electric circuits ecse-2010 spring 2003 class 12
DESCRIPTION
ELECTRIC CIRCUITS ECSE-2010 Spring 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: - PowerPoint PPT PresentationTRANSCRIPT
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