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QUESTION: 1

Mason's rule is applied to

Solution:

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

QUESTION: 2

Assertion (A): Signal flow graph is applicable to the linear systems.

Reason (R): Signal flow graph method of finding the transfer function of a system is very simple and does not require any reduction technique.

Solution:

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)

QUESTION: 3

Consider the following three cases of signal flow graph and their corresponding transfer functions:

Q. Which of the above relations is/are correctly matched?

Solution:

Hence, only 1 is correctly matched.

QUESTION: 4

The signal flow graph shown below has M number of forward path and N number of individual loops.

Q. What are the values of M and N ?

Solution:

QUESTION: 5

The signal flow graph for a certain feedback control system is given below.

Now, consider the following set of equations for the nodes:

- x
_{2}= a_{1}x_{1}+a_{5}x_{3}+a_{6}x_{4}+a_{7}x_{5} - x
_{3}=a_{2}x_{2 } - x
_{4}=a_{3}x_{3 } - x
_{5}=a_{4}x_{4}+a_{8}x_{3}

Q. Which of the above equations are correct?

Solution:

**Correct Answer :- b**

**Explanation : **x_{2} = a_{1}x_{1} + a_{5}x_{3} + a_{6}x_{4} + a_{7}x_{5}

x_{3} = a_{2}x_{2}

x_{4} a_{3}x_{3} + a_{9}x_{5}

x_{5} = a_{4}x_{4} + a_{8}x_{3}

QUESTION: 6

The gain C(s)/R(s) of the signal flow graph shown below is

Solution:

Gain of forward paths are:

P1 = G1G2G3 and P2 = G4

Here, Δ1 = 1

and Δ2 = (1 + G1G2— G2G3)

Individual loops are:

L_{1} = -G_{1}G_{2}

and L_{2} = G_{2}G_{3}

Non-touching loop = Nil

QUESTION: 7

The number of forward paths and the number of non-touching loop pairs for the signal flow graph shown in the figure below are respectively

Solution:

Forward paths are

P_{1} = G_{1}G_{2}G_{3} and P_{2} = G_{3}G_{4 }

Gain product of non-touching loop pairs are:

L_{1} L_{2} = G_{1}H_{1}H_{4}

and L_{1}L_{3} = G_{1}G_{3}H_{1}H_{2}

Thus, there are two forward paths and two non touching loop pairs

QUESTION: 8

The signal flow graph of the RLC circuit of figure (i) is shown in figure (ii)

The values of G_{1} and H_{1} are respectively

Solution:

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

Also, from given SFG, we have

QUESTION: 9

The closed loop transfer function CIR for the signal graph shown below is

Solution:

Number of forward paths are two,

QUESTION: 10

Consider the following statements with regards to the signal flow graph shown below.

1. The number of forward paths are 2.

2. The number of forward paths are 3.

3. The number of loops are 3.

4. The number of loops are 5,

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

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

Q. Which of these statements are correct?

Solution:

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