University:
California State University, Northridge
Course:
ECE 240 | Electrical Engineering Fundamentals
Academic year:

2021
Views:

351

Pages:

2
Author:

esfredint7qo

Nodal Analysis Nodal Analysis (NA) - - A general, systematic procedure for applying Kirchhoff’s laws and Ohm’s law to analyze circuits Pros o Systematic o Useful for developing software to analyze circuits Cons o Not useful for circuit simplification o Does not provide intuition about circuit behavior o Not particularly useful for circuit design Reference nodes and node voltages - NA starts by identifying circuit nodes, choosing one as a reference node, and labeling the reference node with this symbol - Voltages at all other nodes are labeled with node voltage variables 𝑣1, 𝑣2, … o The node voltage is the voltage drop from the node to the reference node In lab terms, the node voltage is what you measure with the red lead of the voltmeter on the node and the black lead on the reference node - Expressing resistor currents in terms of node voltages - When doing NA, it is necessary to use Ohm’s law to express resistor currents in terms of node voltages By KVL, the voltage across the resistor is the difference between the node voltages by Ohm’s law ix = v1 – v2/R1 iy = v2 – v1/R1 NA steps (circuits w/o voltage sources) 1. 2. 3. 4. 5. 6. Select and label a reference node Label all other nodes with node voltage variables 𝑣1, 𝑣2, … Apply KCL at each non-reference node. Express all currents in terms of node voltages Simplify KCL equations to 𝑎1𝑣1 + 𝑎2𝑣2 + ⋯ = 𝑏, where 𝑎1, 𝑎2, … and 𝑏 are constants Solve the system of equations for the node voltages Use the node voltages to calculate any other desired quantities NA with voltage sources - Problem: Expressing current in terms of node voltages is problematic for voltage sources If a voltage source is connected to a node, a KCL equation cannot be written at that node without introducing additional variables (beyond the node voltage variables) - - The solution is broken into two cases o Case 1: One end of the voltage source is connected to the reference node o Case 2: The voltage source is connected between two nonreference nodes Only step 3 of the NA procedure needs modification o 3. If a nonreference node has no voltage sources attached, apply KCL. For nonreference nodes with voltage sources, there are 2 cases  Case 1: voltage source connected to reference node  vn = value of voltage source Case 2: voltage source between two nonreference nodes vm – vn = value of voltage source Enclose nodes 𝑚 and 𝑛 in a supernode, and apply KCL to the supernode -

Lecture 6 Nodal Analysis

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