General Description
Energy Stored – The energy which can be stored in a
capacitor is given by the formula:
I (Ideal)
I (Actual)
E = 1⁄ CV2
2
Loss
Angle
Phase
Angle
E = energy in joules (watts-sec)
V = applied voltage
␦
C = capacitance in farads
f
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:
V
IRs
dV
dt
In practice the current leads the voltage by some other
phase angle due to the series resistance RS. The comple-
ment of this angle is called the loss angle and:
Iideal
=
C
where
I = Current
C = Capacitance
dV/dt = Slope of voltage transition across capacitor
Power Factor (P.F.) = Cos f or Sine ␦
Dissipation Factor (D.F.) = tan ␦
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.
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 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:
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.
C = Capacitance
L = Inductance
Rp = Parallel Resistance
Rs = Series Resistance
R P
E.S.R.
C
L
R S
Dissipation Factor – The DF/PF of a capacitor tells what
percent of the apparent power input will turn to heat in the
capacitor.
C
Reactance – Since the insulation resistance (Rp) is normally
very high, the total impedance of a capacitor is:
E.S.R.
Dissipation Factor =
= (2 π fC) (E.S.R.)
XC
The watts loss are:
2
2
Z = RS + (XC - XL)
ͱ
Watts loss = (2 π fCV2) (D.F.)
where
Z = Total Impedance
Rs = Series Resistance
XC = Capacitive Reactance =
Very low values of dissipation factor are expressed as their
reciprocal for convenience. These are called the “Q” or
Quality factor of capacitors.
1
2 π fC
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:
XL = 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°.
di
dt
V = L
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