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)

Therestofthe

circuit

dt

tdvCti

)()(

Capacitors (cont’d)

t

dxxiC

tv )(1

)(

t

t

dxxiC

tvtv0

)(1

)()( 0

)(2

1)( 2 tCvtwC

Energy stored:

Example

i(t)

+

-

v(t)

Therestofthe

circuit

t

i(t)1A

-1A1s

2s

0.2F

Example (cont’d)

t

v(t)

5V

1s 2s

t

wc(t)

2.5J

1s 2s