22.5 : メイソンの法則

Mason's rule simplifies transfer function calculation from signal-flow graphs, assessing various elements.

Loop gain is calculated by tracing a path from a node back to itself, taking the product of branch gains.

Forward-path gain involves following a path from the input to the output node, computing the product of gains.

Non-touching loops are loops with no common nodes. The gain is the product of loop gains from these separate loops.

The transfer function is computed from these elements using Mason's rule.

Delta is derived from alternating series of sums of loop gains and nontouching-loop gains taken two or more at a time. Delta_k is formed by excluding loop gains from Delta that intersect with the k^th forward path.

To calculate the transfer function of a system, the forward-path gains are identified, and the loop gains are evaluated.

Then, the non-touching loops and their corresponding gains are identified.

Delta is calculated, and Delta_k is evaluated by removing intersecting loop gains.

Finally, these values are substituted into Mason's rule to yield the system's transfer function.