Superposition
Principle of Superposition
When a linear circuit is excited by more than one
independent source of energy, the total response is
the sum of the responses to each source acting
individually.
To find the response due to each independent
sou
Thevenin and Norton Equivalent
Circuits
Voltage Source Model
Current Source Model
ECE 201 Circuit Theory I
1
Why do we need them?
Circuit simplification
Reduce the complicated circuit on the left to a
voltage source in series with a resistor.
ECE 201 Cir
Maximum Power Transfer
Maximize the power delivered to a
resistive load
ECE 201 Circuit Theory I
1
Consider the General Case
A resistive network contains independent
and dependent sources.
A load is connected to a pair of terminals
labeled a b.
What va
PROBLEM #7.55
Assume that the switch in the circuit shown has been in position a for a long time
and that at t = 0 it is moved to position b.
Find
a) vC(0+)
vC (0+ =vC (0 ) =50V
)
b) vC()
20
( 30)
20 +5
vC ( ) = 24V
vC ( ) =
c) for t > 0
t =Req C =( 2
PROBLEM # 7.35
The switch in the circuit shown has been closed for a long time before opening at
t = 0.
a) find the numerical expressions for iL(t) and vO(t) for t>=0.
For t<0, the switch is closed, and the 4 mH inductor appears as a short circuit.
The 5
PROBLEM # 7.81
The voltage waveform is applied to the circuit shown. The initial voltage on the
capacitor is zero.
a) Calculate vo(t).
vs (t ) =0, 0 t
vs (t ) =50V , 0 t 1ms
vs (t ) =0,1ms t
For 0 < t < 1ms
vC (0) =0V
vC ( ) =50V
for t > 1ms
t =RC =(400 1
PROBLEM # 7.34
a) Use component values fromAppendix H to create a firstorder RL circuit (see
Fig. 7.16) with a time constant of 8 s. Use a single inductor and a network of
resistors, if necessary. Draw your circuit.
L
R
L
R=
t
L =1mH
t=
1 10 3
R=
=125W
PROBLEM # 6.40
a) Show that the coupled coils shown below can be replaced by a single coil having an
inductance of Lab = L1 + L2 + 2M.
b) Show that if the connections to the terminals of the coil labeled L2 are reversed,
Lab = L1 + L2 2M.
vab
a)
+

iab
v
PROBLEM # 6.42
The polarity markings on two coils are to be determined experimentally. The
experimental setup is shown below. Assume that the terminal connected to the negative
terminal of the battery has been given a ploarity mark as shown. When the swit
PROBLEM # 6.32
Determine the equivalent circuit for a series connetion of ideal capacitors. Assume that
each capacitor has its own initial voltage.
The current in each capacitor is the same since they are in series and their individual
voltages add togeth
PROBLEM # 6.27
Find the equivalent capacitance with respect to the terminals ab for the circuit
shown.
1
1 1 5
= + =
Ceq1 4 6 12
Ceq1 =2.4 m F .12V
Ceq2 =1.6 m F +2.4 m F =4 m F .12V
1
1 1 16 1
= + = =
Ceq3 4 12 48 3
Ceq3 =3m F .7V
Ceq4 =5m F +3m F =8m F
PROBLEM # 6.3
The voltage at the terminals of the 200H inductor is shown below in (b). The inductor
current is known to be zero for t<=0.
a) Determine the expressions for i for t>=0.
vs (t ) =0, t 0
vs (t ) =5mV , 0 t 2ms
vs (t ) =0, t 2ms
t
1
i (t ) = v(
PROBLEM # 6.28
Use realistic capacitor values from Appendix H to construct series and parallel
combinations of capacitors to yield the equivalent capacitances specified below.
Try to minimize the number of capacitors used. Assume that no initial energy is
Problem # 4.91
a) Use the principle of superposition to find the voltage v in the circuit shown.
b) Find the power dissipated in the 10 resistor.
Consider the voltage source acting alone.
Req (10 (2 12)
(10)(14)
5.833
10 14
v
v'
5.833
5.833
(110V ) 59.2
Problem # 4.93
Use the principle of superposition to find the voltage v 0 in the circuit shown.
The 240 V source acting alone.
'
0
v
(20 5)
(20 5) 12
(240V ) 60V
The 84 V source acting alone
"
0
v
(20 12)
(20 12) 5
( 84V ) 50.4V
The 16 A source acting a
ECE 201
Exam #2
Review
Topics
Thevenins/Nortons Theorem
Maximum Power Transfer
Superposition
OP AMPs
Inverting Amplifier
Non Inverting Amplifier
Relaxation Oscillator
Comparator
Difference Amplifier
Inductance
Henry (H)
mH, H
Magnetic Field
Lines of Flux
Problem # 4.6
Use the nodevoltage method to determine the voltages v 1 and v2 in the circuit
shown below.
The voltages have been identified for you show the ground connection
(voltage=0) and the currents out of the nodes.
The direction of the 3A current
Alternator Problem
1.)
Identify the branch currents and node A.
2.)
Write equations for the branch currents and solve.
A
VA
+
I3
I2
I1
+

16 VA
I1
0.2
12.8 VA
I2
0.1
16 VA 12.8 VA
VA
0.2
0.1
16 VA 25.6 2VA 0.2VA
41.6 3.2VA
VA 13Volts
I3
VA
1
3.)
Calcu
UNIVERSITY OF MASSACHUSETTS DARTMOUTH
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 201
CIRCUIT THEORY I
ALTERNATOR PROBLEM
An automobile alternator with an internal resistance of 0.2 develops an open
circuit voltage of 16.0 Volts. The storage bat
CPRE 381 Lab 4
Sequential Logic Register File
The register file is an elusive creature. Rumor has it nobody has ever seen one in their natural
habitat. This is true for the most part. Because the overwhelming majority of the time people deal
with them, is
CPRE 381 Lab 6
The Arithmetic Logic Unit
This, is a 16bit ALU, implemented on MINECRAFT with RippleCarry
Adders. Amazing
Please watch this video of it before Lab6:
http:/www.youtube.com/watch?v=LGkkyKZVzug
In this lab you will construct a design for an
CPRE 381 Lab 3
Module Reuse Multipurpose Shifter
We put this image here because it demonstrates the operation of a shifter, and, it is an
excellent example of module reuse. Do not try this at home.
In computer engineering, reusability is the likelihood th
Math 267 R: Solutions to even # problems
1.1: Background
2. This equation involves only ordinary derivatives of x with respect to t, and the highest
derivative has the second order. Thus it is an ordinary differential equation of the second
order with ind
Cpr E 381 Lab 10
Pipelined Datapath Implementation
This is the last laboratory of CPRE381. We
are glad to see you all here
and we would like to
congratulate you on your
achievement.
This lab is a culmination of
your
semester
efforts
where you master the I
CPRE 381 Lab 5
Digital Arithmetic Adder/Subtracter Design
Compared to the present day technologies the typical Iowa State University student
hauls around in that backpack, the humble pocket calculator might strike you as
underwhelming. Sure, they make you