English

Noun

capacitors

1. Plural of capacitor

A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors (called "plates"). The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity, building up on each plate.

Capacitors are often used in electric and electronic circuits as energy-storage devices. They can also be used to differentiate between high-frequency and low-frequency signals. This property makes them useful in electronic filters.

Capacitors are occasionally referred to as condensers. This is considered an antiquated term in English, but most other languages use an equivalent, like "condensateur" in French, "Kondensator" in German, "condensador" in Spanish, or "Kondensa" in Japanese.

History

In October 1745, Ewald Georg von Kleist of Pomerania in Germany invented the first recorded capacitor: a glass jar with water inside as one plate was held on the hand as the other plate. A wire in the mouth of the bottle received charge from an electric machine, and released it as a spark.

In the same year, 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 charge storage capacity.

Benjamin Franklin investigated the Leyden jar, and proved that the charge was stored on the glass, not in the water as others had assumed. The earliest unit of capacitance was the 'jar', equivalent to about 1 nanofarad.

Early capacitors were also known as condensers, a term that is still occasionally used today. It was coined by Alessandro 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 European languages still use a word derived from "condensatore".

Theory of operation

A capacitor consists of two conductive electrodes, or plates, separated by a dielectric, which prevents charge from moving directly between the plates. Charge may however be moved indirectly by external influences, such as a battery connecting the terminals. After removing the external influences, the charge on the plates persists. The separated charges attract each other, and an electric field is present between the plates. The simplest practical capacitor consists of two wide, flat, parallel plates separated by a thin dielectric layer.

Assuming that the area of the plates A is much greater than their separation d, the instantaneous electric field between the plates E(t) is identical at any location away from the edges. If the instantaneous charge on a plate -q(t) is spread evenly,

E(t) = -\frac,

where \varepsilon is the permittivity of the dielectric. The voltage v(t) between the plates is given by

v(t) = -\int_0^d E(t)\,\,\,\textz = \frac,

where z is a position between the plates

Capacitance

A property called the capacitance C, which is a measure of the charge stored on each plate for a given voltage such that

q(t)= Cv(t),

where

C = \frac

for an ideal parallel plate capacitor.

In SI units, a capacitor has a capacitance of one farad when one coulomb of charge storage corresponds to one volt between its plates. Since the farad is a very large unit, capacitance is usually expressed in microfarads (µF), nanofarads (nF), or picofarads (pF). In general, capacitance is greater in devices with large plate areas, separated by small distances. When a dielectric is present between two charged plates, its molecules become polarized and reduce the internal electric field and hence the voltage. The capacitance is therefore strongly dependent on the quality of the dielectric.

Energy storage

Work must be done by an external influence to move charge between the plates in a capacitor. When the external influence is removed, the charge separation persists and energy is stored in the electric field. If charge is later allowed to return to its equilibrium position, the energy is released. The work done in establishing the electric field, and hence the amount of energy stored, is given by

W(t) = -q(t) \int_0^d E(t) \textz = = C v(t)^2 =

The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage of the dielectric. Therefore, all capacitors made with a particular dielectric have approximately identical maximum energy density if the dielectric dominates their volume.

Hydraulic analogy

As electrical circuitry can be modeled by fluid flow, a capacitor can be modeled as a chamber with a flexible diaphragm separating the input from the output. As can be determined intuitively as well as mathematically, this provides the correct characteristics:

• The pressure difference (voltage difference) across the unit is proportional to the integral of the flow (current).
• A steady state current cannot pass through it because the pressure will build up across the diaphragm until it equally opposes the source pressure,
• but a transient pulse or alternating current can be transmitted.
• An overpressure results in bursting of the diaphragm, analogous to dielectric breakdown.
• The capacitance of units connected in parallel is equivalent to the sum of their individual capacitances.

Aging

The capacitance of certain capacitors decreases as the component ages. In ceramic capacitors, this is caused by degradation of the dielectric. The type of dielectric and the ambient operating and storage temperatures are the most significant aging factors, while the operating voltage has a smaller effect. The aging process may be reversed by heating the component above the Curie point. Aging is fastest near the beginning of life of the component, and the device stabilizes over time. Electrolytic capacitors age as the electrolyte evaporates. In contrast with ceramic capacitors, this occurs towards the end of life of the component.

Electric circuits

When a capacitor is connected to a current source, charge is transfered between its plates at a rate i(t)=\textq(t)/\textt. As the voltage between the plates is proportional to the charge, it follows that

v(t) = \fracq(t) = \frac\int_0^t i(\tau)\,\,\text\tau.

Conversely, if a capacitor is connected to a voltage source, the resulting current is

i(t) = C\frac

DC sources

A circuit containing only a resistor, a capacitor, a switch and a constant (DC) voltage source v_(t)=V_0 in series is known as a charging circuit. From Kirchhoff's voltage law it follows that

V_0 = v_r(t) + v_c(t) = i(t)R + \frac\int_0^t i(\tau)\,\,\text\tau,

where v_r(t) and v_c(t) are the voltages across the resistor and capacitor respectively. This reduces to a first order differential equation

RC\frac = - i(t)

Assuming that the capacitor is initially uncharged, there is no internal electric field, and the initial current is I_0=V_0/R. This initial condition allows solution of the differential equation as

i(t) = \frac\exp\left(-\frac\right).

The corresponding voltage drop across the capacitor is

v(t) = V_0\left[1-\exp\left(\frac\right)\right].

Therefore, as charge increases on the capacitor plates, the voltage across the capacitor increases, until it reaches a steady-state value of V_0, and the current drops to zero. Both the current, and the difference between the source and capacitor voltage decay exponentially with respect to time. The time constant of the decay is given by \tau = RC.

AC sources

When connected to an AC voltage source, the plates on a capacitor repeatedly charge and discharge relative to each other. The current varies sinusoidally, with a nonzero amplitude. For this reason, capacitors effectively conduct AC although charge ideally never passes directly through the dielectric. Since the current is proportional to the time derivative of the voltage, a sinusoidal current leads the voltage by a 90 degree phase shift, or equivalently a quarter cycle. The amplitude of the voltage depends on the amplitude of the current divided by the product of the frequency of the current with the capacitance, C.

Impedance

The ratio of the phasor voltage across a circuit element to the phasor current through that element is called the impedance Z. For a capacitor, the impedance is given by

Z_C = \frac = \frac = -j X_C ,

where X_C = \frac is the capacitive reactance, \omega = 2 \pi f \, is the angular frequency, f is the frequency), C is the capacitance in farads, and j is the imaginary unit.

While this relation (between the frequency domain voltage and current associated with a capacitor) is always true, the ratio of the time domain voltage and current amplitudes is equal to X_C only for sinusoidal (AC) circuits in steady state.

See derivation Deriving capacitor impedance.

Hence, capacitive reactance is the negative imaginary component of impedance. The negative sign indicates that the current leads the voltage by 90° for a sinusoidal signal, as opposed to the inductor, where the current lags the voltage by 90°.

The impedance is analogous to the resistance of a resistor. The impedance of a capacitor is inversely proportional to the frequency -- that is, for very high-frequency alternating currents the reactance approaches zero -- so that a capacitor is nearly a short circuit to a very high frequency AC source. Conversely, for very low frequency alternating currents, the reactance increases without bound so that a capacitor is nearly an open circuit to a very low frequency AC source. This frequency dependent behaviour accounts for most uses of the capacitor (see "Applications", below).

Reactance is so called because the capacitor doesn't dissipate power, but merely stores energy. In electrical circuits, as in mechanics, there are two types of load, resistive and reactive. Resistive loads (analogous to an object sliding on a rough surface) dissipate the energy delivered by the circuit as heat, while reactive loads (analogous to a spring or frictionless moving object) store this energy, ultimately delivering the energy back to the circuit.

Also significant is that the impedance is inversely proportional to the capacitance, unlike resistors and inductors for which impedances are linearly proportional to resistance and inductance respectively. This is why the series and shunt impedance formulae (given below) are the inverse of the resistive case. In series, impedances sum. In parallel, conductances sum.

Laplace equivalent (s-domain)

When using the Laplace transform in circuit analysis, the capacitive impedance is represented in the s domain by:

Z(s)=\frac

where C is the capacitance, and s (= σ+jω) is the complex frequency.

Displacement current

The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampère's law consistent with conservation of charge in cases where charge is accumulating as in a capacitor. He interpreted this as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the aether. Although this interpretation has been abandoned, Maxwell's correction to Ampère's law remains valid.

Networks

Series or parallel arrangements

Capacitors in a parallel configuration each have the same potential difference (voltage). Their total capacitance (Ceq) is given by:

C_ = C_1 + C_2 + \cdots + C_n \,

The reason for putting capacitors in parallel is to increase the total amount of charge stored. In other words, increasing the capacitance also increases the amount of energy that can be stored. Its expression is:

E_\mathrm = C V^2 .

The current through capacitors in series stays the same, but the voltage across each capacitor can be different. The sum of the potential differences (voltage) is equal to the total voltage. Their total capacitance is given by:

\frac = \frac + \frac + \cdots + \frac

In parallel the effective area of the combined capacitor has increased, increasing the overall capacitance. While in series, the distance between the plates has effectively been increased, reducing the overall capacitance.

In practice capacitors will be placed in series as a means of economically obtaining very high voltage capacitors, for example for smoothing ripples in a high voltage power supply. Three "600 volt maximum" capacitors in series, will increase their overall working voltage to 1800 volts. This is of course offset by the capacitance obtained being only one third of the value of the capacitors used. This can be countered by connecting 3 of these series set-ups in parallel, resulting in a 3x3 matrix of capacitors with the same overall capacitance as an individual capacitor but operable under three times the voltage. In this application, a large resistor would be connected across each capacitor to ensure that the total voltage is divided equally across each capacitor and also to discharge the capacitors for safety when the equipment is not in use.

Another application is for use of polarized capacitors in alternating current circuits; the capacitors are connected in series, in reverse polarity, so that at any given time one of the capacitors is not conducting...

Capacitor/inductor duality

In mathematical terms, the ideal capacitor can be considered as an inverse of the ideal inductor, because the voltage-current equations of the two devices can be transformed into one another by exchanging the voltage and current terms. Just as two or more inductors can be magnetically coupled to make a transformer, two or more charged conductors can be electrostatically coupled to make a capacitor. The mutual capacitance of two conductors is defined as the current that flows in one when the voltage across the other changes by unit voltage in unit time.

Capacitor types

Practical capacitors are available commercially in many different forms. The type of internal dielectric, the structure of the plates and the device packaging all strongly affect the characteristics of the capacitor, and its applications.

Dielectric materials

Most types of capacitor include a dielectric spacer, which increases their capacitance. However, low capacitance devices are available with a vacuum between their plates, which allows extremely high voltage operation and low losses. Air filled variable capacitors are also commonly used in radio tuning circuits.

Several solid dielectrics are available, including paper, plastic, glass, mica and ceramic materials. Paper was used extensively in older devices and offers relatively high voltage performance. However, it is susceptible to water absorption, and has been largely replaced by plastic film capacitors. Plastics offer better stability, and aging performance, which makes them useful in timer circuits although they may be limited to low operating temperatures and frequencies. Ceramic capacitors are generally small, cheap and useful for high frequency applications, although their capacitance varies strongly with voltage, and they age poorly. They are broadly categorized as Class 1 dielectrics, which have predictable variation of capacitance with temperature or Class 2 dielectrics, which can operate at higher voltage. Glass and mica capacitors are extremely reliable, stable and tolerant to high temperatures and voltages, but are too expensive for most mainstream applications.

Electrolytic capacitors use an aluminum or tantalum plate with an oxide dielectric layer. The second electrode is a liquid electrolyte. Electrolytic capacitors offer very high capacitance but suffer from poor tolerances, high instability, gradual loss of capacitance especially when subjected to heat, and high leakage current. The conductivity of the electrolyte drops at low temperatures, which increases equivalent series resistance. While widely used for power-supply conditioning, poor high-frequency characteristics make them unsuitable for many applications. Tantalum capacitors offer better frequency and temperature characteristics than aluminum, but higher dielectric absorption and leakage.. OS-CON (or OC-CON) capacitors are a polymerized organic semiconductor solid-electrolyte type that offer longer life at higher cost than standard electrolytic capacitors.

Several other types of capacitor are available for specialist applications. Supercapacitors made from carbon aerogel, carbon nanotubes, or highly porous electrode materials offer extremely high capacity and can be used in some applications instead of rechargeable batteries. AC capacitors are specifically designed to work on line (mains) voltage AC power circuits. They are commonly used in electric motor circuits and are often designed to handle large currents, so they tend to be physically large. They are usually ruggedly packaged, often in metal cases that can be easily grounded/earthed. They also tend to have rather high DC breakdown voltages.

Structure

Capacitors may have their plates arranged in many configurations, for example axially or radially. Small, cheap discoidal ceramic capacitors have existed since the 1930s, and remain in widespread use. Since the 1980s, surface mount packages for capacitors have been widely used. These packages are extremely small and lack connecting leads, allowing them to be soldered directly onto the surface of printed circuit boards. Surface mount components avoid undesirable high-frequency effects due to the leads and simplify automated assembly, although manual handling is made difficult due to their small size.

Variable capacitors are available in various forms. Mechanically controlled variable capacitors allow the plate spacing to be adjusted, for example by rotating or sliding a set of movable plates into alignment with a set of stationary plates. Very cheap variable capacitors squeeze together alternating layers of aluminum and plastic with a screw, but the resulting capacitance is unstable, and unreproducible. Electrical control of capacitance is achievable with varactors (or varicaps), which are reverse-biased semiconductor diodes whose depletion region width varies with applied voltage. They are used in phase-locked loops, amongst other applications.

Applications

Capacitors have various uses in electronic and electrical systems.

Energy storage

A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary battery. Capacitors are commonly used in electronic devices to maintain power supply while batteries are being changed. (This prevents loss of information in volatile memory.)

Power conditioning

Reservoir capacitors are used in power supplies where they smooth the output of a full or half wave rectifier. They can also be used in charge pump circuits as the energy storage element in the generation of higher voltages than the input voltage.

Capacitors are connected in parallel with the power circuits of most electronic devices and larger systems (such as factories) to shunt away and conceal current fluctuations from the primary power source to provide a "clean" power supply for signal or control circuits. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry. The capacitors act as a local reserve for the DC power source, and bypass AC currents from the power supply. This is used in car audio applications, when a stiffening capacitor compensates for the inductance and resistance of the leads to the lead-acid car battery.

Power factor correction

Capacitors are used in power factor correction. Such capacitors often come as three capacitors connected as a three phase load. Usually, the values of these capacitors are given not in farads but rather as a reactive power in volt-amperes reactive (VAr). The purpose is to counteract inductive loading from electric motors and fluorescent lighting in order to make the load appear to be mostly resistive.

Filtering

Signal coupling

Because capacitors pass AC but block DC signals (when charged up to the applied dc voltage), they are often used to separate the AC and DC components of a signal. This method is known as AC coupling or "capacitive coupling". Here, a large value of capacitance, whose value need not be accurately controlled, but whose reactance is small at the signal frequency, is employed.

Decoupling

A decoupling capacitor is a capacitor used to decouple one part of a circuit from another. Noise caused by other circuit elements is shunted through the capacitor reducing the effect they have on the rest of the circuit. It is most commonly used between the power supply and ground.

An alternative name is bypass capacitor as it is used to bypass the power supply or other high impedance component of a circuit.

Noise filters, motor starters, and snubbers

When an inductive circuit is opened, the current through the inductance collapses quickly, creating a large voltage across the open circuit of the switch or relay. If the inductance is large enough, the energy will generate a spark, causing the contact points to oxidize, deteriorate, or sometimes weld together, or destroying a solid-state switch. A snubber capacitor across the newly opened circuit creates a path for this impulse to bypass the contact points, thereby preserving their life; these were commonly found in contact breaker ignition systems, for instance. Similarly, in smaller scale circuits, the spark may not be enough to damage the switch but will still radiate undesirable radio frequency interference (RFI), which a filter capacitor absorbs. Snubber capacitors are usually employed with a low-value resistor in series, to dissipate energy and minimize RFI. Such resistor-capacitor combinations are available in a single package.

In an inverse fashion, to initiate current quickly through an inductive circuit requires a greater voltage than required to maintain it; in uses such as large motors, this can cause undesirable startup characteristics, and a motor starting capacitor is used to increase the coil current to help start the motor.

Capacitors are also used in parallel to interrupt units of a high-voltage circuit breaker in order to equally distribute the voltage between these units. In this case they are called grading capacitors.

In schematic diagrams, a capacitor used primarily for DC charge storage is often drawn vertically in circuit diagrams with the lower, more negative, plate drawn as an arc. The straight plate indicates the positive terminal of the device, if it is polarized (see electrolytic capacitor).

Signal processing

The energy stored in a capacitor can be used to represent information, either in binary form, as in DRAMs, or in analogue form, as in analog sampled filters and CCDs. Capacitors can be used in analog circuits as components of integrators or more complex filters and in negative feedback loop stabilization. Signal processing circuits also use capacitors to integrate a current signal.

Tuned circuits

Capacitors and inductors are applied together in tuned circuits to select information in particular frequency bands. For example, radio receivers rely on variable capacitors to tune the station frequency. Speakers use passive analog crossovers, and analog equalizers use capacitors to select different audio bands.

In a tuned circuit such as a radio receiver, the frequency selected is a function of the inductance (L) and the capacitance (C) in series, and is given by:

f = \frac

This is the frequency at which resonance occurs in an LC circuit.

Other applications

Sensing

Most capacitors are designed to maintain a fixed physical structure. However, various factors can change the structure of the capacitor; the resulting change in capacitance can be used to sense those factors.

Changing the dielectric: the effects of varying the physical and/or electrical characteristics of the dielectric can also be of use. Capacitors with an exposed and porous dielectric can be used to measure humidity in air.

Changing the distance between the plates: Capacitors are used to accurately measure the fuel level in airplanes. Capacitors with a flexible plate can be used to measure strain or pressure. Capacitors are used as the sensor in condenser microphones, where one plate is moved by air pressure, relative to the fixed position of the other plate. Some accelerometers use MEMS capacitors etched on a chip to measure the magnitude and direction of the acceleration vector. They are used to detect changes in acceleration, eg. as tilt sensors or to detect free fall, as sensors triggering airbag deployment, and in many other applications. Some fingerprint sensors use capacitors. Additionally, a user can adjust the pitch of a theremin musical instrument by moving his hand since this changes the effective capacitance between the user's hand and the antenna.

Changing the effective area of the plates: capacitive touch switches http://discovercircuits.com/C/capacitance-sw.htm http://mobilehandsetdesignline.com/showArticle.jhtml?articleID=185300662 http://edn.com/article/CA6343249.html?industryid=2282.

Pulsed power and weapons

Groups of large, specially constructed, low-inductance high-voltage capacitors (capacitor banks) are used to supply huge pulses of current for many pulsed power applications. These include electromagnetic forming, Marx generators, pulsed lasers (especially TEA lasers), pulse forming networks, radar, fusion research, and particle accelerators.

Large capacitor banks(Reservoir) are used as energy sources for the exploding-bridgewire detonators or slapper detonators in nuclear weapons and other specialty weapons. Experimental work is under way using banks of capacitors as power sources for electromagnetic armour and electromagnetic railguns or coilguns.

See also Explosively pumped flux compression generator.

Hazards and safety

Capacitors may retain a charge long after power is removed from a circuit; this charge can cause shocks (sometimes fatal) or damage to connected equipment. For example, even a seemingly innocuous device such as a disposable camera flash unit powered by a 1.5 volt AA battery contains a capacitor which may be charged to over 300 volts. This is easily capable of delivering an extremely painful shock.

Care must be taken to ensure that any large or high-voltage capacitor is properly discharged before servicing the containing equipment. For board-level capacitors, this is done by placing a bleeder resistor across the terminals, whose resistance is large enough that the leakage current will not affect the circuit, but small enough to discharge the capacitor shortly after power is removed. High-voltage capacitors should be stored with the terminals shorted, since temporarily discharged capacitors can develop potentially dangerous voltages when the terminals are left open-circuited.

Large oil-filled old capacitors must be disposed of properly as some contain polychlorinated biphenyls (PCBs). It is known that waste PCBs can leak into groundwater under landfills. If consumed by drinking contaminated water, PCBs are carcinogenic, even in very tiny amounts. If the capacitor is physically large it is more likely to be dangerous and may require precautions in addition to those described above. New electrical components are no longer produced with PCBs. ("PCB" in electronics usually means printed circuit board, but the above usage is an exception.) Capacitors containing PCB were labelled as containing "Askarel" and several other trade names.

High voltage

Above and beyond usual hazards associated with working with high-voltage high-energy circuits, there are a number of dangers that are specific to high-voltage capacitors. High-voltage capacitors may catastrophically fail when subjected to voltages or currents beyond their rating, or as they reach their normal end of life. Dielectric or metal interconnection failures may create arcing called an arc fault; within oil-filled units, that vaporizes dielectric fluid, resulting in case bulging, rupture, or even an explosion, called flash meltdown, that disperses flammable oil, starts fires, and damages nearby equipment. Rigid cased cylindrical glass or plastic cases are more prone to explosive rupture than rectangular cases due to an inability to easily expand under pressure. Capacitors used in RF or sustained high-current applications can overheat, especially in the center of the capacitor rolls. The trapped heat may cause rapid interior heating and destruction, even though the outer case remains relatively cool. Capacitors used within high-energy capacitor banks can violently explode when a fault in one capacitor causes sudden dumping of energy stored in the rest of the bank into the failing unit. And, high voltage vacuum capacitors can generate soft X-rays even during normal operation. Proper containment, fusing, and preventative maintenance can help to minimize these hazards.

High-voltage capacitors can benefit from a pre-charge to limit in-rush currents at power-up of HVDC circuits. This will extend the life of the component and may mitigate high-voltage hazards.

See also

• Capacitance
• Capacitor plague: capacitor failures on computer motherboards
• Circuit design
• Decoupling capacitor
• Electronic component
• Electric displacement field
• Electronics
• Electronic oscillator
• Filter capacitor
• Light emitting capacitor
• Reservoir capacitor
• Supercapacitor
• Vacuum variable capacitor
• Variable capacitor
• Capacitance meter

Notes

References

• The ARRL Handbook for Radio Amateurs
• Basic Circuit Theory with Digital Computations
• Philosophical Transactions of the Royal Society LXXII, Appendix 8, 1782 (Volta coins the word condenser)
• A. K. Maini "Electronic Projects for Beginners", "Pustak Mahal", 2nd Edition: March, 1998 (INDIA)
• Spark Museum (von Kleist and Musschenbroek)
• Biography of von Kleist

External links

• The Capacitor Tutorial
• Capacitance and Inductance - a chapter from an online textbook
• Howstuffworks.com: How Capacitors Work
• CapSite 2007: Introduction to Capacitors
• AC circuits
• Capacitor Tutorial - Includes how to read capacitor temperature codes
• Capacitors in Circuits by Ernest Lee, The Wolfram Demonstrations Project.