L-05(GDR)(ET) ((EE)NPTEL)

L-05(GDR)(ET) ((EE)NPTEL) - Module 2 DC Circuit Version 2...

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Module 2 DC Circuit Version 2 EE IIT, Kharagpur

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Lesson 5 Node-voltage analysis of resistive circuit in the context of dc voltages and currents Version 2 EE IIT, Kharagpur
Objectives To provide a powerful but simple circuit analysis tool based on Kirchhoff’s current law (KCL) only. L.5.1 Node voltage analysis In the previous lesson-4, it has been discussed in detail the analysis of a dc network by writing a set of simultaneous algebraic equations (based on KVL only) in which the variables are currents, known as mesh analysis or loop analysis. On the other hand, the node voltage analysis (Nodal analysis) is another form of circuit or network analysis technique, which will solve almost any linear circuit. In a way, this method completely analogous to mesh analysis method, writes KCL equations instead of KVL equations, and solves them simultaneously. L.5.2 Solution of Electric Circuit Based on Node Voltage Method In the node voltage method, we identify all the nodes on the circuit. Choosing one of them as the reference voltage (i.e., zero potential) and subsequently assign other node voltages (unknown) with respect to a reference voltage (usually ground voltage taken as zero (0) potential and denoted by ( ). If the circuit has “n” nodes there are “n-1” node voltages are unknown (since we are always free to assign one node to zero or ground potential). At each of these “n-1” nodes, we can apply KCL equation. The unknown node voltages become the independent variables of the problem and the solution of node voltages can be obtained by solving a set of simultaneous equations. Let us consider a simple dc network as shown in Figure 5.1 to find the currents through different branches using “Node voltage” method. Version 2 EE IIT, Kharagpur

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KCL equation at “Node-1”: 13 12 1 2 3 42 2 4 4 2 11 1 1 0; 0 ss VV II V V V RR R R R R ⎛⎞ −− = →−− + = ⎜⎟ ⎝⎠ 1 3 11 1 12 2 13 3 I IG V G V G V −= (5.1) where = sum of total conductance (self conductance) connected to Node-1. ii G KCL equation at “Node-2”: 23 22 1 2 43 4 3 4 3 3 I IV V R R R R = = + + V 3 1 1 2 2 2 2 3 s I GV GV GV + (5.2) KCL equation at “Node-3”: 3 33 1 2 32 1 2 3 1 2 3 111 1 1 V 3 I V R R R R R R ++− = = + + + V 3 1 1 3 2 2 3
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L-05(GDR)(ET) ((EE)NPTEL) - Module 2 DC Circuit Version 2...

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