Nodal Analysis (3.1)

1
Nodal Analysis (3.1)

• Prof. Phillips
• February 7, 2003

2
Advantages of Nodal Analysis

• Solves directly for node voltages.
• Current sources are easy.
• Voltage sources are either very easy or somewhat
  difficult.
• Works best for circuits with few nodes.
• Works for any circuit.

3
Where We Are

• Nodal analysis is a technique that allows us to
  analyze more complicated circuits than those in
  Chapter 2.
• We have developed nodal analysis for circuits
  with independent current sources.
• We now look at circuits with dependent sources
  and with voltage sources.

4
Example Transistor Circuit
10V
Common Collector (Emitter Follower) Amplifier
1kW

Vin

2kW
Vo

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Why an Emitter Follower Amplifier?

• The output voltage is almost the same as the
  input voltage (for small signals, at least).
• To a circuit connected to the input, the EF
  amplifier looks like a 180kW resistor.
• To a circuit connected to the output, the EF
  amplifier looks like a voltage source connected
  to a 10W resistor.

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A Linear Large Signal Equivalent
0.7V
Ib


50W
2kW
1kW
5V

Vo
100Ib

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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.

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A Linear Large Signal Equivalent
0.7V
Ib
V2
V1
V3
V4

1

50W
1kW
2
3
4

5V
Vo
100Ib
2kW

9
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.

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KCL _at_ Node 4
0.7V
Ib
V2
V1
V3
V4

1

50W
1kW
2
3
4

5V
Vo
100Ib
2kW

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The Dependent Source

• We must express Ib in terms of the node voltages
• Equation from Node 4 becomes

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How to Proceed?

• The 0.7V voltage supply makes it impossible to
  apply KCL to nodes 2 and 3, since we dont know
  what current is passing through the supply.
• We do know that
• V2 - V3 0.7V

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The Supernode!
0.7V
Ib
V2
V1
V3
V4

1

50W
1kW
4

Vo
100Ib
2kW

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KCL _at_ the Supernode
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Class Examples