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 curren
17、t and I for a branch current. Its evident from Fig. 3.17 that,PSUT,Methods of Analysis,41,Find the branch current I1, I2, and I3 using mesh analysis.,PSUT,Methods of Analysis,42,For mesh 1,For mesh 2,We can find i1 and i2 by substitution method or Cramers rule. Then,PSUT,Methods of Analysis,43,Use m
18、esh analysis to find the current I0 in the circuit.,PSUT,Methods of Analysis,44,Apply KVL to each mesh. For mesh 1,For mesh 2,PSUT,Methods of Analysis,45,For mesh 3,In matrix from become we can calculus i1, i2 and i3 by Cramers rule, and find I0.,PSUT,Methods of Analysis,46,3.5 Mesh Analysis with Cu
19、rrent Sources,PSUT,Methods of Analysis,47,A circuit with a current source.,Case 1 Current source exist only in one meshOne mesh variable is reduced Case 2 Current source exists between two meshes, a super-mesh is obtained.,PSUT,Methods of Analysis,48,a supermesh results when two meshes have a (depen
20、dent , independent) current source in common.,PSUT,Methods of Analysis,49,Properties of a Supermesh,The current is not completely ignored provides the constraint equation necessary to solve for the mesh current. A supermesh has no current of its own. Several current sources in adjacency form a bigge
21、r 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; one is obtained using KVL and Ohms law to the supermesh and the other is obtained by relation regulated due
22、to the current source.,PSUT,Methods of Analysis,52,Similarly, a supermesh formed from three meshes needs three equations: one is from the supermesh and the other two equations are obtained from the two current sources.,PSUT,Methods of Analysis,53,PSUT,Methods of Analysis,54,3.6 Nodal and Mesh Analys
23、is by Inspection,PSUT,Methods of Analysis,55,For circuits with only resistors and independent current sources For planar circuits with only resistors and independent voltage sources,The analysis equations can be obtained by direct inspection,the circuit has two nonreference nodes and the node equati
24、ons,PSUT,Methods of Analysis,56,In general, the node voltage equations in terms of the conductances is,PSUT,Methods of Analysis,57,or simplyGv = i,where G : the conductance matrix, v : the output vector, i : the input vector,The circuit has two nonreference nodes and the node equations were derived
25、as,PSUT,Methods of Analysis,58,In general, if the circuit has N meshes, the mesh-current equations as the resistances term is,PSUT,Methods of Analysis,59,or simplyRv = i,where R : the resistance matrix, i : the output vector, v : the input vector,Write the node voltage matrix equations,PSUT,Methods
26、of Analysis,60,The circuit has 4 nonreference nodes, soThe off-diagonal terms are,PSUT,Methods of Analysis,61,The input current vector i in amperesThe node-voltage equations are,PSUT,Methods of Analysis,62,Write the mesh current equations,PSUT,Methods of Analysis,63,The input voltage vector v in vol
27、tsThe mesh-current equations are,PSUT,Methods of Analysis,64,3.7 Nodal Versus Mesh Analysis,Both nodal and mesh analyses provide a systematic way of analyzing a complex network. The choice of the better method dictated by two factors. First factor : nature of the particular network. The key is to se
28、lect the method that results in the smaller number of equations. Second factor : information required.,PSUT,Methods of Analysis,65,3.10 Summery,Nodal analysis: the application of KCL at the nonreference nodes A circuit has fewer node equations A supernode: two nonreference nodes Mesh analysis: the application of KVL A circuit has fewer mesh equations A supermesh: two meshes,PSUT,Methods of Analysis,66,
