation to
DC (direct current). We will consider that initially
the capacitor is uncharged, that is, without electric charge and therefore the voltage
between its terminals is equal to zero. When not is the case,
we will explain the initial condition.
Below are two fundamental properties of a capacitor.
Based on the above properties the capacitor assumes characteristics
when subjected to voltage variations at its terminals. Normally,
a resistor in series with the capacitor is used to limit the current
in the capacitor. Thus, when the capacitor is subjected,
abruptly, at a variation of electric voltage, it behaves like
a SHORT-CIRCUIT. This is due to the fact that at the moment a voltage is applied
power to the capacitor terminals, the speed that the battery draws electrons from a
of the capacitor plates, is very large, decreasing with the passage of time. And after a long
time, when the capacitor is fully charged, there is no more movement of electrons and,
therefore, the capacitor assumes the role of an OPEN CIRCUIT.
Thus, we can see in the Figure 03-05, a classic circuit
to study the behavior of the capacitor.
Figure 03-05
In this circuit we have a key S that allows to turn on and off the voltage source
which feeds the circuit. When closed it applies a voltage from the voltage source V
in the circuit formed by the resistor in series with the capacitor. In the technical literature
the closing time of the key S is represented as the time equal to
t = 0+.
At the time of closing the S key, at t = 0+, as the capacitor is initially
uncharged (q = 0 and VC = 0), its behavior will be a short circuit.
Hence, the voltage on the capacitor, VC, will be equal to zero, and
therefore, all of the source voltage will be applied to the R resistor. So we can calculate the current electric current flowing through the circuit at time t = 0+. For this, just apply
the Ohm law, or:
I = V / R
At the instant immediately after t = 0+, the capacitor starts
then to be charged electrically by the electric current I. Since the capacitor
has electric charge, then it must also have a certain electrical voltage. This voltage
in the capacitor grows exponentially. And, of course, about the
resistor, the voltage decreases exponentially. The speed with which the capacitor
electric charge, depends on the capacitance values of the capacitor and the
electrical resistance of the resistor that is in series with the capacitor.
The values of these two components determine the time constant call of the
circuit and is represented by the greek letter τ (tau). So we can write that:
τ = R C
Knowing the time constant of the circuit, we can write the equation that
determines the current through the capacitor at any instant. See the equation below.
As we said earlier, for t = 0, the current through the circuit is
maximum and equal to I = V / R, since we know that the exponential function raised to
power zero (t = 0) equals ONE.
eq. 03-08
Figure 03-06
We see in the Figure 03-06, the graph of how the capacitor acquires its electric charge
over time. Notice in the figure, that for a time equal to a time constant,
the capacitor acquires 63.2% of its total charge. After two time constants,
already reaches 86.5% of its total charge. In practice, we consider that after five
time constant, the capacitor reaches its maximum electric charge.
When the capacitor reaches its maximum electric charge, we say that the circuit has reached
the state of permanent scheme. This means that if the circuit does not suffers any
electrical perturbation, the circuit tends to remain in this state
indefinitely.
Now, stay tuned for the fact that as the voltage in the
capacitor grows, obviously the voltage on the resistor decreases, since the voltage source has
a fixed (constant) value. Then, the sum VC + VR
must be equal to V. Below we have the equation that determines the voltage
on the capacitor at any time. Note that when t = 0, the voltage across the capacitor is
zero, as we have already commented.
eq. 03-09
Figure 03-07
In the Figure 03-07, we have the graph of the electric current through the capacitor.
Since resistor and capacitor form a series circuit, then this electric current is
same that circulates through the resistor. Thus, we conclude that the voltage on the resistor
has the same appearance as the electric current on the capacitor.
Realize that when the voltage
on the capacitor increases (see Figure 03-07), simultaneously the voltage
over the resistor decreases.
Notice that this graph also represents the voltage drop on the resistor,
just replace on the vertical axis ic by
VR.
This was a brief approach on the behavior of a capacitor when this
is in a circuit that uses DC only. We will soon address
with this problem, using
the solution of differential equations, as well as to demonstrate where the above equations came from.
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