NETWORKS 1

1
CHAPTER 4

• NETWORKS 1
• Professor Linda Head
• ROWAN UNIVERSITY, COLLEGE OF ENGINEERING
• DEPARTMENT OF ELECTRICAL COMPUTER ENGINEERING
• FALL SEMESTER, 2001

2
METHODS OF ANALYSIS RESISTIVE CIRCUITS

• We will now learn techniques for circuit analysis
  that do not require us to reduce the entire
  circuit a single element with power supply.
• These new techniques are applications of the
  principles that we already know KCL, KVL, Ohms
  Law, current divider, voltage divider, series and
  parallel element reduction.

3
NODE-VOLTAGE METHOD(Ohms Law plus KCL)
R3
R1
b
c
a
_
_





V
R4
R2

_
_
Reference or Ground
4
DEFINING THE VOLTAGES(All node voltage are taken
wrt the Reference node)
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



V
R4
va
vb
vc
R2

_
_
Reference or Ground
5
WRITE KCL AT EACH NODE
node a node c node b
3 equations/4unknowns iv, va, vb, vc
6
WRITE SUPPLEMENTARY EQUATIONS
7
NODE-VOLTAGE WITH CURRENT SOURCES
R3
R1
I
R4
R2
SET UP THE PROBLEM AS AN EXERCISE
8
NODE-VOLTAGE WITH CURRENT SOURCES
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



I
R4
va
vb
vc
R2
_
_
_
Reference or Ground
9
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
10
NODE-VOLTAGE WITH DEPENDENT SOURCES
R3
R1
2i2
R4
i2
R2
SET UP THE PROBLEM AS AN EXERCISE
11
NODE-VOLTAGE WITH DEPENDENT SOURCES
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb
R4
va
vc
2i2
_
R2
_
_
Reference or Ground
12
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
13
DEPENDENT VOLTAGE SOURCE EXAMPLE
R3
R1

2i2
R4
i2
R2
_
SET UP THE PROBLEM AS AN EXERCISE
14
DEPENDENT VOLTAGE SOURCE EXAMPLE
R3
R1
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb

R4
va
vc
2i2
_
_
R2
_
_
Reference or Ground
15
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
16
SUPPLEMENTAL EQUATIONS
R1
R3
b
c
a
_
_


(va - vb)
(vb - vc)



i2
vb

R4
va
vc
2i2
_
_
R2
_
_
Reference or Ground
17
MESH-CURRENT METHOD(Ohms Law plus KVL)
R3
R1

V
R4
R2

18
MESH-CURRENT METHOD
Current in R1 is i1 Current in R3 is i2 But what
is the current in R2?
19
MESH-CURRENT METHOD
The two currents, i1 and i2, are flowing through
R2 in opposite directions. The current in R2 is
the difference between i1 and i2. But which one
is positive and which one is negative?
20
MESH-CURRENT METHOD
It depends on which mesh you are adding voltages
in. In mesh 1 i1 is positive, in mesh 2 i2 is
positive.
21
MESH-CURRENT METHOD





Mesh 1
Mesh 2
22
MESH-CURRENT METHOD





Mesh 1
Mesh 2
23
MESH-CURRENT METHODWITH A CURRENT SOURCE
I
Mesh 1
2 eq. / 3 unk.?
No, i1 I
Mesh 2
24
MESH-CURRENT METHODWITH A DEPENDENT SOURCE
R3
R1




ia
R4
R2
2ia

2 eq. / 3 unk.?
Mesh 1
No i1 2ia
Mesh 2
ia -i2
i1 -2i2
25
MESH-CURRENT METHODWITH A DEPENDENT V-SOURCE
R3
R1




ia

R4
R2
2ia
_

2 eq. / 3 unk.?
Mesh 1
No ia -i2
Mesh 2
2ia -2i2
26
IMPORTANT CONCEPTSFROM CHAPTER 4

• Node Voltage Method is an easy combination of KCL
  and Ohms Law.
• Mesh Current Method is an easy combination of KVL
  and Ohms Law.
• Handling dependent voltage and current sources
  when adding currents and/or voltages.