Circuit Analysis Techniques
Key Concepts
Node voltage analysis and equations
Super node
Mesh current analysis and equations
Super mesh
Source transformation
Linearity
Nonlinear loads
Superposition
Thevenin and Norton models
Maximum Signal Transfer
Interface Design
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Circuit Analysis Techniques
Key Words
Node-voltage
KVL constraint
KCL constraint
Reference node
Supernode
Supermesh
Nonreference nodes
Mesh currents
Planar circuit
Source transformation
Linear circuits.
Homogeneity
Additivity
Proportionality
Superposition
Unit output method
Lookback resistance
Maximum signal transfer
Maximum power transfer
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Circuit Analysis Techniques
Reading
The Analysis & Design of Linear Circuits
Sections 3-1 to 3-6 Pages 73-153.
Roland E. Thomas, Albert J. Rosa Gregory J. Toussaint,
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Circuit Analysis Techniques
Node Voltage Analysis and Equations
Node Voltage Analysis – Getting Started
• What is a node?
• What does node-voltage analysis find?
• Using KCL what do we know about node currents?
• What is the current that flows through the resistor?
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Circuit Analysis Techniques
Node Voltage Analysis and Equations
Node Voltage Analysis – Doing the Analysis
1. Find ground
2. Assume currents leaving a node are positive and those entering are
negative
3. Let’s analyze the circuit…
V V
A
S
V V
V V
V 0
B
S  B
C 0
 B
R
R
R
1
2
3
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Circuit Analysis Techniques
Super Node
Working with Super Nodes
The circuit has a voltage source between two non-ground nodes
1. Draw a node around the non-grounded source
2. Treat the exiting currents as if they were exiting from one node
VA  0 VA  VS1 VC  VS1


 IS  0
R2
R1
R3
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Circuit Analysis Techniques
Mesh Current Analysis and Equations
Mesh Current Analysis – Getting Started
• How many loops?
• How many meshes?
• How many KVL equations?
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Circuit Analysis Techniques
Mesh Current Analysis and Equations
Mesh Current Analysis – Multiple Currents in one Branch
There are two types of voltage drops in a branch element
• The drop with one mesh current flowing through that element
• The drop with two branch currents flowing in opposite directions
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Circuit Analysis Techniques
Super Mesh
Mesh Current Analysis – Working with Super Meshes
• The super mesh is the dual of the super node
R2I A  R1 ( I A  IC )  R3 ( IB  IC )  R4IB  0
VS  R3 ( IC  IB )  R1 ( IC  I A )  0
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Circuit Analysis Techniques
Linearity
Linear Circuit Analysis – Proportionality
•
•
•
•
The relationship between input and output – Gain
We call the gain K
Gain may be positive or negative
What is the gain – K – in this circuit?
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Circuit Analysis Techniques
Linearity
Linear Circuit Analysis – Superposition
• For a linear circuit with multiple sources….
• We can compute the desired output by
-Turning off all sources but one
- Computing the output from the one remaining source
- Repeating for each source
- Summing the results
• What are the outputs Vx and Vy
Current Source  0 : VXV 
100 10
5V
100  100
1
 0.1
Voltage Source  0 : VXI  100 100
 5 V
1
1

100 100
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Circuit Analysis Techniques
Linearity
Linear Circuit Analysis – Unit Output Modeling
Unit Output Modeling – An application of proportionality
1. Objective is to find the gain – K of a circuit
2. Once K is known – we can find the output for any input
3. Start with easy numbers
- Let i0 = 1A
- Work backwards…
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Circuit Analysis Techniques
Thévenin and Norton Equivalent Models
Thévenin and Norton Equivalent Circuits
1. The key initial concept…Any linear circuit can be represented by
- A Thévenin source VT in series with a Thévenin resistor RT
2. The key to the solution…
- Find VT and RT
Problem…
What value of RL will give us Vout of 2V?
Solution…
Find the Thévenin equivalent circuit then RL
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Circuit Analysis Techniques
Interface Design
Interface Circuit Design
Things to think about when designing an interface to a load…
1. What i, V, or p is available without the interface?
- This is the maximum i, V, or p available from the source
2. Does the load require less than the maximum?
Design an interface that will enable 3 V across the load
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Circuit Analysis Techniques
SUMMARY:
This unit introduced basic functional circuit analysis, developed the
Thevenin and Norton circuit models, then extended these concepts and
techniques to interface circuit design.
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Circuit Analysis Techniques
REMINDERS:
Assignments from Unit 1 are due at start of next unit.
Prepare for the next unit by reading:
Thomas, Rosa, and Toussaint, Sections 4-1 to 4-6 and 5-1 to 5-6, prior to
coming to class.
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