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hw4_ext_sol

# hw4_ext_sol - EE 101 Professor Abbas El Gamal Handout 12-a...

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EE 101 Handout # 12-a Professor Abbas El Gamal Feb. 11, 2003 Homework #4 Extra Problem Solutions 1. We chose the node and branch labels as shown below. ( You could choose any others!) 1A - 2A i 1 i 2 i 3 i 4 i 5 n 1 n 2 We can write down the reduced incidence matrix A directly from the schematic above. A = " 1 0 0 1 1 0 1 1 - 1 - 1 # . If you used a different labeling or orientation of branches, you’d get a different matrix here! We get 12 equations from the 2 (independent) KCL equations, 5 (independent) KVL equations, and the 5 branch relations. The KCL equations are: i 1 + i 4 + i 5 = 0 , i 2 + i 3 - i 4 - i 5 = 0 The KVL equations are: v 1 = e 1 v 2 = e 2 v 3 = e 2 v 4 = e 1 - e 2 v 5 = e 1 - e 2 The branch relations are: 0 = v 1 - i 1 0 = v 2 - 3 i 2 2 = i 3 0 = v 4 - 2 i 4 - 1 = i 5 1

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In matrix form, we have Ai = 0 , v = A T e, Mi + Nv = S, where the incidence matrix A is given above and M = - 1 - 3 1 - 2 1 , N = 1 1 0 1 0 , S = 0 0 2 0 - 1
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hw4_ext_sol - EE 101 Professor Abbas El Gamal Handout 12-a...

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