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## Capacitors

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**Capacitors**Energy Storage Devices**Objective of Lecture**• Describe the construction of a capacitor and how charge is stored. • Introduce several types of capacitors • Discuss the electrical properties of a capacitor • The relationship between charge, voltage, and capacitance • Charging and discharging of a capacitor • Relationship between voltage, current, and capacitance; power; and energy • Equivalent capacitance when a set of capacitors are in series and in parallel**Capacitors**• Composed of two conductive plates separated by an insulator (or dielectric). • Commonly illustrated as two parallel metal plates separated by a distance, d. C = e A/d where e = ereo er is the relative dielectric constant eo is the vacuum permittivity**Effect of Dimensions**• Capacitance increases with • increasing surface area of the plates, • decreasing spacing between plates, and • increasing the relative dielectric constant of the insulator between the two plates.**Types of Capacitors**• Fixed Capacitors • Nonpolarized • May be connected into circuit with either terminal of capacitor connected to the high voltage side of the circuit. • Insulator: Paper, Mica, Ceramic, Polymer • Electrolytic • The negative terminal must always be at a lower voltage than the positive terminal • Plates or Electrodes: Aluminum, Tantalum**Nonpolarized**• Difficult to make nonpolarized capacitors that store a large amount of charge or operate at high voltages. • Tolerance on capacitance values is very large • +50%/-25% is not unusual PSpice Symbol http://www.marvac.com/fun/ceramic_capacitor_codes.aspx**Electrolytic**Pspice Symbols Fabrication http://www.digitivity.com/articles/2008/11/choosing-the-right-capacitor.html**Variable Capacitors**• Cross-sectional area is changed as one set of plates are rotated with respect to the other. PSpice Symbol http://www.tpub.com/neets/book2/3f.htm**MEMS Capacitor**• MEMS (Microelectromechanical system) • Can be a variable capacitor by changing the distance between electrodes. • Use in sensing applications as well as in RF electronics. http://www.silvaco.com/tech_lib_TCAD/simulationstandard/2005/aug/a3/a3.html**Electric Double Layer Capacitor**• Also known as a supercapacitor or ultracapacitor • Used in high voltage/high current applications. • Energy storage for alternate energy systems. http://en.wikipedia.org/wiki/File:Supercapacitor_diagram.svg**Electrical Properties of a Capacitor**• Acts like an open circuit at steady state when connected to a d.c. voltage or current source. • Voltage on a capacitor must be continuous • There are no abrupt changes to the voltage, but there may be discontinuities in the current. • An ideal capacitor does not dissipate energy, it takes power when storing energy and returns it when discharging.**Properties of a Real Capacitor**• A real capacitor does dissipate energy due leakage of charge through its insulator. • This is modeled by putting a resistor in parallel with an ideal capacitor.**Energy Storage**• Charge is stored on the plates of the capacitor. Equation: Q = CV Units: Farad = Coulomb/Voltage Farad is abbreviated as F**Sign Conventions**• The sign convention used with a capacitor is the same as for a power dissipating device. • When current flows into the positive side of the voltage across the capacitor, it is positive and the capacitor is dissipating power. • When the capacitor releases energy back into the circuit, the sign of the current will be negative.**Charging a Capacitor**• At first, it is easy to store charge in the capacitor. • As more charge is stored on the plates of the capacitor, it becomes increasingly difficult to place additional charge on the plates. • Coulombic repulsion from the charge already on the plates creates an opposing force to limit the addition of more charge on the plates. • Voltage across a capacitor increases rapidly as charge is moved onto the plates when the initial amount of charge on the capacitor is small. • Voltage across the capacitor increases more slowly as it becomes difficult to add extra charge to the plates.**Adding Charge to Capacitor**• The ability to add charge to a capacitor depends on: • the amount of charge already on the plates of the capacitor and • the force (voltage) driving the charge towards the plates (i.e., current)**Discharging a Capacitor**• At first, it is easy to remove charge in the capacitor. • Coulombic repulsion from charge already on the plates creates a force that pushes some of the charge out of the capacitor once the force (voltage) that placed the charge in the capacitor is removed (or decreased). • As more charge is removed from the plates of the capacitor, it becomes increasingly difficult to get rid of the small amount of charge remaining on the plates. • Coulombic repulsion decreases as charge spreads out on the plates. As the amount of charge decreases, the force needed to drive the charge off of the plates decreases. • Voltage across a capacitor decreases rapidly as charge is removed from the plates when the initial amount of charge on the capacitor is small. • Voltage across the capacitor decreases more slowly as it becomes difficult to force the remaining charge out of the capacitor.**General Equations for Ceq**Parallel Combination Series Combination • If P capacitors are in parallel, then • If S capacitors are in series, then:**Summary**• Capacitors are energy storage devices. • An ideal capacitor act like an open circuit at steady state when a DC voltage or current has been applied. • The voltage across a capacitor must be a continuous function; the current flowing through a capacitor can be discontinuous. • The equations for equivalent capacitance for capacitors in parallel capacitors in series