2. Lecture 3
Capacitance
Capacitors
Capacitors are passive components that can store energy in an electric field
between two ‘plates’. The electric field is generated by building up charge on
the plates, called charging.
+ C
Capacitance, C, is measured in Farads (F) and is given by the following
expression.
Where:
C is the capacitance in Farads
Q is the charge in Coulombs
V is the Voltage across the plates in Volts
What is the charge built up on a 47nF capacitor plate with 5V
across it?
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3. Types of Capacitors
There are many different varieties of capacitors for different applications.
Some of the more common types:
• Ceramic: Cheap, low voltage and normally high tolerances. Come in a
range of values from a few pico-Farads to hundreds of nano-Farads.
• Metallised Plastic Film: Higher quality and more expensive than
ceramic capacitors. This range includes polyester, polypropylene and
others.
• Electrolytic: These capacitors are polarised, and are available in
higher capacitances. They have a slightly different symbol to indicate it
must be placed in the circuit in the correct orientation:
C
+
Capacitors in Parallel
To find the equivalent capacitance of capacitors side by side simply add the
capacitances:
C1 C2 Cparallel
(is equivalent to)
Find the capacitance of circuit that has 1nF, 220pF and 47pf
resistors in parallel.
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4. Capacitors in Series
When capacitors are connected end to end the inverse of the combined
capacitance is found by adding the inverse of the capacitances:
C1
Cseries
C2
(is equivalent to)
Find the capacitance of circuit that has three 22nF and a 47nF
capacitor in series.
Note that the series/parallel equations for capacitors are the opposite of those
for resistance.
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5. Charging and Discharging
When a voltage is put across the capacitor, the plates will charge up. To
discharge the capacitor you must provide another circuit path for the charge to
flow off again. This will be explored in the practical later this session.
The time it takes for the capacitor to charge/discharge is dependent on the
circuit resistance. The time it takes for the capacitor to charge to 63% of its
value (or discharge to 37%) is called the RC time constant, and the product
of the resistance and capacitance:
Where:
τ, (‘tau’) is the time constant in seconds
R is the resistance in Ohms
C is the capacitance in Farads
The voltage across the capacitor as it charges is given by the expression:
And to discharge:
Where:
Vc is the voltage across the capacitor in Volts
Vin is the input voltage in Volts
t is the time taken in seconds
e is a constant = 2.718
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6. Find the voltage after 2 micro-seconds across a 1nF capacitor as it
charges in a 12V circuit with resistance of 10k.
Find the time it takes for a 22nF capacitor in a 1k circuit and charged to
5V to discharge to 1V.
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7. Capacitors and Power Supplies
Capacitors are used for decoupling (smoothing) power rails. For example in
a simple voltage regulator circuit, where the input voltage is dropped to 5V for
example, a capacitor is used on either side of the regulator to smooth the
input and output voltages.
IN OUT
GND
Vin
Vout
A similar effect could be achieved with a potential divider resistor network, but
using a voltage regulator or other DC-DC power supply unit allows:
• Variable input voltage.
• Variations in the input voltage will not appear on the output.
• The output voltage will not be dependent on the load circuitry.
• Lower power.
Modern DC-DC converters will not use a voltage regulator, they will use a
switch-mode system. These devices have the following advantages:
• Even lower power
• Wider range of input voltages
• Devices are often programmable or controllable
• Some will offer multiple output voltages
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8. Practical: Capacitors Charging and Discharging
Read the Health and Safety Information on page 5.
• Choose a capacitor and resistor values and build the following
circuit:
R
Vin C Vc
• Measure the voltage, Vc, under charge and discharge and draw
graphs for both.
• Calculate the time constant for your circuit.
• Use your time constant to estimate the voltage after one time
constant period. Measure this and confirm it is 63% of Vin.
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9. Extended Practical: Build a 5V Power Supply
• Build the following voltage regulator circuit (see datasheet for
capacitor values):
IN OUT
+ 7805 +
Vin = GND
6-15V Vout = 5V
• Measure the output voltage, Vout for a range of input voltages, Vin.
• What is the dropout voltage of the regulator?
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10. Health & Safety Considerations
Soldering and de-soldering:
Solder melts at between 180 and 200°C. Soldering irons will heat up to
between 250 and 400°C. Be extremely careful when soldering and take the
following precautions:
• Switch off the soldering iron at the mains when not in use
• Always keep the iron in its stand
• Make sure your workspace is clear, well lit and well ventilated
• Never solder while your circuit is powered up
• Never solder without tutor supervision
• Only apply the soldering iron for the minimum amount of time
• Keep your soldering tidy and use the minimum amount of solder
• Avoid breathing in solder fumes
• You must only use the lead-free solder provided
• You must use tools e.g. pliers to support components that are
being soldered and ensure the board is secure.
Switching it on:
Powering up a circuit that is incorrectly connected can cause components or
equipment to get extremely hot or even ‘blow’. A short circuit (where
unintended electrical connections are made) for example may damage
equipment or blow components causing them to behave in an unpredictable
way.
• Before powering up your circuit you MUST have it checked by the
tutor
• Have your neighbour physically inspect your work before
powering on
• If your circuit does not behave as you expect, switch it off
immediately
• Use your nose! A faulty circuit with hot components will often
smell or smoke
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11. If your circuit does not behave as you expect:
• With the power off, confirm by eye that your circuit is connected
correctly and that you are using all the correct components and
mounted with the correct polarities
• Inspect your circuit closely for short circuits, soldering faults and
dry joints:
• Do all the testing on your circuit that you can with it powered off.
• Be extremely careful when probing your circuit live as the probe
itself can cause short circuits
• When probing with an oscilloscope ensure the earth connection is
applied safely
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