nodal analysis for kcl and kvl
DESCRIPTION
Nodal analysis using KCL and KVL for a simple circuitTRANSCRIPT
NODAL AND LOOP ANALYSIS TECHNIQUES
LEARNING GOALS
Develop systematic techniques to determine all the voltagesand currents in a circuit
NODAL ANALYSISLOOP ANALYSIS
NODE ANALYSIS
• One of the systematic ways to determine every voltage and current in a circuit
The variables used to describe the circuit will be “Node Voltages” -- The voltages of each node with respect to a pre-selected reference node
1 1 21@ : 4 0
6 12
V V VV mA
k k
USING KCL
2 2 12@ : 2 0
6 12
V V VV mA
k k
BY “INSPECTION”
1 2
1 1 14
6 12 12V V mA
k k k
1 2
1 1 12
12 6 12V V mAk k k
LEARNING EXAMPLE
VV
VV
4
6
4
1
SOURCES CONNECTED TO THE
REFERENCE
SUPERNODE
CONSTRAINT EQUATION VVV 1223
KCL @ SUPERNODE
02
)4(
212
63322
k
V
k
V
k
V
k
Vk2/*
VVV 22332VVV 12
32 add and 3/*
VV 385 3
mAk
VIO
8.323 LAW SOHM'
OIV FOR NEEDED NOT IS
2
LEARNING EXAMPLE
CIRCUITS WITH DEPENDENT SOURCESPRESENT NO SIGNIFICANT ADDITIONAL COMPLEXITY. THE DEPENDENT SOURCESARE TREATED AS REGULAR SOURCES
WE MUST ADD ONE EQUATION FOR EACHCONTROLLING VARIABLE
VOLTAGE SOURCE CONNECTED TO REFERENCE
VV 31
0263
: 212
xI
k
V
k
VV VKCL@ 2
CONTROLLING VARIABLE IN TERMS OF NODE VOLTAGES k
VIx 6
2
REPLACE
062
632212
k
V
k
V
k
VVk6/*
VVVV 602212
mAk
VVIO
13
21
OI FIND
LEARNING EXAMPLE
SUPER NODE WITH DEPENDENT SOURCE
VOLTAGE SOURCE CONNECTED TO REFERENCE
VV 63
SUPERNODE CONSTRAINT xVVV 2
21
KCL AT SUPERNODE
k12/*
062)6(22211
VVVV
CONTROLLING VARIABLE IN TERMS OF NODES
2VV
x
213VV
183321 VV 184
1 V
LEARNING EXAMPLE FIND THE VOLTAGE Vo
AT SUPER NODE
1 22
XV V V
2 3 1 32 14
2 01 1 1 1
V V V VV V VmA
k k k k
3 2 3 1
3@ : 2 0
1 1
V V V VV mA
k k
4 4@ : 4V V V
CONTROLLING VARIABLE2X
V V
1k
1k
SOLVE EQUATIONS NOW
1
1 3
1 3
3
2 2 2 6
2 2
X
X
X
V V
V V V V
V V V V
VARIABLE OF INTEREST 1 3OV V V
LEARNING EXAMPLE Find the current Io
FIND NODES – AND SUPER NODES
2 2@ : 12V V V
3 3@ : 2
XV V V
4 1
1 3 4 3 4 51 2 4
@super node:
6 (constraint eq.)
21 1 1 1 10
X
V V V
V V V V V VV V VI
k k k k k
5 4 5
5@ : 2 0
1 1X
V V VV I
k k
1 2
4
CONTROLLING VARIABLES
1
X
X
V V V
VI
k
7 eqs in 7 variables
VARIABLE OF INTEREST 5
1O
VI
k