Mason's Rule - Formula

Formula

The gain formula is as follows:


where:

  • Δ = the determinant of the graph.
  • yin = input-node variable
  • yout = output-node variable
  • G = complete gain between yin and yout
  • N = total number of forward paths between yin and yout
  • Gk = gain of the kth forward path between yin and yout
  • Li = loop gain of each closed loop in the system
  • LiLj = product of the loop gains of any two non-touching loops (no common nodes)
  • LiLjLk = product of the loop gains of any three pairwise nontouching loops
  • Δk = the cofactor value of Δ for the kth forward path, with the loops touching the kth forward path removed. *

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