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For the signal flow diagram shown in the given figure, the transmittance between x2 and x1 is



  • a)

  • b)
     

  • c)

  • d)

Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For the signal flow diagram shown in the given figure, the transmittan...
Concept:
According to Mason’s gain formula, the transfer function is given by
Where, n = no of forward paths
M= kth forward path gain
Δ= the value of Δ which is not touching the kth forward path
Δ = 1 – (sum of the loop gains) + (sum of the gain product of two non-touching loops) – (sum of the gain product of three non-touching loops)
Calculation:
From the given signal flow graph, the forward paths are
P= rsu, P2 = efh
The loops are
L1 = st, L2 = fg
Two non-touching loops = L1L2 = stfg
Δ = 1 – st – fg + stfg
= 1 – st – fg (1 – st) = (1 – st) (1 – fg)
Δ= 1 – fg
Δ2 = 1 – st
Transmittance between Xand X2 is,
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For the signal flow diagram shown in the given figure, the transmittan...
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For the signal flow diagram shown in the given figure, the transmittan...
Concept:
According to Mason’s gain formula, the transfer function is given by
Where, n = no of forward paths
M= kth forward path gain
Δ= the value of Δ which is not touching the kth forward path
Δ = 1 – (sum of the loop gains) + (sum of the gain product of two non-touching loops) – (sum of the gain product of three non-touching loops)
Calculation:
From the given signal flow graph, the forward paths are
P= rsu, P2 = efh
The loops are
L1 = st, L2 = fg
Two non-touching loops = L1L2 = stfg
Δ = 1 – st – fg + stfg
= 1 – st – fg (1 – st) = (1 – st) (1 – fg)
Δ= 1 – fg
Δ2 = 1 – st
Transmittance between Xand X2 is,
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