Ee 240 - homework - solution 3

EE 240 - HOMEWORK - Solution 3
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EE240-A2-2010 Assignment #3 SOLUTION 1. Nodal Analysis Problem: Find the matrix equations for V 1 , V 2 , and V 4 by NODAL analysis. ANS: (1) At the supernode: 6A = V1/4 + (V1-V2)/8 + (V4-V2)/2 + (V4-20)/5 (2) Constraint: V1-V4 = 4 Ix = 4(20-V2)/10 (3) V2 Node: 2Vx = 2(V4-20)/5 = (V2-V1)/8 + (V2-V4)/2 + (V2-20)/10 (1)' V1(1/4+1/8) + V2(-1/8-1/2) + V4(1/2+1/5) = 10 (2)' V1 + V2(4/10) + V4(-1) = 8 (3)' V1(-1/8) + V2(1/8+1/2+1/10) + V4(-1/2-2/5) = -8+2 = -6 Matrix form: 3/8 -5/8 7/10 V1 10 1 2/5 -1 V2 = 8 -1/8 29/40 -7/10 V4 -6
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