Capacitance And Capacitors
A system of two conducting bodies (which are frequently identified as plates) located in an electromagnetic field and having equal charges of opposite signs +Q and –Q can be called a capacitor. The capacitance C of this system is equal to the ratio of the charge Q (absolute value) to the voltage V (again, absolute value) between the bodies; that is,
Capacitance C depends on the size and shape of the bodies and their mutual location. It is proportional to the dielectric permittivity ε of the media where the bodies are located. The capacitance is measured in farads (F) if the charge is measured in coulombs (C) and the voltage in volts (V). One farad is a very big unit; practical capacitors have capacitances that are measured in micro- (μF, or 10–6F), nano- (nF, or 10–9F), and picofarads (pF, or 10–12F).
The calculation of capacitance requires knowledge of the electrostatic field between the bodies. The following two theorems  are important in these calculations. The integral of the flux density D over a closed surface is equal to the charge Q enclosed by the surface (the Gauss theorem), that is,
This result is valid for linear and nonlinear dielectrics. For a linear and isotropic media D = εE, where E is the electric field. The magnitude E of the field is measured in volt per meter, the magnitude D of the flux in coulomb per square meter, and the dielectric permittivity has the dimension of farad per meter. The dielectric permittivity is usually represented as ε = ε0Kd where ε0 is the permittivity of air (ε0 = 8.86 × 10–12 F/m) and Kd is the dielectric constant.
The electric field is defined by an electric potential φ. The directional derivative of the potential taken with the minus sign is equal to the component of the electric field in this direction. The voltage VAB between the points A and B, having the potentials φA and φB, respectively (the potential is also measured in volts), is equal to
This result is the second basic relationship. The left hand side of equation above is a line integral. At each point of the line AB there exist two vectors: E defined by the field and dl that defines the direction of the line at this point.
A wide variety of capacitors are in common usage. Capacitors are passive components in which current leads voltage by nearly 90° over a wide range of frequencies. Capacitors are rated by capacitance, voltage, materials, and construction.
A capacitor may have two voltage ratings:
- Working voltage—the normal operating voltage that should not be exceeded during operation
- Test or forming voltage—which stresses the capacitor and should occur only rarely in equipment operation
Good engineering practice dictates that components be used at only a fraction of their maximum ratings. The primary characteristics of common capacitors are given in the following table.
Some common construction practices are illustrated in the following figure.
Losses in capacitors occur because an actual capacitor has various resistances. These losses are usually measured as the dissipation factor at a frequency of 120 Hz. Leakage resistance in parallel with the capacitor defines the time constant of discharge of a capacitor. This time constant can vary between a small fraction of a second to many hours depending on capacitor construction, materials, and other electrical leakage paths, including surface contamination.
The equivalent series resistance of a capacitor is largely the resistance of the conductors of the capacitor plates and the resistance of the physical and chemical system of the capacitor. When an alternating current is applied to the capacitor, the losses in the equivalent series resistance are the major causes of heat developed in the device. The same resistance also determines the maximum attenuation of a filter or bypass capacitor and the loss in a coupling capacitor connected to a load.
The dielectric absorption of a capacitor is the residual fraction of charge remaining in a capacitor after discharge. The residual voltage appearing at the capacitor terminals after discharge is of little concern in most applications but can seriously affect the performance of analog-to-digital (A/D) converters that must perform precision measurements of voltage stored in a sampling capacitor.
The self-inductance of a capacitor determines the high-frequency impedance of the device and its ability to bypass high-frequency currents. The self-inductance is determined largely by capacitor construction and tends to be highest in common metal foil devices.
Plastic is a preferred dielectrical material for capacitors because it can be manufactured with minimal imperfections in thin films. A metal-foil capacitor is constructed by winding layers of metal, plastic, metal, and plastic into a cylinder and then making a connection to the two layers of metal. A metallized foil capacitor uses two layers, each of which has a very thin layer of metal evaporated on one surface, thereby obtaining a higher capacity per volume in exchange for a higher equivalent series resistance. Metallized foil capacitors are self-repairing in the sense that the energy stored in the capacitor is often sufficient to burn away the metal layer surrounding the void in the plastic film.
Depending on the dielectric material and construction, capacitance tolerances between 1 and 20 percent are common, as are voltage ratings from 50 to 400 V. Construction types include axial leaded capacitors with a plastic outer wrap, metal-encased units, and capacitors in a plastic box suitable for printed circuit board insertion.
Polystyrene has the lowest dielectric absorption of 0.02 percent, a temperature coefficient of –20 to –100 ppm/°C, a temperature range to 85°C, and extremely low leakage. Capacitors between 0.001 and 2 μF can be obtained with tolerances from 0.1 to 10 percent.
Polycarbonate has an upper temperature limit of 100°C, with capacitance changes of about 2 percent up to this temperature. Polypropylene has an upper temperature limit of 85°C. These capacitors are particularly well suited for applications where high inrush currents occur, such as switching power supplies. Polyester is the lowest-cost material with an upper temperature limit of 125°C. Teflon and other high-temperature materials are used in aerospace and other critical applications.
Mica capacitors are made of multiple layers of silvered mica packaged in epoxy or other plastic. Available in tolerances of 1 to 20 percent in values from 10 to 10,000 pF, mica capacitors exhibit temperature coefficients as low as 100 ppm. Voltage ratings between 100 and 600 V are common. Mica capacitors are used mostly in high-frequency filter circuits where low loss and high stability are required.
Aluminum foil electrolytic capacitors can be made nonpolar through use of two cathode foils instead of anode and cathode foils in construction.With care in manufacturing, these capacitors can be produced with tolerance as tight as 10 percent at voltage ratings of 25 to 100 V peak. Typical values range from 1 to 1000 μF.
Barium titanate and other ceramics have a high dielectric constant and a high breakdown voltage. The exact formulation determines capacitor size, temperature range, and variation of capacitance over that range (and consequently capacitor application). An alphanumeric code defines these factors, a few of which are given here.
- Ratings of Y5V capacitors range from 1000 pF to 6.8 μF at 25 to 100 V and typically vary +22 to –82 percent in capacitance from –30 to + 85°C.
- Ratings of Z5U capacitors range to 1.5 μF and vary +22 to –56 percent in capacitance from +10 to +85°C. These capacitors are quite small in size and are used typically as bypass capacitors.
- X7R capacitors range from 470 pF to 1 μF and vary 15 percent in capacitance from –55 to + 125°C.
Nonpolarized (NPO) rated capacitors range from 10 to 47,000 pF with a temperature coefficient of 0 to +30 ppm over a temperature range of –55 to +125°C.
Ceramic capacitors come in various shapes, the most common being the radial-lead disk. Multilayer monolithic construction results in small size, which exists both in radial-lead styles and as chip capacitors for direct surface mounting on a printed circuit board.
Polarized capacitors have a negative terminal—the cathode—and a positive terminal—the anode—and a liquid or gel between the two layers of conductors. The actual dielectric is a thin oxide film on the cathode, which has been chemically roughened for maximum surface area. The oxide is formed with a forming voltage, higher than the normal operating voltage, applied to the capacitor during manufacture. The direct current flowing through the capacitor forms the oxide and also heats the capacitor.
Whenever an electrolytic capacitor is not used for a long period of time, some of the oxide film is degraded. It is reformedwhen voltage is applied again with a leakage current that decreases with time. Applying an excessive voltage to the capacitor causes a severe increase in leakage current,which can cause the electrolyte to boil. The resulting steam may escape by way of the rubber seal or may otherwise damage the capacitor. Application of a reverse voltage in excess of about 1.5Vwill cause forming to begin on the unetched anode electrode. This can happenwhen pulse voltages superimposed on a dc voltage cause a momentary voltage reversal.
Aluminum Electrolytic Capacitors
Aluminum electrolytic capacitors use very pure aluminum foil as electrodes, which are wound into a cylinder with an interlayer paper or other porous material that contains the electrolyte. Aluminum ribbon staked to the foil at the minimum inductance location is brought through the insulator to the anode terminal, while the cathode foil is similarly connected to the aluminum case and cathode terminal.
Electrolytic capacitors typically have voltage ratings from 6.3 to 450Vand rated capacitances from 0.47 μF to several hundreds of microfarads at the maximum voltage to several farads at 6.3 V. Capacitance tolerance may range from ±20 to +80/–20 percent. The operating temperature range is often rated from –25 to +85°C or wider. Leakage current of an electrolytic capacitor may be rated as low as 0.002 times the capacity times the voltage rating to more than 10 times as much.
Tantalum Electrolytic Capacitors
Tantalum electrolytic capacitors are the capacitors of choice for applications requiring small size, 0.33- to 100-μF range at 10 to 20 percent tolerance, low equivalent series resistance, and low leakage current. These devices are well suited where the less costly aluminum electrolytic capacitors have performance issues. Tantalum capacitors are packaged in hermetically sealed metal tubes or with axial leads in epoxy plastic, as illustrated in the following figgure.
Capacitor Failure Modes
Mechanical failures relate to poor bonding of the leads to the outside world, contamination during manufacture, and shock-induced short-circuiting of the aluminum foil plates. Typical failure modes include short-circuits caused by foil impurities, manufacturing defects (such as burrs on the foil edges or tab connections), breaks or tears in the foil, and breaks or tears in the separator paper.
Short-circuits are the most frequent failure mode during the useful life period of an electrolytic capacitor. Such failures are the result of random breakdown of the dielectric oxide film under normal stress. Proper capacitor design and processing will minimize such failures. Short-circuits also can be caused by excessive stress,where voltage, temperature, or ripple conditions exceed specified maximum levels.
Open circuits, although infrequent during normal life, can be caused by failure of the internal connections joining the capacitor terminals to the aluminum foil. Mechanical connections can develop an oxide film at the contact interface, increasing contact resistance and eventually producing an open circuit. Defective weld connections also can cause open circuits. Excessive mechanical stress will accelerate weld-related failures.
Like semiconductor components, capacitors are subject to failures induced by thermal cycling. Experience has shown that thermal stress is a major contributor to failure in aluminum electrolytic capacitors. Dimensional changes between plastic and metal materials can result in microscopic ruptures at termination joints, possible electrode oxidation, and unstable device termination (changing series resistance). The highest-quality capacitor will fail if its voltage and/or current ratings are exceeded. Appreciable heat rise (20°C during a 2-hour period of applied sinusoidal voltage) is considered abnormal and may be a sign of incorrect application of the component or impending failure of the device.
The figure above is illustrates the effects of high ambient temperature on capacitor life. Note that operation at 33 percent duty cycle is rated at 10 years when the ambient temperature is 35°C, but the life expectancy drops to just 4 years when the same device is operated at 55°C. A common rule of thumb is this: In the range of +75°C through the full-rated temperature, stress and failure rates double for each 10°C increase in operating temperature. Conversely, the failure rate is reduced by half for every 10°C decrease in operating temperature.
Failure of the electrolyte can be the result of application of a reverse bias to the component, or of a drying of the electrolyte itself. Electrolyte vapor transmission through the end seals occurs on a continuous basis throughout the useful life of the capacitor. This loss has no appreciable effect on reliability during the useful life period of the product cycle. When the electrolyte loss approaches 40 percent of the initial electrolyte content of the capacitor, however, the electrical parameters deteriorate and the capacitor is considered to be worn out.
As a capacitor dries out, three failure modes may be experienced: leakage, a downward change in value, or dielectric absorption. Any one of these can cause a system to operate out of tolerance or fail altogether.
The most severe failure mode for an electrolytic is increased leakage, illustrated in the figure above. Leakage can cause loading of the power supply, or upset the dc bias of an amplifier. Loading of a supply line often causes additional current to flow through the capacitor, possibly resulting in dangerous overheating and catastrophic failure.
A change of device operating value has a less devastating effect on system performance. An aluminum electrolytic capacitor has a typical tolerance range of about ±20 percent. A capacitor suffering from drying of the electrolyte can experience a drastic drop in value (to just 50 percent of its rated value, or less). The reason for this phenomenon is that after the electrolyte has dried to an appreciable extent, the charge on the negative foil plate has no way of coming in contact with the aluminum oxide dielectric.
Failure mechanism of an electrolytic capacitor exhibiting a loss of capacitance. After the electrolyte dries, the plates can no longer come in contact with the aluminum oxide. The result is a decrease in capacitor value.
This failure mode is illustrated in the figure above. Remember, it is the aluminum oxide layer on the positive plate that gives the electrolytic capacitor its large rating. The dried-out paper spacer, in effect, becomes a second dielectric,which significantly reduces the capacitance of the device.
Capacitor Life Span
The life expectancy of a capacitor—operating in an ideal circuit and environment—will vary greatly, depending upon the grade of device selected. Typical operating life,according to capacitor manufacturer data sheets, range from a low of 3 to 5 years for inexpensive electrolytic devices, to a high of greater than 10 years for computer-grade products. Catastrophic failures aside, expected life is a function of the rate of electrolyte loss by means of vapor transmission through the end seals, and the operating or storage temperature. Properly matching the capacitor to the application is a key component in extending the life of an electrolytic capacitor. The primary operating parameters include:
Rated voltage—the sum of the dc voltage and peak ac voltage that can be applied continuously to the capacitor. Derating of the applied voltage will decrease the failure rate of the device.
Ripple current—the rms value of the maximum allowable ac current, specified by product type at 120 Hz and +85°C (unless otherwise noted). The ripple current may be increased when the component is operated at higher frequencies or lower ambient temperatures.
Reverse voltage—the maximum voltage that can be applied to an electrolytic without damage. Electrolytic capacitor are polarized, and must be used accordingly.