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?In matrix from bee we can calculus i1, i2 and i3 by Cramer’s rule, and find I0. PSUT Methods of Analysis 46 020)(4)(12)(4, A, n o d eA t 0)(4)(12432123132121023130?????????????????iiiiiiiiiiIIiiiiI???????????????????????????????001221121956511321iii Mesh Analysis with Current Sources PSUT Methods of Analysis 47 A circuit with a current source. ?Case 1 ● Current source exist only in one mesh ● One mesh variable is reduced ?Case 2 ● Current source exists between two meshes, a supermesh is obtained. PSUT Methods of Analysis 48 A21 ??i?a supermesh results when two meshes have a (dependent , independent) current source in mon. PSUT Methods of Analysis 49 Properties of a Supermesh 1. The current is not pletely ignored ● provides the constraint equation necessary to solve for the mesh current. 2. A supermesh has no current of its own. 3. Several current sources in adjacency form a bigger supermesh. PSUT Methods of Analysis 50 ?For the circuit below, find i1 to i4 using mesh analysis. PSUT Methods of Analysis 51 ? If a supermesh consists of two meshes, two equations are needed。 express currents in terms of node voltages. 4. Solve the resulting system of linear equations for the nodal voltages. Lect4 EEE 202 7 2. Node Voltages V1, V2, and V3 are unknowns for which we solve using KCL 500W 500W 1kW 500W 500W I1 I2 1 2 3 V1 V2 V3 Lect4 EEE 202 8 Steps of Nodal Analysis 1. Choose a reference (ground) node. 2. Assign node voltages to the other nodes. 3. Apply KCL to each node other than the reference node。Methods of Analysis PSUT 1 Basic Nodal and Mesh Analysis AlQaralleh Methods of Analysis PSUT Methods of Analysis 2 ? Introduction ? Nodal analysis ? Nodal analysis with voltage source ? Mesh analysis ? Mesh analysis with current source ? Nodal and mesh analyses by inspection ? Nodal versus mesh analysis Lect4 EEE 202 3 Steps of Nodal Analysis 1. Choose a reference (ground) node. 2. Assign node voltages to the other nodes. 3. Apply KCL to each node other than the reference node。 express currents in terms of node voltages. 4. Solve the resulting system of linear equations for the nodal voltages. PSUT Methods of Analysis 4 Common symbols for indicating a reference node, (a) mon ground, (b) ground, (c) chassis. Lect4 EEE 202 5 1. Reference Node The reference node is called the ground node where V = 0 + – V 500W 500W 1kW 500W 500W I1 I2 Lect4 EEE 202 6