Mason's Gain Formula

A portion of the code for this site was taken from an open source resource that requires attribution. View attribution.

from	to	gain

Enter the consecutive connections first in descending order (0, 1, etc), then the nonconsecutive ones.

Submit Values Through Table
Submit Values Through File

The gain formula is as follows:

$$G = \frac{y_\text{out}}{y_\text{in}} = \frac{ \sum_{k=1}^N {G_k \Delta _k} }{ \Delta\ }$$
$$\Delta = 1 - \sum L_i + \sum L_iL_j- \sum L_iL_jL_k + \cdots + (-1)^m \sum \cdots +\cdots$$

where:

Δ = the determinant of the graph.
y_in = input-node variable
y_out = output-node variable
G = complete gain between y_in and y_out
N = total number of forward paths between y_in and y_out
G_k = path gain of the kth forward path between y_in and y_out
L_i = loop gain of each closed loop in the system
L_iL_j = product of the loop gains of any two non-touching loops (no common nodes)
L_iL_jL_k = product of the loop gains of any three pairwise nontouching loops
Δ_k = the cofactor value of Δ for the k^th forward path, with the loops touching the k^th forward path removed.

Descripton Liscenced under Wikipedia's Creative Commons Attribution-ShareAlike License
Original Ariticle.

Top Menu

Signal Flow Graph: