seconds, then leave the capacitor to
recover for 60 seconds.- Connect a high-resistance voltmeter
to the capacitor terminals and readthe
recovery voltage present.
The value of dielectric absorption can
be determined from:VR is the recovery voltage and VS is the
charging supply voltage.
For example, if a capacitor is charged
from a 63V supply (its rated working
voltage) and it exhibits a recovery
voltage of 9V, then the value of dielectric
absorption will be given by:Equivalent series inductance
A capacitor’s equivalent series inductance
(ESL) is the effective inductance of
the capacitor expressed as a single
inductance considered to be connected
in series with a perfect inductor (see
Fig.6.8). It is important to note that ESL
is made up of the sum of the internal
inductance and the inductance of the
conducting path between the capacitor
plates and its external connections. ESL
reduces the effectiveness of a capacitor
at high frequencies. It is also responsible
for a sharp dip in impedance that occurs
at the series resonant frequency of some
types of capacitor. Depending on the
component type and value, this resonant
effect occurs at frequencies of between
about 700kHz for a small axial lead
electrolytic capacitor to around 40MHz
for small PCB-mounting film dielectric
capacitors. ESL is mostly of concern for
power-supply filtering in high-frequency
switched-mode power supplies.Insulation resistance
A capacitor’s insulation resistance (IR)
is the parallel (or ‘shunt’) resistance
of a capacitor (see Fig.6.8). Insulation
resistance is usually specified in MΩ (a
typical value for an electrolytic capacitor
being in the range 1MΩ to 10MΩ). The
lower values of insulation resistance
are associated with higher values ofefficiency is mainly determined by
the dielectric constant (k) and the
construction of the capacitor. It’s worth
noting that for a given dielectric material,
the volume of a capacitor varies roughly
with the square of its maximum voltage
rating. Thus a 63V capacitor is likely to
have around 100 times the volume of a
similar component rated at a mere 6.3V!
The energy density (ED) of a capacitor
is related to its volumetric efficiency.
Energy density is given by:where C is the capacitance and V is the
working voltage.Maximum ripple current
The maximum ripple current of a
capacitor is the maximum RMS current
(usually quoted in amps) that can be
allowed to flow in the capacitor at
a specified frequency. Note that the
permissible ripple current for a capacitor
is limited by the capacitor’s internal
temperature, which increases due to
internal power dissipation associated
with its ESR.Dielectric absorption (DA)
Few electronic enthusiasts can fail
to have noticed that, once charged, a
capacitor seems to retain some of the
charge, even after a concerted attempt
is made to discharge it! Even shorting
its terminals for several seconds can
stubbornly fail to remove the charge from
a large value capacitor. The reason for
this puzzling phenomenon is dielectric
absorption (sometimes referred to as
‘voltage retention’ or ‘soakage’) resulting
in the generation of a potential between
the terminals of a capacitor after it has
been discharged.
Dielectric absorption can be checked
using the following simple procedure:- Charge the capacitor to its rated
voltage (eg, 63V, 100V or 150V) for
five minutes. - Disconnect the capacitor from its
charging supply. - Short the capacitor’s terminals for five
power supplies (ie, 50kHz to 150kHz).
Note also that the power loss in a capacitor
increases with ESR. Because ESR is so
important to the correct operation of a
capacitor (it is often the reason why an
apparently ‘good’ component fails to
work) we shall examine this in much
greater detail later.Dissipation factor
The dissipation factor (D or DF) of a
capacitor is the ratio of the effective
series resistance (ESR) of a capacitor to
its reactance (XC) at a specified frequency.
Dissipation factor is sometimes also
referred to as ‘tanδ’, i.e. the tangent of the
angle in which ESR (RE) and XC are the
adjacent sides of a right-angle triangle.D = tan δNote that dissipation factor is usually
quoted for sinusoidal AC power
applications and is less meaningful
when conditions are non-sinusoidal
(as in switched-mode power supplies).
Dissipation factor is given by:To help put this into context, consider
the following example. A capacitor of
68μF with an ESR of 1.5Ω is used at a
frequency of 50Hz. The dissipation factor
can be determined from:Quality factor
The quality factor (Q or QF) is the ratio
of capacitive reactance (XC) to ESR (RE)
at a specified frequency. QF is the inverse
of the dissipation factor, hence:Volumetric efficiency and
energy density
The volumetric efficiency (VE) of
a capacitor is a measure of how
much capacitance is provided for a
given component volume. Volumetric×
−××−
−−
×× × −
−EE
E
C2
1
2RR
DF fCR
X
fCππ== =
⎛⎞
⎜⎟
⎝⎠π ××× ×−1 1××× × ××⎛⎞
⎜⎟⎝⎠× ×⎛⎞
⎜⎟
⎝⎠× ×⎛⎞
⎜⎟
⎝⎠×
−××−
−−
×× × −
−ππ⎛⎞
⎜⎟
⎝⎠π ××× ×−1
Q
D= and1
D
Q=^CV××× × ××⎛⎞
⎜⎟
⎝⎠× ×⎛⎞
⎜⎟⎝⎠× ×⎛⎞
⎜⎟
⎝⎠×
−××−
−−
×× × −
−ππ⎛⎞
⎜⎟
⎝⎠π ××× ×−EDCV
volume×
=×× × ××⎛⎞
⎜⎟
⎝⎠× ×⎛⎞
⎜⎟
⎝⎠× ×⎛⎞
⎜⎟⎝⎠×
−××−
−−
×× × −
−ππ⎛⎞
⎜⎟
⎝⎠π ××× ×−××(^71) 100% 100%
63 9
DA= × = × = ×
×⎛⎞
⎜⎟
⎝⎠
× ×⎛⎞
⎜⎟
⎝⎠
× ×⎛⎞
⎜⎟
⎝⎠
×
−
××−
−
−
×× × −
−
π
π
⎛⎞
⎜⎟
⎝⎠
π ××× ×−
×
×
× ×100% 0.11 100% 11%= × =
×⎛⎞
⎜⎟
⎝⎠
× ×⎛⎞
⎜⎟⎝⎠
× ×⎛⎞
⎜⎟⎝⎠
×
−
××−
−
−
×× × −
−
π
π
⎛⎞
⎜⎟
⎝⎠
π ××× ×−
×
R
S
100%
V
DA
V
= ×
× × ×
×⎛⎞
⎜⎟⎝⎠
× ×⎛⎞
⎜⎟
⎝⎠
× ×⎛⎞
⎜⎟
⎝⎠
×
−
××−
−
−
×× × −
−
π
π
⎛⎞
⎜⎟
⎝⎠
DF== 2 πfCRE 6.28 50 68 10××× ×−^6 1.5=
1 1
×
×
× × ×
×⎛⎞
⎜⎟⎝⎠
× ×⎛⎞
⎜⎟
⎝⎠
× ×⎛⎞
⎜⎟
⎝⎠
×
−
××−
−
−
×× × −
−
π
π
⎛⎞
⎜⎟
⎝⎠
π ××× ×− 1.5 0.032= or 3.2%
1 1
×
×
× × ×
×⎛⎞
⎜⎟
⎝⎠
× ×⎛⎞
⎜⎟
⎝⎠
× ×⎛⎞
⎜⎟⎝⎠
Fig.6.6. Four large electrolytic
capacitors connected in parallel to
form a large reservoir capacitance at
the high-voltage DC input of a high-
current switched-mode power supply.
Fig.6.7. Surface-mounte reservoir
capacitors in a low-power switched-
mode power supply.
Fig.6.8. Equivalent circuit of a
capacitor.