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# PowerPedia:Capacitors

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A capacitor consists of two conductive electrodes, or plates, separated by an insulator or dielectric. Capacitors are electrical "condensers". A capacitor can be seen as similiar to a battery in that it is a medium for storing electrical energy. Capacitors are used in electrical circuits as energy-storage devices. However, a capacitor is a much simpler device than a battery, it cannot produce new electrons -- it only stores them. They can also be used to differentiate between high-frequency and low-frequency signals and this makes them useful in electronic filters.

A capacitor is an electrical device that can store energy in the electric field between a pair of closely spaced conductors (called 'plates'). When voltage is applied to the capacitor, electric charges of equal magnitude, but opposite polarity, build up on each plate. Practical capacitors are often classified according to the material used as the dielectric with the dielectrics divided into two broad categories: bulk insulators and metal-oxide films (so-called electrolytic capacitors). Capacitors are used in electrical circuits as energy-storage devices. They can also be used to differentiate between high-frequency and low-frequency signals and this makes them useful in electronic filters. Capacitors are occasionally referred to as condensers. This is now considered an antiquated term.

Large-scale capacitors designed for use in hybrids or on the power grid are far more powerful than small capacitors used in electronics. These large capacitors are called ultracapacitors. An ultracapacitor (or supercapacitor) is an electrochemical capacitor that has an unusually large amount of energy storage capability relative to its size when compared to common capacitors. These are of particular interest in automotive applications for hybrid vehicles and as supplemental storage for battery electric vehicles.

## History

In October 1745, Ewald Georg von Kleist of Pomerania invented the first recorded capacitor: a glass jar coated inside and out with metal. The inner coating was connected to a rod that passed through the lid and ended in a metal sphere. By having this thin layer of glass insulation (a dielectric) between two large, closely spaced plates, von Kleist found the energy density could be increased dramatically compared with the situation with no insulator. In January 1746, before Kleist's discovery became widely known, a Dutch physicist Pieter van Musschenbroek independently invented a very similar capacitor. It was named the Leyden jar, after the University of Leyden where van Musschenbroek worked. Daniel Gralath was the first to combine several jars in parallel into a "battery" to increase the total possible stored charge. The earliest unit of capacitance was the 'jar', equivalent to about 1 nF.

The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampere's law consistent with conservation of charge in cases where charge is accumulating, for example in a capacitor. He interpreted this as a real motion of charges, where he corresponded the concept to motion of dipole charges in the aether. This interpretation is viable and Maxwell's correction to Ampere's law remains valid (a changing electric field produces a magnetic field). Maxwell's equation combining Ampere's law with the displacement current concept is given as curl H = dD/dt + J, where, in keeping with notational stricture, curl is emboldened because it is a vector operator. (Integrating both sides, the integral of curl H can be replaced—courtesy of Stokes's theorem—with the integral of H ? dl over a closed contour, thus demonstrating the interconnection with Ampere's formulation.)

The first supercapacitor based on a double layer mechanism was developed in 1957 by General Electronics in a patent using a porous carbon electrode (Becker, H.I., “Low voltage electrolytic capacitor?, U.S. Patent 2800616 (G.patent; PDF), 23 July 1957). It was believed that the energy was stored in the carbon pores and it exhibited "exceptionally high capacitance", although the mechanism was unknown at that time. It was the Standard Oil of Ohio|Standard Oil Company, Cleveland (SOHIO) in 1966 that patented a device that stored energy in the double layer interface (Rightmire, R.A., “Electrical energy storage apparatus?, U.S. Patent 3288641 (G.patent; PDF), 29 Nov 1966). First trials of using the supercapacitors in industrial applications were carried out for supporting the energy supply to robots. (PDF) In 2005, leading producer of aerospace systems and controls Diehl Luftfahrt Elektronik GmbH chose ultracapacitors Boostcap® (of Maxwell Technologies) to power emergency actuation systems for doors and evacuation slides in passenger aircraft, including the new Airbus 380 jumbo jet. [1]

## Capacitors Overview

A capacitor is an electrical device that can store energy in the electric field between a pair of closely spaced conductors (called 'plates'). When current is passed through the capacitor, electric charges of equal magnitude, but opposite sign, build up on each plate. Early capacitors were also known as condensers, a term that is still occasionally used today. It was coined by Volta in 1782 (derived from the Italian condensatore), with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor. Most non-English languages still use a word derived from "condensatore", like the French "condensateur", the German or Polish "Kondensator", or the Spanish "condensador".

When the capacitor is in its minimum-energy state, each plate contains equal densities of electrons and protons and is therefore, overall, electrically neutral. When an electric field is applied across the terminals by an external circuit, excess electrons are forced into one plate, giving it a net negative charge, and some are forced out of the other plate, giving it a net positive charge. Assuming that the entire circuit is electrically neutral, as is usually the case, the number of electrons added to one plate is equal to the number removed from the other. Therefore, the net charge on the capacitor, even when it is energised, remains zero.

Because of the electric field between the two plates of an energised capacitor, the electrons in the negative plate are attracted towards the positive plate, but they cannot cross the dielectric, so their concentration is highest at the edge of the negative plate facing the gap. Conversely, the electrons in the positive plate are repelled from the negative plate by the electric field, so their concentration is lowest at the edge of the positive plate nearest the gap. The protons in both plates are fixed in position by the atomic structure of the material.

A large capacitors can hold a very large charge, sufficient for many tasks performed by heavey-duty batteries. The difference between a capacitor and a battery is that a capacitor can dump its entire charge in a tiny fraction of a second. A battery of similiar storage capacity would take minutes to completely discharge itself. This quality makes capacitors especially useful for applications that require quick bursts of energy, such as a camera flash.

## Capacitor construction

Capacitors have thin conducting plates (usually made of metal), separated by a layer of dielectric, then stacked or rolled to form a compact device. Many types of capacitor are available commercially, with capacitances ranging from the picofarad range to more than a farad, and voltage ratings up to hundreds of kilovolts. In general, the higher the capacitance and voltage rating, the larger the physical size of the capacitor and the higher the cost. Tolerances in capacitance value for discrete capacitors are usually specified as a percentage of the nominal value. Tolerances ranging from 50% (electrolytic types) to less than 1% are commonly available.

Another figure of merit for capacitors is stability with respect to time and temperature, sometimes called drift. Variable capacitors are generally less stable than fixed types. The electrodes need round edges to avoid field emission. Air has low breakdown voltage, so any air inside a capacitor - especially at plate edges - will reduce the voltage rating. Even closed air bubbles in the insulator or between the insulator and the electrode lead to gas discharge, particularly in AC or High Frequency applications. Groups of identically constructed capacitor elements are often connected in series for operation at higher voltage.

## Variable capacitors

Main article: Variable capacitor

Variable capacitors may have their capacitance intentionally and repeatedly changed over the life of the device. They include capacitors that use a mechanical construction to change the distance between the plates, or the amount of plate surface area which overlaps, and variable capacitance diodes that change their capacitance as a function of the applied reverse bias voltage.

Variable capacitance is also used in sensors for physical quantities, including microphones, pressure and hygro sensors.

## Types of dielectric

• Air-gap: An air-gap capacitor has a low dielectric loss. Large-valued, tunable capacitors that can be used for resonating HF antennas can be made this way.
• Ceramic: The main differences between ceramic dielectric types are the temperature coefficient of capacitance, and the dielectric loss. C0G and NP0 (negative-positive-zero, i.e. ±0) dielectrics have the lowest losses, and are used in filters, as timing elements, and for balancing crystal oscillators. Ceramic capacitors tend to have low inductance because of their small size. NP0 refers to the shape of the capacitor's temperature coefficient graph (how much the capacitance changes with temperature). NP0 means that the graph is flat and the device is not affected by temperature changes.
• C0G or NP0 — Typically 4.7 pF to 0.047 µF, 5%. High tolerance and temperature performance. Larger and more expensive.
• X7R — Typical 3300 pF to 0.33 µF, 10%. Good for non-critical coupling, timing applications. Subject to microphonics.
• Z5U or 2E6 — Typical 0.01 µF to 2.2 µF, 20%. Good for bypass, coupling applications. Low price and small size. Subject to microphonics.
• Ceramic chip: 1% accurate, values up to about 1 µF, typically made from Lead zirconate titanate (PZT) ferroelectric ceramic
• Glass — used to form extremely stable, reliable capacitors.
• Paper — common in antique radio equipment, paper dielectric and aluminum foil layers rolled into a cylinder and sealed with wax. Low values up to a few μF, working voltage up to several hundred volts, oil-impregnated bathtub types to 5,000 V used for motor starting and high-voltage power supplies, and up to 25,000 V for large oil-impregnated energy discharge types.
• Polycarbonate good for filters, low tempco, good aging, expensive
• Polyester, (PET film): (from about 1 nF to 1 μF) signal capacitors, integrators.
• Polystyrene: (usually in the picofarad range) stable signal capacitors.
• Polypropylene: low-loss, high voltage, resistant to breakdown, signal capacitors.
• PTFE or Teflon ™: higher performing and more expensive than other plastic dielectrics.
• Silvered mica: These are fast and stable for HF and low VHF RF circuits, but expensive.
• Electrolytic capacitors have a larger capacitance per unit volume than other types, making them valuable in relatively high-current and low-frequency electrical circuits, e.g. in power-supply filters or as coupling capacitors in audio amplifiers. High-capacity electrolytics, also known as supercapacitors or ultracapacitors, have applications similar to those of rechargable batteries, e.g. in electrically powered vehicles;
• Printed circuit board: Metal conductive areas in different layers of a multi-layer printed circuit board can act as a highly stable capacitor. It is common industry practice to fill unused areas of one PCB layer with the ground conductor and another layer with the power conductor, forming a large distributed capacitor between the layers, or to make power traces broader than signal traces.
• In integrated circuits, small capacitors can be formed through appropriate patterns of metallization on an isolating substrate.
• Vacuum: Expensive, housed in glass or ceramic body, typically rated for 5kV - 30kV. Typically used in high power RF transmitters because the dielectric has virtually no loss and is self-healing. May be fixed or adjustable.

## Capacitors - A Description About How They Function

A capacitor consists of two conductive electrodes, or plates, separated by an insulator. Like a battery, a capacitor has two terminals. Inside the capacitor, the terminals connect to two metal plates separated by a dielectric. The dielectric can be anything that does not conduct electricity and keeps the plates from touching each other. The plate on the capacitor that attaches to the negative terminal of the battery accepts electrons that the battery is producing. The plate on the capacitor that attaches to the positive terminal of the battery loses electrons to the battery. Once it's charged, the capacitor has the same voltage as the battery (3 volts on the battery means 3 volts on the capacitor). The ideal capacitance can be considered as an inverse of the ideal inductance, because the voltage-current equations of the two phenomena can be transformed into one another by exchanging the voltage and current terms.

Capacitance measures the amount of electric charge stored (or separated) for a given electric potential. The capacitance is usually defined as the ratio of the total electric charge placed on the object to its voltage:

$C = \frac{Q}{V}$

or, according to Gauss's law, the capacitance can be expressed as the electric flux per volt

$C = \frac{\Phi}{V}$

where

C is the capacitance in farads, F
Q is the charge in coulombs, C
V is the potential in volts, V
$\Phi\,$ is the electric flux associated with the charge Q in coulombs

The above uses SI units; an alternative unit to measure capacitance is the centimetre in the cgs system of measurement. It should be noted that 1 F = 9 × 1011 cm.

It is instructive to use the farad to test the claim that all units can be reduced to the SI minima of kilograms, meters, seconds, and coulombs. For our purposes, we start with the equations W = QV and Q = CV, whence the units of capacitance (C) are those of Q squared over W (work). Now, Q squared is measured in coulombs squared (fundamental SI units), while W is measured in newton-meters, with one newton equating to one kilogram-meter per second squared, whence the units of W are kilogram-meters squared per second squared. Dividing through, one finds that the farad is equivalent to one coulomb squared-second squared per kilogram-meter squared in base SI units.

It should be noted that the above equation (C = Q/V) is only applicable for values of Q which are much larger than the electron charge e = 1.602×10-19 C. For example, if a capacitance of 1 pF is charged to a voltage of 100 nV, the equation would predict a charge Q = 10-19 C, which is smaller than the charge on a single electron.

The capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. Indeed, for ideal dielectrics, capacitance is strictly a function of the geometry of the system. The capacitance of a parallel-plate capacitor is given by:

$C \approx \frac{\epsilon A}{d}; A \gg d^2$ [2]

where ε is the permittivity of the dielectric, A is the area of the plates and d is the spacing between them.

The capacitance of a parallel-plate capacitor constructed of two identical plane electrodes of area A at constant spacing d is approximately equal to the following:

$C = \epsilon_0 \epsilon_r \frac{A}{d}$

where

C is the capacitance in farads, F
ε0 is the permittivity of free space, measured in farads per meter
εr is the dielectric constant or relative permittivity of the insulator used
A is the area of each plane electrode, measured in square metres
d is the separation between the electrodes, measured in metres

It should be noted that the dielectric constant for a number of very useful dielectrics (ferroelectric materials) changes as a function of the applied electrical field, so the capacitance for these devices is no longer purely a function of device geometry.

The energy (measured in joules) stored in a capacitance is equal to the work done to charge it. Consider a capacitance C, holding a charge +q on one plate and -q on the other. Moving a small element of charge dq from one plate to the other against the potential difference V = q/C requires the work dW:

$dW = \frac{q}{C}dq$

where

W is the work measured in joules
q is the charge measured in coulombs
C is the capacitance, measured in farads

The energy stored in a capacitance in terms of work is found by integrating this equation. Starting with an uncharged capacitance (q=0) and moving charge from one plate to the other until the plates have charge +Q and -Q requires the work W:

$W_{charging} = \int_{0}^{Q} \frac{q}{C} dq = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}CV^2 = W_{stored}$

Stated as how much energy stored, the equation is given by:

$E_{stored} = {1 \over 2} C V^2 = {1 \over 2} {Q^2 \over C} = {1 \over 2} {V Q}$

where $V\,$ is the voltage across the capacitor.

The amount of work stored is given by:

$W_{stored} = \frac{1}{2} \epsilon_0 \epsilon_r \frac{A}{d} V^2$

As opposite charges accumulate on the plates of a capacitor due to the separation of charge, a voltage develops across the capacitor owing to the electric field of these charges. Ever-increasing work must be done against this ever-increasing electric field as more charge is separated. The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish the voltage across the capacitor, and therefore the electric field.

## Non-ideal properties of practical capacitors

### Q factor, dissipation and tan-delta

Capacitors have "Q" (quality) factor (and the inverse, dissipation factor , D or tan-delta) which relates capacitance at a certain frequency to the combined losses due to dielectric leakage and series internal resistance( also known as ESR) dissipation factor (dielectric loss). The lower the 'Q', the lossier the capacitor. Aluminum Electrolytic types have typically low Q factors. High Q capacitors tend to exhibit low DC leakage currents. Tan-delta is the tangent of the phase angle between voltage and current in the capacitor. This angle is sometimes called the loss angle. It is related to the power factor which is zero for an ideal capacitor.

### Equivalent series resistance (ESR)

This is an effective resistance that is used to describe the resistive parts of the impedance of certain electronic components. The theoretical treatment of devices such as capacitors and inductors tends to assume they are ideal or "perfect" devices, contributing only capacitance or inductance to the circuit. However, all physical devices are constructed of materials with finite electrical resistance, which means that all real-world components contain some resistance in addition to their other properties. A low ESR capacitor typically has an ESR of 0.01 Ω. Low values are preferred for high-current, pulse applications. Low ESR capacitors have the capability to deliver huge currents into short circuits, which can be dangerous.

For capacitors, ESR takes into account the internal lead and plate resistances and other factors. An easy way to deal with these inherent resistances in circuit analysis is to express each real capacitor as a combination of an ideal component and a small resistor in series, the resistor having a value equal to the resistance of the physical device.

### Equivalent series inductance (ESL)

ESL in signal capacitors is mainly caused by the leads used to connect the plates to the outside world and the series interconnects used to join sets of plates together internally. For any real-world capacitor, there is a frequency above DC at which it ceases to behave as a pure capacitance. This is called the (first) resonant frequency. This is critically important with decoupling high-speed logic circuits from the power supply. The decoupling capacitor supplies transient current to the chip. Without decouplers, the IC demands current faster than the connection to the power supply can supply it, as parts of the circuit rapidly switch on and off. Large capacitors tend to have much higher ESL than small ones. As a result, electronics will frequently use multiple bypass capacitors — a small 0.1 µF rated for high frequencies and a large electrolytic rated for lower frequencies, and occasionally, an intermediate value capacitor.

### Maximum voltage and current

Important properties of capacitors are the maximum working voltage (potential, measured in volts) and the amount of energy lost in the dielectric. For high-power or high-speed capacitors, the maximum ripple current, peak current, fault current, and percent voltage reversal are further considerations.

### Temperature dependence

Another major non-ideality is temperature coefficient (change in capacitance with temperature) which is usually quoted in parts per million (ppm) per degree Celsius.

### Aging

When refurbishing old (especially audio) equipment, it is a good idea to replace all of the electrolyte-based capacitors. After long storage, the electrolyte and dielectric layer within electrolytic capacitors may deteriorate; before powering up equipment with old electrolytics, it may be useful to apply low voltage to allow the capacitors to reform before applying full voltage. Deteriorating capacitors are a frequent cause of hum in aging audio equipment. Non polarised capacitors also suffer from aging, changing their values slightly over long periods of time. In high voltage DC applications, accumulated capacitor stress due to in-rush currents at circuit power-up can be minimized with a pre-charge circuit.

### Dielectric absorption (soakage)

In the construction of long-time-constant integrators, it is important that the capacitor will not retain a residual charge when shorted. This phenomenon of unwanted charge storage is called dielectric absorption or soakage, and it effectively creates a memory effect in the capacitor. This is a non-linear phenomenon, and is also important when building very low distortion filters. This is also why, for safety, high voltage capacitors are stored with their terminals short circuited.

### Non-linearity

Capacitors may also change capacitance with applied voltage. This effect is more prevalent in high 'k' ceramic and some high voltage capacitors. This can be another small source of non-linearity when building low distortion filters.

### Leakage

Capacitors also have some level of parasitic resistance across the terminals which is called 'leakage'. This fundamentally limits how long capacitors can store charge. Historically, this was a major source of problems in some types of applications (long RC timers, sample-and-holds, etc.)

## Component values and identification

### Standard values

In the early days of electronics, components were often made to fit a specific need, the values of early capacitors were of arbitrary (usually integer) base numbers. The more common values included 1.0, 1.5, 2.0, 3.0, 5.0, 6.0, and 8.0 as base numbers, but they were not necessarily limited to these values. Values were generally in microfarads (µF) and could be multiplied by any power of ten; picofarads were often called micro-microfarads (µµF) then.

In the late 1960s, a standardized set of geometrically increasing base values was introduced. According to the number of values per decade, these were called the E3, E6 or E12 series:

 Series Values E3 1.0 2.2 4.7 E6 1.0 1.5 2.2 3.3 4.7 6.8 E12 1.0 1.2 1.5 1.8 2.2 2.7 3.3 3.9 4.7 5.6 6.8 8.2

The same series are used for resistors, where E24/E48/E96 series are additionally used for even lower-tolerance components. These number series are known as preferred values.

Since most electrolytic capacitors have a tolerance range of ±20%, meaning that the manufacturer guarantees that the actual value of the capacitor lies within ±20% of its nominal value, they are normally available in E6 (or even just E3) series values only (e.g. 2200 µF, 3300 µF, 4700 µF)  – the tolerance ranges overlap the intermediate values from the next higher series anyway.

Other types of capacitors, e.g. ceramic, can be manufactured to tighter tolerances and are available in E12 values (e.g. 47 pF, 56 pF, 68 pF).

Capacitors were once specified by their values in either microfarads or picofarads, which meant that both very small (such as 0.01 µF) and very large (such as 10,000 pF) numbers were in common use. Nowadays, it is considered preferable to use the nanofarad as well, and specify all values in the numeric range 1 - 999 only; this makes the examples given above equal to 10 nF (yes, they are both the same!). Above 999 µF, the practice is not yet in common use; capacitors are not usually specified in millifarads (mF), probably because it would be too easily confused with microfarads (for which mF was once an acceptable abbreviation).

A table giving translations of previous commonly used multiples is as follows:

 preferred in pF in nF in µF 1pF 1 0.001 0.000,001 10pF 10 0.01 0.000,01 100pF 100 0.1 0.000,1 1nF 1000 1 0.001 10nF 10,000 10 0.01 100nF 100,000 100 0.1 1µF 1,000,000 1000 1

### Colour coding

ColourSignificant digitsMultiplierCapacitance toleranceCharacteristicDC working voltageOperating temperatureEIA/vibration
Black 0 1 ±20% −55 °C to +70 °C 10 to 55 Hz
Brown 1 10 ±1% B 100
Red 2 100 ±2% C −55 °C to +85°C
Orange 3 1,000 D 300
Yellow 4 10,000 E −55 °C to +125°C 10 to 2000 Hz
Green 5 ±5% F 500
Blue 6 −55 °C to +150°C
Violet 7
Grey 8
White 9 EIA
Gold ±0.5%* 1000
Silver ±10%
*Or ±0.5 pF, whichever is greater.

## Capacitors - Role In Alternative Energy

Ultracapacitors might one day play a larger role in regenerative braking in vehicles and providing power, when necessary, for hybrid vehicles. Ultracapacitors might also play a role in utility scale batteries and other large battery storage scenarios required to store energy created by alternative means. It is unlikely that ultracapacitors will entirely replace batteries, but for functions that require a high burst of energy, an ultracapacitor has many advantages over battery technology.

Carbon nanotubes and polymers, or carbon aerogels, are practical for supercapacitors. Carbon nanotubes have excellent nanoporosity properties, allowing tiny spaces for the polymer to sit in the tube and act as a dielectric. Polymers have a redox (reduction-oxidation) storage mechanism along with a high surface area. MIT's Laboratory of Electromagnetic and Electronic Systems (LEES) is researching using carbon nanotubes.

Supercapacitors are also being made of carbon aerogel. Carbon aerogel is a unique material providing extremely high surface area of about 400-1000 m2/g. Capacitances of up to 104 F/g and 77 F/cm3 have been achieved. Some corporations, such as Cooper Electronic Technologies, are already producing aerogel-based supercapacitors. Their maximum voltage is 2.5 V (or 2.7 V), but they can achieve an energy density of 325 kJ/kg (disputed as 10.6 kJ/kg, see Discussion), which is about 70% of that provided by the state-of-the-art lithium polymer batteries. Power densities achieved are even higher, up to 20 kW/kg, orders of magnitude higher than what Li-poly offers. Small aerogel supercapacitors are being used as backup batteries in microelectronics, but applications for electric vehicles are expected.

The electrodes of aerogel supercapacitors are usually made of non-woven paper made from carbon fibers and coated with organic aerogel, which then undergoes pyrolysis. The paper is a composite material where the carbon fibers provide structural integrity and the aerogel provides the required large surface.

Ultracapacitor storage has several advantages and disadvantages relative to batteries as follows:

• Very high rates of charge and discharge.
• Little degradation over hundreds of thousands of cycles.
• Good reversibility
• Low toxicity of materials used.
• High cycle efficiency (95% or more)
• The amount of energy stored per unit weight is considerably lower than that of an electrochemical battery (3-5 W.h/kg for a UC compared to 30-40 W.h/kg for a battery).
• The voltage varies with the energy stored. To effectively store and recover energy requires sophisticated electronic control and switching equipment.
• Exhibits the highest dielectric absorption of all types of capacitors.

## External articles and references

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