Capacitor

Various types of capacitors

A high voltage (15 kV AC) capacitor

A capacitor (occasionally referred to using the older term condenser) is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. Capacitors have thin conducting plates (usually made of metal), separated by a layer of dielectric, then stacked or rolled to form a compact device.

## History of the capacitor

We know from reports of the lost writings of Thales of Miletus (around 600 BC) that the Ancient Greeks knew how to generate sparks by rubbing balls of amber on spindles. This is the triboelectric effect, the mechanical separation of charge in a dielectric.

The ancient experimenters, however, did not know that the charge density could be dramatically increased by sandwiching the insulator between two metal plates. This was the basis of the capacitor. Ewald Georg von Kleist of Pomerania invented the first recorded capacitor in October 1745. It was 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 ball.

Before Kleist's discovery became widely known, a capacitor essentially the same as his was invented independently in January 1746 by the Dutch physicist Pieter van Musschenbroek of the University of Leyden and was named by Abbe Nollet as the Leyden jar.

Benjamin Franklin investigated the Leyden jar, and proved that the charge was stored on the glass, not in the water as others had assumed. Originally, the units of capacitance were in 'jars'. A jar is equivalent to about 1 nF.

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 or the German kondensator.

Physics of the capacitor

Overview

A capacitor consists of two electrodes or plates, each of which stores an opposite charge. These two plates are conductive and are separated by an insulator or dielectric. The charge is stored at the surface of the plates, at the boundary with the dielectric. Because each plate stores an equal but opposite charge, the total charge in the capacitor is always zero.

When electric charge accumulates on the plates, an electric field is created in the region between the plates that is proportional to the amount of accumulated charge. This electric field creates a potential difference V = E·d between the plates of this simple parallel-plate capacitor.

The electrons in the molecules move or rotate the molecule toward the positively charged left plate. This process creates an opposing electric field that partially annuls the field created by the plates. (The air gap is shown for clarity; in a real capacitor, the dielectric is in direct contact with the plates.)

Capacitance of a capacitor

The capacitor's capacitance (C) is a measure of the amount of charge (Q) stored on each plate for a given potential difference or voltage (V) which appears between the plates:

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

In SI units, a capacitor has a capacitance of one farad when one coulomb of charge causes a potential difference of one volt across the plates. Since the farad is a very large unit, values of capacitors are usually expressed in microfarads (µF), nanofarads (nF) or picofarads (pF).

The capacitance is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates. It is also proportional to the permittivity of the dielectric (that is, non-conducting) substance that separates the plates.

Stored energy

As electric charge accumulates on the plates of a capacitor, a voltage develops across the capacitor due to the electric field of the accumulated charge. Ever increasing work must be done against this ever increasing electric field as more charge accumulates. 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. The energy stored is given by:

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

where V is the voltage across the capacitor.

### In electric circuits

For an ideal capacitor, the capacitor current is proportional to the time rate of change of the voltage across the capacitor where the constant of proportionality is the capacitance, C:

$i(t) = C \frac{dv(t)}{dt}$

The impedance in the frequency domain can be written as

$Z = \frac{1}{j \omega C} = - j X_C$.

This shows that a capacitor has a high impedance to low-frequency signals (when ω is small) and a low impedance to high-frequency signals (when ω is large). This frequency dependent behavior accounts for most uses of the capacitor (see "Applications", below).

Applying the Laplace transform, the impedance becomes:

$Z=\frac{1}{sC}$

### Capacitors and 'displacement current'

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, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. Although this interpretation has been abandoned, Maxwell's correction to Ampere's law remains valid (a changing electric field produces a magnetic field).

The displacement current must be included, for example, to apply Kirchhoff's current law to the interior of a capacitor (e.g. to only one of the plates).

## Capacitor networks

A capacitor can be used to block the DC Current flowing within the circuit and therefore have important applications in coupling of ac signals between amplifier stages, whilst preventing dc from passing.

Capacitors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent capacitance (Ceq):

$C_{eq} = C_1 + C_2 + \cdots + C_n \,$

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. To find their total capacitance:

$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}$

One possible reason to connect capacitors in series is to increase the overall voltage rating. In practice, a very large resistor might be connected across each capacitor to divide the total voltage appropriately for the individual ratings.

## 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.

Non-idealities of capacitors

Important properties of capacitors, apart from the capacitance, 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 and equivalent series resistance (ESR) are further considerations. A typical ESR for most capacitors is between 0.0001 and 0.01 ohm, low values being preferred for high-current, or long term integration applications.

Since capacitors have such low ESRs, they have the capacity to deliver huge currents into short circuits, which can be dangerous. For safety purposes, all large capacitors should be discharged before handling. For board-level capacitors, this is done by placing a high-power 1 to 10 ohm resistor across the terminals.

When rehabilitating old (especially audio) equipment, it is a good idea to replace all of the electrolyte-based caps. After long storage electrolytic capacitors may deteriorate; when first powering up equipment with old electrolytics, it may be useful to apply low voltage at first to allow the capacitors to reform before applying full voltage.

ESL (equivalent series inductance) is also important for signal capacitors. 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 also critically important with local supply decoupling for high-speed logic circuits. This 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, instrumentation electronics will frequently use multiple bypass capacitors — a small 0.1 uF for high frequencies, a large electrolytic for low frequencies, and occasionally, an intermediate value.

In the construction of long-time-constant integrators, it is important that the capacitor does not retain a residual charge when shorted. This phenomenon of unwanted charge storage is called dielectric absorption or soakage, and it creates a memory effect in the capacitor. This is a non-linear phenomenon, and is important when building very low distortion filters.

Capacitors may also change capacitance with applied voltage. This is another major source of non-linearity when building low distortion filters. In the case of some types of audio equipment, capacitor non-linearity in the signal path is the dominant source of distortion.

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.). Most of these problematic applications are now performed with digital techniques.

Another major non-ideality is temperature coefficient (change in capacitance with temperature).

Practical capacitors

Common types of fixed capacitor

Many types of Discrete capacitors are available commercially, with capacitances ranging from the picofarad range to more than a Farad, and voltage ratings up to many 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%(electrolystic 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.

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 using bulk insulators

• Air-gap: An air-gap capacitor is highly resistant to breakdown from arcing, because any air that becomes ionized is soon replaced by fresh air . Large-valued tunable capacitors can be made this way. Good for resonating HF antennas.
• 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 - 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.
• Polyester, Mylar®: (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.

• Printed circuit board: Finally, 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.

#### Electrolytic capacitors

main article: electrolytic capacitor

Unlike capacitors that use a bulk dielectric made from an intrinsically insulating material, the dielectric in electrolytic capacitors depends on the formation and maintenance of a microscopic metal oxide layer. Compared to bulk dielectric capacitors, this very thin dielectric allows for much more capacitance in the same unit volume, but maintaining the integrity of the dielectric usually requires the steady application of the correct polarity of direct current else the oxide layer will break down and rupture, causing the capacitor to fail. In addition, electrolytic capacitors generally use an internal wet chemistry and they will eventually fail as the water within the capacitor evaporates.

Electrolytic capacitance values are not as tightly-specified as with bulk dielectric capacitors. Especially with aluminum electrolytics, it is quite common to see an electrolytic capacitor specified as having a "guaranteed minimum value" and no upper bound on its value. For most purposes (such as power supply filtering and signal coupling), this type of specification is acceptable.

As with bulk dielectric capacitors, electrolytic capacitors come in several varieties:

• Aluminum electrolytic: compact but lossy, these are available in the range of <1 μF to 1,000,000 μF with working voltages up to several hundred volts dc. The dielectric is a thin layer of aluminum oxide. They contain corrosive liquid and can burst if the device is connected backwards. Over a long time the liquid can dry out, causing the capacitor to fail. Bipolar electrolytics contain two capacitors connected in series opposition and are used for coupling AC signals.
• Tantalum: compact, low-voltage devices up to about 100 μF, these have a lower energy density and are more accurate than aluminum electrolytics. Compared to aluminum electrolytics, tantalum capacitors have very stable capacitance and little DC leakage, and very low impedance at low frequencies. However, unlike aluminum electrolytics, they are intolerant of voltage spikes and are destroyed (often exploding violently) if connected backwards or exposed to spikes above their voltage rating. Tantalum capacitors are also polarized because of their dissimilar electrodes. The cathode electrode is formed of sintered tantalum grains, with the dielectric electrochemically formed as a thin layer of oxide. The thin layer of oxide gives this type a very high capacitance per unit volume. The anode electrode is formed of a chemically deposited semi-conductive layer of manganese dioxide, which is then connected to an external wire lead. A development of this type replaces the manganese dioxide with a conductive plastic polymer (polypyrrole) that eliminates a self-ignition failure mode of capacitor failure. One vendor's web site refers to the advantage of this new design as "suppression of combustion" [1].
• Supercapacitor or electrical double layer capacitor: extreme high capacitance values up to ten farads but low voltage. They are based on the huge surface area of pucks of activated charcoal immersed in electrolyte, with the voltage of each puck being kept below 1 volt. Current is carried through the non-metallic but conductive granular carbon.
• Ultracapacitor or aerogel capacitor. Huge values, up to thousands of farads. Similar to supercapacitors, but using carbon aerogel to attain immense electrode surface area.

### Variable capacitors

Variable capacitors.

There are two distinct types of variable capacitors, whose capacitance may be intentionally and repeatedly changed over the life of the device:

• Those that use a mechanical construction to change the distance between the plates, or the amount of plate surface area which overlaps. These devices are called tuning capacitors or simply "variable capacitors", and are used in telecommunication equipment for tuning and frequency control. Small variable capacitors which are mounted directly to PCBs (for instance, to precisely set a resonant frequency at the factory and then never be adjusted again) are called trimmer capacitors.
• Those that use the fact that the thickness of the depletion layer of a diode varies with the DC voltage across the diode. These diodes are called variable capacitance diodes, varactors or varicaps. Any diode exhibits this effect, but devices specifically sold as varactors have a large junction area and a doping profile specifically designed to maximize capacitance.

Variable capacitance is sometimes used to convert physical phenomena into electrical signals.

• In a capacitor microphone (commonly known as a condenser microphone), the diaphragm acts as one plate of a capacitor, and vibrations produce changes in the distance between the diaphragm and a fixed plate, changing the voltage maintained across the capacitor plates.
• In process industry instruments,some types of pressure transmitter use a capacitor element to measure pressure and convert to an electrical signal.
• Some forms of tank level gauge detect the change in capacitance between two electrodes which are immersed in a varying depth of liquid.
• A shell may be equipped with a proximity fuse which sets off the explosive charge when a tuned circuit's frequency changes because of an approaching target.
• Variable capacitance can be used to detect objects [proximity switch], or as the operating principle of a keyboard.

### Electric double-layer capacitors (EDLCs)

These devices, often called supercapacitors or ultracapacitors for short, are capacitors that use a molecule-thin layer of electrolyte, rather than a manufactured sheet of material, as the dielectric. As the energy stored is inversely proportional to the thickness of the dielectric, these capacitors have an extremely high energy density. The electrodes are made of activated carbon, which has a high surface area per unit volume, further increasing the capacitor's energy density. Individual EDLCs have capacitances of hundreds or even thousands of farads. For example, the Korean company NessCap offers units up to 5000 farads (5 kF) at 2.7 V, useful for electric vehicles and solar energy applications.

EDLCs can be used as replacements for batteries in applications where a high discharge current is required. They can also be recharged hundreds of thousands of times, unlike conventional batteries which last for only a few hundred or thousand recharge cycles. But capacitor voltage drops faster than battery voltage during discharge so a DC-to-DC inverter may be used to maintain voltage and to make more of the energy stored in the capacitor usable. Shanghai is testing trolleybuses employing supercapacitors.

### Less-conventional capacitors

• Capacitors can also be fabricated in semiconductor integrated circuit devices using metal lines and insulators on a substrate. Such capacitors are used to store analogue signals in switched-capacitor filters, and to store digital data in dynamic random-access memory (DRAM). Unlike discrete capacitors, however, in most fabrication processes, tolerances much lower than 15-20% are not possible.

Other circuit elements or devices exhibit capacitive impedance. These include:

• stubs: In RF circuits, a length of transmission line less than a quarter-wave, that is open at the far end, or a length equal to a quarter-wave which is shorted, has the electrical properties of a capacitor. Transmission line transformers could also be used to tune a resistive load into looking like a capacitor, if the value of the resistor was distinct from the characteristic impedance to the T-line. Video typically uses a 75-ohm T-line, RF 50, UHF pairs (ladder line) are typically 300 ohms.
• electrically short antennas: Dipole and monopole antennas, as well as other types, can be made 'electrically short', which means that they are shorter than one quarter of the wavelength of the radio signal. This makes them look capacitive to their driving amplifiers. A small, tunable shunt inductor can be added to match the antenna to the amplifier. Nulling out the capacitance also has the effect of greatly increasing the effective size of the antenna.
• phosphors: Electro-luminescent displays, used in computers before the availability of light-emitting diodes, are made from photo-emissive capacitors with a visible phosphor-based dielectric. When stimulated with ca. 100 V AC they glow. When left floating afterward they gradually diminish in brightness. If shunted with a resistor after being stimulated, they stop glowing immediately. They come in glowstick-like colors, and lately they take the form of long filaments containing a center conductor and a transparent conductive coating.
• human body: The human body can be modeled as a capacitor of about 10 pF in parallel with a 1 MΩ resistor for the purposes of ESD (electrostatic discharge) studies.
• piezoelectric crystals: Capacitors with a piezoelectric crystal as the dielectric can induce movements in the crystal or sense external strains on it. Devices based on this principle are called capacitive transducers. Applications of capacitive transducers include ceramic phonograph pickups, hi-fi tweeters, and microscope stage positioners. Generally they operate across short distances, but can generate high pressure with good linearity.
• parasitics: These are generally unwanted. The nature of the electromagnetic field makes space itself capacitive and inductive by nature. Processing for faster semiconductors generally involves reducing stored charge at the electrodes, to reduce parasitic capacitance. RF connectors are designed to have low capacitance.
• vacuum: if empty space lacks charge carriers (an electron cloud or mobile ions), it will serve as an excellent insulator which lacks dielectric absorption or dielectric losses. Vacuum capacitors are typically used in high voltage, high power applications. Since a vacuum lacks a breakdown voltage, the typical failure mode is either an arc developing in the supporting enclosure, or a "vacuum arc" breaking out when the work function of the metal electrode surfaces is exceeded.

## Applications

 Capacitor Polarized Capacitor Variable Capacitor
Capacitor symbols

A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a fast battery.

In AC or signal circuits a capacitor induces a phase difference of 90 degrees, current leading voltage.

The energy stored in a capacitor can be used to represent information, either in binary form, as in computers, or in analogue form, as in switched-capacitor circuits and bucket-brigade delay lines.

Capacitors are commonly used in power supplies where they smooth the output of a full or half wave rectifier.

Capacitors can be used in analog computers as components of integrators. Signal processing circuits also use capacitors to integrate a current signal.

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.

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

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 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). Non-polarized electrolytic capacitors used for signal filtering are typically drawn with two curved plates. Other non-polarized capacitors are drawn with two straight plates.

Because capacitors pass AC but block DC signals, they are often used to separate the AC and DC components of a signal. This method is known as AC coupling. (Sometimes transformers are used for the same effect.) Here, a large value of capacitance, whose value need not be accurately controlled, but whose reactance is small at the signal frequency, is employed. Capacitors for this purpose designed to be fitted through a metal panel are called feed-through capacitors, and have a slightly different schematic symbol.

Capacitors with an exposed and porous dielectric can be used to measure humidity in air. Capacitors with a flexible plate can be used to measure strain or pressure.

Capacitors are used in condenser microphones.

Capacitors are also 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 match the inductive loading of machinery which contains motors, to return the load to a purely resistive state.

An obscure but illustrative military application of the capacitor is in an EMP weapon. A plastic explosive is used for the dielectric. The capacitor is charged up and the explosive is detonated. The capacitance becomes smaller, but the charge on the plates stays the same. This creates a high-energy electromagnetic shock wave capable of destroying unprotected electronics for miles around. These devices were first employed by the US in the 2003 invasion of Iraq.

## Capacitor hazards

Capacitors may retain a charge long after power is removed from a circuit; this charge can cause shocks (up to and including electrocution) or damage to connected equipment. Take care to ensure that any large or high-voltage capacitor is properly discharged before servicing the containing equipment.

Dispose of large oil-filled old capacitors properly; some contain polychlorinated biphenyls (PCBs). The reason many older large capacitors and transformers were oil-filled is that the normal usage of these devices can generate a great deal of heat. Oil is an inexpensive heat-dissipating substance that is resistant to boiling within these components' heat range. However, if overheated, the oil can ignite. PCBs were an inexpensive additive that dramatically reduced the oil's ignitability. It was later discovered 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.