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43321311vvvvii x????????At node 2 PSUT Methods of Analysis 25 40822322132????????vvvvviii x?At node 3 PSUT Methods of Analysis 26 2)(284221323121vvvvvviii x?????????In matrix form: PSUT Methods of Analysis 27 ??????????????????????????????????????????003838943818721412143321vvv Nodal Analysis with Voltage Sources ?Case 1: The voltage source is connected between a nonreference node and the reference node: The nonreference node voltage is equal to the magnitude of voltage source and the number of unknown nonreference nodes is reduced by one. ?Case 2: The voltage source is connected between two nonreferenced nodes: a generalized node (supernode) is formed. PSUT Methods of Analysis 28 Nodal Analysis with Voltage Sources 5608042323231213241??????????????vvvvvvvviiiiPSUT Methods of Analysis 29 A circuit with a supernode. ?A supernode is formed by enclosing a (dependent or independent) voltage source connected between two nonreference nodes and any elements connected in parallel with it. ?The required two equations for regulating the two nonreference node voltages are obtained by the KCL of the supernode and the relationship of node voltages due to the voltage source. PSUT Methods of Analysis 30 Example ?For the circuit shown in Fig. , find the node voltages. 204272021722121???????????vvvviiPSUT Methods of Analysis 31 i1 i2 PSUT Methods of Analysis 32 Find the node voltages in the circuit below. ?At suopernode 12, PSUT Methods of Analysis 33 20231062114123???????vvvvvvv?At supernode 34, PSUT Methods of Analysis 34 )(341634143342341vvvvvvvvvv???????? Mesh Analysis ?Mesh analysis: another procedure for analyzing circuits, applicable to planar circuit. ?A Mesh is a loop which does not contain any other loops within it PSUT Methods of Analysis 35 PSUT Methods of Analysis 36 (a) A Planar circuit with crossing branches, (b) The same circuit redrawn with no crossing branches. PSUT Methods of Analysis 37 A nonplanar circuit. ? Steps to Determine Mesh Currents: 1. Assign mesh currents i1, i2, .., in to the n meshes. 2. Apply KVL to each of the n meshes. Use Ohm’s law to express the voltages in terms of the mesh currents. 3. Solve the resulting n simultaneous equations to get the mesh currents. PSUT Methods of Analysis 38 Fig. PSUT M