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Chapter 4 Methods of Analysis of Resistive Circuits

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Node voltage analysis - with independent source : current source / voltage source - with dependent source Mesh current analysis - with independent source : voltage source / current source - with dependent source Resistive Circuit Analysis

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Figure 4.2-1 (a) A circuit with three nodes. (b) The circuit after the nodes have been labeled and a reference node has been selected and marked. (c) Using voltmeters to measure the node voltages. Node Voltage Analysis – with current sources To write a set of node equations, we do two things: 1. Express element currents as functions of the node voltages. 2. Apply KCL at each of the nodes of the circuits, except for the reference node.

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Figure 4.2-2 Node voltages, v 1 and v 2, and element voltage, v a, of a circuit element. Figure 4.2-3 Node voltages, v 1 and v 2, and element voltage, v 1 - v 2, of a (a) generic circuit element, (b) voltage source, and (c) resistor. Node Voltage Analysis – with current sources

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Figure 4.2-4 (a) A circuit with three resistors. (b) The resistor voltages expressed as functions of the node voltages. (c) The resistor currents expressed as functions of the node voltages. Node Voltage Analysis – with current sources KCL If node (a) node (b)

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Example 4.2-1 Node Voltage Analysis – with current sources node (a) node (b)

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Example 4.2-2 Example 4.2-3 Node Voltage Analysis – with current sources node (a) node (b) node (c)

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Exercise 4.2-1 Exercise 4.2-2 Node Voltage Analysis – with current sources node (a) node (b)

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Figure 4.3-1 Circuit with an independent voltage source and an independent current sources. Figure 4.3-2 Circuit with a supernode that incorporate v a and v b. Node Voltage Analysis – with current and voltage sources A supernode consists of two nodes connected by an independent or a dependent voltage source

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Example 4.3-1 Example 4.3-2 Node Voltage Analysis – with current and voltage sources Method #1 Apply KCL to the Supernode Method #2 Method #1 Method #2 : apply KCL to the Supernode

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Example 4.3-3 Exercise 4.3-1Exercise 4.3-2 Node Voltage Analysis – with current and voltage sources Let Supernode be the 10V source Apply KCL to the Supernode

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Example 4.4-1 Example 4.4-2 Example 4.4-3 Node Voltage Analysis – with dependent sources KCL at node (b) KCL at supernode KCL at node (b) KCL at node (a)

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Exercise 4.4-1 Exercise 4.4-2 Node Voltage Analysis – with dependent sources KCL at node (a)

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Figure 4.5-1 Nonplanar circuit with a crossover. Figure 4.5-2 Circuit with four meshes. Each mesh is identified by dashed lines. - Loop - Mesh : 다른 loop 를 포함하고 있지 않은 loop (cross over 가 없는 circuit 에만 적용 가능 ) Mesh Current Analysis – with independent voltage source

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Figure 4.5-3 (a) A circuit with two meshes (b) Inserting ammeters to measure the mesh currents. Figure 4.5-4 Mesh currents, i 1 and i 2, and element current, i 1 – i 2, of a (a) generic circuit element, (b) current source, and (c) resistor. Mesh Current Analysis – with independent voltage source To write a set of mesh equations, we do two things: 1. Express element voltages as functions of the mesh currents. 2. Apply KVL to each of the meshes of the circuits.

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Figure 4.5-5 Mesh Current Analysis – with independent voltage source Figure 4.5-6 Mesh #1 Mesh #2 Mesh #1 Mesh #2 Mesh #3

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Exercise 4.5-1 Mesh Current Analysis – with two independent voltage sources

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Figure 4.6-2 Circuit with an independent current source common to both meshes. Figure 4.6-1 Circuit with an independent voltage source and an independent current source. Mesh Current Analysis – with current and voltage source Mesh #1 Mesh #2 Mesh #1

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Example 4.6-1 Figure 4.6-4 Circuit with a supermesh that incorporates mesh 1 and mesh 2, indicated by the dashed line. Mesh Current Analysis – with current and voltage source Mesh #2 Mesh #3 A Supermesh is one larger mesh created from two meshes that have an independent or dependent current source in common. Supermesh Mesh #3 Current source Supermesh Mesh #3

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Example 4.6-2 Mesh Current Analysis – with current and voltage source Method #1 Method #2

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Exercise 4.6-1 Exercise 4.6-2 Mesh Current Analysis – with current and voltage source

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Example 4.7-1 Mesh Current Analysis – with dependent source KVL to mesh #1 KVL to mesh #2

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Example 4.7-2 Mesh Current Analysis – with dependent source KVL to mesh #1 KVL to mesh #2

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Example 4.8-1 Figure 4.8-1 Node Voltage & Mesh Current Analysis – comparison Figure 4.8-2 KVL to mesh #3

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Example 4.8-2 Figure 4.8-4 Node Voltage & Mesh Current Analysis – comparison Figure 4.8-3 KCL at node 3

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Mesh Current Analysis – MATLAB

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Node Voltage and Mesh Current Analysis – PSpice Example 4.10-1

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Example 4.11-1 Example 4.11-2 Node Voltage and Mesh Current Analysis – MATLAB

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Figure 4.12-1 Proposed circuit for measuring and displaying the angular position of the potentiometer shaft. Potentiometer Angle Display Figure 4.12-2 Circuit diagram containing models of the power supplies, voltmeter, and potentiometer. Figure 4.12-3 The redrawn circuit showing the mode v 1. where Angle varies from toPotentiometer varies from to

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Potentiometer Angle Display Figure 4.12-3 The redrawn circuit showing the mode v 1. Assumption Then, Let

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Figure 4.12-4 The final designed circuit. Potentiometer Angle Display Suppose

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ProblemsP4.2-4 / P4.2-7 / P4.3-5 / P4.3-11 / P4.4-7 / P4.4-10 / P4.4-17 / P4.5-6 / P4.6-10 / P4.7-10 / P4.8-2 Homework #4

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Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 4 Basic Nodal and Mesh Analysis.

Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 4 Basic Nodal and Mesh Analysis.

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