NETWORKS 1: ECE 09'201'01

1
CHAPTER 4

• NETWORKS 1 ECE 09.201.01
• 26 SEPTEMBER 2006 Lecture 6
• ROWAN UNIVERSITY
• College of Engineering
• Dr Peter Mark Jansson, PP PE
• Associate Professor - DEPARTMENT OF ELECTRICAL
  COMPUTER ENGINEERING
• Autumn Semester 2006 - Quarter One

2
Admin

• HW 2 returned upfront
• LC returned pick-up
• Test 1 chapters 1-3
• returned pick-up
• HW 3 due tomorrow at 9.25 AM
• LAB HW3 and review/master test 1 problems

3
networks I

• Todays learning objectives
• define and apply new methods for analyzing
  circuits node voltage
• w/ current sources
• w/ current and voltage sources
• w/ dependent sources

4
first test NICE WORK!!!

• 3 YEARS 2YEARS LAST YR THIS YEAR
• As 3 2 7(21) 6(21)
• Bs 7 12 9(27) 10(34)
• Cs 9 8 6(18) 8(28)
• Ds 2 6 4(12) 4(14)
• Fs 6 7 7(21) 1(3)
• TOT 27 35 33 29

5
Test Review

• TEST 1 AVERAGE 81 vs. 76 2005
• Reduced Ds and Fs by 50 from
• 33 2005 to 17 2006

6
any concepts still unclear?

• from Chapters 1-3.

7
key concepts in ch 4

• node voltage analysis of circuits
• began last week
• current sources
• voltage sources
• dependent sources
• mesh current analysis of circuits w/
• current sources
• voltage sources
• dependent sources

8
What is node voltage?

• the voltage at any node in the system with
  respect to the reference node

9
NODE-VOLTAGE METHOD(Ohms Law plus KCL)
R3
R1
b
c
a
_
_





V
R4
R2

_
_
Reference or Ground
10
DEFINING THE VOLTAGES(All node voltage are taken
wrt the Reference node)
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)


iv

V
R4
va
vb
vc
R2

_
_
Reference or Ground
11
WRITE KCL AT EACH NODE
iv
node a node c node b
3 equations/4unknowns iv, va, vb, vc
12
WRITE SUPPLEMENTARY EQUATIONS
iv
13
learning exercise

• exercise 4.2-2
• p. 111 in text
• Learning check 1 KCLa KCLb
• focus on delta V that drives current flow from
  node

14
new concept supernode

• What is it? Two nodes connected by a dependent
  or independent voltage source
• Why is it helpful? You can apply KCL (nodal
  analysis) to the supernode just as though it was
  one node

15
How to recognize a supernode
16
exercise

• exercise 4.3-1, page 115
• LC 2 KCLsupernode

17
Hw preview

• lets do a supernode hw problem 4.3-3

Give Solution as LC 3
18
NODE-VOLTAGE WITH CURRENT SOURCES
R3
R1
I
R4
R2
SET UP THE PROBLEM AS AN EXERCISE
19
NODE-VOLTAGE WITH CURRENT SOURCES
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



I
R4
va
vb
vc
R2
_
_
_
Reference or Ground
20
WRITE KCL
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



I
R4
va
vb
vc
R2
_
_
_
Reference or Ground
node a node c node b
3 equations/3unknowns va, vb, vc
21
NODE-VOLTAGE WITH DEPENDENT SOURCES
R3
R1
2i2
R4
i2
R2
SET UP THE PROBLEM AS AN EXERCISE
22
NODE-VOLTAGE WITH DEPENDENT SOURCES
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb
R4
va
vc
2i2
_
R2
_
_
Reference or Ground
23
WRITE KCL
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb
R4
va
vc
2i2
_
R2
_
_
Reference or Ground
node a node c node b
3 equations/4unknowns i2, va, vb, vc i2 vb/R2
24
Lets solve this one.
25
Lets do a KCL at node a
Three (3) terms (Va-6)/10 ia (Va-Vb)/20 0
What is relationship of Va to reference node?
26
Lets do a KCL at node b
Two (2) terms 5ia (Vb-Va)/20 0
Combine what we know and solve for Vb as LC 4
27
DEPENDENT VOLTAGE SOURCE EXAMPLE
R3
R1

2i2
R4
i2
R2
_
SET UP THE PROBLEM AS AN EXERCISE
28
DEPENDENT VOLTAGE SOURCE EXAMPLE
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb

R4
va
vc
2i2
_
_
R2
_
_
Reference or Ground
29
WRITE KCL
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb

R4
va
vc
2i2
_
_
R2
_
_
Reference or Ground
node a node c node b
3 equations/4unknowns i2i2, va, vb, vc
30
SUPPLEMENTAL EQUATIONS
R1
R3
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb

R4
va
vc
2i2
_
_
R2
_
_
Reference or Ground
31
example

• problem 4.4-5

32
example

• where do we begin?

Va
Vb
What do we know? Va 12V, What does Vb ?
Vb 2ix and Va 3ix - WHY? solve for ix as
LC 5
33
hw problem 4.4-3
34
Take KCL at node b
Three (3) terms (vb 2)/4000 vb/2000 -5ia 0
One equation Two unknowns? Or do we know
something else about ia ??
35
Take KCL at node b
Three (3) terms (vb 2)/4000 vb/2000 -5ia 0
ia (2-vb)/4000 from Ohms Law
36
tomorrow

• mesh current analysis of circuits w/
• current sources
• voltage sources
• dependent sources

37
Assignment 3

• Due Wednesday, 28 September, 9.25 AM at Lecture
•  Dorf Svoboda, pp. 142-144 4.3-2, 4.3-3,
  4.3-4, 4.3-7, 4.3-12, 4.4-1, 4.4-3, 4.4-4,
  4.4-7