Lecture 6
Nodal/Mesh Analysi
4.2,4.3, 4.5 &4.6
Definitions
Nodes
Node: a point where two or more circuit elements join
Essential Node
Essential Node: a node where three or more circuit elements join
Step 1:
Number of Nodal Voltage
Equations
• ne is essential nodes
• Number of nodal voltage Equations is
ne-1
ne = 3
ne-1 =2 nodal voltage equations are required.
Step 2: Designate a node as the
reference node.
• Suggestion: Select the node with the
most branches.
(3 branches)
(4 branches)
(3 branches)
Step 3:
Define the Node Voltage on the
Diagram
Step 4: Apply KCL
• Apply KCL to essential nodes.
R1
VS
R2
R5
R10
IS
Simulation Results
Solve ia, ib and ic
Hints
ne=2
Need ne-1=1 equation
Mesh Analysis
Definitions
Branch
Branch: a path that connects two nodes.
Essential Branch
Essential branch: a path which connects two essential nodes
without passing through an essential node.
Mesh
Mesh: a loop that does not enclose any other loops
Step 1: Determine the number of
essential nodes
ne=3
Step 2: Determine the number of
essential branches
be=5
# of equations: be-(ne-1)=5-(3-1)=3
Step 3: Apply KVL Around Loop b
+
+
-
a. Focus initially on ia.
b. Account for ib.
40-iaR2-(ia )8=0
40-iaR2-(ia-ib)8=0
Step 4: Apply KVL Around Loop b
+
+
a. Focus initially on ib.
b. Account for ia.
c. Account for ic.
+
-
-(ib )8-ib6-(ib )6=0
-(ib-ia)8-ib6-(ib )6=0
-(ib-ia)8-ib6-(ib-ic )6=0
Step 5: Apply KVL Around Loop c
+
+
a. Focus initially on ic.
b. Account for ib
-(ic )6-ic4-20=0
-(ic- ib)6-ic4-20=0
-
Solve 3 EQ and 3 Unknowns
Using Mathematica
3 Unknown equations
3 unknowns
Get Mathematica Through SSU
Step 1
# of essential branch: 6
# of essential nodes: 4
# of equations: 6-(4-1)=3
Step 2
See in the handout.
Use Mathematica to Solve
Equations
Format: Solve[{equations separated by a comma},{list of unknowns}]
To solve an equation: Evaluation→Evaluate Cells
Mesh Analysis
ne=2 essential nodes
be=3 essential branches
3-(2-1)=2 equations
Mesh Analysis
1
2
Loop 1: clockwise
Loop 2: counter-clockwise
Clockwise around loop 1:
+Vin-i1rπ-(i1+i2)RE=0
i2=gmi1rπ
Vout=-i2RC