The Capacitor reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

# Capacitor

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Various types of capacitors

A capacitor (historically known as a "condenser") is a device that stores energy in an electric field, by accumulating an internal imbalance of electric charge.

Sometimes, other types of natural or man-made structures that store electric charge are also called capacitors. Examples include thunderclouds (separated from each other and from the earth by an air dielectric), and an automobile and the earth (separated by tires and air).

Capacitors are most often used as electrostatic devices, but at high frequencies their inductive and electrodynamic properties also become significant.

## 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.

When a potential difference V = Ed is applied to the plates of this simple parallel-plate capacitor, an electric field must arise between them. This electric field is produced by the accumulation of a charge on the plates.

### 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 above equation is only accurate 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 1 µV, the equation would predict a charge Q = 10-19 C, but this is impossible as it is smaller than the charge on a single electron. However, recent experiments and theories (e.g. the fractional quantum Hall (FQH) effect) have suggested the existence of fractional charges.

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:

where C is the capacitance in farads, ε0 is the electrostatic permittivity of vacuum or free space, and εr is the dielectric constant or relative permittivity of the insulator used.

### Energy

The energy (in SI, measured in joules) stored in a capacitor is equal to the work done to charge it up. Consider a capacitor with 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:

We can find the energy stored in a capacitor by integrating this equation. Starting with an uncharged capacitor (q=0) and moving charge from one plate to the other until the plates have charge +Q and -Q requires the work W:

The electrons in the molecules shift toward the positively charged left plate. The molecules then create a leftward 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.)

### In electric circuits

where I is the current flowing in the conventional direction, and dV/dt is the time derivative of voltage.

In the case of a constant voltage (DC) soon an equilibrium is reached, where the charge of the plates corresponds with the applied voltage by the relation Q=CV, and no further current will flow in the circuit. Therefore direct current cannot pass. However, effectively alternating current (AC) can: every change of the voltage gives rise to a further charging or a discharging of the plates and therefore a current. The amount of "resistance" of a capacitor to AC is known as capacitive reactance, and varies depending on the AC frequency. Capacitive reactance is given by this formula:

where:
Thus the reactance is inversely proportional to the frequency. Since DC has a frequency of zero, the formula confirms that capacitors completely block direct current. For high-frequency alternating currents the reactance is small enough to be considered as zero in approximate analyses.

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 energy that enters them, ultimately by electromagnetic emission (see Black body radiation), while reactive loads (analogous to a spring or frictionless moving object) retain the energy.

The impedance of a capacitor is given by:

where j is the imaginary number.

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

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 shunt, conductances sum.

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

This is the frequency at which resonance occurs in a RLC series circuit.

### Capacitor networks

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

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:

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.

## Practical capacitors

### Common types of fixed capacitor

Discrete capacitors of various types are available commercially with capacitances ranging from the pF range to more than a farad, and voltage ratings up to hundreds of volts. In general, the higher the capacitance and voltage rating, the larger the physical size of the capacitor and the higher the cost. If two capacitors have the same potential rating and capacity, the smaller one has greater volumetric efficiency. Tolerances for discrete capacitors are usually specified as 5 or 10%, and adjustable versions have stability issues. Another figure of merit for analog components is derivative accuracy, or drift.

Capacitors are often classified according to the material used as the dielectric.  The following types of dielectric are used.

The main differences between ceramic dielectric types are the temperature coefficient of capacitance, and the dielectric loss. COG and NPO 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.

• Ceramic chip: 1% accurate, values up to about 1μF
• C0G or NP0 - Typically 4.7pF to .047uF, 5%. High tolerance and temperature performance. Larger and more expensive.
• X7R - Typical 3300pF to .33uF, 10%. Good for non-critical coupling, timing applications.
• Z5U - Typical .01uF to 2.2uF, 20%. Good for bypass, coupling applications. Low price and small size.
• Polystyrene: (usually in the picofarad range) stable signal capacitors.
• Polyester, Mylar: (from about 1nF to 1μF) signal capacitors.
• Polypropylene low-loss, high voltage, resistant to breakdown, signal capacitors.
• PTFE or Teflon ™: higher performing and more expensive than other plastic dielectrics.
• Tantalum: compact, low-voltage devices up to about 100μF, lower energy density and more accurate than electrolytics, but less accurate and higher energy density than signal capacitors. These capacitors are polarized, meaning that they can only support a potential in one direction and are suitable only for DC applications.
• Electrolytic: high-power, compact but lossy, in the 1μF-1000μF range. 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.
• 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.
• stubs: In RF circuits, a length of transmission line less than a quarter-wave, that is shorted at the end, or a length greater than a quarter-wave left open, 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 ohm.
• 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.
• 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 c. 100V 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.
• human body: The human body can be modeled as a capacitor of about 10pF in parallel with a 1M 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.

### 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 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 rehabilating old (especially audio) equipment, it is a good idea to replace all of the electrolyte-based caps out of hand. Dispose of old cap of these types 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. The local decoupler (a 0.1 ~ 1.0 μF capacitor placed near a power pin of a digital IC) must look like a capacitor at 10x the highest (usually clock) frequency associated with the logic chip, down to DC. 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.

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.

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:

### 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.

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.

## Applications

A capacitor can store electronic 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. This use is called integration or filtering, which is a basic analog signal computation function. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry.

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. The effect of such capacitors can be thought of in two different ways. One way of thinking about it is that the capacitors act as a local reserve for the DC power source, to smooth out fluctuations by charging and discharging each cycle. The other way to think about it is that the capacitor and resistance of the power supply circuitry acts as a filter and removes high frequencies, leaving only DC. This is called an 'AC short' in industrial parlance.

Capacitors and inductors are applied together in AC 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. Signal circuits also use capacitors to integrate a current signal.

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 capacitors used for signal filtering are typically 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 volts-amps 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 to use a plastic explosive for the dielectric in an EMP weapon. Charge it up and detonate the explosive. The capacitor gets (electronically) smaller, but the energy stays the time. This drives a potential spike capable of destroying non-hardened electronics for miles around. These were the first devices the US employed 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.

### 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 a capacitor.