lesson 10: nodal analysis i
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Lesson 10: Nodal Analysis I. Learning Objectives. Apply Ohm’s Law using nodal voltages. Apply the Nodal Analysis method to determine an unknown node voltage and branch currents in a simple DC circuit. - PowerPoint PPT PresentationTRANSCRIPT
Learning Objectives
Apply Ohm’s Law using nodal voltages.
Apply the Nodal Analysis method to
determine an unknown node voltage and branch currents in a simple DC circuit
Nodal analysisBased on a systematic application of KCL, nodal analysis allows us to obtain a set of simultaneous equations to solve for voltages and current in any linear circuit.
Nodal analysis steps In nodal analysis we are interested in finding
node voltages.
Given a circuit with n nodes,
1. Select a reference node. Assign voltages va, vb, vc …. to the remaining nodes.
2. Apply KCL to each node expressing branch currents in terms of node voltages.
3. Solve the resulting simultaneous equations to obtain unknown node voltages.
1. Identify the nodes
What are the voltages of the three nodes a,b,c below?
6
12
a
b
c
V V
V unknown
V V
2. Write equations for branch currents
In nodal analysis, we usually write the branch currents directly in terms of node voltages and branch resistances.
Care must be taken in keeping the polarity correct!
You can make the problem simpler by always arbitrarily assuming current leaves each node
This simplifies writing the resulting equations and prevents polarity errors.
1
2
3
6
4 40
3 312
8 8
b a b a
b b
b c b
V V Vi
V Vi
V V Vi
2. Write equations for branch currents
3. Substitute into KCL and solve for the unknowns
1 2 3 0
6 120
4 3 8b bb
i i i
V VV
current out = current in
You can solve this with some simple algebra…
6 120
4 3 81 1 1 6 12
4 3 8 4 8
0.7083 3
4.235
b bb
b
b
b
V VV
V
V
V V
1
2
3
6
4 40
2 2
8 8
8 8 8
b a b a
b b
bb c b
V V Vi
V Vi
VV V Vi
Making it tougher… The polarity of the voltage supplies changes how you
write the equations Notice the inverted supply on the right and how you write
the equation
You can solve this with some simple algebra…
6 80
4 2 81 1 1 6 8
4 2 8 4 8
0.875 0.5
0.571 571
b bb
b
b
b
V VV
V
V
V V mV