ELECTRIC CIRCUITSECSE-2010Spring 2003

Class 12

ASSIGNMENTS DUE• Today (Monday):

• Exam I, 7-9 pm, DCC 308• Homework #4 Due• Experiment #3 Report Due• Activities 12-1, 12-2 (In Class)

• Tuesday/Wednesday:• Will do Experiment #5 in Class (EP-5)• Activity 13-1 (In Class)

• Thursday:• Experiment #4 Report Due• Will do Experiment #6 in Class (EP-6)• Activity 14-1 (In Class)

REVIEW• Operational Amplifiers:

• High Gain, Differential Voltage Amplifiers:• Real Op Amp Has:

• “High” Input Resistance (~10 Mohms)• “Low” Output Resistance (~100 ohms) • “High” Voltage Gain (105-106)

• Will Usually Model with Ideal Op Amps:• Ideal Op Amp Has:

• Infinite Input Resistance• Zero Output Resistance• Infinite Gain

REVIEW• Operational Amplifiers:

• If Add Negative Feedback => Virtual Short at Input• vp= vn; ip = in = 0• Leads to Useful Circuits

• Use Virtual Short and Circuit Analysis to find Output

• Effects of Real Op Amps => Use PSpice• Ideal Op Amp is a Very Good Model for a

Real Op Amp (Saw this in Computer Project #1)

CIRCUITS WITH R, L, & C• For Resistive Circuits: (No L or C)

• v = i R; => v(t) = i(t) R• Resistor does not affect time behavior• Resistors only absorb energy (get hot)• Resistors convert electrical energy to

thermal energy

CIRCUITS WITH R, L, & C

• R, L, C Circuits:• L = Inductor; C = Capacitor • v, i are now time dependent• v(t) and i(t) may be quite different

waveforms• L and C can store electrical energy!• Makes circuits far more interesting• Must find Time Behavior of circuit

ACTIVITY 12-1

Let's Begin with an ILM Go to: http://www.academy.rpi.edu/projects/ccli Click on Capacitors and Inductors Module It should download quickly You can access this website at any time

ACTIVITY 12-1

C C

Capacitors: Change DC voltage to .5 V Takes time to reach DC Steady State Sketch v and i vs. time for DC Input In DC Steady State, current 0! In DC Steady State, voltage Constant O

C C

bserve current and voltage with AC Input Sketch v and i vs. time for AC Input

ACTIVITY 12-1

L L

Inductors: Change DC current to .5 A Takes time to reach DC Steady State Sketch v and i vs. time for DC Input In DC Steady State, voltage 0! In DC Steady State, current Constant Ob

L L

serve current and voltage with AC Input Sketch v and i vs. time for AC Input

CAPACITANCE

cc

dvi Cdt

cv

ci

C [Farads]

CAPACITANCE

• See Symbol:• Relationship Between i and v:

• ic= C dvc/dt

• Measure C in Farads:• 1 farad = 1 amp-sec/volt

CAPACITANCE• DC Steady State:

• d /dt = 0• => iC = CdvC/dt = 0 in DC Steady State• Capacitor is an Open Circuit in DC

Steady State• If apply a DC source, Capacitor will

charge up to some voltage and stay there in the Steady State

CAPACITANCE

cc

dvi Cdt

cv

ci

C [Farads]

CSS

dIn DC Steady State; 0dt

i 0 Open Circuit

CAPACITANCE

• Capacitors in Series:• 1 / Ceq = 1 / C1 + 1 / C2 + 1 / C3 + ..• Similar to Resistors in Parallel

• Capacitors in Parallel:• Ceq = C1 + C2 + C3 + …• Similar to Resistors in Series

CAPACITANCE• Energy Stored in Capacitor:

• wc = (1/2 ) C vC2

• Energy stored in Electric Field• Voltage Across Capacitor

Cannot Change Instantaneously:• Capacitor voltage must be continuous

in time• No instantaneous jumps

INDUCTANCE

LL

div Ldt

L [Henries]Lv

Li

INDUCTANCE

• See Symbol:• Relationship Between i and v:

• vL = L diL/dt

• Measure L in Henries:• 1 henry = 1 volt-sec/amp

INDUCTANCE• DC Steady State:

• d /dt = 0• => vL= LdiL/dt = 0 in DC Steady State• Inductor is a Short Circuit in DC Steady

State• If apply a DC Source, Inductor will have

current flowing in it, but no voltage across it in the Steady State

INDUCTANCE

LL

div Ldt

L [Henries]Lv

Li

LSS

dIn DC Steady State; 0dt

v 0 Short Circuit

INDUCTANCE

• Inductors in Series:• Leq = L1 + L2 + L3 + …• Similar to Resistors in Series

• Inductors in Parallel:• 1 / Leq = 1 / L1 + 1 / L2 + 1 / L3 + ..• Similar to Resistors in Parallel

INDUCTANCE• Energy Stored in Inductor:

• wL = (1/2 ) L iL2

• Energy Stored in Magnetic Field• Current Through Inductor

Cannot Change Instantaneously:• Inductor Current must be continuous in

time• No instantaneous jumps

ACTIVITY 12-2

siC

Lv

Ci LiLi A cos t

sFind such that i 0

2 ff frequency

Angular Frequency

ACTIVITY 12-2

• v = vL = L diL/dt:

• iC = C dvC/dt = C dvL/dt

• is = iC + iL ; If is = 0; iC = - iL

L v LA sin t

2ci L C A cos t

2 1LC 1 L C

Li A cos t

ACTIVITY 12-2

c

Have current flowing in C and L with No Input Will see this circuit again later Called a Resonant Circuit

1 Resonant FrequencyLC

"Natural" frequency for this circuit Give Energy to Cir

c

cuit Circuit will Oscillate at