## Capacitors and Ultracapacitors

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# CAPACITORS AND ULTRACAPACITORS

Capacitors store electrical energy in the form of an electric field between two electrically conducting plates. The simplest capacitor is two electrically conducting plates separated spatially. By inserting a dielectric material (a poor conductor of electricity) between the two plates the capacity can be greatly increased (Figure 1). The dielectric material used determines the major characteristics of the capacitor: capacitance, maximum voltage or breakdown voltage, and response time or frequency. The first capacitor, the Leyden jar accidentally discovered in 1745, is a glass jar coated with copper on the inside and outside. The inside and outside copper coatings are electrically connected to a battery. The two spatially separated copper plates are the electrodes, and the glass is the dielectric of the Leyden jar capacitor. The capacity to store electrical energy at certain frequencies and to provide high-power discharges makes a capacitor an essential component in most electrical circuits used in electronics, communication, computers, manufacturing, and electric vehicles.

Capacitance is related to the area of the plates (A), the distance between the plates (d), and the dielectric constant (ε) of the material between the plates (Figure 2, equation I). The dielectric constant or permittivity of a material is the increased capacitance observed compared to the condition if a vacuum was present between the plates. Common dielectric materials are polystyrene (ε = 2.5), mylar (ε = 3), mica (ε = 6), aluminum oxide (ε = 7), tantalum oxide (ε = 25), and titania (ε = 100). In the Leyden jar the dielectric is silica. A capacitor, previously called a condenser, stores electrical energy based on the relationship between voltage (V) and stored charge (Q) in coulombs as shown in the equation C=QU. One farad of capacitance is a coulomb per volt of stored charge. The voltage limit of a capacitor is determined by the breakdown potential of the dielectric material.

Like a battery, a capacitor is an electrical energy storage device. There are, however, significant differences in how a battery and a capacitor store and release electrical energy. A battery stores electrical energy as chemical energy and can be viewed as a primary source. Capacitors need to be charged from a primary electrical source. During a constant current discharge, a battery will maintain a relatively constant voltage. In contrast, a capacitor's voltage is dependent on the "state of charge," decreasing linearly during a constant current discharge (Figure 3). The energy of a capacitor in joules is defined in the equation

Capacitors are often combined in series or parallel, with the resulting circuit capacitance calculated as depicted in Figure 4. An important relationship is the time constant of a capacitor. The time constant is based on the product of the resistance and capacitance and is known as the RC time constant. A capacitor in a dc circuit will charge or discharge 63.2 percent in one RC time constant. The time dependence of a capacitor is shown in the equations. and

Electrochemical capacitors are also known as double layer capacitors, ultracapacitors, or supercapacitors. These devices are based on either double-layer charge storage or pseudocapacitance. Electrochemical double-layer capacitors, originally developed by Standard Oil Company during the 1960s, store charge at the interface between an electrically conducting electrode such as carbon and an ionically conducting electrolyte such as sulfuric acid. The double layer, first described by Hermann von Helmholtz in 1853, can be considered the equivalent of a parallel plate capacitor wherein the distance of charge separation is given by the ionic radius of the electrolyte, while the solvent continuum is the dielectric (Figure 5). The large charge storage offered by electrochemical capacitors is due to amplifying the double-layer capacitance (≃ 15 × 10-6 F/cm2) by a large surface area electrode (≃ 2 × 107 cm2⁄g). Electrochemical capacitors typically have capacitance values of millifarads to tens of farads, in contrast to electrolytic capacitors, which typically have values in the range of picofarads to microfarads.

The single cell of an electrochemical capacitor consists of two electrodes separated by an electrolyte (Figure 6). The cell voltage is limited to the oxidation and reduction limit of the electrolyte, about 1.2V for aqueous and 3-4V for organic electrolytes. To obtain high-voltage electrochemical capacitor devices, single cells are connected in series to achieve the desired voltage. In contrast, electrolytic capacitors can have single-cell voltages of several hundred volts, depending on the dielectric.

Pseudocapacitance is used to describe electrical storage devices that have capacitor-like characteristics but that are based on redox (reduction and oxidation) reactions. Examples of pseudocapacitance are the overlapping redox reactions observed with metal oxides (e.g., RuO2) and the p- and n-dopings of polymer electrodes that occur at different voltages (e.g. polythiophene). Devices based on these charge storage mechanisms are included in electrochemical capacitors because of their energy and power profiles.

A Ragone plot (Figure 7) compares the power and energy density of electrical energy storage devices. Electrolytic capacitors, based on an oxide dielectric, for example, are associated with high-power densities and low energy densities. Batteries, on the other hand, have high-energy density but limited power. Electrochemical capacitors have good energy and power densities.

Capacitors are used in many applications. Every type of capacitor has an optimum performance, depending on the voltage, capacitance, weight and volume, and frequency criteria. Optimization of circuit design requires knowledge of the performance attributes and limitations of each type of capacitor. Typically electrolytic capacitors are high-voltage, low-capacitance devices used as filters in circuits or for fast-time constant (<10 mS) circuits. Ultracapacitors are lower-voltage high-capacitance devices used as standby power for random access memory devices, power sources for actuators, circuit elements in telephone equipment, and for long-time constant (>10 mS) circuits. Ultracapacitors are used in electric vehicles and cellular phones. The rapid charging characteristics and high energy make ultracapacitors useful in smart-card applications.

Alan B. McEwen

## BIBLIOGRAPHY

Horowitz, P., and Hill, W. (1981). The Art of Electronics. Cambridge, Eng.: Cambridge University Press.

Conway, B. (1999). Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications. New York: Kluwer Academic/Plenum.