0. ECE 1270: Introduction to Electric Circuits
Lecture 6:
Advanced Nodal
Analysis
Chapter 4
Techniques of Circuit Analysis: Sections 4.3,4.4

1. Dependent Sources and Their Applications
____ Controlled Voltage Source
____ Controlled Voltage Source
____ Controlled
Current Source
____ Controlled Current Source
Example:
Voltage Amplifier
Example:
Transimpedance Amplifier
Example: MOSFET Switch
Example:
Bipolar Junction
Transistor

2. 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

3. Node Voltage Method: Independent Sources
Step3: Write Current Leaving Each Branch
Passive Sign Convention
Substitute iϕ with
Step4: Solve Simultaneous Equations in Standard Form
Find the unknown voltage or current

4. AP4.3a: Find power associated with each source
Simultaneous Equations:
Passive Sign Convention
Solution
p50V=
p5A=
p3 i1=

5. Super Node

6. Supernode Circuit with voltage source between two nodes
Combine nodes to form a supernode

7. Fig. 4.13: Voltage Source Between Nodes
Step1: Label Nodes
Step2: Define Node Voltages

8. Fig. 4.13: Voltage Source Between Nodes
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:
Step4: Solve Simultaneous Equations in Standard Form
What about Eq. 2?

9. Alternative: Create a Supernode
- Now we can write Eq.1 directly as …
- What about Eq. 2?

10. AP4.5 (create super node): Find v
Passive Sign Convention
Simultaneous Equations:
Students do this example
Solution v=

11. Passive Sign Convention
AP4.6: Find v1
Passive Sign Convention
Simultaneous Equations:
Solution
v1=

12. Passive Sign Convention
AP4.4: Find vo
Passive Sign Convention
Simultaneous Equations:
Students do this example, Help set it up first
Solution
vo=

13. Example: Transistor Circuit* *=if time permits
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 for equations
Find Vo if Vcc=15 V, R1=100 kΩ, R2=50 kΩ, Rc=10 kΩ, RE=4.25 kΩ, β=300