01 February, 2007

The Inspection Method for Nodal Analysis

In the inspection method the constants G11, G12, . . . , Gmm and I1, I2, . . . , Im in the system of equations:

are gotten according to the following rules:
  • To get Gjj, where j = 1, 2, ... m (ie. the diagonal G 's), sum up the admittances of each of the branches attached to node j. (The admittance of a branch is the reciprocal of the impedance of that branch.)

  • To get Ij, where j = 1, 2, ... m (ie. the constants on the right-hand-side), find the value of vs/R for each branch attached to node j and sum these values up. vs is the voltage of the voltage source (if any) in that branch and R is the impedance in that branch. vs is positive if the voltage source's polarity faces the node and is negative if it does not.

  • To get Gjk, where j is not equal to k (ie. the off-diagonal R 's), sum up the admittances of all the branches joining nodes j and k, and multiply this number by -1.
For the above example the equations we get immediately by inspection method are

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