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The sum of the gains of the feedback paths in the signal flow graph shown in the figure is -

The sum of the gains of the feedback paths in the signal flow graph shown in the figure is - Correct Answer af + be + cd

Concept:

Any feedback path is considered as a valid feedback path if it does not touches any single node twice in its path.

Calculation:

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Feedback paths in the above diagram are af, be, cd, abef, bcde, and abcdef.

  • abef is not a valid feedback path because node 'Q' is repeated twice in the path.
  • bcde is not a valid feedback path because node 'R' is repeated twice in the path.
  • abcdef is not a valid feedback path because node 'Q' and 'R' is repeated twice in the path.

​So af, be and cd are the only valid feedback paths.

The sum of the gains of the feedback paths in the signal flow graph is af + be + cd.

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