Chapter 4 Methods of Analysis of Resistive Circuits

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

Figure (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.

Figure Node voltages, v 1 and v 2, and element voltage, v a, of a circuit element. Figure 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

Figure (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)

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

Example Example Node Voltage Analysis – with current sources node (a) node (b) node (c)

Exercise Exercise Node Voltage Analysis – with current sources node (a) node (b)

Figure Circuit with an independent voltage source and an independent current sources. Figure 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

Example Example 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

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

Example Example Example Node Voltage Analysis – with dependent sources KCL at node (b) KCL at supernode KCL at node (b) KCL at node (a)

Exercise Exercise Node Voltage Analysis – with dependent sources KCL at node (a)

Figure Nonplanar circuit with a crossover. Figure 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

Figure (a) A circuit with two meshes (b) Inserting ammeters to measure the mesh currents. Figure 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.

Figure Mesh Current Analysis – with independent voltage source Figure Mesh #1 Mesh #2 Mesh #1 Mesh #2 Mesh #3

Exercise Mesh Current Analysis – with two independent voltage sources

Figure Circuit with an independent current source common to both meshes. Figure 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

Example Figure 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

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

Exercise Exercise Mesh Current Analysis – with current and voltage source

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

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

Example Figure Node Voltage & Mesh Current Analysis – comparison Figure KVL to mesh #3

Example Figure Node Voltage & Mesh Current Analysis – comparison Figure KCL at node 3

Mesh Current Analysis – MATLAB

Node Voltage and Mesh Current Analysis – PSpice Example

Example Example Node Voltage and Mesh Current Analysis – MATLAB

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

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

Figure The final designed circuit. Potentiometer Angle Display Suppose

ProblemsP4.2-4 / P4.2-7 / P4.3-5 / P / P4.4-7 / P / P / P4.5-6 / P / P / P4.8-2 Homework #4