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Notes

This lecture outlines the node analysis and mesh analysis methods used in circuit analysis. It covers examples, including the use of dependent sources, and provides step-by-step explanations. Don't forget to bring your completed pre-lab sheet to each lab!

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  1. Notes • Be sure to take your completed Pre-Lab sheet to each lab! • Here are some useful books in the Engineering Library: • On 2-hr reserve for EE40: • “The Art of Electronics” by Horowitz and Hill • “Electrical Engineering Uncovered” by White and • Doering • In the Reference section with Dictionaries: • “Newton’s Telecom Dictionary” TK5102 N486 2002 • Course grading weightings: Labs 30%, Midterm 1 15%, • Midterm 2 15%, Final 35%, Homework 5%

  2. Lecture #5 OUTLINE • Node Analysis, examples • Node Analysis with dependent sources • Mesh Analysis Reading Chapter 2

  3. Node-Voltage Circuit Analysis Method • Choose a reference node (“ground”) Look for the one with the most connections! • Define unknown node voltages those which are not fixed by voltage sources • Write KCL at each unknown node, expressing current in terms of the node voltages (using the I-V relationships of branch elements) Special cases: floating voltage sources • Solve the set of independent equations N equations for N unknown node voltages

  4. R1 R 3 + IS V1 R R - 2 4 Nodal Analysis: Example #1 • Choose a reference node. • Define the node voltages (except reference node and the one set by the voltage source). • Apply KCL at the nodes with unknown voltage. • Solve for unknown node voltages.

  5. R 1 R 5 R I 3 1 V V R R 2 1 2 4 Nodal Analysis: Example #2 Va

  6. V V LL V a b - + I R I R 1 2 2 4 Nodal Analysis w/ “Floating Voltage Source” A “floating” voltage source is one for which neither side is connected to the reference node, e.g. VLL in the circuit below: Problem: We cannot write KCL at nodes a or b because there is no way to express the current through the voltage source in terms of Va-Vb. Solution: Define a “supernode” – that chunk of the circuit containing nodes a and b. Express KCL for this supernode. Incorporate voltage source constraint into KCL equation.

  7. Nodal Analysis: Example #3 supernode V V LL V a b - + I R I R 1 2 2 4 Eq’n 1: KCL at supernode Substitute property of voltage source:

  8. Node-Voltage Method and Dependent Sources • If a circuit contains dependent sources, what to do? Example: iD 20 W 10 W 200 W – + 2.4 A 80 V – + 5iD

  9. Node-Voltage Method and Dependent Sources • Dependent current source: treat as independent current source in organizing and writing node eqns, but include (substitute) constraining dependency in terms of defined node voltages. • Dependent voltage source: treat as independent voltage source in organizing and writing node eqns, but include (substitute) constraining dependency in terms of defined node voltages.

  10. iD 20 W 10 W – + 200 W 2.4 A 80 V – + 5iD Example:

  11. Formal Circuit Analysis Methods • MESH ANALYSIS • (“Mesh-Current Method”) • 1) Select M independent mesh currents such that at least one mesh current passes through each branch* • M = #branches - #nodes + 1 • 2) Apply KVL to each mesh, • expressing voltages in terms of • mesh currents • => M equations for • M unknown mesh currents • 3) Solve for mesh currents • => determine node voltages • NODAL ANALYSIS • (“Node-Voltage Method”) • 0) Choose a reference node • 1) Define unknown node voltages • 2) Apply KCL to each unknown • node, expressing current in • terms of the node voltages • => N equations for • N unknown node voltages • 3) Solve for node voltages • => determine branch currents *Simple method for planar circuits A mesh current is not necessarily identified with a branch current.

  12. Mesh Analysis: Example #1 • Select M mesh currents. • Apply KVL to each mesh. • Solve for mesh currents.

  13. Mesh Analysis with a Current Source ia ib Problem: We cannot write KVL for meshes a and b because there is no way to express the voltage drop across the current source in terms of the mesh currents. Solution: Define a “supermesh” – a mesh which avoids the branch containing the current source. Apply KVL for this supermesh.

  14. Mesh Analysis: Example #2 ia ib Eq’n 1: KVL for supermesh Eq’n 2: Constraint due to current source:

  15. Mesh Analysis with Dependent Sources • Exactly analogous to Node Analysis • Dependent Voltage Source: (1) Formulate and write KVL mesh eqns. (2) Include and express dependency constraint in terms of mesh currents • Dependent Current Source: (1) Use supermesh. (2) Include and express dependency constraint in terms of mesh currents

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