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Understanding Node Voltage and Mesh Current Techniques in Circuit Analysis

In this lecture, we discuss the Node Voltage Method and the Mesh Current Method for analyzing electrical circuits. Key topics include identifying essential nodes, formulating node-voltage equations using Kirchhoff's current law, and the application of these methods to circuits with dependent sources. We also delve into the concept of supernodes and provide details on setting up mesh-current equations for planar circuits. Homework assignments and assessment problems will enhance your understanding of these fundamental techniques used in electrical engineering.

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Understanding Node Voltage and Mesh Current Techniques in Circuit Analysis

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  1. ECE410 Spring 2012 Lecture #12 Node Voltage – Supernode Current Mesh Technique

  2. Announcements • Homework #4 – Due next Monday 2-20-2012. Chapter 4 – 6, 8, 9, 13, 17, 20, 26, 32, 34, 38, 41, 45, 51 • Verify your answers to problems 8 (same as problem 41) and problem 13 (same as problem 32) with PSpice. Print and attach the schematics with required voltages and currents labeled.

  3. Node-Voltage Review • Find essential nodes of your circuit • Designate a reference node • Label node voltages as voltage between your reference node and the other essential nodes in the circuit

  4. Node-Voltage Method Continued • With the node voltages labeled in your circuit you are ready to generate your node-voltage equations • This is done by writing each of the essential branch currents leaving the essential nodes in terms of the node voltages and then summing them to zero in accordance with Kirchoff’s current law.

  5. Write Node Voltage Equations (3) (1) (2) Write branch currents exiting each essential node in terms of the node voltages and sum them to zero in accordance with KCL.

  6. Using N-V Method with dependent sources • In order to solve a circuit with dependent sources, the node-voltage equations must also include the constraint equation that governs the dependent source written in terms of the node voltage. • Work Assessment 4.3 to show how this is done.

  7. Special Cases and Supernode Technique • Sometimes a current flowing out of a node cannot be expressed in terms of the node voltages due to a voltage source between essential nodes • These nodes can then be treated as a single ‘supernode’. An example is shown below and will be worked out in class.

  8. Current Mesh Method • Mesh-Current Method lets you describe the circuit in be-(ne-1) equations. • Only applicable to planar circuits. • Mesh current is the current that exists around the loop of a mesh.. It is not necessarily a branch current. • Apply KVL around each mesh loop, expressing all voltages in terms of the mesh current. • This will create enough equations to solve the circuit • Once mesh currents are determined, the branch currents (and voltages) can be determined.

  9. Mesh-Current Setup Example 4 equations, 4 Unknowns (i1, i2, i3, and i4)

  10. Example Continued • With mesh currents found, group current terms in each equation Solve equations for four mesh currents

  11. Work an Example • Assessment Problem 4.7

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