General Description
Energy Stored –
The energy which can be stored in a
capacitor is given by the formula:
I (Ideal)
I (Actual)
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
shown by the equation for the linear charge of a capacitor:
Loss
Angle
Phase
Angle
f
IR
s
V
I
ideal
=
C dV
dt
where
In practice the current leads the voltage by some other
phase angle due to the series resistance R
S
. The comple-
ment of this angle is called the loss angle and:
Power Factor (P.F.) = Cos
f
or Sine
Dissipation Factor (D.F.) = tan
for small values of the tan and sine are essentially equal
which has led to the common interchangeability of the two
terms in the industry.
Equivalent Series Resistance –
The term E.S.R. or
Equivalent Series Resistance combines all losses both
series and parallel in a capacitor at a given frequency so
that the equivalent circuit is reduced to a simple R-C series
connection.
I
= Current
C
= Capacitance
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.
Equivalent Circuit –
A capacitor, as a practical device,
exhibits not only capacitance but also resistance and induc-
tance. A simplified schematic for the equivalent circuit is:
C
= Capacitance
L
= Inductance
R
p
= Parallel Resistance
R
s
= Series Resistance
R
P
E.S.R.
C
L
R
S
C
Dissipation Factor –
The DF/PF of a capacitor tells what
percent of the apparent power input will turn to heat in the
capacitor.
Dissipation Factor
=
E.S.R.
=
(2
π
fC) (E.S.R.)
X
C
The watts loss are:
Watts loss
=
(2
π
fCV
2
) (D.F.)
Very low values of dissipation factor are expressed as their
reciprocal for convenience. These are called the “Q” or
Quality factor of capacitors.
Parasitic Inductance –
The parasitic inductance of capac-
itors is becoming more and more important in the decou-
pling of today’s high speed digital systems. The relationship
between the inductance and the ripple voltage induced on
the DC voltage line can be seen from the simple inductance
equation:
V = L
di
dt
Reactance –
Since the insulation resistance (R
p
) is normally
very high, the total impedance of a capacitor is:
Z=
where
Z
= Total Impedance
R
2
+ (X
C
- X
L
)
2
S
R
s
= Series Resistance
X
C
= Capacitive Reactance =
X
L
= Inductive Reactance
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 identi-
cal in value. In a “perfect” capacitor the current in the
capacitor will lead the voltage by 90°.
39
ETC [ ETC ]
