Chapter 5: CAPACITANCE and INDUCTANCE Capacitors Inductors Capacitor Inductor Combinations

Review So far, we have talked about two kinds of circuit elements: Sources (independent and dependent) active, can provide power to the circuit. Resistors passive, can only dissipate power.

Energy Storage Elements Capacitors store energy in an electric field Inductors store energy in a magnetic field Capacitors and inductors are passive elements: Can store energy supplied by circuit Can return stored energy to circuit Cannot supply more energy to circuit than is stored Voltages and currents in a circuit with energy storage elements are solutions to linear, constant coefficient differential equations!

For Practical Solutions Practicing engineers almost never solve the differential equations directly. Instead, they use: LaPlace transforms (covered in EEE 302) AC steady-state analysis These techniques covert the solution of differential equations into algebraic problems-circuit analysis.

Example Applications Capacitors and inductors are used to build filters and amplifiers with desired frequency responses: RF and IF amplifiers in a superhetrodyne receiver Instrumentation amplifiers Capacitors are used in A/D converters to hold a sampled signal until it can be converted into bits Integrated circuits have layers of conductors (metal, silicon with impurities) with insulators (glass) between. This is a capacitor! This capacitance is one of the limiting factors in processor speeds This capacitance is used to create RAM’s

Capacitance Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator). Charge on the two conductors creates an electric field that stores energy. The voltage difference between the two conductors is proportional to the charge: q = C v The proportionality constant C is called capacitance. Units of Farads (F) - C/V

Capacitors i(t) + - v(t) The rest of the circuit

Capacitors (cont’d) Energy stored:

Example i(t) The rest of the circuit + 0.2F v(t) - t i(t) 1A -1A 1s 2s

Example (cont’d) t v(t) 5V 1s 2s wc(t) 2.5J 2s 1s t