A capacitor 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. Intentional capacitors have thin conducting plates (usually made of metal) stacked or rolled to form a compact device, but every multi-conductor geometry has capacitance.

Contents

1 Physics of the capacitor 1.1 Overview 1.2 Capacitance 1.3 Energy 1.4 In electric circuits 2 Practical capacitors 2.1 Common types of fixed capacitor 2.2 Properties of capacitors 2.3 Variable capacitors 2.4 Electric Double Layer Capacitors (EDLCs) 3 Applications 4 History 4.1 Displacement current 5 See also 6 External links 7 References

Physics of the capacitor

Overview

Typical designs consist 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 device is always zero.

Capacitance

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

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.

Energy

The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish voltage, and therefore the electric field. This is given by:

where V is the voltage across the capacitor.

In electric circuits

The transfer function for an ideal capacitor can be written as a differential equation in time domain:

The impedance in frequency domain can be written as

Applying the Laplace transform, the impedance becomes:

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 kilovolts. In general, the higher the capacitance and voltage rating, the larger the physical size of the capacitor and the higher the cost. Tolerances for discrete capacitors are usually specified such as 5 or 10%, or broader ranges for some types. Adjustable versions have stability issues. Another figure of merit for analog components is stability with respect to time and temperature,or drift.

Capacitors are often classified according to the material used as the dielectric.

• 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.
  • Z5U - Typical 0.01 µF to 2.2 µF, 20%. Good for bypass, coupling applications. Low price and small size.
  • Ceramic chip: 1% accurate, values up to about 1 μF, typically made from Lead zirconate titanate (PZT) ferroelectric ceramic
• Polystyrene : (usually in the picofarad range) stable signal capacitors.
• Polyester , Mylar®: (from about 1 nF to 1 μF) signal capacitors, integrators.
• Polypropylene low-loss, high voltage, resistant to breakdown, signal capacitors.
• PTFE or Teflon ™: higher performing and more expensive than other plastic dielectrics.
• 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.
• Tantalum: compact, low-voltage devices up to about 100 μF, lower energy density and more accurate than aluminum electrolytics, but less accurate and higher energy density than signal capacitors. Since these capacitors rely on an electrolyte, they are polarized, meaning that they can only support a potential in one direction and are suitable only for DC applications. Compared to aluminum electrolytics, tantalum capacitors have very stable capacitance and 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 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 depositied semi-conductive layer of magnese dioxide, which is then connected to an external wire lead. A development of this type replaces the magnese dioxide with a conductive plastic polymer which eliminates a self-ignition failure mode of capacitor failure.

• Aluminum electrolytic: compact but lossy, in the 1 μF to 1,000,000 μF range, up to several hundred volts. The dielectric is a thin oxide layer. Like tantalum capacitors, these are polarized. 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.
• 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.
• 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.
• Silver mica: These are fast and stable for HF and low VHF RF circuits, but expensive.
• Printed circuit board: Metal plates 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, or to make power traces broader than signal traces.

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 (electro-static 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 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.

Properties 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 out of hand. 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.

Dispose of large oil-filled old capacitors properly; some have PCBs. If the capacitor is physically large it is more likely to be dangerous and may require precautions in addition to those described above.

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, 0.1uF for high frequencies, a large electrolytic for low frequencies, and occasionally, an intermediate.

In the construction of long-time-constant integrators, it is important that the capacitor does not retain a residual charge when shorted. This phenomenon is called dielectric absorption or soakage, and it creates a memory effect in the capacitor. This is a non-linear phenomenon, and is also 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 will also have leakage --- some level of parasitic resistance across the terminals. 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 applications have since moved to digital.

Other major non-idealities include temperature coefficient (change in capacitance with temperature).

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.

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.

Applications

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 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 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 drives a potential spike capable of destroying non-hardened electronics for miles around. These devices were first employed by the US in the 2003 invasion of Iraq.

History

The ancient Greeks used balls of amber on spindles that they rubbed to generate sparks. This is the triboelectric effect, mechanical separation of charge in a dielectric. Their work was a precursor to the development of the capacitor.

The Leyden jar, the first form of capacitor, was invented at Leiden University in the Netherlands. 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. Benjamin Franklin was known to experiment with Leyden jars.

Early capacitors were also known as "condensers".

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).

See also

• Capacitance
• Electromagnetism
• Electricity
• Electronics
• Inductor
• Ark of the Covenant (thought by some to be a capacitor)

External links

• Caltech: Practical capacitor properties
• FaradNet: The Capacitor Resource
• NessCap, maker of 5000 farad capacitors
• General Atomics Electronic Systems, inc. High Voltage Pulsed Power Capacitors and Systems.
• Skeleton NanoLab, Research & Development of advanced capacitors

References

• Glenn Zorpette "Super Charged: A Tiny South Korean Company is Out to Make Capacitors Powerful enough to Propel the Next Generation of Hybrid-Electric Cars", "IEEE Spectrum", January, 2005 Vol 42, No. 1, North American Edition.
• "The ARRL Handbook for Radio Amateurs, 68th ed", The Amateur Radio Relay League, Newington CT USA, 1991
• "Basic Circuit Theory with Digital Computations", Lawrence P. Huelsman, Prentice-Hall, 1972