Capacitor

Objective
 Describe the construction of a capacitor and
how charge is stored.
 Introduce several types of capacitors.
 Discuss the electrical properties of a capacitor
The relationship between charge, voltage,
and capacitance.
Charging and discharging of a capacitor.
Relationship between voltage, current, and
capacitance; power; and energy.
Equivalent capacitance when a set of
capacitors are in series and in parallel.

Capacitors
 Composed of two conductive plates separated
by an insulator (or dielectric).
Commonly illustrated as two parallel metal
plates separated by a distance, d.
C = e A/d
where e = er eo
er is the relative dielectric
constant.
eo is the vacuum permittivity.

Dielectrics
 A dielectric is an insulating material (e.g.
paper, plastic, glass).
 A dielectric placed between the conductors of
a capacitor increases its capacitance by a
factor κ, called the dielectric constant.
 C= κCo (Co=capacitance without dielectric)
 For a parallel-plate capacitor:
ε = κεo = permittivity of the material.
d
A
d
A
C 

  0

Effect of Dimensions
 Capacitance increases with
increasing surface area of the plates,
decreasing spacing between plates, and
increasing the relative dielectric constant of
the insulator between the two plates.

Types of Capacitors
 Fixed Capacitors
Nonpolarized
May be connected into circuit with either
terminal of capacitor connected to the
high voltage side of the circuit.
Insulator: Paper, Mica, Ceramic, Polymer
Electrolytic
The negative terminal must always be at a
lower voltage than the positive terminal
Plates or Electrodes: Aluminum, Tantalum.

Nonpolarized
 Difficult to make nonpolarized capacitors that
store a large amount of charge or operate at
high voltages.
Tolerance on capacitance values is very large
+50%/-25% is not unusual.
PSpice Symbol

Electrolytic
Pspice
Symbols
Fabricatio
n

Types of Capacitors
Parallel-Plate Capacitor
A cylindrical capacitor is a parallel-plate
capacitor that has been rolled up with
an insulating layer between the plates.
Cylindrical Capacitor

Variable Capacitors
 Cross-sectional area is changed as one set of
plates are rotated with respect to the other.
PSpice Symbol

Electric Double Layer
Capacitor
 Also known as a supercapacitor or
ultracapacitor
Used in high voltage/high current
applications.
Energy storage for alternate energy
systems.

MEMS Capacitor
 MEMS (Microelectromechanical system)
Can be a variable capacitor by changing the
distance between electrodes.
Use in sensing applications as well as in RF
electronics.

Electrical Properties of a
Capacitor
 Acts like an open circuit at steady state when
connected to a d.c. voltage or current source.
 Voltage on a capacitor must be continuous
 There are no abrupt changes to the voltage,
but there may be discontinuities in the
current.
 An ideal capacitor does not dissipate energy,
it takes power when storing energy and
returns it when discharging.

Properties of a Real
Capacitor
 A real capacitor does dissipate energy due
leakage of charge through its insulator.
 This is modeled by putting a resistor in
 parallel with an ideal capacitor.

Energy Storage
 Charge is stored on the plates of the
capacitor.
 Equation : Q = CV
 Units:
Farad = Coulomb/Voltage
Farad is abbreviated as F

Sign Conventions
The sign convention used with a
capacitor is the same as for a
power dissipating device.
When current flows into the
positive side of the voltage
across the capacitor, it is
positive and the capacitor is
dissipating power.
When the capacitor releases
energy back into the circuit, the
sign of the current will be
negative.

Charging a capacitor
 Current flow
Initially High
Finally Zero
 Charging factors
Capacitance
Resistance
I
t

Charging a Capacitor
 It is easy to store charge in the capacitor.
 As more charge is stored on the plates of the
capacitor, it becomes increasingly difficult to place
additional charge on the plates.
Coulombic repulsion from the charge already on
the plates creates an opposing force to limit the
addition of more charge on the plates.
Voltage across a capacitor increases rapidly as
charge is moved onto the plates when the initial
amount of charge on the capacitor is small.
Voltage across the capacitor increases more
slowly as it becomes difficult to add extra
charge to the plates.

Adding Charge to
Capacitor
The ability to add charge to a
capacitor depends on:
The amount of charge already on the
plates of the capacitor and the force
(voltage) driving the charge towards
the plates (i.e., current)

Discharging a capacitor
 Current flow
Initially High
Opposite to
charging
Finally zero
 Discharging factors
Capacitance
Resistance
I
t

Discharging a Capacitor
 At first, it is easy to remove charge in the capacitor.
 Coulombic repulsion from charge already on the plates creates a
force that pushes some of the charge out of the capacitor once
the force (voltage) that placed the charge in the capacitor is
removed (or decreased).
 As more charge is removed from the plates of the capacitor, it
becomes increasingly difficult to get rid of the small amount of
charge remaining on the plates.
 Coulombic repulsion decreases as charge spreads out on the
plates. As the amount of charge decreases, the force needed to
drive the charge off of the plates decreases.
 Voltage across a capacitor decreases rapidly as charge is
removed from the plates when the initial amount of charge on
the capacitor is small.
 Voltage across the capacitor decreases more slowly as it
becomes difficult to force the remaining charge out of the
capacitor.

Current~Voltage
Relationships




1
1
t
t
CC
C
C
C
C
o
dti
C
v
dt
dv
Ci
dt
dq
i
Cvq
Power and
Energy
dt
dv
Cvp
vip
C
CC
CCC


C
q
w
Cvw
C
CC
2
2
1
2
2



Capacitors in Parallel


P
p
Peq CC
1

Ceq for Capacitors in Parallel
i
4321eq
4321
4433
2211
4321
C CCCC
dt
dv
Ci
dt
dv
C
dt
dv
C
dt
dv
C
dt
dv
Ci
dt
dv
Ci
dt
dv
Ci
dt
dv
Ci
dt
dv
Ci
iiiii
eqin
in
in







Capacitors in Series
1
1
1








 
S
s s
eq
C
C

Ceq for Capacitors in Series
i
         1
4321eq
t
t
t
t4
t
t3
t
t2
t
t1
t
t4
4
t
t3
3
t
t2
2
t
t1
1
4321
1111C
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
1
o
1
o
1
o
1
o
1
o
1
o
1
o
1
o
1
o











CCCC
C
v
CCCC
v
C
v
C
v
C
v
C
v
vvvvv
eq
in
in
in

Summary
 Capacitors are energy storage devices.
 An ideal capacitor act like an open circuit at
steady state when a DC voltage or current has
been applied.
 The voltage across a capacitor must be a
continuous function; the current flowing
through a capacitor can be discontinuous.

1
1
t
t
CC
C
C
o
dti
C
v
dt
dv
Ci

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