Mallory Aluminum Electrolytic Capacitors Application Guide

Application Guide Aluminum Electrolytic Capacitors

This Application Guide

This guide is a full handbook on aluminum electrolytic
capacitors, of course with emphasis on Cornell
Dubilier’s types. It covers construction in depth and
discloses the latest information on performance and

application for the major aluminum electrolytic types
made worldwide. We encourage you to tell us what more
you’d like to know, so we can improve this guide.

Aluminum Electrolytic Capacitor Overview

Except for a few surface-mount technology (SMT) alu­minum electrolytic capacitor types with solid electro
lyte systems an aluminum electrolytic capacitor con
sists of a wound capacitor element, impregnated with
liquid electrolyte, connected to terminals and sealed in
a can. The element is comprised of an anode foil, paper
separators saturated with electrolyte and a cathode foil.
The foils are high-purity aluminum and are etched with
billions of microscopic tunnels to increase the surface
area in contact with the electrolyte.

While it may appear that the capacitance is between the
two foils, actually the capacitance is between the anode
foil and the electrolyte. The positive plate is the anode
foil; the dielectric is the insulating aluminum oxide on
the anode foil; the true negative plate is the conductive,
liquid electrolyte, and the cathode foil merely connects
to the electrolyte.

They are polar devices, having distinct positive and neg­ative terminals, and are offered in an enormous va

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riety of styles which include molded and can-style SMT
devices, axial and radial-leaded can styles, snap-in ter­minals styles and large-can, screw terminal styles. Rep
resentative capacitance-voltage combinations include

330 µF at 100 V and 6800 µF at 10 V for SMT
devices

100 µF at 450 V, 6,800 µF at 50 V and 10,000
µF at 10 V for miniature-can styles,

1200 µF at 450 V and 39,000 µF at 50 V for
snap-in can styles and

9000 µF at 450 V and 390,000 µF at 50 V for
large-can, screw-terminal styles.

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This construction delivers colossal capacitance because
etching the foils can increase surface area more than
100 times and the aluminum-oxide dielectric is less
than a micrometer thick. Thus the resulting capacitor
has very large plate area and the plates are awfully close
together.

These capacitors routinely offer capacitance values from

0.1 µF to 3 F and voltage ratings from 5 V to 550V.

Capacitor Construction

Rilled

Construction

If two, same-value, aluminum electrolytic capacitors are
connected in series, back-to-back with the positive ter
minals or the negative terminals connected, the result
ing single capacitor is a non-polar capacitor with half
the capacitance. The two capacitors rectify the applied
voltage and act as if they had been bypassed by diodes.
When voltage is applied, the correct-polarity capacitor
gets the full voltage. In non-polar aluminum electrolytic
capacitors and motor-start aluminum electrolyte capaci
tors a second anode foil substitues for the cathode foil to
achieve a non-polar capacitor in a single case.

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Application Guide Aluminum Electrolytic Capacitors

Miniature,

Radial-Leaded T

ype

Snap-in T

ype

Aluminum

Lead Wire

Tabs

Sleeve

Rubber

Can

Capacitor

Element

Terminal

Rubber

Top Disc

Phenolic Disc

Aluminum Tabs

Capacitor Element

Tape

Can

Sleeve

Capacitor Construction

Conventional Cornell Dubilier
Construction Thermal Pak

These figures show typical constructions of the
non-surface-mount aluminum electrolytic capacitors.
Most Cornell Dubilier capacitors use compression-fit
construction so there is no thermoplastic potting com
pound to interfere with safety-vent operation. Thermal
Pak™ and Rilled are Cornell Dubilier’s unique con
structions for computergrade, screw terminal capaci­tors. Compared to conventional, potted construction,
they operate cooler, provide longer life, withstand
higher shock and vibration, deliver more reliable safe
ty vent operation and are lighter weight.

Etching

The anode and cathode foils are made of high purity,
thin aluminum foil, 0.02 to 0.1 mm thick. To increase
the plate area and the capacitance, the surface area in
contact with the electrolyte is increased by etching the
foils to dissolve aluminum and create a dense network
of billions of microscopic tunnels penetrating through
the foil. Etching involves pulling the aluminum foil on
rollers through a chloride solution while applying an
AC, DC or AC-and-DC voltage between the etch solu­tion and the aluminum foil. Surface area can increase

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as much as 100 times for foil in low-voltage capacitors
and 20 to 25 times for high-voltage capacitors.

Forming

The anode foil carries the capacitor’s dielectric. The di
electric is a thin layer of aluminum oxide, Al

2O3

is chemically grown on the anode foil during a process
called “formation.” Formation is accomplished by pull
ing the anode foil on rollers through an electrolyte bath
and continuously applying a DC voltage between the
bath and the foil. The voltage is 135% to 200% of the
final capacitor’s rated voltage. The thickness of the alu
minum oxide is about 1.4 to 1.5 nm for each volt of
the formation voltage, e.g., the anode foil in a 450 V
capacitor may get a formation voltage in excess of 600
V and have an oxide thickness of about 900 nm. That’s
less than a hundredth the thickness of a human hair.

Formation reduces the effective foil surface area be­cause the microscopic tunnels are partially occluded by
the oxide. The tunnel etch pattern is adjusted by choice
of foil and etching process so that low-voltage anodes
have dense tunnel patterns compatible with thin oxide
and high-voltage anodes have coarse tunnel patterns
compatible with thick oxide. The cathode foil is not
formed and it retains its high surface area and dense
etch pattern.

Slitting

­Foil is etched and formed in jumbo rolls of 40 to 50 cm

wide and then slit into various widths according to the

­lengths of the final capacitors.

Winding

The capacitor element is wound on a winding machine

­with spindles for one-to-four separator papers, the an-

ode foil, another set of one-to-four separator papers and
the cathode foil. These are wound into a cylinder and
wrapped with a strip of pressure-sensitive tape to pre­vent unwinding. The separators prevent the foils from
touching and shorting, and the separators later hold the
reservoir of electrolyte.

Before or during winding aluminum tabs are attached
to the foils for later connection to the capacitor termi­nals. The best method is by cold-welding of the tabs to
the foils with tab locations microprocessor controlled
during winding so that the capacitor element’s induc­tance can be less than 2 nH.

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, that

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Application Guide Aluminum Electrolytic Capacitors

The older method of attachment is by staking, a process
of punching the tab through the foil and folding down
the punched metal. Cold welding reduces short-circuit
failures and performs better in high-ripple current and
discharge applications in which the individual stakes
may fail from high current like buttons popping off one
at a time from a fat-man’s vest.

Wound Capacitor Elements

Connecting Terminals

conduction. Common solvents are ethylene glycol
(EG), dimethylformamide (DMF) and gammabutyro
lactone (GBL). Common solutes are ammonium borate
and other ammonium salts. EG is typically used for ca
pacitors rated –20 °C or –40 °C. DMF and GBL are
often used for capacitors rated –55 °C.

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In SMT capacitors and miniature capacitors with rub
ber bungs, extensions of the tabs are the capacitor ter­minals. But in large can capacitors like snap-ins and
screw terminal styles, the tabs are riveted or welded
on the underside of the capacitor tops to terminal in­serts. Welding produces the lowest contact resistance
and highest current handling. Both resistive welding
and ultrasonic welding are used. The up to 12 tab pairs
that may be used in large screw terminal capacitors of­ten require more mechanical support during assembly
so the tabs in such capacitors may be both riveted to
post extensions on the terminals and then welded. In an
axial-leaded capacitor the cathode tab is welded to the
can before sealing.

Impregnation

The capacitor element is impregnated with electrolyte
to saturate the paper separators and penetrate the etch
tunnels. The method of impregnation may involve
immersion of the elements and application of vacuum­pressure cycles with or without heat or, in the case of
small units, just simple absorption. The electrolyte is
a complex blend of ingredients with different formu
lations according to voltage and operating temperature
range. The principal ingredients are a solvent and a
conductive salt – a solute – to produce electrical

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Water in the electrolyte plays a big role. It increases
conductivity thereby reducing the capacitor’s resis
tance, but it reduces the boiling point so it interferes
with high temperature performance, and it reduces
shelf life. A few percent of water is necessary because
the electrolyte maintains the integrity of the aluminum
oxide dielectric. When leakage current flows, water is
broken into hydrogen and oxygen by hydrolysis, and
the oxygen is bonded to the anode foil to heal leakage
sites by growing more oxide. The hydrogen escapes by
passing through the capacitor’s rubber seal.

Sealing

The capacitor element is sealed into a can. While most
cans are aluminum, phenolic cans are often used for
motorstart capacitors. In order to release the hydrogen
the seal is not hermetic and it is usually a pressure clo
sure made by rolling the can edge into a rubber gasket,
a rubber end-plug or into rubber laminated to a phe­nolic board. In small capacitors molded phenolic resin
or polyphenylene sulfide may replace the rubber. Too

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tight a seal causes pressure build up, and too loose a
seal shortens the life by permitting drying out, loss of
electrolyte.

Capacitor-Element Materials

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Application Guide Aluminum Electrolytic Capacitors

Aging

Here the capacitor assembly comes full circle. The last
manufacturing step is “aging” during which a DC voltage
greater than the rated voltage but less than the formation
voltage is applied to the capacitor. Usually the voltage is ap
plied at the capacitor’s rated temperature, but other tem­peratures and even room temperature may be used. This

step reforms the cut edges and any damaged spots on the an
ode foil and covers any bare aluminum with aluminum oxide
dielectric. Aging acts as burn-in and reduces or eliminates
early life failures (infant mortals). Low, initial DC leakage

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current is a sign of effective aging.

Comparison to Other Types of Capacitors

Ceramic Capacitors

Ceramic capacitors have become the preeminent, general
purpose capacitor, especially in SMT chip devices where
their low cost makes them especially attractive. With the
emergence of thinner-dielectric, multilayer units with rated
voltages of less than 10 V capacitance values in the hundreds
of microfarads have become available. This intrudes on the
traditional, high-capacitance province of aluminum electro
lytic capacitors.

Ceramic capacitors are available in three classes according
to dielectric constant and temperature performance. Class 1
(NPO, COG) is suitable for low capacitance, tight tolerance
applications in the range of 1 pF to a few mF. Class 2 (X7R)
has 20 to 70 times as much capacitance per case size, but ca
pacitance typically varies about ± 10% over its –55 to 125 °C
temperature range. The maximum change is +15 % to –25%.
Class 3 (Z5U) with about 5 times the capacitance of Class
2 has wild swings of capacitance with voltage and tempera­ture. The temperature range is –25 °C to 85 °C, and capaci­tance varies about +20% –65% over the range. Ceramic chip
capacitors are brittle and sensitive to thermal shock, so pre­cautions need to be taken to avoid cracking during mounting,
especially for high-capacitance large sizes.

The typical temperature range for aluminum electrolytic
capacitors is –40 °C to 85 °C or 105 °C. Capacitance var
ies about +5% –40% over the range with the capacitance
loss all at cold temperatures. Capacitors rated –55 °C gener­ally only have –10 % to –20 % capacitance loss at –40 °C.
Cold temperature performance for rated voltages of 300 V
and higher is often worse, and temperature performance var
ies by manufacturer. Thus Class 1 and 2 ceramic capacitors
perform better than aluminum electrolytic capacitors at cold
temperatures, and Class 3 ceramic capacitors perform worse
at all temperatures.

Aluminum electrolytic capacitors readily deliver much
more capacitance. Aluminum electrolytic capacitors give
more capacitance and energy storage per unit volume than
ceramic capacitors for all types except for low-voltage,
Class 3 ceramic SMT chip capacitors. While tolerances of
±5% and ±10% are routine for ceramic capacitors, ± 20%
and –10% +50% are the norms for aluminum electrolytic.

This makes aluminum electrolytics the choice for high ca­pacitance applications like rectification filters and power
holdup where more capacitance is a bonus. Ceramic ca
pacitors are not polarized and therefore can be used in AC
applications. The low DF and high capacitance stability of
Class 1 and 2 are especially suited to AC and RF applica

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tions. By comparison, aluminum electrolytic capacitors are
polarized and cannot withstand voltage reversal in excess of

1.5 V. While non-polar aluminum electrolytics are available
for momentary-duty AC applications like motor starting and
voltage-reversing applications, the high DF of aluminum
electrolytic capacitors – from 2% to 150% – causes excess
heating and short life in most AC applications.

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Ceramic capacitors are generally no more reliable than alu
minum electrolytic capacitors because aluminum electrolyt­ics self heal. Since high-capacitance ceramic capacitors may
develop micro-cracks, aluminum electrolytic capacitors are
preferred for high capacitance values. However, small sizes
of aluminum electrolytic capacitors may have limited life
due to dry out, so consider reliability in your choice for ap­plications operating at high temperatures, over 65 °C.

Film Capacitors

Film capacitors offer tight capacitance tolerances, very low

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leakage currents and small capacitance change with temper­ature. They are especially suited to AC applications through
their combination of high capacitance and low DF that per­mits high AC currents. However, they have relatively large
sizes and weights.

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The popular polymers used for plastic-film dielectric
tors are polyester and polypropylene. The popular polymer
for SMT devices is polyphenylene sulfide (PPS). While film/
foil construction is often used for small capacitance values
– less than 0.01 µF – and for high-current applications, met­allized-film is usually preferred because it gives smaller size,
lower cost and is self healing. Film capacitors are general­purpose capacitors for through-hole applications and have
special uses for tight-tolerance, AC voltage, high voltage and
snubbing.

Polyester film capacitors operate from –55 °C to 85 °C at

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capaci-

CDM Cornell Dubilier • 140 Technology Place • Liberty, SC 29657 • Phone: [phone] • Fax: [phone] • www.cde.com

Application Guide Aluminum Electrolytic Capacitors

rated voltage; +85 °C to 125 °C with linear voltage derating­to 50% rated voltage. The typical capacitance change over
the entire range is less than –5% +15% with ±1% from 0 °C
to 50 °C. Capacitance values are readily available up to 10
µF with special large sections to 100 µF. Generally available
voltages are 50 to 1000 Vdc and 35 to 600 Vac. AC current
handling is limited by polyester’s high temperature DF of
about 1%.

Polypropylene film capacitors operate from –55 °C to 85 °C
at rated voltage; 85 °C to 105 °C with linear voltage derating
to 50% rated voltage. The typical capacitance change over
the entire range is less than +2% –4% with ±1% from –20
°C to 60 °C. Capacitance values are readily available up to
65 µF with special large sections to 1000 µF. Generally avail
able voltages are 100 to 3000 Vdc and 70 to 500 Vac. AC
current handling permits use in motor-run and other continu
ous duty AC applications.

Compared to aluminum electrolytic capacitors, film capaci
tors take teh lead in high voltage, AC voltage and tight toler
ance applications. Aluminum electrolytics excel in capaci­tance and energy storage.

Solid Tantalum Capacitors

Like aluminum electrolytic capacitors solid tantalum
capacitors are polar devices (1 V maximum reverse voltage),
having distinct positive and negative terminals and are of
fered in a variety of styles. Case styles include both molded
and conformal-coated versions of

radial, axial and surface

mount configurations. Typical capacitance values are from

0.1 µF to 1000 µF in voltage ratings from 2 V to 50 V. Typi­cal maximum capacitance-voltage combinations are ap­proximately 22 µF at 50 V for leaded styles and 22 µF at
35 V for surface mount. Strengths are temperature stability,
volumetric efficiency and compatibility with all automated
assembly systems. Weaknesses are the limited voltage and
capacitance ranges and a short-circuit failure mode accom­panied by catching fire.

The operating temperature range is –55 °C to 85 °C at rated
voltage; +85 °C to 125 °C with linear voltage derating to
2/3 rated voltage. The typical capacitance change over the
entire range is less than ±5%. Thus aluminum electrolytic

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capacitors have a much broader voltage and capacitance
ranges than solid tantalum capacitors but perform worse at

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cold temperature.

Solid tantalum capacitors are generally considered more re

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liable than aluminum electrolytic capacitors because solid

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tantalum capacitors do not wear out. Their failure rate de­creases with time, while aluminum electrolytic capacitors
wear out by drying out. As a practical matter, dry-out only
affects the smallest capacitors operating in high-temperature
environments.

Larger aluminum electrolytics do not dry out in the 10 to 20

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years expected of most applications, and the open-circuit,
dry-out failure is benign compared to solid-tantalum’s short
circuit failure mode.

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Characterization

Resistance Rs is the equivalent series resistance, and it

CIRCUIT MODEL

Capacitance occurs when two electrical conductors are sepa­rated by an insulator. A capacitor is an electronic component
optimized to deliver capacitance. The capacitance in pF is

C = 0.08855(n-1) ε A/d

Where n is the number of plates for electrodes, ε is the
dielectric constant, A is the plate surface area in cm
is the thickness of the dielectric between the plates in cm.
Dielectric constant is the multiplier increase in capacitance
that the dielectric delivers compared to a vacuum. The
dielectric constant for aluminum oxide is about 8.

The circuit at the right models the aluminum electrolytic
capacitor’s normal operation as well as overvoltage and
reverse-voltage behavior. Capacitance C is the equivalent
capacitance and it decreases with increasing frequency.
Common values range from

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1 µF to 1 F, a six-decade range.

2

and d

decreases with increasing frequency and temperature. It in­creases with rated voltage. Typical values range from 10 m�
to 1 Ω , and Rs is inversely proportional to capacitance for a
given rated voltage.

Inductance Ls is the equivalent series inductance, and it is
relatively independent of both frequency and temperature.
Typical values range from 10 nH to 30 nH for radial-leaded
types, 20 to 50 nH for screw-terminal types, and up to 200
nH for axial-leaded types. It increases with terminal spac­ing.

Equivalent Circuit

Application Guide Aluminum Electrolytic Capacitors

Resistance Rp is the equivalent parallel resistance and ac­counts for leakage current in the capacitor. It increases with
increasing capacitance, temperature and voltage, and it de
creases with time. Typical values are on the order of 100/C
MΩ with C in µF.

Zener diode D models overvoltage and reverse voltage be
havior. Application of overvoltage on the order of 50 V be
yond the capacitor’s surge voltage rating causes high leak
age current and a constant-voltage operating mode quite like
the reverse conduction of a zener diode.

Parameter Unit Symbol Formula Approximately

Capacitance farads (F) C

Capacitive reactance

ohms (Ω)

Current amperes (A) I C(dV/dt), Vz/Z

Dissipation factor none DF

Energy

Equivalent series resistance

joules (J) E ½CV²

ohms (Ω)

Frequency hertz (Hz) f

Impedance

ohms (Ω)

Inductance henries (H) Ls

Inductive reactance

ohms (Ω)

Loss angle degrees (°)

Phase angle degrees (°)

Power watts (W) P I²Rs, I²XcDF,(VA)(PF)

Power factor none PF

Quality factor none Q

Self-resonant frequency hertz (Hz)

Voltage

volts (V) V Vc=IXc, Vz=IZ

Volt-amperes V-A VA

Application of reverse voltage much beyond 1.5 V causes
high leakage current quite like the forward conduction of a
diode. Neither of these operating modes can be maintained

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for long because hydrogen gas is produced by the capaci
tor, and the pressure build up will cause failure. In terms
of parameters in the next section, Rated Capacitance is C,
Dissipation Factor is 2

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is Rs, Impedance is

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and Inductance is Ls. The table below expresses these and
other parameters in terms of the equivalent-circuit model.

[(Rs)2 + (1/(2πfC) – 2πfLs)2 ]

Xc

Rs/Xc, 2πfCRs, tan δ, cot θ

Rs

Z [Rs²+ (Xc–XL)²]

X

L

δ

θ

Rs/Z, sin δ, cos θ

Xc/Rs, 1/DF, cot

ω

o

πfCRs, Equivalent Series Resistance

1⁄2

1/(2πfC)

PF

DF/(2πfC)

½

Xc

2πfLs

tan-1 DF
cot-1 DF

DF

δ, tan θ

1/PF

1/[2π(LC)½]

Z

IVz, I²Z

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Parameters

TEMPERATURE RANGE

Operating Temperature Range

The Operating Temperature Range is the temperature range
over which the part will function, when electrified, within
the limits given in the specification. It is the range of ambient
temperatures for which the capacitor has been designed to
operate continuously. Largely the formation voltage sets the
high-temperature limit. Higher formation voltages permit
higher operating temperatures but reduce the capacitance.
The low-temperature limit is set largely by the cold resistiv­ity of the electrolyte. The higher cold resistivity increases
the capacitor’s ESR 10 to 100 fold and reduces the available
capacitance.

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Typical temperature ranges are –20 °C to 55 °C, –25 °C
to 85 °C, –40 °C to 85 °C, –55 °C to 85 °C, –40 °C to
105 °C, –55 °C to 105 °C and –55 °C to 125 °C.

Storage Temperature Range

The Storage Temperature Range is the temperature range to
which the part can be subjected unbiased, and retain confor­mance to specified electrical limits. It is the range of ambient
temperatures over which the capacitor may be stored without
damage for short periods. For long periods of storage keep
capacitors at cool room temperatures and in an atmosphere
free of halogen gases like chlorine and fluorine that can cor­rode aluminum. Storage temperature ranges are from –55
°C to the upper limit of the operating-temperature ranges.

Application Guide Aluminum Electrolytic Capacitors

CAPACITANCE

The rated capacitance is the nominal capacitance and it is
specified at 120 Hz and a temperature of 25 °C. The rated
capacitance is also the capacitance marked on the unit.

here DF is a unit-less number express in percent, test fre
quency f is

i

n Hz, capacitance C

is in µF and ESR is in

Ω.

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Capacitance Tolerances

Capacitance tolerance is the permitted minimum and maxi
mum capacitance values expressed as the percentage de­crease and increase from the rated capacitance, ΔC/C. Typi­cal capacitance tolerances are ±20%, –10% +50%, and –10%
+75%.

Tighter tolerances are more readily available in high volt
age capacitors, e.g., above 150 V, but tolerances tighter than
±10% are generally not available. Note that tighter tolerance
parts may meet other tolerance requirements and are readily
substitutable. The capacitance varies with temperature and
frequency. This variation itself is also dependent on the rated
voltage and capacitor size.

Capacitance Measurement

For aluminum electrolytic capacitors, capacitance is mea
sured as the capacitance of the equivalent series circuit at 25
°C in a measuring bridge supplied by a 120 Hz source free of
harmonics with maximum AC signal voltage of 1 V rms and
no forward-bias voltage.

DF Measurement

The measurement of DF is carried out at +25 °C, 120 Hz,

­and no voltage bias, with a maximum 1 Vac rms signal volt

age free of harmonics. The value of DF is temperature and
frequency dependent.

DF Temperature Characteristics

The dissipation factor decreases with increasing temperature.

­DF declines about 50% from 25 °C to the high-temperature

limit, but increases more than 10 fold at the low temperature
limit. The DF of the better devices rated –55 °C increases
less than 5 times at –40 °C.

DF

defined in the next paragraph, varies little with tem-

lf,

perature and ESR

, also in the next paragraph, increases 10

hf

to 100 times from 25 °C to the low-temperature limit. The
increase in DF at cold temperatures is set by the ESRhf.

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DF Frequency Characteristics

The dissipation factor varies with frequency at high frequen
cies. DF can be modeled as below:

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Capacitance Temperature Characteristics

The capacitance varies with temperature. This variation it
self is dependent to a small extent on the rated voltage and
capacitor size. Capacitance increases less than 5% from 25
ºC to the high-temperature limit. For devices rated –40 °C
capacitance typically declines 20% at –40 °C for low-volt
age units and up to 40% for high-voltage units. Most of the
decline is between –20 °C and –40 °C. For devices rated
–55 °C capacitance typically declines less than 10% at –40
°C and less than 20% at –55 °C.

Capacitance Frequency Characteristics

The effective capacitance decreases as frequency increases.
Self-resonance is typically below 100 kHz depending on ca­pacitance. At self-resonance the device is resistive and be
yond it is inductive. The termination style (i.e., axial, radial,
screw-terminal) will influence the inductive characteristics.
Small radial-leaded capacitors have inductance of less than
20 nH. Larger capacitors have more inductance according to
terminal spacing.

DISSIPATION FACTOR (DF)

Dissipation factor is the measurement of the tangent of the
loss angle (tan

δ) expressed as a percentage. It is also the ratio

of the ESR to the capacitive reactance and is thus related to
ESR by this equation:
DF = 2πfC(ESR)/10,000

DF = DFlf + 2πfC(ESRhf)/10,000

­Where DF is a the total dissipation factor in percent, DF

the low-frequency dissipation factor in percent, ESR
high-frequency ESR in
C is the capacitance in µF at the test frequency. DF

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Ω, f is the test frequency in Hz and

hf

results

lf

from the power lost by the applied electric field in orient­ing he molecules of the aluminum oxide dielectric. ESR
results from the resistive losses in the foils, connections and
the electrolyte/separator pad. The electrolyte/ separator pad
resistance usually dominates and its resistance varies little
with frequency. DF

ranges from about 1.5% to 3%. ESRhf

lf

ranges from 0.002 to 10 and decreases with temperature.

The DF equation above shows that DF is constant for low fre

­quencies and crosses over to increasing-DF, constant ESR, at

a crossover frequency inversely proportional to capacitance.
Since high-capacitance capacitors have low crossover fre
quencies, DF increases more with increasing frequency than
for lower-capacitance capacitors.

EQUIVALENT SERIES RESISTANCE (ESR)

The equivalent series resistance (ESR) is a single resistance
representing all of the ohmic losses of the capacitor and con
nected in series with the capacitance.

is

lf

is the

hf

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