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An electrolytic capacitor is a polarized capacitor which anode electrode is made of a special metal on which by anodically oxidation (forming) an insulating oxide layer originates, which acts as the dielectric of the electrolytic capacitor. A non-solid or solid electrolyte which covers the surface of the oxide layer serves as second electrode (cathode) of the capacitor.

Depending on the used nature of the anode metal the family of electrolytic capacitors are divided into three family members:

• Aluminum electrolytic capacitors,
• Tantalum electrolytic capacitors and
• Niobium electrolytic capacitors

Electrolytic capacitors store the electric energy statically by charge separation in an electric field in the dielectric oxide layer between two electrodes like other conventional capacitors. The non-solid or solid electrolyte is the cathode and thus forms the second electrode of the capacitor. This and the storage principle distinguishes them from electrochemical supercapacitors, in which the electrolyte is the conductive connection between two electrodes and the storage occur with double-layer capacitance and pseudocapacitance.

Electrolytic capacitors have - based on the volume - a much higher specific electric capacitance compared to ceramic capacitors and film capacitors, but articulately smaller capacitance than supercapacitors.

All electrolytic capacitors are polarized components by the manufacturing principle and may only be operated with DC voltage. Voltages with reverse polarity, voltage or ripple current higher than specified can destroy the dielectric and thus the capacitor. A possible ripple voltage must not cause reversal. The destruction of electrolytic capacitors can have catastrophic consequences (explosion, fire).

Bipolar electrolytic capacitors which may be operated with AC voltage are special constructions with two anodes connected in revers polarity.

The large capacitance of electrolytic capacitors makes them particularly suitable for passing or bypassing low-frequency signals and storing large amounts of energy. They are widely used in power supplies, and interconnecting stages of amplifiers at audio frequencies.

Basic informations

Basic principle

Electrolytic capacitors are using a chemical feature of some special metals, earlier called “valve metals”, on which by anodically oxidation an insulating oxide layer serves as dielectric originates. Applying a positive voltage to the anode material in an electrolytic bath an oxide barrier layer with a thickness corresponding to the applied voltage will be formed (formation). This oxide layer acts as dielectric in an electrolytic capacitor.

Main difference of the three types of electrolytic capacitors is the used anode material and their oxide as dielectric:

• Aluminum electrolytic capacitors use a high purity etched aluminum foil with aluminum oxide as dielectric
• Tantalum electrolytic capacitors use a sintered pellet (“slug”) out of high purity tantalum powder with tantalum pentoxide as dielectric
• Niobium electrolytic capacitors use a sintered “slug” out of high purity niobium or niobium oxide powder with niobium pentoxide as dielectric.

All anode materials are either etched or sintered and have a rough surface structure with a much higher surface compared to a smooth surface of the same area or the same volume. Applying a positive voltage to the above mentioned anode material in an electrolytic bath an oxide barrier layer with a thickness corresponding to the applied voltage will be formed (formation). This oxide layer acts as dielectric in an electrolytic capacitor. The properties of this oxide layers are given in the following table:

After forming a dielectric oxide on the rough anode structure a counter-electrode has to match the rough insulating oxide surface. This will be done by the electrolyte which acts as cathode electrode of an electrolytic capacitor. There are a lot of different electrolytes in use. Generally they will be distinguished into two species, “non-solid” and “solid” electrolytes. Non-solid electrolytes as a liquid medium which have a ion conductivity by moving ions can fit the rough structures easily. Solid electrolytes which have an electron conductivity can fit the rough structures by special chemical processes like pyrolysis for manganese dioxide or polymerization for conducting polymers.

The anodic generated insulating oxide layer becomes destroyed if the polarity of the applied voltage changes.

Every electrolytic capacitor in principle forms a "plate capacitor" whose capacitance is greater, the larger the electrode area A and the permittivity ε are and the thinner the thickness (d) of the dielectric is.

${\displaystyle C=\varepsilon \cdot {\frac {A}{d}}}$

The dielectric thickness of electrolytic capacitors is very thin in the range of nano-meter per volt. Otherwise the voltage strengths of these oxide layers are quite high. With this very thin dielectric oxide layer combined with a sufficient high dielectric strength the electrolytic capacitors can already achieve a high volumetric capacitance. This is one reason for the high capacitance values of electrolytic capacitors compared to conventional capacitors.

All etched or sintered anodes have a much higher surface compared to a smooth surface of the same area or the same volume. That increases the later capacitance value, depending on the rated voltage, by the factor of up to 200 for non-solid aluminum electrolytic capacitors as well as for solid tantalum electrolytic capacitors. The large surface compared to a smooth one is the second reason for the relatively high capacitance values of electrolytic capacitors compared with other capacitor families.

One special advantage is given for all electrolytic capacitors. Because the forming voltage defines the oxide layer thickness the voltage proof of the later electrolytic capacitor can be produced very simple for the desired rated value. Therefore the volume of a capacitor is defined by the product of capacitance and voltage, the so-called “CV-Volume”.

However, comparing the permittivities of the different oxide materials it is seen that tantalum pentoxide has an approximately 3 times higher permittivity than aluminum oxide. Tantalum electrolytic capacitors of a given CV value therefore are smaller than aluminum electrolytic capacitors but tantalum and niobium electrolytic capacitors may have similar CV-volumes.

Basic construction of non-solid aluminum electrolytic capacitors

Basic construction of solid tantalum electrolytic capacitors

Types and features of electrolytic capacitors

Electrolytic capacitors family tree

Out of the basic construction principles of electrolytic capacitors it has grown three different types: aluminum, tantalum and niobium electrolytic capacitors. Each of this three capacitor families uses non-solid and solid manganese dioxide or solid polymer electrolytes so that now a great spread of different types as combination of anode material and solid or non-solid electrolyte are available.

Properties of electrolytic capacitor types

The non-solid or so-called "wet" aluminum electrolytic capacitors were and are the cheapest among all other conventional capacitors. They not only provide the cheapest solutions for high capacitance or voltage values for decoupling and buffering purposes but are also insensitive to low ohmic charging and discharging as well as to low-energy transients. The non-solid electrolytic capacitors can be found in nearly all areas of electronic devices with the exception of military applications.

Tantalum electrolytic capacitors with solid electrolyte as surface-mountable chip capacitors are mainly used in electronic devices in which little space is available or a low profile is required. They operate reliable over a wide temperature range without large parameter deviations. In military and space applications only tantalum electrolytic capacitors do have the necessary approvals.

Niobium electrolytic capacitors are in direct competition with industrial tantalum electrolytic capacitors because niobium is more readily available. Their properties are comparable to each other.

The electrical properties of aluminum, tantalum and niobium electrolytic capacitors have been greatly improved by the polymer electrolyte.

Comparison of electrolytic capacitor types

The combination of anode materials for electrolytic capacitors and the electrolytes used a wide variety of capacitor types with different properties has formed. An outline of the main characteristics of the different types is shown in the table below.

The non-solid or so-called "wet" aluminum electrolytic capacitors were and are the cheapest among all other conventional capacitors. They not only provide the cheapest solutions for high capacitance or voltage values for decoupling and buffering purposes but are also insensitive to low ohmic charging and discharging as well as to low-energy transients. The non-solid electrolytic capacitors can be found in nearly all areas of electronic devices with the exception of military applications.

Tantalum electrolytic capacitors with solid electrolyte as surface-mountable chip capacitors are mainly used in electronic devices in which little space is available or a low profile is required. They operate reliable over a wide temperature range without large parameter deviations. In military and space applications only tantalum electrolytic capacitors do have the necessary approvals.

Niobium electrolytic capacitors are in direct competition with industrial tantalum electrolytic capacitors because niobium is more readily available. Their properties are comparable to each other.

The electrical properties of aluminum, tantalum and niobium electrolytic capacitors have been greatly improved by the polymer electrolyte.

Comparison of electrical parameters

In order to compare the different characteristics of the different electrolytic capacitor types capacitors with the same dimensions and of similar capacitance and voltage are compared in the following table. In such a comparison the values for ESR and ripple current load are the most important parameters for the use of electrolytic capacitors in modern electronic equipment. The lower the ESR the higher the ripple current per volume the better the functionality of the capacitor in the circuit. However, better electrical parameters mostly are combined with the higher price. In the first line of the table is to see a capacitor out of 1976, all other are today’s available products.

) 100 µF/10 V, unless otherwise specified,

) calculated for a capacitor 100 µF/10 V,

) out of a datasheet from 1976

Styles of aluminum and tantalum electrolytic capacitors

Aluminum electrolytic capacitors form the bulk of the electrolytic capacitors used in electronics because of the large diversity of sizes and of its inexpensive production. Tantalum electrolytic capacitors, usually used in the SMD version, have a higher specific capacitance than the aluminum electrolytic capacitors and are used in devices with limited space or flat design such as laptops. They are also used in military technology, mostly in axial style hermetic sealed. Niobium electrolytic chip capacitors are a new development in the market, and are intended as a replacement for tantalum electrolytic chip capacitors.

History

The phenomenon that can form an oxide layer on aluminum and other metals like tantalum, niobium, manganese, titanium,zinc, cadmium etc. in an electrochemical process, which block an electric current to flow in one direction but allow to flow in the other direction, however, it was discovered in 1875 by the French researcher and founder Eugène Ducretet. He coined for this kind of metals the term „valve metal“.

Charles Pollak (born Karol Pollak), a producer of accumulators, found out, that that the oxide layer on an aluminum anode remained stable in a neutral or alkaline electrolyte, even when the power was switched off. In 1896 he handed out this idea of an Electric liquid capacitor with aluminium electrodes (de: Elektrischer Flüssigkeitskondensator mit Aluminiumelektroden) as a patent of using the oxide layer in a polarized capacitor in combination with a neutral or slightly alkaline electrolyte.

The first industrial realized electrolytic capacitors consisted out of a metallic box used as cathode, filled with a borax electrolyte solved in water, in which a folded aluminum anode plate was inserted. Applying a DC voltage from outside the oxide layer was formed on the surface of the anode. The advantage of these capacitors was that they were significantly smaller and cheaper than all other capacitors at this time related on the realized capacitance value. This construction with different styles of anode construction but with a case as cathode and as container for the electrolyte would be used up to the 1930s years and was called “wet” electrolytic capacitor, in the sense of containing a high water content.

The first more common application of wet aluminum electrolytic capacitors was in large telephone exchanges, to reduce relay hash (noise) on the 48 volt DC power supply. The development of AC-operated domestic radio receivers in the late 1920s created a demand for large-capacitance (for the time) and high-voltage capacitors for the valve amplifier technique, typically at least 4 microfarads and rated at around 500 volts DC. Waxed paper and oiled silk film capacitors were available, but devices with that order of capacitance and voltage rating were bulky and prohibitively expensive.

The ancestor of the modern electrolytic capacitor was patented by Samuel Ruben in 1925. teamed with Philip Mallory, the founder of the battery company that is now known as Duracell International. Rubens idea adopted the stacked construction of a silver mica capacitor. He introduce a separated second foil to contact the electrolyte adjacent the anode foil instead of using the electrolyte filled container as cathode of the capacitor. The stacked second foil got it's own terminal additional to the anode terminal and the container had no electrical function any more. This type of electrolytic capacitors combined with an employed liquid or gel-like electrolyte of a non-aqueous nature, which is therefore dry, in the sense of containing a very low water content, was became known as the “dry” type of electrolytic capacitor.

With Rubens invention, together with the invention of wound foils separated with a paper spacer 1927 by A. Eckel, Hydra-Werke (Germany) the actual development of e-caps began.

William Dubilier whose first patent for electrolytic capacitors was fined in 1928 and Ezra Cornell industrialized the new ideas for electrolytic capacitors and started the first larger commercial production in 1931 as Cornell-Dubilier (CD) factory in Plainfield, NJ. At the same time in Germany, Berlin, the “Hydra-Werke”, an AEG company, has started the production of e-caps in larger quantities.

Even in his patent from 1896 Pollak wrote, that the capacitance of the capacitor increase by roughen the surface of the anode foil. Today (2014) the electro-chemically etching of low voltage foils can be reached an up to 200 fold increase in surface area compared to a smooth surface. The progress of the etching process is the reason for the ongoing dimension reductions in the aluminum electrolytic capacitors over the last decades.

The first tantalum electrolytic capacitors were developed in 1930 by Fansteel Metallurgical Corporation for military purposes They adopt the basic construction of a wound cell and used a tantalum anode foil together with a tantalum cathode foil separated with a paper spacer impregnated with a liquid electrolyte.

The relevant development of solid electrolyte tantalum capacitors began some years after William Shockley, John Bardeen and Walter Houser Brattain invented the transistor 1947. It was invented by Bell Laboratories in the early 1950s as a miniaturized, more reliable low-voltage support capacitor to complement their newly invented transistor. The solution R. L. Taylor and H. E. Haring from the Bell labs found for the new miniaturized capacitor found in early 1950 was based on experiences with ceramics. They grind down tantalum to a powder, pressed this powder into a cylindrical form and then sintered the powder particles at high temperature between 1500 and 2000 °C under vacuum conditions to a pellet (“slug”).

These first sintered tantalum capacitors used a non-solid electrolyte, what don’t fit the concept of solid electronics. 1952 a targeted search in the Bell Labs for a solid electrolyte by D. A. McLean and F. S. Power led to the invention of manganese dioxide as a solid electrolyte for a sintered tantalum capacitor.

Although the fundamental inventions came from the Bell Labs the inventions for manufacturing commercially viable tantalum electrolytic capacitors was done by researchers of Sprague Electric Company. Preston Robinson, Spragues Director of Research is considered to be the actual inventor of tantalum capacitors 1954 His invention was supported by R. J. Millard, who introduced the “reform” step 1955 , a significant improvement in which the dielectric of the capacitor was repaired after each dip-and-convert cycle of MnO2 deposition which dramatically reduced the leakage current of the finished capacitors. This first solid electrolyte manganese dioxide had a 10 times better conductivity than all other types of non-solid electrolyte. It also influenced the development of aluminum electrolytic capacitors. 1964 came, developed by Philips, the first aluminum electrolytic capacitors with solid electrolyte Solid aluminum capacitors (SAL) on the market.

With the beginning of the digitalization, 1971 launched Intel his first microcomputer MCS 4 and 1972 Hewlett Packard one of the first pocket calculator HP 35 the requirements for capacitors increases in terms of lower losses. The equivalent series resistance (ESR) for bypass and decoupling capacitors of standard electrolytic capacitors should be decreases.

Although solid tantalum capacitors offered smaller capacitors with lower ESR values than the aluminum e-caps, a gambling at the stock exchange 1980 followed by a price shock the industry were somewhat cautiously towards tantalum, so that the mass production came to a standstill. +

For aluminum electrolytic capacitor the decades from 1970 to 1990 were marked by the development of various new professional series with f. e. very low leakage currents or with long life characteristics or for higher temperatures up to 125 °C, which were specifically suited to certain industrial applications.

It was not until 1983, by Sanyo with its "OS-CON" aluminum electrolytic capacitors, a new step of ESR reduction was developed. These capacitors are used an solid organic conductor, the charge transfer salt TTF-TCNQ (tetracyanoquinodimethane), which provided an improvement in conductivity by a factor of 10 with respect to the manganese dioxide electrolyte.

The next step in ESR reduction takes place with the development of conducting polymers by Alan J. Heeger, Alan MacDiarmid and Hideki Shirakawa in 1975. The conductivity of conductive polymers such as polypyrrole (PPy) or PEDOT are by a factor of 100 to 500 better than that of TCNQ, and are close to the conductivity of metals.

In 1991 Panasonic with its "SP-Cap" called polymer aluminum electrolytic capacitors came on the market. These aluminum electrolytic capacitors with polymer electrolytes reached very low ESR values direct comparable to ceramic multilayer capacitors (MLCCs). They were still less expensive than tantalum capacitors and with their flat design for laptops and cell phones a competition to tantalum chip capacitors, too..

Tantalum electrolytic capacitors with PPy polymer electrolyte cathode followed three years later. In 1993 NEC introduced his SMD polymer tantalum electrolytic capacitors called "NeoCap". 1997 followed Sanyo with the "POSCAP" polymer tantalum chips.

A new conductive polymer for tantalum polymer capacitors was presented by Kemet at the "1999 Carts" conference. This capacitors used the new developed organic conductive polymer PEDT Poly(3,4-ethylenedioxythiophene), also known as PEDOT (trade name Baytron®)

An another price explosion for tantalum in 2000/2001 forces the new development of niobium electrolytic capacitors with manganese dioxide electrolyte which are available since 2002. Niobium is a sister metal to tantalum and serves as valve metal and generates an oxide layer during anodic oxidation. Niobium as raw material is much more abundant in nature than tantalum and is less expensive. It was a question of the availability of the base metal in the late '60s led to developed and implemented the niobium electrolytic capacitors in the former Soviet Union instead of tantalum capacitors in the West. The materials and processes used to produce niobium-dielectric capacitors are essentially the same as for existing tantalum-dielectric capacitors. The characteristics of this niobium electrolytic capacitors and tantalum electrolytic capacitors are roughly comparable.

With the goal of reducing ESR for inexpensive non-solid e-caps from the mid-1980s in Japan new water-based electrolytes were developed. Water is inexpensive, is an effective solvent for electrolytes and improves the conductivity of the electrolyte significantly. The Japanese manufacturer Rubycon was a leader in the development of new water-based electrolyte systems with enhanced conductivity in the late 1990s. The new series of non-solid e-caps with water-based electrolyte was called in the data sheets "Low-ESR", "Low-Impedance", "Ultra-Low-Impedance" or "High-Ripple Current" series.

A stolen recipe of such a water-based electrolyte, in which important stabilizing substances were absent, has led in the years 2000 to 2005 to the problem of mass-bursting capacitors in computers and power supplies, which became known under the term "Capacitor Plague". In this e-caps the water react quite aggressively and even violently with aluminum accompanied by strong heat and gas development in the capacitor, and often has led to the explosion of the capacitor.

Electrical characteristics

Series-equivalent circuit

The electrical characteristics of capacitors are harmonized by the international generic specification IEC 60384-1. In this standard, the electrical characteristics of capacitors are described by an idealized series-equivalent circuit with electrical components which model all ohmic losses, capacitive and inductive parameters of an electrolytic capacitor:

• C, the capacitance of the capacitor
• R_ESR, the equivalent series resistance which summarizes all ohmic losses of the capacitor, usually abbreviated as "ESR"
• L_ESL, the equivalent series inductance which is the effective self-inductance of the capacitor, usually abbreviated as "ESL".
• R_leak, the resistance representing the leakage current of the capacitor

Capacitance, standard values and tolerances

The electrical characteristics of electrolytic capacitors depend on structure of the anode and used electrolyte. This influences the capacitance value of electrolytic capacitors which depends on measuring frequency and temperature. Electrolytic capacitors with non-solid electrolytes show a broader aberration over frequency and temperature than capacitors with solid electrolytes.

The basic unit of electrolytic capacitors capacitance is microfarad (μF, or less correctly uF). The capacitance value specified in the data sheets of the manufacturers is called rated capacitance C_R or nominal capacitance C_N and is the value for which the capacitor has been designed.

Standardized measuring condition for e-caps is an AC measuring method with 0.5 V at a frequency of 100/120 Hz and a temperature of 20 °C. For tantalum capacitors a DC bias voltage of 1.1 to 1.5  V for types with a rated voltage of ≤2.5 V or 2.1 to 2.5 V for types with a rated voltage of >2.5 V may be applied during the measurement to avoid reverse voltage.

The capacitance value measured at the frequency of 1 kHz is about 10% less than the 100/120 Hz value. Therefore the capacitance values of electrolytic capacitors are not direct comparable and differ from those of film capacitors or ceramic capacitors , whose capacitance is measured at 1 kHz or higher.

Measured with an AC measuring method with 100/120 Hz the measured capacitance value is the closest value to the electrical charge stored in the e-caps. The stored charge is measured with a special discharge method and is called DC capacitance. The DC capacitance is about 10% higher than the 100/120 Hz AC capacitance. The DC capacitance is of interest for discharge applications like photoflash.

The percentage of allowed deviation of the measured capacitance from the rated value is called capacitance tolerance. Electrolytic capacitors are available in different tolerance series, whose values are specified in the E series specified in IEC 60063. For abbreviated marking in tight spaces, a letter code for each tolerance is specified in IEC 60062.

• rated capacitance, series E3, tolerance ±20%, letter code "M“
• rated capacitance, series E6, tolerance ±20%, letter code "M“
• rated capacitance, series E12, tolerance ±10%, letter code "K“

The required capacitance tolerance is determined by the particular application. Electrolytic capacitors, which are often used for filtering and bypassing capacitors don’t have the need for narrow tolerances because they are mostly not used for accurate frequency applications like oscillators.

Rated and category voltage

Referring to IEC/EN 60384-1 standard the allowed operating voltage for electrolytic capacitors is called "rated voltage U_R " or "nominal voltage U_N". The rated voltage U_R is the maximum DC voltage or peak pulse voltage that may be applied continuously at any temperature within the rated temperature range T_R.

The voltage proof of electrolytic capacitors decreases with increasing temperature. For some applications it is important to use a higher temperature range. Lowering the voltage applied at a higher temperature maintains safety margins. For some capacitor types therefore the IEC standard specify a "temperature derated voltage" for a higher temperature, the "category voltage U_C". The category voltage is the maximum DC voltage or peak pulse voltage that may be applied continuously to a capacitor at any temperature within the category temperature range T_C. The relation between both voltages and temperatures is given in the picture right.

Applying a higher voltage than specified may destroy electrolytic capacitors.

Lower voltage applied may have positive influences to electrolytic capacitors. For aluminum electrolytic capacitors in some cases a lower voltage applied can extend the lifetime.For tantalum electrolytic capacitors lowering the voltage applied increases the reliability and reduce the expected failure rate. I

Surge Voltage

The surge voltage indicates the maximum peak voltage value that may be applied to electrolytic capacitors during their application for a limited number of cycles. The surge voltage is standardized in IEC/EN 60384-1. For aluminum electrolytic capacitors with a rated voltage of up to 315 V, the surge voltage is 1.15 times the rated voltage, and for capacitors with a rated voltage exceeding 315 V, the surge voltage is 1.10 times the rated voltage.

For tantalum electrolytic capacitors the surge voltage shall be 1.3 times of the rated voltage, rounded off to the nearest volt. The surge voltage applied to tantalum capacitors may influence the capacitors failure rate.

Transient Voltage

Aluminum electrolytic capacitors with non-solid electrolyte are relatively insensitive to high and short-term transient voltages higher than surge voltage, if the frequency and the energy content of the transients is low. This ability depends on rated voltage and component size. Low energy transient voltages lead to a voltage limitation similar like a zener diode. An unambiguously and general specification of tolerable transients or peak voltages is not possible. In every case, transients arises, the application has to be approved very carefully.

Electrolytic capacitors with solid manganese oxide or polymer electrolyte, aluminum as well as tantalum electrolytic capacitors can not withstand transients or peak voltages higher than surge voltage. Transients for this type of e-caps may destroy the components.

Reverse voltage

Standard electrolytic capacitors, aluminum as well as tantalum and niobium electrolytic capacitors are polarized capacitors and generally require anode electrode voltage to be positive relative to the cathode voltage.

Nevertheless, electrolytic capacitors can withstand for short instants a reverse voltage for a limited number of cycles. In detail aluminum electrolytic capacitors with non-solid electrolyte can withstand a reverse voltage of about 1 V to 1.5 V. This reverse voltage should never be used to determine the maximum reverse voltage under which a capacitor can be used permanently.

Also solid tantalum capacitors can withstand for short periods reverse voltages. The most common guidelines for tantalum reverse voltage are:

• 10 % of rated voltage to a maximum of 1 V at 25 °C,
• 3 % of rated voltage to a maximum of 0.5 V at 85 °C,
• 1 % of rated voltage to a maximum of 0.1 V at 125 °C.

These guidelines apply for short excursion and should never be used to determine the maximum reverse voltage under which a capacitor can be used permanently.

But in no case, for aluminum as well as for tantalum and niobium electrolytic capacitors, a reverse voltage may be used for a permanent AC application.

To minimize the likelihood of a polarized electrolytic being incorrectly inserted into a circuit, polarity has to be very clearly indicated on the case, see #Polarity marking.

Special bipolar aluminum electrolytic capacitors designed for bipolar operation are available, usually referred to as "non-polarized" or "bipolar" types. In these, the capacitors have two anode foils with full-thickness oxide layers connected in revers polarity. On the alternate halves of the AC cycles, one of the oxide on the foil acts as a blocking dielectric, preventing reverse current from damaging the electrolyte of the other one. But these bipolar electrolytic capacitors are not adaptable for main AC applications instead of power capacitors with metallized polymer film or paper dielectric.

Impedance

In general, a capacitor is seen as a storage component for electric energy. But this is only one capacitor function. A capacitor can also act as an AC resistor. Especially aluminum electrolytic capacitors in many applications are used as a decoupling capacitors to filter or bypass undesired biased AC frequencies to the ground or for capacitive coupling of audio AC signals. Than the dielectric is used only for blocking DC. For such applications the AC resistance, the impedance is as important as the capacitance value.

The impedance Z is the vector sum of reactance and resistance, describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. In this sense impedance is a measure of the ability of the capacitor to pass alternating currents and can be used like Ohms law.

${\displaystyle Z={\frac {\hat {u}}{\hat {\imath }}}={\frac {U_{\mathrm {eff} }}{I_{\mathrm {eff} }}}.}$

With other words, the impedance is a frequency dependent AC resistance and possesses both magnitude and phase at a particular frequency.

In data sheets of electrolytic capacitors only the impedance magnitude |Z| is specified, and simply written as "Z". Regarding to the IEC/EN 60384-1 standard, the impedance values of electrolytic capacitors are measured and specified at 10 kHz or 100 kHz depending on the capacitance and voltage of the capacitor.

Besides measuring the impedance can be calculated using the idealized components out of a capacitor's series-equivalent circuit, including an ideal capacitor C, a resistor ESR, and an inductance ESL. In this case the impedance at the angular frequency ω therefore is given by the geometric (complex) addition of ESR, by a capacitive reactance X_C

${\displaystyle X_{C}=-{\frac {1}{\omega C}}}$

and by an inductive reactance X_L (Inductance)

${\displaystyle X_{L}=\omega L_{\mathrm {ESL} }}$.

Then Z is given by

${\displaystyle Z={\sqrt {{ESR}^{2}+(X_{\mathrm {C} }+(-X_{\mathrm {L} }))^{2}}}}$.

In the special case of resonance, in which the both reactive resistances X_C and X_L have the same value (X_C=X_L), then the impedance will only be determined by ESR. With frequencies above the resonance the impedance increases again due to the ESL of the capacitor. The capacitor becomes to an inductance.

ESR and dissipation factor tan δ

The equivalent series resistance (ESR) summarizes all resistive losses of the capacitor. These are the terminal resistances, the contact resistance of the electrode contact, the line resistance of the electrodes, the electrolyte resistance, and the dielectric losses in the dielectric oxide layer.

For electrolytic capacitors generally the ESR decreases with increasing frequency and temperature.

ESR influences the remaining superimposed AC ripple behind smoothing and may influence the circuit functionality. Related to the capacitor ESR is accountable for internal heat generation if a #ripple current flow over the capacitor. This internal heat reduces the #lifetime of non-solid aluminum electrolytic capacitors or influences the reliability of solid tantalum electrolytic capacitors.

For electrolytic capacitors, out of historical reasons sometimes the dissipation factor tan δ will be specified in the relevant data sheets, instead of the ESR. The dissipation factor is determined by the tangent of the phase angle between the capacitive reactance X_C minus the inductive reactance X_L and the ESR. If the inductance ESL is small, the dissipation factor can be approximated as:

${\displaystyle \tan \delta ={\mbox{ESR}}\cdot \omega C}$

The dissipation factor is used for capacitors with very low losses in frequency determining circuits where the reciprocal value of the dissipation factor is called the quality factor (Q) which represents a resonator's bandwidth.

Ripple current

A "ripple current" is the RMS value of a superimposed AC current of any frequency and any waveform of the current curve for continuous operation within the specified temperature range. It arises mainly in power supplies (including switched-mode power supplies) after rectifying an AC voltage and flows as charge and discharge current through the decoupling or smoothing capacitor.

Ripple currents generates heat inside the capacitor body. These dissipation power loss P_L is caused by ESR and is the squared value of the effective (RMS) ripple current I_R.

${\displaystyle P_{L}=I_{R}^{2}\cdot ESR}$

This internal generated heat, additional to the ambient temperature and possibly other external heat sources leads to a capacitor body temperature having a temperature difference of Δ T against the ambient. This heat has to be distributed as thermal losses P_th over the capacitors surface A and the thermal resistance β to the ambient.

${\displaystyle P_{th}=\Delta T\cdot A\cdot \beta }$

The internal generated heat has to be distributed to the ambient by thermal radiation, convection, and thermal conduction. The temperature of the capacitor, which is established on the balance between heat produced and distributed, shall not exceed the capacitors maximum specified temperature.

The ripple current is specified as an effective (RMS) value at 100 or 120 Hz or at 10 kHz at upper category temperature. Non-sinusoidal ripple currents have to be analyzed and separated into their single sinusoidal frequencies by means of Fourier analysis and summarized by squared addition the single currents.

${\displaystyle Z={\sqrt {{i_{1}}^{2}+{i_{2}}^{2}+{i_{3}}^{2}+{i_{n}}^{2}}}}$

In non-solid electrolytic capacitors the heat generated by the ripple current force the evaporation of electrolytes, shortening the life time of the capacitors. Exceeding the limit tends to result in explosive failure.

In solid tantalum electrolytic capacitors with manganese dioxide electrolyte the heat generated by the ripple current influences the reliability of the capacitors. Exceeding the limit tends to result in catastrophic failures with shorts and burning components.

The heat generated by the ripple current also influences the life time of aluminum and tantalum electrolytic capacitors with solid polymer electrolytes. Exceeding the limit tends to result in catastrophic failures with short components.

Current surge, peak or pulse current

Aluminum electrolytic capacitors with non-solid electrolytes normally can be charged up to the rated voltage without any current surge, peak or pulse limitation. This property is a result of the limited ion movability in the liquid electrolyte, which slow down the voltage ramp across the dielectric, and the capacitors ESR. Only the frequency of peaks integrated over the time must not exceed the maximal specified ripple current.

Solid tantalum electrolytic capacitors with manganese dioxide electrolyte as well as with polymer electrolyte are damageable against peak or pulse currents. Solid Tantalum capacitors which are exposed to surge, peak or pulse currents, f. e. in in highly inductive circuits, should be used with a voltage derating. If possible the voltage profile should be a ramp turn-on, as this reduces the peak current seen by the capacitor.

Leakage current

For electrolytic capacitors the DC leakage current (DCL) is a special characteristic the other conventional capacitors don’t have. This current is represented by the resistor R_leak in parallel with the capacitor in the series-equivalent circuit of electrolytic capacitors.

The reasons for leakage current are different between electrolytic capacitors with non-solid and with solid electrolyte or more common for “wet” aluminum and for “solid” tantalum electrolytic capacitors with manganese dioxide electrolyte as well as for electrolytic capacitors with polymer electrolytes. For non-solid aluminum electrolytic capacitors the leakage current includes all weakened imperfections of the dielectric caused by unwanted chemical processes happened during the time without voltage applied (storage time) between operating cycles. This unwanted chemical processes depend on the kind of electrolyte. Electrolytes with water contend or water based electrolytes are more aggressive against the aluminum oxide layer than electrolytes based on organic liquids. This is the reason different electrolytic capacitor series specify different storage time without reforming instructions.

Applying a positive voltage to a "wet" capacitor a reforming process (self-healing) repairs all weakened dielectric layers, and the leakage current remain on a low level.

Although the leakage current of non-solid e-caps is higher than current flow over insulation resistance in ceramic or film capacitors, the self-discharge of modern non-solid electrolytic capacitors with organic electrolytes takes several weeks.

The main causes of DCL for solid tantalum capacitors are f. e. electrical breakdown of the dielectric, conductive paths due to impurities or due to poor anodization, bypassing of dielectric due to excess manganese dioxide, due to moisture paths or due to cathode conductors (carbon, silver). This “normal” leakage current in solid electrolyte capacitors couldn’t be reduced by “healing”, because under normal conditions solid electrolytes don’t can deliver oxygen for forming processes. This statement should not be confused with the self-healing process during field crystallization, see #Reliability, Failure rate.

The specification of the leakage current in datasheets often will be given by multiplication of the rated capacitance value C_R with the value of the rated voltage U_R together with an addendum figure, measured after a measuring time of 2 or 5 minutes, for example:

${\displaystyle I_{\mathrm {Leak} }=0{,}01\,\mathrm {{A} \over {V\cdot F}} \cdot U_{\mathrm {R} }\cdot C_{\mathrm {R} }+3\,\mathrm {\mu A} }$

The leakage current value depends on the voltage applied, on temperature of the capacitor, and on measuring time. Leakage current in solid MnO₂ tantalum electrolytic capacitors generally drops very much faster than for non-solid electrolytic capacitors but remain on the reached level.

Dielectric absorption (soakage)

Dielectric absorption occurs when a capacitor that has remained charged for a long time discharges only incompletely when briefly discharged. Although an ideal capacitor would reach zero volts after discharge, real capacitors develop a small voltage from time-delayed dipole discharging, a phenomenon that is also called dielectric relaxation, "soakage" or "battery action".

Dielectric absorption may a problem in circuits, were very small currents are used for in the function of an electronic circuit such as long-time-constant integrators or sample-and-hold circuits. In most applications of electrolytic capacitors supporting power supply lines dielectric absorption is not a problem.

But especially for electrolytic capacitors with high rated voltage the voltage at the terminals generated by the dielectric absorption can be a safety risk to personnel or circuits. In order to prevent shocks most very large capacitors are shipped with shorting wires that need to be removed before they are used.

Reliability and life time

Reliability (failure rate]

The reliability of a component is a property that indicates how reliable this component performs its function in a time interval. It is subject to a stochastic process and can be described qualitatively and quantitatively; it is not directly measurable. The reliability of electrolytic capacitors are empirically determined by identifying the failure rate in production accompanying endurance tests, see Reliability engineering#Reliability testing

The reliability normally is shown in a bathtub curve and is divided into three areas: Early failures or infant mortality failures, constant random failures and wear out failures. Failures totalized in a failure rate are short circuit, open circuit and degradation failures (exceeding electrical parameters).

The reliability prediction is generally expressed in a Failure rate λ, abbreviation FIT (Failures In Time]. This is the number of failures that can be expected in one billion (10) component-hours of operation (e.g. 1000 components for 1 million hours, or 1  million components for 1000 hours which is 1 ppm/1000 hours) at fixed working conditions during the period of constant random failures. These failure rate model implicitly assume the idea of "random failure". Individual components fail at random times but at a predictable rate.

Billions of tested capacitors unit-hours would be needed to establish failure rates in the very low level range which are required today to ensure the production of large quantities of components without failures. This requires about a million units over a long time period which needs great personal staff and a lot of money. The tested failure rates often are complemented with figures resulting from big users feedback of failed component returns from the field (field failure rate) which mostly results in a lower failure rate than tested.

The reciprocal value of FIT is MTBF (Mean Time Between Failures).

The standard operation conditions for the failure rate FIT are 40 °C and 0.5 U_R. For other conditions of applied voltage, current load, temperature, capacitance value, circuit resistance (for tantalum capacitors), mechanical influences and humidity the FIT figure can recalculated with acceleration factors standardized for industrial or military contexts. As higher f. e. temperature and applied voltage as higher is the failure rate.

The most often cited source for recalculation the failure rate is the MIL-HDBK-217F, the “bible” of failure rate calculations for electronic components. SQC Online, the online statistical calculators for acceptance sampling and quality control gives an online tool for short examination to calculate given failure rate values to application conditions.

Some manufacturers may have their own FIT calculation tables, for tantalum capacitors or for aluminum capacitors

It is good to know that for tantalum capacitors often the failure rate is specified in essence at 85 °C and rated voltage U_R as reference conditions and expressed as per cent failed components per thousand hours (n %/1000 h). That is “n” number of failed components per 10 hours or in FIT the ten-thousand-fold value per 10 hours.

It should be noted that industrial produced tantalum capacitors nowadays are very reliable components. Continuous improvement in tantalum powder and capacitor technologies have resulted in a significant reduction in the amount of impurities present which formerly have caused most of the field crystallization failures. Commercial available industrial produced tantalum capacitors now have reached as standard products the high MIL standard “C” level which is 0.01 %/1000h at 85 °C and U_R or 1 failure per 10 hours at 85 °C and U_R. Recalculated in FIT with the acceleration factors coming from MIL HDKB 217F at 40 °C and 0.5 U_R is this failure rate for a 100 µF/25 V tantalum chip capacitor used with a series resistance of 0.1 Ω the failure rate is 0.02 FIT.

Aluminum electrolytic capacitors are not familiar with the specification in "% per 1000 h at 85 °C and U_R". They use the FIT specification with 40 °C and 0.5 U_R as reference conditions. Also for aluminum electrolytic capacitors should be noted that they are very reliable components. Published figures show for low voltages types (6.3…160 V) FIT rates in the range of 1 to 20 FIT and for high voltage types (>160 …550 V) FIT rates in the range of 20 to 200 FIT.Field failure rates for aluminum e-caps are in the range of 0.5 to 20 FIT.

The published figures show that both capacitor types, tantalum and aluminum, are reliable components, comparable with other electronic components achieving safe operations of decades under normal conditions. But it exist a great difference in case of wear-out failures. Tantalum capacitors with solid electrolyte have no wear-out mechanism so that the constant failure rate least up to the point all capacitors have failed. Electrolytic capacitors with non-solid electrolyte however have a limited time of constant random failures up to that point the wear-out failures starts. This time of the constant random failure rate correspondents with the life time or service life of “wet” aluminum electrolytic capacitors.

Life time

The life time, service life, load life or useful life of electrolytic capacitors is a special characteristic of non-solid aluminum electrolytic capacitors, which liquid electrolyte can evaporate over the time. Lowering the electrolyte influences the electrical parameters of the capacitors. The capacitance decreases and the impedance and ESR increases with decreasing electrolyte. This very slowly electrolyte drying-out depends on the temperature, the applied ripple current load, and the applied voltage. The lower these parameters compared with their maximum values the longer the capacitors “life”. The “end of life” point is defined by the appearance of wear-out failures or degradation failures when either capacitance, impedance, ESR or leakage current exceed their specified change limits.

The life time is a specification of a collective of tested capacitors and delivers an expectation of the behavior of similar types. This life time definition corresponds with the time of the constant random failure rate in the bathtub curve.

But even after exceeding the specified limits and the capacitors have reached their “end of life” the electronic circuit is not in an immediate danger, only the functionality of the capacitors are reduced. With today's high levels of purity in the manufacture of electrolytic capacitors it is not to be expected that after end-of-life-point with progressive evaporation combined with parameter degradation short circuits occur.

The life time of non-solid aluminum electrolytic capacitors is specified in terms of “hours per temperature" like “2,000h/105 °C”. With this specification the life time at operational conditions can be estimated by special formulas or graphs specified in the data sheets of serious manufacturers. They use different ways for specification, some give special formulas, others specify their e-caps life time calculation with graphs, which consider the influence of applied voltage.. Basic principle for calculating the time under operational conditions is the so called “10-degree-rule”.

This rule also is well known as Arrhenius rule. It characterizes the change of thermic reactions speed. For every 10 °C lower temperature evaporation halves. That means for every 10 °C lower temperature the life time of capacitors doubles. That means if a life time specification of an electrolytic capacitor is f. e. 2000  h/105 °C the capacitors life time at 45 °C can be ”calculated” with 128,000 hours – that is roughly 15 years - by using the 10-degrees-rule.

However, also solid polymer electrolytic capacitors, aluminum as well as tantalum and niobium electrolytic capacitors do have a life time specification. The polymer electrolyte have a small deterioration of conductivity by a thermal degradation mechanism of the conductive polymer. The electrical conductivity decreased, as a function of time, in agreement with a granular metal type structure, in which aging is due to the shrinking of the conductive polymer grains. The life time of polymer electrolytic capacitors is specified in similar terms like non-solid e-caps but it’s life time calculation follows other rules leading to much longer operational life times.

Tantalum electrolytic capacitors with solid manganese dioxide electrolyte don't have wear-out failures so they don't have a life time specification in the sense of non-solid aluminum electrolytic capacitors. Also tantalum capacitors with non-solid electrolyte, the “wet tantalums” don’t have a life time specification because they are hermetically sealed and evaporation of electrolyte is minimized.

Electrolytic capacitors with solid electrolyte don't have wear-out failures so they don't have a life time specification in the sense of non-solid aluminum electrolytic capacitors. Also tantalum capacitors with non-solid electrolyte, the “wet tantalums” don’t have a life time specification because they are hermetically sealed and evaporation of electrolyte is minimized.

Failure modes, self-healing mechanism and application rules

The many different types of electrolytic capacitors show a different behavior in point of electrical long-term behavior, their inherent failure modes and their self-healing mechanism. Application rules for types with an inherent failure mode are specified to ensure capacitors high reliability and long life.

Additional informations

Capacitor symbols

Electrolytic capacitor	Electrolytic capacitor	Electrolytic capacitor	Bipolar electrolytic capacitor

Parallel connection

Smaller or low voltage electrolytic capacitors may be connected in parallel without any safety correction action. Large sizes capacitors, especially large sizes and high voltage types should be individual guarded against sudden energy charge of the whole capacitor bank due to a failed specimen.

Series connection

Some applications like AC/AC converters with DC-link for frequency controls in three-phase grids needs higher voltages aluminum electrolytic capacitors usually offer. For such applications electrolytic capacitors can be connected in series for increased voltage withstanding capability. During charging, the voltage across each of the capacitors connected in series is proportional to the inverse of the individual capacitor’s leakage current. Since every capacitor differs a little bit in individual leakage current the capacitors with a higher leakage current will get less voltage. The voltage balance over the series connected capacitors is not symmetrically. Passive or active voltage balance has to be provided in order to stabilize the voltage over each individual capacitor .

Performance after storage

All electrolytic capacitors with non-solid as well as with solid electrolyte are "aged" during manufacturing by applying rated voltage at high temperature for a sufficient time to repair all cracks and weaknesses that may have occurred during production. However, a particular problem with non-solid aluminum electrolytic capacitors may occur after storage or unused times without voltage applied. During storage or unused times potentially chemical processes (corrosion) can weaken the oxide layer, which may lead to a higher leakage current. However, today’s most electrolytic systems are chemically inert and don’t generate any corrosion problems, even after storage times of two years or longer. Especially non-solid electrolytic capacitors using organic solvents like GBL as electrolyte do not have problems with high leakage current after longer storage times. They can be specified with storage times up to 10 years without leakage current problems

The ability to reach longer storage times can be tested using an accelerated shelf-life testing, which requires the storage of capacitors without applied voltage at its upper category temperature for a certain period, usually 1000 hours. This shelf life test is a good indicator for the chemical stability of the electrolytic system and the protecting aluminum oxide layer because all chemical reactions are accelerated by high temperatures. Since decades nearly all today’s series of non-solid e-caps fulfill the 1000 hours shelf life test which comply with minimum fife years storage at room temperature. However, many e-cap series are specified only for a two years storage time. This is a standard storage time for electronic components for storing at room temperature caused by the oxidation of the terminals to ensure the solderability of the terminals.

Only for antique radio equipment or for very old e-caps built in the 1970s or earlier, "pre-conditioning" may be recommended. For this purpose, the rated voltage is applied to the capacitor via a series resistance of approximately 1 kΩ for a period of one hour. Applying a voltage via a safety resistor repairs the oxide layer by self-healing. If the capacitors don’t meet the leakage current requirements after preconditioning, it may be an indication of a mechanical damage.

Electrolytic capacitors with solid electrolytes don’t have any precondition instructions.

Polarity marking

Imprinted markings

Electrolytic capacitors, like most other electronic components and if enough space is available, have imprinted markings to indicate manufacturer, type, electrical and thermal characteristics, and date of manufacture. If they are large enough the capacitor is marked with:

• manufacturer's name or trademark;
• manufacturer's type designation;
• polarity of the terminations (for polarized capacitors)
• rated capacitance;
• tolerance on rated capacitance
• rated voltage and nature of supply (AC or DC)
• climatic category or rated temperature;
• year and month (or week) of manufacture;
• certification marks of safety standards (for safety EMI/RFI suppression capacitors)

Polarized capacitors have polarity markings, usually "−" (minus) sign on the side of the negative electrode for electrolytic capacitors or a stripe or "+" (plus) sign, see #Polarity marking. Also, the negative lead for leaded "wet" e-caps is usually shorter.

Smaller capacitors use a shorthand notation. The most commonly used format is: XYZ J/K/M “V”, where XYZ represents the capacitance (calculated as XY × 10 pF), the letters K or M indicate the tolerance (±10 % and ±20 % respectively) and “V” represents the working voltage.

Examples:

• 105K 330V implies a capacitance of 10 × 10 pF = 1 µF (K = ±10%) with a working voltage of 330 V.
• 476M 100V implies a capacitance of 47 × 10 pF = 47 µF (M = ±20%) with a working voltage of 100 V.

Capacitance, tolerance and date of manufacture can be indicated with a short code specified in IEC/EN 60062. Examples of short-marking of the rated capacitance (microfarads): µ47 = 0,47 µF, 4µ7 = 4,7 µF, 47µ = 47 µF

The date of manufacture is often printed in accordance with international standards.

• Version 1: coding with year/week numeral code, "1208" is "2012, week number 8".
• Version 2: coding with year code/month code. The year codes are: "R" = 2003, "S"= 2004, "T" = 2005, "U" = 2006, "V" = 2007, "W" = 2008, "X" = 2009, "A" = 2010, "B" = 2011, "C" = 2012, "D" = 2013, “E” = 2014 etc. Month codes are: "1" to "9" = Jan. to Sept., "O" = October, "N" = November, "D" = December. "X5" is then "2009, May"

For very small capacitors no marking is possible. Here only the traceability of the manufacturers can ensure the identification of a type.

Standardization

The standardization for all electrical, electronic components and related technologies follows the rules given by the International Electrotechnical Commission (IEC), a non-profit, non-governmental international standards organization.

The definition of the characteristics and the procedure of the test methods for capacitors for use in electronic equipment are set out in the Generic specification:

• IEC/EN 60384-1 - Fixed capacitors for use in electronic equipment

The tests and requirements to be met by aluminum and tantalum electrolytic capacitors for use in electronic equipment for approval as standardized types are set out in the following sectional specifications:

• IEC/EN 60384-3—Surface mount fixed tantalum electrolytic capacitors with manganese dioxide solid electrolyte
• IEC/EN 60384-4—Aluminium electrolytic capacitors with solid (MnO₂) and non-solid electrolyte
• IEC/EN 60384-15—Fixed tantalum capacitors with non-solid and solid electrolyte
• IEC/EN 60384-18—Fixed aluminium electrolytic surface mount capacitors with solid (MnO₂) and non-solid electrolyte
• IEC/EN 60384-24—Surface mount fixed tantalum electrolytic capacitors with conductive polymer solid electrolyte
• IEC/EN 60384-25—Surface mount fixed aluminium electrolytic capacitors with conductive polymer solid electrolyte
• IEC/EN 60384-26—Fixed aluminium electrolytic capacitors with conductive polymer solid electrolyte

Market

The market of electrolytic capacitors in 2008 reach roughly 30% of the total market in value

• Aluminum electrolytic capacitors—US$3.9 billion (22%);
• Tantalum electrolytic capacitors—US$2.2 billion (12%);

In number of pieces this capacitors cover about 10% of the total capacitor market, which are about 100 to 120 billion pieces.

See also

• Aluminum electrolytic capacitor
• Niobium capacitor
• Polymer capacitor
• Solid Aluminum Capacitor (SAL)
• Tantalum capacitor
• Types of capacitor

References

1. ^ A. Albertsen, Jianghai Europe, Keep your distance – Voltage Proof of Electrolytic Capacitors, PDF
2. ^ KDK, Specifications for Etched Foil for Anode, Low Voltage
3. I.Horacek, T.Zednicek, S.Zednicek, T.Karnik, J.Petrzilek, P.Jacisko, P.Gregorova, AVX, High CV Tantalum Capacitors - Challenges and Limitations
4. Charles Pollack: D.R.P. 92564, filed 14. Januar 1896, granted 19. Mai 1897 D.R.P. 92564
5. US Patent Nr. 1774455, Electric condenser, filed October 19,1925, granted August 26, 1930
6. Samuel Ruben: Inventor, Scholar, and Benefactor by Kathryn R. Bullock PDF www.electrochem.org
7. ^ P. McK. Deeley, Electrolytic Capacitors, The Cornell-Dubilier Electric Corp. South Plainfield New Jersey, 1938
8. Elektrolytischer Kondensator mit aufgerollten Metallbändern als Belegungen, Alfred Eckel Hydra-Werke, Berlin-Charlottenburg, DRP 498 794, filed 12.Mai 1927, granted 8.Mai 1930
9. William Dubilier, Electric Condenser, US Patent 468787
10. D. F. Tailor, Tantalum and Tantalum Compounds, Fansteel Inc., Encyclopedia of Chemical Technology, Vol. 19, 2nd ed. 1969 John Wiley & sons, Inc.
11. R. L. Taylor and H. E. Haring, “A metal semi-conductor capacitor,” J. Electrochem. Soc., vol. 103, p. 611, November, 1956.
12. E. K. Reed, Jet Propulsion Laboratory, Characterization of Tantalum Polymer Capacitors, NEPP Task 1.21.5, Phase 1, FY05]
13. D. A. McLean, F. S. Power, Proc. Inst. Radio Engrs. 44 (1956) 872
14. Preston Robinson, Sprague, US Patent 3066247, 25. Aug. 1954 - 27. Nov. 1962
15. Sprague, Dr. Preston Robinson Granted 103rd Patent Since Joining Company In 1929
16. A. Fraioli, Recent Advances in the Solid-State Electrolytic Capacitor, IRE Transactions on Component Parts, June 1958
17. R. J. Millard, Sprague, US Patent 2936514, October 24, 1955 - May 17, 1960
18. J.Both, Valvo, SAL contra Tantal, Zuverlässige Technologien im Wettstreit, nachrichten elektronik 35, 1981
19. Computerposter,
20. K. Lischka, Spiegel 27.09.2007, 40 Jahre Elektro-Addierer: Der erste Taschenrechner wog 1,5 Kilo,
21. Larry E. Mosley, Intel Corporation, Capacitor Impedance Needs For Future Microprocessors, CARTS USA 2006,
22. W. Serjak, H. Seyeda, Ch. Cymorek, Tantalum Availability: 2000 and Beyond, PCI,March/April 2002,
23. The Tantalum Supply Chain: A Detailed Analysis, PCI, March/April 2002,
24. Philips Data Handbook PA01, 1986, the first 125 °C series “118 AHT”
25. Shinichi Niwa, Yutaka Taketani, Development of new series of aluminium solid capacitors with organic Semiconductive electrolyte (OS-CON), Journal of Power Sources, Volume 60, Issue 2, June 1996, Pages 165–171,
26. Kuch, Investigation of charge transfer complexes:TCNQ-TTF,
27. Sanyo, OS-CON, Technical Book Ver. 15, 2007
28. About the Nobel Prize in Chemistry 2000, Advanced Information, October 10, 2000,
29. Y. K. ZHANG, J. LIN，Y. CHEN, Polymer Aluminum Electrolytic Capacitors with Chemically-Polymerized Polypyrrole (PPy) as Cathode Materials Part I. Effect of Monomer Concentration and Oxidant on Electrical Properties of the Capacitors, PDF
30. U. Merker, K. Wussow, W. Lövenich, H. C. Starck GmbH, New Conducting Polymer Dispersions for Solid Electrolyte Capacitors, PDF
31. Panasonic, SP-Caps
32. John Prymak, Kemet, Replacing MnO2 with Polymers, 1999 CARTS
33. F. Jonas, H.C.Starck, Baytron, Basic chemical and physical properties, Präsentation 2003,
34. Ch. Schnitter, A. Michaelis, U. Merker, H.C. Starck, Bayer, New Niobium Based Materials for Solid Electrolyte Capacitors, Carts 2002
35. T. Zednicek, S. Sita, C. McCracken, W. A. Millman, J. Gill, AVX, Niobium Oxide Technology Roadmap, CARTS 2002
36. Y. Pozdeev-Freeman, P. Maden, Vishay, Solid-Electrolyte Niobium Capacitors Exhibit Similar Performance to Tantalum, Feb 1, 2002,
37. Shigeru Uzawa, Akihiko Komat-u, Tetsushi Ogawara, Rubycon Corporation, Ultra Low Impedance Aluminum Electrolytic Capacitor with Water based Electrolyte
38. J.L. Stevens, T. R. Marshall, A.C. Geiculescu m, C.R. Feger, T.F. Strange, Carts USA 2006, The Effects of Electrolyte Composition on the Deformation Characteristics of Wet Aluminum ICD Capacitors,
39. Alfonso Berduque, Zongli Dou, Rong Xu, KEMET, Electrochemical Studies for Aluminium Electrolytic Capacitor Applications: Corrosion Analysis of Aluminium in Ethylene Glycol-Based Electrolytes PDF
40. Hillman; Helmold (2004), Identification of Missing or Insufficient Electrolyte Constituents in Failed Aluminum Electrolytic Capacitors (PDF), DFR solutions
41. Ch. Reynolds, AVX, Technical Information, Reliability Management of Tantalum Capacitors, PDF
42. ^ J. Gill, AVX, Surge in Solid Tantalum Capacitors,
43. ^ A. Teverovsky, Perot Systems Code 562, NASA GSFCE, Effect of Surge Current Testing on Reliability of Solid Tantalum Capacitors PDF
44. Imam, A.M., Condition Monitoring of Electrolytic Capacitors for Power Electronics Applications, Dissertation, Georgia Institute of Technology (2007) PDF
45. Nichicon. "General Description of Aluminum Electrolytic Capacitors" PDF section "2-3-2 Reverse Voltage".
46. Rubycon. "Aluminum Electrolytic Capacitors FAQ"
47. CDM Cornell Dubilier. "Aluminum Electrolytic Capacitor Application Guide"p. 4 and p. 6 and p. 9
48. I. Bishop, J. Gill, AVX Ltd., Reverse Voltage Behavior of Solid Tantalum Capacitors PDF
49. P. Vasina, T. Zednicek, Z. Sita, J. Sikula, J. Pavelka, AVX, Thermal and Electrical Breakdown Versus Reliability of Ta2O5 Under Both – Bipolar Biasing Conditions PDF
50. A. Berduque, Kemet, Low ESR Aluminium Electrolytic Capacitors for Medium to High Voltage Applications, PDF
51. Joelle Arnold, Uprating of Electrolytic Capacitors, DfR Solutions
52. ^ Vishay BCcomponents, Introduction Aluminum Capacitors, Revision: 10-Sep-13 1 Document Number: 28356, PDF
53. Vishay, Engineering Solutions, Aluminum Capacitors in Power Supplies
54. Panasonic, Use technique of Aluminum Electrolytic Capacitors
55. CDE, Aluminum Electrolytic Capacitor Application Guide
56. Nichicon, Application Guidelines for Aluminum Electolytic Capacitors
57. Evox Rifa,Electrolytic Capacitors Application Guide
58. I. Salisbury, AVX, Thermal Management of Surface Mounted Tantalum Capacitors
59. R.W. Franklin, AVX , Ripple Rating of Tantalum Chip Capacitors,
60. Vishay, Application Notes, AC Ripple Current, Calculations Solid Tantalum Capacitors
61. KEMET, Ripple Current Capabilities, Technical Update 2004
62. E. Vitoratos, S. Sakkopoulos, E. Dalas, N. Paliatsas, D. Karageorgopoulos, F. Petraki, S. Kennou, S.A. Choulis, Thermal degradation mechanisms of PEDOT:PSS, Organic Electronics Volume 10, Issue 1, February 2009, Pages 61–66, Organic ElectronicsVolume 10, Issue 1, February 2009, Pages 61–66,
63. Vishay, Aluminium capacitors, Introduction, Revision: 10-Sep-13 1 Document Number: 28356, Chapter Storage, page 7
64. ^ Ch. Baur, N. Will, Epcos, Long-term stability of aluminum electrolytic capacitors Built to last
65. R.W. Franklin, AVX, AN EXPLORATION OF LEAKAGE CURRENT
66. Kemet, Polymer Tantalum Chip Capacitors
67. AVX, ANALYSIS OF SOLID TANTALUM CAPACITOR LEAKAGE CURRENT
68. "Understand Capacitor Soakage to Optimize Analog Systems" by Bob Pease 1982
69. * "Modeling Dielectric Absorption in Capacitors", by Ken Kundert
70. NIC, Failure Rate Estimation,
71. IEC/EN 61709, Electric components. Reliability. Reference conditions for failure rates and stress models for conversion
72. MIL-HDBK-217F Reliability Prediction of Electronic Equipment
73. SQC online table calculator, Capacitor Failure Rate Model, MIL-HDBK-217, Rev. F - Notice 2
74. Vishay, Fit Calculator,
75. Hitachi, Precautions in using Tantalum Capacitors, 4.2 Failure Rate Calculation Formula
76. KEMET FIT Calculator Software
77. ^ Sam G. Parler, Cornell Dubilier, Reliability of CDE Aluminum Electrolytic Capacitors (PDF)
78. ^ T.Zednicek, AVX, A Study of Field Crystallization in Tantalum Capacitors and its effect on DCL and Reliability,
79. ^ A. Albertsen, Jianghai Europe, Reliability of Electrolytic Capacitors, PDF
80. Hitachi aic-europe, Explanations to the useful life, PDF
81. NCC, Technical Note Judicious Use of Aluminum Electrolytic Capacitors PDF
82. Rubycon, LIFE OF ALUMINUM ELECTROLYTIC CAPACITORS, S. 9 (PDF)
83. A. Albertsen, Jianghai, Electrolytic Capacitor Lifetime Estimation PDF
84. "Snap-In HU". aic-europe.com.
85. ^ Epcos, Aluminum electrolytic capacitors, General technical informations PDF
86. Panasonic (10-degree-rule; PDF)
87. NIC Life expectancy of aluminum electrolytic capacitors (rev.1) (PDF)
88. Gregory Mirsky, Determining end-of-life, ESR, and lifetime calculations for electrolytic capacitors at higher temperatures, EDN, August 20, 2008,
89. E. Vitoratos, S. Sakkopoulos, E. Dalas, N. Paliatsas, D. Karageorgopoulos, F. Petraki, S. Kennou, S.A. Choulis, Thermal degradation mechanisms of PEDOT:PSS, Organic Electronics, Volume 10, Issue 1, February 2009, Pages 61–66,
90. Nichicon, Technical Guide, Calculation Formula of Lifetime PDF
91. Estimating of Lifetime FUJITSU MEDIA DEVICES LIMITED PDF
92. NIC Technical Guide, Calculation Formula of Lifetime
93. ^ VISHAY, DC LEAKAGE FAILURE MODE, PDF
94. ^ J.Gill, T. Zednicek, AVX, VOLTAGE DERATING RULES FOR SOLID TANTALUM AND NIOBIUM CAPACITORS,
95. ^ R. Faltus, AVX, Advanced capacitors ensure long-term control-circuit stability, 7/2/2012, EDT
96. IEC Homepage
97. IEC Webstore
98. IEC/EN/DIN Standards, Beuth-Verlag
99. Electronic Capacitors, SIC 3675, NAICS 334414: Electronic Capacitor Manufacturing, Industry report:

• Capacitors