ECE 2006
Lecture for Chapter 3
S.Norr
S.Norr - UMD - Fall,
2006
Circuit Analysis Methods
• Nodal Analysis:
– Applicable to ANY circuit
– Uses KCL to determine voltages in cricuit
• Mesh Analysis:
– ONLY applicable to planar circuits
– Uses KVL to determine currents in circuit
S.Norr - UMD - Fall,
2006
Nodal Analysis
• Procedure:
1. Select One Node as Reference
2. Assign a Voltage Variable to each
remaining Node
3. Apply KCL at each non-reference Node
4. Solve the resulting set of simultaneous
equations
S.Norr - UMD - Fall,
2006
Grounding
• Any SINGLE node in a circuit can be
grounded without impact on the
performance of the circuit.
• Connecting one node of a circuit to ground
provides a Zero Voltage reference at that
point
• Symbols for the Ground Plane:
S.Norr - UMD - Fall,
2006
Example of Nodal Analysis
• Assign a Reference Node
S.Norr - UMD - Fall,
2006
Nodal Analysis Example
• Assign a Voltage to all Other Nodes:
S.Norr - UMD - Fall,
2006
Nodal Example (Cont.)
• Write KCL at One or More Nodes:
i1 + i2 + i3 = 0
• Re-Write the Currents using Ohm’s Law:
i1 = (Va - 5)/2 ; i2 = (Va + 3)/4 ; i3 = (Va – 0)/8
• Substitute:
(Va - 5)/2 + (Va + 3)/4 + (Va – 0)/8 = 0
S.Norr - UMD - Fall,
2006
Va = 2 Volts
Nodal Analysis Example…
• Use the Resulting Node Voltages to Solve
for Currents:
Example:
i3 = (Va – 0)/8 = (2 – 0)/8 = 1/4 Amps
S.Norr - UMD - Fall,
2006
Example of Nodal Analysis
with a Dependent Source
• Establish a Reference Node:
S.Norr - UMD - Fall,
2006
Example of Dependent (Cont.)
• Assign a voltage at all other nodes:
S.Norr - UMD - Fall,
2006
Example of Dependent (Cont.)
• Applying KCL at Node V2:
ix + i + 2i = 0
S.Norr - UMD - Fall,
2006
Example of Dependent (Cont.)
Describe Ix using Ohm’s Law:
ix = Vx/5 ; Vx = V2 – V1 = V2 – 5 Volts
ix = (V2 – 5) /5
Also, Relate i to V2:
V2 = i * 10
Result:
ix = (i * 10 – 5) /5 = 2i -1
Substitute back into KCL:
ix + i + 2i = 0
2i -1 + i + 2i = 0
i = 1/5 Amps ; V2 = 2 Volts
S.Norr - UMD - Fall,
2006
MESH Analysis
• ONLY used with PLANAR circuits
– Planar meaning the circuit can be drawn
on a two-dimensional plane without any
branches crossing over another branch
• A MESH is a Loop that contains no
other Loops within it.
S.Norr - UMD - Fall,
2006
MESH Analysis:
• Assign a current variable to each MESH in
a circuit
• Apply KVL to each Mesh, using Ohm’s law
to express each Voltage in terms of the
assigned currents
• Solve the resulting set of simultaneous
equations
S.Norr - UMD - Fall,
2006
Mesh Example:
• Assign Mesh Currents:
S.Norr - UMD - Fall,
2006
MESH Example…
• Write KVL in terms of Mesh Currents:
• Mesh 1:
-5 + 2i1 + 8(i1 –i2) = 0
S.Norr - UMD - Fall,
2006
Mesh Example….
• Mesh 2 Equation:
8(i2 – i1) + 4i2 – 3 = 0
S.Norr - UMD - Fall,
2006
Mesh Example…
• Solve the Set of Simultaneous Equations:
10i1 – 8i2 = 5
-8i1 + 12i2 = 3
14i1 + 0i2 = 21
i1 = 3/2 Amps
i2 = 5/4 Amps
S.Norr - UMD - Fall,
2006