Q3Control System
Question
Q.3. State Mason's gain formula.
Answer
Mason's gain formula gives the overall transfer function as T = (1/Δ)·ΣPkΔk, where Pk is each forward path gain, Δ = 1 − Σ(loop gains) + Σ(products of non-touching loop pairs) − ..., and Δk is Δ evaluated after removing loops touching path k.
Mason's gain formula computes the overall gain (transfer function) between an input and output node of a signal flow graph as:
where Pk is the gain of the k-th forward path, Δ (the graph determinant) = 1 − (sum of all individual loop gains) + (sum of gain products of all possible pairs of non-touching loops) − (sum of gain products of all possible triples of non-touching loops) + ⋯, and Δk is the value of Δ computed by deleting from the graph all loops that touch (share a node with) the k-th forward path.