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1、Methods of Analysis,PSUT,1,Basic Nodal and Mesh Analysis,Al-Qaralleh,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,EE
2、E 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
3、 of Analysis,4,Common symbols for indicating a reference node, (a) common 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,Steps of Nodal Analysis,1. Choose a reference (groun
4、d) 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.,Lect4,EEE 202,7,2. Node Voltages,V1, V2, and V3 are unknowns for which w
5、e 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; express currents in terms of node voltages. 4. Solve the re
6、sulting system of linear equations for the nodal voltages.,Lect4,EEE 202,9,Currents and Node Voltages,500W,V1,500W,V1,V2,Lect4,EEE 202,10,3. KCL at Node 1,500W,500W,I1,V1,V2,Lect4,EEE 202,11,3. KCL at Node 2,500W,1kW,500W,V2,V3,V1,Lect4,EEE 202,12,3. KCL at Node 3,500W,500W,I2,V2,V3,Lect4,EEE 202,13
7、,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.,Lect4,EEE 202,14,+,
8、V,500W,500W,1kW,500W,500W,I1,I2,4. Summing Circuit Solution,Solution: V = 167I1 + 167I2,PSUT,Methods of Analysis,15,Typical circuit for nodal analysis,PSUT,Methods of Analysis,16,PSUT,Methods of Analysis,17,Calculus the node voltage in the circuit shown in Fig. 3.3(a),PSUT,Methods of Analysis,18,At
9、node 1,PSUT,Methods of Analysis,19,At node 2,PSUT,Methods of Analysis,20,In matrix form:,PSUT,Methods of Analysis,21,Practice,PSUT,Methods of Analysis,22,Determine the voltage at the nodes in Fig. below,PSUT,Methods of Analysis,23,At node 1,PSUT,Methods of Analysis,24,At node 2,PSUT,Methods of Analy
10、sis,25,At node 3,PSUT,Methods of Analysis,26,In matrix form:,PSUT,Methods of Analysis,27,3.3 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 t
11、he 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,28,3.3 Nodal Analysis with Voltage Sources,PSUT,Methods of Analysis,29,A circuit with a supernode.,A
12、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 relation
13、ship of node voltages due to the voltage source.,PSUT,Methods of Analysis,30,Example 3.3,For the circuit shown in Fig. 3.9, find the node voltages.,PSUT,Methods of Analysis,31,i1,i2,PSUT,Methods of Analysis,32,Find the node voltages in the circuit below.,At suopernode 1-2,PSUT,Methods of Analysis,33
14、,At supernode 3-4,PSUT,Methods of Analysis,34,3.4 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 c
15、rossing branches, (b) The same circuit redrawn with no crossing branches.,PSUT,Methods of Analysis,37,A nonplanar circuit.,Steps to Determine Mesh Currents: Assign mesh currents i1, i2, , in to the n meshes. Apply KVL to each of the n meshes. Use Ohms law to express the voltages in terms of the mesh
16、 currents. Solve the resulting n simultaneous equations to get the mesh currents.,PSUT,Methods of Analysis,38,Fig. 3.17,PSUT,Methods of Analysis,39,A circuit with two meshes.,Apply KVL to each mesh. For mesh 1, For mesh 2,PSUT,Methods of Analysis,40,Solve for the mesh currents. Use i for a mesh current and I for a branch current. Its evident from Fig. 3.17 that,PSUT,
