General Description
Effe c ts o f Me c ha nic a l Stre s s – High “K” dielectric
ceramic capacitors exhibit some low level piezoelectric
reactions under mechanical stress. As a general statement,
the piezoelectric 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 capaci-
tors in extremely low level applications.
Energy Stored – The energy which can be stored in a
capacitor is given by the formula:
2
E = 1⁄
2
CV
E = energy in joules (watts-sec)
V = applied voltage
C = capacitance in farads
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:
Potential Change – A capacitor is a reactive component
which reacts against a change in potential across it. This is
shown by the equation for the linear charge of a capacitor:
Lo
Lt
V
X
Tt
Y
t
=
ꢁ ꢁ
ꢁV ꢁ
T
o
o
dV
dt
Iideal
=
C
where
Lo = operating life
Lt = test life
Tt = test temperature and
To = operating temperature
in °C
where
I = Current
C = Capacitance
V = test voltage
t
Vo = operating voltage
X,Y = see text
dV/dt = Slope of voltage transition across capacitor
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.
Historically for ceramic capacitors exponent X has been
considered as 3. The exponent Y for temperature effects
typically tends to run about 8.
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:
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 = Capacitance
L = Inductance
Rs = Series Resistance
Rp = Parallel Resistance
.224 KA
C =
t
R P
C = capacitance (picofarads)
K = dielectric constant (Vacuum = 1)
A = area in square inches
t = separation between the plates in inches
(thickness of dielectric)
L
R S
.224 = conversion constant
C
(.0884 for metric system in cm)
Reactance – Since the insulation resistance (Rp) is normal-
Capacitance – The standard unit of capacitance is the
farad. A capacitor has a capacitance of 1 farad when 1
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.
ly very high, the total impedance of a capacitor is:
2
Z = R2S + (X - X )
C
L
ꢀ
where
Z = Total Impedance
Dielectric Constant – In the formula for capacitance given
above the dielectric constant of a vacuum is arbitrarily cho-
sen as the number 1. Dielectric constants of other materials
are then compared to the dielectric constant of a vacuum.
Rs = Series Resistance
XC = Capacitive Reactance =
1
2 π fC
XL = Inductive Reactance = 2 π fL
Dielectric Thickness – Capacitance is indirectly propor-
tional to the separation between electrodes. Lower voltage
requirements mean thinner dielectrics and greater capaci-
tance per volume.
The variation of a capacitor’s impedance with frequency
determines its effectiveness in many applications.
Phas e 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°.
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
a material group.
68
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