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General Description
Effects of Mechanical Stress – High “K” dielectric ceramic
capacitors exhibit some low level piezoelectric reactions
under mechanical stress. As a general statement, the piezo-
electric output is higher, the higher the dielectric constant of
the ceramic. It is desirable to investigate this effect before
using high “K” dielectrics as coupling capacitors in extremely
low level applications.
Reliability – Historically ceramic capacitors have been one
of the most reliable types of capacitors in use today.
The approximate formula for the reliability of a ceramic
capacitor is:
Energy Stored – The energy which can be stored in a
capacitor is given by the formula:
E = 1 ? 2 CV 2
E = energy in joules (watts-sec)
V = applied voltage
C = capacitance in farads
Potential Change – A capacitor is a reactive component
which reacts against a change in potential across it. This is
I ideal = C dV
where
L o
L t
=
V t
V o
X
T t
T o
Y
shown by the equation for the linear charge of a capacitor:
dt
L o = operating life
L t = test life
V t = test voltage
V o = operating voltage
T t = test temperature and
T o = operating temperature
in °C
X,Y = see text
where
I = Current
C = Capacitance
dV/dt = Slope of voltage transition across capacitor
Historically for ceramic capacitors exponent X has been
considered as 3. The exponent Y for temperature effects
typically tends to run about 8.
A capacitor is a component which is capable of storing
electrical energy. It consists of two conductive plates (elec-
trodes) separated by insulating material which is called the
dielectric. A typical formula for determining capacitance is:
C = .224 KA
t
C = capacitance (picofarads)
K = dielectric constant (Vacuum = 1)
Thus an infinite current would be required to instantly change
the potential across a capacitor. The amount of current a
capacitor can “sink” is determined by the above equation.
Equivalent Circuit – A capacitor, as a practical device,
exhibits not only capacitance but also resistance and
inductance. A simplified schematic for the equivalent circuit
is:
C = Capacitance L = Inductance
R P
A = area in square inches
t = separation between the plates in inches
L
R S
(thickness of dielectric)
.224 = conversion constant
(.0884 for metric system in cm)
Capacitance – The standard unit of capacitance is the
farad. A capacitor has a capacitance of 1 farad when 1
C
R s = Series Resistance R p = Parallel Resistance
Reactance – Since the insulation resistance (R p ) is nor-
mally very high, the total impedance of a capacitor is:
coulomb charges it to 1 volt. One farad is a very large unit
and most capacitors have values in the micro (10 -6 ), nano
(10 -9 ) or pico (10 -12 ) farad level.
where
Z=
R S 2 + (X C - X L ) 2
X C = Capacitive Reactance =
X L = Inductive Reactance
Dielectric Constant – In the formula for capacitance given
above the dielectric constant of a vacuum is arbitrarily chosen
as the number 1. Dielectric constants of other materials are
then compared to the dielectric constant of a vacuum.
Dielectric Thickness – Capacitance is indirectly proportional
to the separation between electrodes. Lower voltage require-
ments mean thinner dielectrics and greater capacitance per
volume.
Area – Capacitance is directly proportional to the area of the
electrodes. Since the other variables in the equation are
usually set by the performance desired, area is the easiest
parameter to modify to obtain a specific capacitance within
Z = Total Impedance
R s = Series Resistance
1
2 π fC
= 2 π fL
The variation of a capacitor’s impedance with frequency
determines its effectiveness in many applications.
Phase Angle – Power Factor and Dissipation Factor are
often confused since they are both measures of the loss in
a capacitor under AC application and are often almost
identical in value. In a “perfect” capacitor the current in the
capacitor will lead the voltage by 90°.
a material group.
107
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