# EECS 40

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```					                            Notes

1. Be sure to take your completed Pre-Lab sheet to each lab!
2. Here are some useful books in the Engineering Library:
On 2-hr reserve for EE40:
“The Art of Electronics” by Horowitz and Hill
“Electrical Engineering Uncovered” by White and
Doering
In the Reference section with Dictionaries:
“Newton’s Telecom Dictionary” TK5102 N486 2002
3. Course grading weightings: Labs 30%, Midterm 1 15%,
Midterm 2 15%, Final 35%, Homework 5%

EECS40, Fall 2004          Lecture 5, Slide 1             Prof. White
Lecture #5
OUTLINE
• Node Analysis, examples
• Node Analysis with dependent
sources
• Mesh Analysis
Chapter 2

EECS40, Fall 2004      Lecture 5, Slide 2   Prof. White
Node-Voltage Circuit Analysis Method
1. Choose a reference node (“ground”)
Look for the one with the most connections!

2. Define unknown node voltages
those which are not fixed by voltage sources

3. Write KCL at each unknown node, expressing
current in terms of the node voltages (using the
I-V relationships of branch elements)
Special cases: floating voltage sources

4. Solve the set of independent equations
N equations for N unknown node voltages

EECS40, Fall 2004          Lecture 5, Slide 3            Prof. White
Nodal Analysis: Example #1
R1             R
3

+
-   V1               R             R    IS
2             4

1. Choose a reference node.
2. Define the node voltages (except reference node and
the one set by the voltage source).

3. Apply KCL at the nodes with unknown voltage.

4. Solve for unknown node voltages.
EECS40, Fall 2004                 Lecture 5, Slide 4             Prof. White
Nodal Analysis: Example #2
R1
Va    R5

R3       I1
V        R2                         R4        V2
1

EECS40, Fall 2004              Lecture 5, Slide 5             Prof. White
Nodal Analysis w/ “Floating Voltage Source”
A “floating” voltage source is one for which neither side is
connected to the reference node, e.g. VLL in the circuit below:
Va         VLL       Vb
- +

I1         R2                  R4      I2

Problem: We cannot write KCL at nodes a or b because
there is no way to express the current through the voltage
source in terms of Va-Vb.
Solution: Define a “supernode” – that chunk of the circuit
containing nodes a and b. Express KCL for this supernode.
Incorporate voltage source constraint into KCL equation.
EECS40, Fall 2004        Lecture 5, Slide 6             Prof. White
Nodal Analysis: Example #3
supernode

Va         VLL        Vb
-   +

I1         R2                   R4    I2

Eq’n 1: KCL at supernode

Substitute property of voltage source:

EECS40, Fall 2004         Lecture 5, Slide 7             Prof. White
EECS40, Fall 2004   Lecture 5, Slide 8   Prof. White
Node-Voltage Method and Dependent Sources
• If a circuit contains dependent sources, what to do?

Example:
iD

20 W
10 W
200 W
+
2.4 A                                         –   80 V
–
+ 5iD

EECS40, Fall 2004       Lecture 5, Slide 9                   Prof. White
Node-Voltage Method and Dependent Sources
• Dependent current source: treat as independent current
source in organizing and writing node eqns, but include
(substitute) constraining dependency in terms of defined
node voltages.
• Dependent voltage source: treat as independent voltage
source in organizing and writing node eqns, but include
(substitute) constraining dependency in terms of defined
node voltages.

EECS40, Fall 2004      Lecture 5, Slide 10          Prof. White
Example:
iD

20 W
10 W     +
2.4 A          200 W                       –   80 V
–
+ 5iD

EECS40, Fall 2004   Lecture 5, Slide 11                   Prof. White
EECS40, Fall 2004   Lecture 5, Slide 12   Prof. White
Formal Circuit Analysis Methods
MESH ANALYSIS
NODAL ANALYSIS
(“Mesh-Current Method”)
(“Node-Voltage Method”)
1) Select M independent mesh
0) Choose a reference node                  currents such that at least one
1) Define unknown node voltages             mesh current passes through each
branch*
2) Apply KCL to each unknown
M = #branches - #nodes + 1
node, expressing current in
terms of the node voltages               2) Apply KVL to each mesh,
=> N equations for                        expressing voltages in terms of
N unknown node voltages                mesh currents
=> M equations for
3) Solve for node voltages
M unknown mesh currents
=> determine branch currents
3) Solve for mesh currents
=> determine node voltages
*Simple method for planar circuits
A mesh current is not necessarily identified with a branch current.
EECS40, Fall 2004             Lecture 5, Slide 13                      Prof. White
Mesh Analysis: Example #1

1. Select M mesh currents.
2. Apply KVL to each mesh.

3. Solve for mesh currents.

EECS40, Fall 2004      Lecture 5, Slide 14   Prof. White
EECS40, Fall 2004   Lecture 5, Slide 15   Prof. White
Mesh Analysis with a Current Source

ia                         ib

Problem: We cannot write KVL for meshes a and b
because there is no way to express the voltage drop
across the current source in terms of the mesh currents.
Solution: Define a “supermesh” – a mesh which avoids the
branch containing the current source. Apply KVL for this
supermesh.
EECS40, Fall 2004        Lecture 5, Slide 16        Prof. White
Mesh Analysis: Example #2

ia                         ib

Eq’n 1: KVL for supermesh

Eq’n 2: Constraint due to current source:

EECS40, Fall 2004        Lecture 5, Slide 17        Prof. White
EECS40, Fall 2004   Lecture 5, Slide 18   Prof. White
Mesh Analysis with Dependent Sources
• Exactly analogous to Node Analysis
• Dependent Voltage Source: (1) Formulate
and write KVL mesh eqns. (2) Include and
express dependency constraint in terms of
mesh currents
• Dependent Current Source: (1) Use
supermesh. (2) Include and express
dependency constraint in terms of mesh
currents

EECS40, Fall 2004   Lecture 5, Slide 19   Prof. White

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