CAPACITORS
Capacitors are devices which can store electric charge. They have many
applications in electronic circuits. They include:
•
•
•
forming timing elements,
waveform shaping,
limiting current in AC circuits.
CHARGING AND DISCHARGING A CAPACITOR
Capacitors are made up from two metal plates separated by a thin
insulating layer. The insulator is called the dielectric.
Electron
flow
+
DC
SUPPLY
1
2
+
123456789
123456789
-
-
1
+
DC
SUPPLY
2
Electron
flow
++ ++
123456789
123456789
- - - -
-
Fig. 1a Charging a capacitor
Fig. 1b Discharging a capacitor
Consider an uncharged capacitor in the circuit shown in Fig 1a. When the
switch is moved to position 1, the positive terminal of the battery draws
electrons off the top plate of the capacitor and transfers the same number
to the bottom plate. As a result, the top plate becomes positively charged
and the bottom plate becomes negatively charged. Lamp LP1 would glow
while electrons are being transferred from one plate to the other. The build
up of charge on the plates develops a voltage across the capacitor. Transfer
of charge continues until the voltage across the capacitor is the same as the
battery voltage. The capacitor is then fully charged.
When the switch is moved to position 2 (Fig 1b), the capacitor provides a
voltage across lamp LP2. Electrons on the bottom plate are attracted to the
top plate through the filament of the lamp. The lamp would glow brightly
for a while then gradually dim as the voltage across the capacitor falls.
When all of the electrons have been transferred back to the top plate the
capacitor is fully discharged.
The action can be repeated by moving the switch to position 1 then back to
position 2. When used in this way the capacitor behaves like a small
rechargeable battery.
1
UNITS OF CAPACITANCE
The value of a capacitor is governed by its ability to store charge. The unit
used for capacitance is the farad.
A capacitor has a capacity of 1 farad if the addition, or removal, of 1
coulomb of charge changes the voltage across it by 1V.
The farad (F) is a very large unit. Capacitor values are usually given in
microfarads (mF), nanofarads (nF) or picofarads (pF).
1µF
=
1
1,000,000
F
=
10 -6F
1nF
=
1
1,000,000,000
F
=
10 -9F
1µF
=
1pF
=
1
F
1,000,000,000,000
=
10 -12F
1µF
=1,000,000pF
1,000nF
DIELECTRICS
The insulator, or dielectric, between the plates of a capacitor is strained by
the electric field formed by the charges. The field draws electrons from their
normal orbit, centred on the nucleus, towards the positive plate. Electric
dipoles are formed in the dielectric. This has the effect of reducing the
voltage across the capacitor. The capacitor is now able to hold more charge
at a certain voltage.
Various types of dielectrics are used in capacitors. Each will have advantages
and disadvantages. The material selected will depend upon the application
required for the capacitor.
It can be shown that in order to provide high capacitance, the area of the
plate should be large and the separation small. Rolling the plates into a
spiral enables a large area to be fitted into a small volume. Some insulating
materials, e.g. mica, are not flexible enough for this technique to be used.
2
CIRCUIT SYMBOLS
There are two main types of capacitors, polarised and non-polarised.
Polarised capacitors are usually referred to as electrolytic capacitors.
Symbols used for the two types are shown below.
+
General symbol
Electrolytic capacitor
Fig. 2 Symbols used for capacitors
In the next Exercise you will be using electrolytic capacitors. They are used
because they provide a much larger capacity than non-polarised capacitors
of the same physical size.
Considerable care is required when using electrolytic capacitors. Their
positive terminal must be nearer the positive supply rail than their negative
terminal.
If electrolytic capacitors are connected the wrong way around they
will heat up and probably explode.
IDENTIFYING THE LEADS ON ELECTROLYTIC CAPACITORS.
Polarity is always clearly marked on electrolytic capacitors. The following
diagrams illustrate some conventions in common use. Ask your tutor for
examples of axial and radial aluminium type.
Axial
Radial
Tantalum
Fig. 3 Polarity of electrolytic capacitors
3
TYPES AND SPECIFICATION
A good Electronic Components catalogue will offer a wide range of capacitor
types. Technical specification will usually provide the following data:
•
values available in the range.
•
tolerance.
•
working voltage.
•
leakage current.
•
physical size.
All of these must be considered when making your selection. The working
voltage is the maximum voltage that the capacitor can withstand before its
dielectric breaks down. Care must be taken to ensure that the working
voltage is higher than any DC voltage that will be applied across the
capacitor. In AC circuits, it must be remembered that the maximum voltage
applied on the capacitor is û2 times the RMS voltage.
Leakage current provides a value for the current that flows directly between
the plates through the dielectric. Its value depends upon the dielectric used
and the voltage on the capacitor.
The following table provides information about types of capacitor that are
often used in electronic circuits.
TYPE
Polar Aluminium
Electrolytic
4
APPEARANCE
PROPERTIES AND APPLICATIONS
Available in range of values from
1µF - 50,000µF.
Tolerance about -10% to +50%.
Working voltage from about 6V to
400V available. Size increases with
working voltage value.
Main advantage is small size for
capacitance provided.
Used for smoothing in power power
supplies.
Not suitable for high frequency
operation.
TYPE
APPEARANCE
PROPERTIES AND APPLICATIONS
Tantalum
Available in range of values from
about 0.1µF to 100µF.
Tolerance +20%.
Working voltage from about 6V to
35V available.
Smaller in size than aluminium
type of same value.
Very easily damaged by reverse
voltage.
Often used in timing circuits.
Polyester
Available in range of values from
about 0.01µF to 4.7µF. Colour
code often used to indicate value.
Tolerance +5% to +20%.
Working voltage from about 250V
to 400V.
Disc Ceramic
Available in range of values from
about 2.2pF to 0.1µF.
Tolerance 10% to 50%.
Working voltage up to 10kV
available.
Often used to remove high
frequency noise signals in
switching circuits.
Variable
Capacitors
Used in tuning stages of radio
receivers. Rotating the shaft varies
area of overlap between plates. This
sets value of capacitance.
Air, or thin sheets of mica, used as
dielectric.
Also available as trimmer capacitors
for direct mounting onto printed
circuit boards (PCB).
Values available up to 500pF.
5
COLOUR CODING ON POLYESTER CAPACITORS
A five band colour code is often used to indicate the value, tolerance and
working voltage of polyester capacitors. The numbers associated with the
colours in the value code are the same as for resistors.
Band
Band
Band
Band
Band
1
2
3
4
5
}
Value Code
Tolerance
Working Voltage
Fig. 4 Capacitor colour code
COLOR
Bands 1,2 & 3
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Grey
White
VALUE
COLOR
Band 4
0
1
2
3
4
5
6
7
8
9
Green
White
TOLERANCE
± 5%
±10%
COLOR
Band 5
WORKING
VOLTAGE
Red
Yellow
250V DC
400V DC
Value code is used in the same way as for resistors. Bands 1 and 2 indicate
the first two digits and band 3 indicates the number of 0’s. Value of the
capacitor is given in picofarads (pF).
6
EXAMPLE
Yellow
Violet
Orange
White
Red
(4)
(7)
(3)
Value = 47000pF = 0.047µF
Tolerance = ±10%
Working voltage = 250V DC
PRINTED CODE
Printed code is used in a similar way to that for resistors e.g. 4u7 is used
to indicate a value of 4.7µF.
Ceramic disc capacitors often carry a 3-digit code to indicate their values
in picofarads. The first digits indicate the first two numbers and the third
the number of zeros to be added e.g. 223 indicates 22000pF
7
USING CAPACITORS AS TIMING ELEMENTS
We shall now investigate how the voltage across a capacitor varies with time
as it is being charged and discharged from a constant voltage source.
A.
CHARGING A CAPACITOR FROM A CONSTANT VOLTAGE SOURCE
+
VR
VS
+
VC
Fig. 5 Charging a capacitor
Let us assume that the capacitor carries no initial charge. When the switch
is closed, there is no voltage across the capacitor and all of the supply
voltage will appear across R. In this case VR = VS. The initial charging
current is given by:
I
=
VR
R
=
VS
R
As time goes by, the voltage across the capacitor will increase, due to the
build up of charge, and the voltage across the resistor will decrease. When
the voltage across the capacitor has reached a value V C, the charging
current is given by:
I’ = VR = VS - VC
R
R
Since the charging current decreases, the rate of flow of charge on to the
capacitor plates will decrease. As a result, the rate at which the voltage
increases across the capacitor will decrease. A graph of voltage against time
will be steep when the switch is closed and the slope will decrease as time
goes by (Fig 6). It can be shown that the charging curve is an exponential
curve and that the voltage across the capacitor and resistor at a time t are
given by:
V C = V S (1 - e-t/RC)
and
8
V R = VS e-t/RC
You will not be expected to use these equations in any test. If you would
like to know how they are used, consult your tutor.
VS
.
.
.
VC
VS
2 .
.
0 .
0
.
RC
.
.
2RC 3RC
0.69RC
.
.
4RC 5RC
time
Fig. 6 Charging curve
RC (R x C) is called the time constant of the circuit.
Remember the following points about an exponential charging curve:
•
Voltage across capacitor reaches half way to the supply voltage,
V S, in a time 0.69RC.
•
Voltage across capacitor reaches 0.63V S after a time RC
•
Voltage across capacitor reaches 0.99VS after a time 5RC.
9
B.
DISCHARGING A CAPACITOR THROUGH A RESISTOR
Consider a capacitor being charged up from a voltage source Vo.
1
Vo
2
Vo
C
R
VC
Vo
2
0
0
RC
2RC 3RC
4RC 5RC
0.69RC
time
Fig. 7 Discharging a capacitor
When the switch is moved over to position 2, the capacitor discharges
through resistor R. A voltage Vo is applied across the resistor and the initial
discharging current I is given by :
I
=
Vo
R
Voltage across the capacitor starts to fall at a rapid rate. As charge flows
off the capacitor, the voltage across the resistor is reduced. The discharging
current reduces and the slope of a graph of Vc against time would
decreases. It can be shown (proof provided on request) that:
VC
=
VR
=
V o e-t/RC
Vo has been used in this case to serve as a reminder that it is the starting,
or original, voltage across the capacitor.
The curve in Fig 7 is known as an exponential decay curve. You should
be able to show that:
•
the voltage falls to Vo/2 after a time 0.69RC.
•
the voltage across the capacitor is 0.37V o after a time RC.
•
the voltage across the capacitor is near zero after 5RC.
RC is the time constant of the circuit.
10