EEE 302
Electrical Networks II
Dr. Keith E. Holbert
Summer 2001
Lecture 2
1
Circuit Analysis Techniques
•
•
•
•
While Obeying Passive Sign Convention
Ohm’s Law; KCL; KVL
Voltage and Current Division
Series/Parallel Impedance combinations
Z series  Z1  Z 2    Z N   Z j
1
1
1
1
1




Z par Z1 Z 2
ZM
Zi
Lecture 2
2
Kirchoff’s Current Law (KCL)
i1(t)
i5(t)
i2(t)
i4(t)
i3(t)
The sum of currents entering the node is zero:
n
 i (t )  0
j 1
j
Analogy: mass flow at pipe junction
Lecture 2
3
Kirchoff’s Voltage Law (KVL)
+
+
v(t)1
v(t)2
-
+
v(t)3
-
-
• The sum of voltages around a loop is zero:
n
v
j 1
j
(t )  0
• Analogy: pressure drop thru pipe loop
Lecture 2
4
In General: Voltage Division
Consider N impedances in series:
Zi
VZ i   VS k
Z j
Source voltage(s) are divided between the
resistors in direct proportion to their
resistances
Lecture 2
5
In General: Current Division
Consider N impedances in parallel:
I Z j   I Sk
1
Z par
Z par
Zj
1
1
1
1




Z1 Z 2
ZN
Zi
Special Case (2 resistors in parallel)
I Z1
Z2
 IS
Z1  Z 2
Lecture 2
6
Class Example
• Extension Exercise E8.12
Lecture 2
7
Steps of Nodal Analysis
1. Choose a reference node.
2. Assign node voltages to the other nodes.
3. Apply KCL to each node other than the
reference node; express currents in terms of
node voltages.
4. Solve the resulting system of linear
equations.
Lecture 2
8
Class Example
• Extension Exercise E8.13
Lecture 2
9
Steps of Mesh/Loop Analysis
1. Identify mesh (loops).
2. Assign a current to each mesh.
3. Apply KVL around each loop to get an
equation in terms of the loop currents.
4. Solve the resulting system of linear
equations.
Lecture 2
10
Class Example
• Extension Exercise E8.14
Lecture 2
11
Nodal and Loop Analyses
Nodal Analysis Recipe
1&2) Identify and label
N nodal voltages plus
the ground node (V=0)
3) Apply KCL at N
nodes (supernode
makes constraint eq.)
4) Solve for the nodal
voltages
Loop Analysis Recipe
1&2) Identify and label
N mesh currents
3) Apply KVL at the N
meshes
4) Solve for the mesh
currents
Lecture 2
12