Test: Signal Flow Graphs - 2 - Electronics and Communication Engineering (ECE) MCQ

Mason's rule or Mason’s gain formula is applied to signal flow graph for finding the transfer function.

Signal flow graph is applicable to the linear systems because output is proportional to gain of the system

Reason (R) is also true but is not a correct explanation of assertion (A)

Hence, only 1 is correctly matched.

There are three forward paths. The gain of the forward path are:

• M1 = G1G2G3G4G5
• M2 = G1G6G4G5
• M3 = G1G2G7

There are four loops with loop gains:
N1= - G4H1

N2= - G2G7H2

N3= - G6G4G5H2

N4= - G2G3G4G5H2

Correct Answer :- b

Explanation : x₂ = a₁x₁ + a₅x₃ + a₆x₄ + a₇x₅

x₃ = a₂x₂

x₄  a₃x₃ + a₉x₅

x₅ = a₄x₄ + a₈x₃

Gain of forward paths are:
P1 = G1G2G3 and P2 = G4
Here, Δ1 = 1
and Δ2 = (1 + G1G2— G2G3)
Individual loops are:
L₁ = -G₁G₂
and L₂ = G₂G₃
Non-touching loop = Nil

Converting the given circuit in s-domain and writing the equations, we get:

Also, from given SFG, we have

Explanation: Given signal flow graph properties:

• Forward paths: Paths from input to output that do not revisit any node.
• Loops: Closed paths that start and end at the same node.
• Non-touching loop pairs: Sets of loops that do not share any common node.

Let's evaluate each statement:

1. The number of forward paths are 2.

   • To verify the number of forward paths, we need to count distinct paths from input to output that do not revisit nodes.
   • By tracing in the graph, we can identify 2 such paths.

   Conclusion: This statement is correct.

2. The number of forward paths are 5.

   • Given that we found 2 forward paths, this statement contradicts the first statement.

   Conclusion: This statement is incorrect.

3. The number of loops are 3.

   • Loops are closed paths. Counting the distinct loops in the graph reveals 3 closed loops.

   Conclusion: This statement is correct.

4. The number of loops are 5.

   • If there are only 3 loops, this statement is incorrect.

   Conclusion: This statement is incorrect.

5. The number of non-touching loop pairs is 1.

   • Non-touching loop pairs are sets of loops that do not share any node.
   • Counting such pairs in the graph shows there is 1 pair.

   Conclusion: This statement is correct.

6. The number of non-touching loop pairs is nil.

   • If we identified 1 non-touching loop pair, this statement contradicts that observation.

   Conclusion: This statement is incorrect.

Therefore, the correct answer is: a) 2, 3 and 5

• Signal flow graphs are used to represent systems and their interconnections through nodes and directed branches.


• They provide a visual representation of mathematical relationships in a control system.


• The main application of signal flow graphs is to find the transfer function of a system.


• The transfer function, which is the ratio of the output to the input of a system, can be derived using Mason's Gain Formula applied to the signal flow graph.


 

• Realizing Transfer Functions:
  You can realize a product of two transfer functions, such as G₁(s) G₂(s), by cascading systems.


• Additive Operations:
  Summing or differencing operations allow expressions like G₁(s)(1/G₁(s) ± G₂(s)).


• Division Limitation:
  Direct division, such as G₁(s) / G₂(s) (Option B), cannot be realized using only cascading and summing/differencing, since division is not a supported operation in these configurations.