Mason Gain Formula

Definition :

Mason gain formula is used to determine the overall gain of the system between input and output nodes.

Mason Gain Formula Limitation

1. Output node to input node
2. Intermediate node to input node

P _k =  Gain of K ^th forward path

n  = Number of forward paths from X to Y

Δ =  It is independent of the Forward path

It considers all the loops present in SFG

• Δ _k It is dependent on a forward path:
• Δ _k = 1 – (sum of all loop gains not touching k ^th forward path) + (sum of the product of 2 non-touching loop gains not touching k ^th forward path) – (sum of the product of 3 non-touching loop gains not touching k ^th forward path)

Mason Gain Formula Steps

1. Applicable
2. Calculate the total no of  forward paths
3. Calculate all types of loops.
4. Calculate Δ and Δ _k

Note :

• Self-loop at the initial (first) node of unity /non-unity can always be ignored.
• Self loop at intermediate nodes having unity gain

• To obtain finite such loops can be ignored.
• MGF cannot be applied between two intermediate nodes.

Mason Gain formula – Points to remember

• Carefully observe the forward path (arrow direction)
• Carefully observe the loops/non-touching loops
• Take care of the loop at the input node