EE 1270: Introduction to Electric Circuits
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Lecture 6:
Advanced Nodal
Analysis
Chapter 4
Techniques of Circuit
Analysis: Sections 4.3,4.4
EE 1270 Introduction to Electric Circuits
Suketu Naik
Dependent Sources
____ Controlled
Voltage Source
____ Controlled
Voltage Source
____ Controlled
Current Source
EE 1270 Introduction to Electric Circuits
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____ Controlled
Current Source
Suketu Naik
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Node Voltage Method: Dependent Sources
Find unknown voltages by summing the currents leaving each node
Example 4.3
Step1: Label Nodes
Step2: Define Node
Voltages
EE 1270 Introduction to Electric Circuits
Suketu Naik
Node Voltage Method: Independent Sources
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Step3: Write
Current Leaving
Each Branch
v1  20 v1  v2 v1  0


 0 Substitute iϕ with
2
5
20
v1  v2
i 
v2  v1 v2  0 v2  8i
5


0
5
10
2
1 1 1 
 1
v1      v2     10
 2 5 20 
 5
 1 8
 1 1 13 
v1      v2      0
 5 10 
 5 10 10 
Step4: Solve
Simultaneous
Equations in
Standard Form
EE 1270 Introduction to Electric Circuits
Passive Sign
Convention
Find the
unknown
voltage or
curent
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AP4.3a: Find power associated with each source
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Simultaneous Equations:
Passive Sign
Convention
Solution
p50V=
p5A=
p3 i1=
EE 1270 Introduction to Electric Circuits
Suketu Naik
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Super Node
EE 1270 Introduction to Electric Circuits
Suketu Naik
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Supernode
Circuit with voltage
source between two
nodes
Combine nodes to form a
supernode
EE 1270 Introduction to Electric Circuits
Suketu Naik
Voltage Source Between Nodes
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Step1: Label Nodes
Step2: Define Node
Voltages
EE 1270 Introduction to Electric Circuits
Suketu Naik
Voltage Source Between Nodes
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Step3: Write
Current Leaving
Each Branch
At Node 2
Passive Sign
Convention
At Node 3
Now add them together (or isolate i and
equate them) to get Eq.1:
Eq.2?
EE 1270 Introduction to Electric Circuits
Step4: Solve
Simultaneous
Equations in
Standard Form
Suketu Naik
Alternative: Create a Supernode
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Now we can write Eq.1 directly as …
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example: Transistor Circuit*
*=if time permits
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Note: When a signal level is low, it can be passed through an amplifier to increase its level.
An amplifier can be built from BJT transistor. The following schematic represents a part of the amplifier.
See page 98-99 for equations
EE 1270 Introduction to Electric Circuits
Suketu Naik
AP4.5 (create super node): Find v
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Passive Sign
Convention
Simultaneous Equations:
Solution
v=
EE 1270 Introduction to Electric Circuits
Suketu Naik
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AP4.4: Find vo
Passive Sign
Convention
Simultaneous Equations:
Solution
vo =
EE 1270 Introduction to Electric Circuits
Suketu Naik
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AP4.6: Find v1
Passive Sign
Convention
Simultaneous Equations:
Solution
v1 =
EE 1270 Introduction to Electric Circuits
Suketu Naik