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EE302Lecture11

# EE302Lecture11 - Nodal Analysis the Basics Suppose we had...

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Nodal Analysis – the Basics: Suppose we had this simple circuit – which is two independent circuits: Then v 1 = I 1 R 1 and v 2 = I 2 R 2 using Ohm’s Law Usually I 1 I 2 R 1 and R 2 are known circuit values. The above circuit is easy to solve for the node voltages because the two circuits are not connected. What would we do if the circuits are connected as shown below? 1 v 1 I 1 R 1 I 2 R 2 v 2 0 Volts v 1 I 1 R 1 I 2 R 2 v 2 R 3

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Let’s write KCL for each node. The sum of currents away from node 1 is equal to zero. –I 1 + ( v 1 /R 1 ) + ( v 1 v 2 )/R 3 = 0 The sum of currents away from node 2 is also equal to zero. –I 2 + ( v 2 /R 2 ) + ( v 2 v 1 )/R 3 = 0 2 – is for current I 1 into node 1 current flow from node 1 to ground through R 1 current flow from node 1 to node 2 through R 3 note that v 1 and v 2 are reversed in the node 2 equation v 1 I 1 R 1 I 2 R 2 v 2 R 3
Now let’s rearrange the terms in the equations, grouping the coefficients of the unknowns v 1 and v 2 together, and

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