Lecture 101 Introduction to Energy Storage Elements: The Capacitor

Lecture 102 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.

Lecture 103 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.

Lecture 104 Energy Storage is Fun! Voltages and currents in a circuit without energy storage elements are linear combinations of source voltages and currents. Voltages and currents in a circuit with energy storage elements are solutions to linear, constant coefficient differential equations!

Lecture 105 Even More Fun! Practicing engineers almost never solve the differential equations directly. They also almost never use the techniques in Chapter 6. Instead, they use: –LaPlace transforms (covered in EEE 302) –AC steady-state analysis These techniques convert the solution of differential equations into algebraic problems- circuit analysis (eg the voltage divider) can be applied directly.

Lecture 106 Power Generation and Distribution Energy storage elements model electrical loads: –Capacitors model computers and other electronics (power supplies). –Inductors model motors.

Lecture 107 Signal Processing Communication Instrumentation Capacitors and inductors are used to build filters and amplifiers with desired frequency responses: –RF and IF amplifiers in a superhetrodyne receiver. –Instrumentation amplifiers.

Lecture 108 Signal Processing Communication Instrumentation Capacitors are used in A/D converters (PCM encoders) to hold a sampled signal until it can be converted into bits.

Lecture 109 Solid State Digital Design 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.

Lecture 1010 Electromagnetics For high frequency signals, inductance and capacitance are more significant effects than resistance.

Lecture 1011 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

Lecture 1012 Capacitance The proportionality constant C is called capacitance. Units of Farads (F) - C/V

Lecture 1013 Capacitor i(t) + - v(t) The rest of the circuit

Lecture 1014 Capacitor Voltage

Lecture 1015 Energy Stored

Lecture 1016 Example i(t) + - v(t) The rest of the circuit t i(t) 1A -1A 1s 2s 0.2F

Lecture 1017 Find v(t) Find w c (t)

Lecture 1018 Solution t v(t) 5V 1s 2s t w c (t) 2.5J 1s 2s