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EE302Lecture12 new

# EE302Lecture12 new - Mesh Analysis A structured form of...

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Mesh Analysis – A structured form of Kirchhoff's Voltage Law ( Σ loop V’s = 0). In KVL we know that the sum of voltages around any loop is zero. Consider this problem: v 2 + v 5a V a = 0 or 2 i a + 5( i a i b ) = 10 v 5b + v 7 + v 8 = 0 or 5( i b i a ) + 7 i b + 8 i b = 0 These equations can be put in a convenient matrix form. If we collect the i a terms together in the first column and the i b terms together in the second column, we get the following: 2 + 5 –5 i a 10 = –5 5 + 7 + 8 i b 0 and now we see there is a simple formula for writing loop equations by inspection: V a R’s (loop a) –R ab i a = V b –R ab R’s (loop b) i b 1 8 i a + V a = 10 V 2 5 7 i b + + + + + v 2 v 5a v 5b v 7 v 8 8 i a + 10 2 5 7 i b Note: If a resistance is shown without the ohms sign, assume the value shown is in ohms. Likewise, a voltage source is in volts. independent sources

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The writing of KVL loop equations by inspection works if you:
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EE302Lecture12 new - Mesh Analysis A structured form of...

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