Control Systems Signal Flow Graph and Block Diagram Mason's Gain Formula

The overall transfer function for the signal flow graph shown, is:-

1
\(\frac{{{G_1}{G_2}}}{{\left( {1 - {G_1}{G_2}{H_1} + {G_2}{H_2}} \right)}}\)
2
\(\frac{{{G_1}{G_2}}}{{\left( {1 + {G_1}{G_2}{H_1} + {G_2}{H_2}} \right)}}\)
3
\(\frac{{{G_1}{G_2}}}{{\left( {1 - {G_1}{G_2}{H_1} - {G_2}{H_2}} \right)}}\)
4
\(\frac{{{G_1}{G_2}}}{{\left( {1 + {G_1}{G_2}{H_1} + {G_2}{H_1}} \right)}}\)
5
\(\frac{{{G_1}{G_2}}}{{\left( {1 + {G_1}{G_2}{H_1} + {G_1}{H_1}} \right)}}\)

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