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General Description
Energy Stored – The energy which can be stored in a
capacitor is given by the formula:
E = 12CV
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:
I
ideal =
C
dV
dt
where
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
Rs = Series Resistance
Rp = Parallel Resistance
Reactance – Since the insulation resistance (Rp) is normally
very high, the total impedance of a capacitor is:
Z =
R2
S + (XC - XL )
2
where
Z = Total Impedance
R
s = Series Resistance
X
C = Capacitive Reactance
=
1
2
π fC
X
L = Inductive Reactance
= 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°.
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.
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 fCV2) (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
R
L
R
C
P
S
I (Ideal)
I (Actual)
Phase
Angle
Loss
Angle
V
IR
s
f
E.S.R.
C