 # Lect4EEE 2021 Nodal Analysis Dr. Holbert January 28, 2008.

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Lect4EEE 2021 Nodal Analysis Dr. Holbert January 28, 2008

Lect4EEE 2022 Node and Loop Analysis Node analysis and loop analysis are both circuit analysis methods which are systematic and apply to most circuits Analysis of circuits using node or loop analysis requires solutions of systems of linear equations These equations can usually be written by inspection of the circuit

Lect4EEE 2023 Steps of Nodal Analysis 1.Choose a reference (ground) 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 for the nodal voltages.

Lect4EEE 2024 Example: A Summing Circuit The output voltage V of this circuit is proportional to the sum of the two input currents I 1 and I 2 This circuit could be useful in audio applications or in instrumentation The output of this circuit would probably be connected to an amplifier

Lect4EEE 2025 1. Reference Node The reference node is called the ground node where V = 0 + – V 500  1k  500  I1I1 I2I2

Lect4EEE 2026 Steps of Nodal Analysis 1.Choose a reference (ground) 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 for the nodal voltages.

Lect4EEE 2027 2. Node Voltages V 1, V 2, and V 3 are unknowns for which we solve using KCL 500  1k  500  I1I1 I2I2 123 V1V1 V2V2 V3V3

Lect4EEE 2028 Steps of Nodal Analysis 1.Choose a reference (ground) 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 for the nodal voltages.

Lect4EEE 2029 Currents and Node Voltages 500  V1V1 V1V1 V2V2

Lect4EEE 20210 3. KCL at Node 1 500  I1I1 V1V1 V2V2

Lect4EEE 20211 3. KCL at Node 2 500  1k  500  V2V2 V3V3 V1V1

Lect4EEE 20212 3. KCL at Node 3 500  I2I2 V2V2 V3V3

Lect4EEE 20213 Steps of Nodal Analysis 1.Choose a reference (ground) 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 for the nodal voltages.

Lect4EEE 20214 + – V 500  1k  500  I1I1 I2I2 4. Summing Circuit Solution Solution: V = 167I 1 + 167I 2

Lect4EEE 20215 A Linear Large Signal Equivalent to a Transistor 5V 100I b + – VoVo 50  IbIb 2k  1k  +–+– + – 0.7V

Lect4EEE 20216 Steps of Nodal Analysis 1.Choose a reference (ground) 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 for the nodal voltages.

Lect4EEE 20217 Linear Large Signal Equivalent 5V 100I b + – VoVo 50  IbIb 2k  1k  0.7V 1 234 V1V1 V2V2 V3V3 V4V4 +–+– + –

Lect4EEE 20218 Steps of Nodal Analysis 1.Choose a reference (ground) 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 for the nodal voltages.

Lect4EEE 20219 KCL @ Node 4 100I b + – VoVo 50  IbIb 2k  1k  +–+– 0.7V 1 234 V1V1 V2V2 V3V3 V4V4 5V + –

Lect4EEE 20220 The Dependent Source We must express I b in terms of the node voltages: Equation from Node 4 becomes

Lect4EEE 20221 How to Proceed? The 0.7-V voltage supply makes it impossible to apply KCL to nodes 2 and 3, since we don’t know what current is passing through the supply We do know that V 2 – V 3 = 0.7 V The above is a needed constraint equation

Lect4EEE 20222 100I b + – VoVo 50  IbIb 2k  1k  0.7V 1 4 V1V1 V2V2 V3V3 V4V4 +–+– + – KCL at Supernode

Lect4EEE 20223 Class Examples Drill Problems P2-8, P2-9, P2-10, P2-11