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GATE 2020 EE – Question 23

Control Systems · Mathematical modelling and representation of systems, Feedback principle, Transfer function, Block diagrams and Signal flow graphs · 1 mark · Multiple choice

Which of the options is an equivalent representation of the signal flow graph shown here?

Diagram for GATE 2020 EE question 23
  1. Graph (A)
  2. Graph (B)
  3. Graph (C)
  4. Graph (D)

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Correct answer: (C) Graph (C)

Explanation

The self-loop $c$ at the node after $d$ gives that node a loop gain of $cd$, so the forward path through it is multiplied by $\frac{1}{1-cd}$. Combining with the gains $a$ and $d$ along the forward path gives $\frac{ad}{1-cd}$, with the outer feedback branch $e$ unchanged, which is graph (C).