Test: Signal Flow Graphs - 1

# Test: Signal Flow Graphs - 1 - Electrical Engineering (EE)

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## 15 Questions MCQ Test GATE Electrical Engineering (EE) 2024 Mock Test Series - Test: Signal Flow Graphs - 1

Test: Signal Flow Graphs - 1 for Electrical Engineering (EE) 2023 is part of GATE Electrical Engineering (EE) 2024 Mock Test Series preparation. The Test: Signal Flow Graphs - 1 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Signal Flow Graphs - 1 MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Signal Flow Graphs - 1 below.
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Test: Signal Flow Graphs - 1 - Question 1

### A signal flow graph is the graphical representation of the relationships between the variables of set linear algebraic equations.

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 1

Explanation: By definition signal flow graphs are the graphical representation of the relationships between the variables of set linear algebraic equations.

Test: Signal Flow Graphs - 1 - Question 2

### A node having only outgoing branches.

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 2

Explanation: Nodes are the point by which the branches are outgoing or ingoing and this can be input or output node and input node is the node having only outgoing branches.

Test: Signal Flow Graphs - 1 - Question 3

### Use mason’s gain formula to find the transfer function of the given signal flow graph:

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 3

Explanation: Using mason’s gain formula transfer function from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

Test: Signal Flow Graphs - 1 - Question 4

Use mason’s gain formula to find the transfer function of the following signal flow graph:

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 4

Explanation: Using mason’s gain formula transfer functionThe given signal flow graph can be represented by the transfer function:

T(s) = (abcd + efg) / (1 - cd - fg - cdfg)

We can rearrange this equation as follows:

T(s) = (abcd + efg) / (1 - (cd + fg) - cdfg)

We need to find the transfer function using Mason's Gain formula. Mason's Gain formula is given by:

T(s) = Σ(Pk * Δk) / Δ

where T(s) is the transfer function, Pk is the gain of the kth forward path, Δk is the determinant of the kth forward path, and Δ is the overall determinant.

Step 1: Identify the forward paths and their gains
- Forward path 1: abcd, gain = abcd
- Forward path 2: efg, gain = efg

Step 2: Identify the loops and their gains
- Loop 1: cd, gain = cd
- Loop 2: fg, gain = fg

Step 3: Calculate the overall determinant (Δ)
Δ = 1 - (sum of loop gains) + (sum of product of gains of non-touching loops) - ...
Δ = 1 - (cd + fg) + (0) - ...
Δ = 1 - cd - fg

Step 4: Calculate the determinants for each forward path (Δk)
Δ1 = 1 - fg (since loop 1 touches forward path 1)
Δ2 = 1 - cd (since loop 2 touches forward path 2)

Step 5: Calculate the transfer function using Mason's Gain formula
T(s) = (abcd * Δ1 + efg * Δ2) / Δ
T(s) = (abcd * (1 - fg) + efg * (1 - cd)) / (1 - cd - fg)

Now, let's compare the given options with the calculated transfer function:

Option A: abcd + efg / (1 - cd - fg - cdfg)
Option B: abcd(1 - fg) + efg(1 - cd) / (1 - cd - fg)
Option C: abef + bcd / (1 - cd - fg - cdfg)
Option D: adcdefg / (1 - cd - fg - cdfg)

The correct answer is Option B, as it matches the calculated transfer function. from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

Test: Signal Flow Graphs - 1 - Question 5

Loop which do not possess any common node are said to be ___________ loops.

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 5

Explanation: Loop is the part of the network in which the branch starts from the node and comes back to the same node and non touching loop must not have any node in common.

Test: Signal Flow Graphs - 1 - Question 6

Signal flow graphs:

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 6

Explanation: Signal flow graphs are used to find the transfer function of control system by converting the block diagrams into signal flow graphs or directly but cannot be used for nonlinear systems.

Test: Signal Flow Graphs - 1 - Question 7

Signal flow graphs are reliable to find transfer function than block diagram reduction technique.

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 7

Explanation: As one set technique and formula is used here but in block diagram technique various methods are involved which increases complexity.

Test: Signal Flow Graphs - 1 - Question 8

The relationship between an input and output variable of a signal flow graph is given by the net gain between the input and output node is known as the overall______________

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 8

Explanation: The relationship between input and output variable of a signal flow graph is the overall gain of the system.

Test: Signal Flow Graphs - 1 - Question 9

Loop which do not possess any common node are said to be ___________ loops.

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 9

Explanation: Loop is the part of the network in which the branch starts from the node and comes back to the same node and non touching loop must not have any node in common.

Test: Signal Flow Graphs - 1 - Question 10

Signal flow graphs:

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 10

Explanation: Signal flow graphs are used to find the transfer function of control system by converting the block diagrams into signal flow graphs or directly but cannot be used for nonlinear systems.

Test: Signal Flow Graphs - 1 - Question 11

Signal flow graphs are reliable to find transfer function than block diagram reduction technique.

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 11

Explanation: As one set technique and formula is used here but in block diagram technique various methods are involved which increases complexity.

Test: Signal Flow Graphs - 1 - Question 12

The relationship between an input and output variable of a signal flow graph is given by the net gain between the input and output node is known as the overall______________

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 12

Explanation: The relationship between input and output variable of a signal flow graph is the overall gain of the system.

Test: Signal Flow Graphs - 1 - Question 13

Use mason’s gain formula to calculate the transfer function of given figure:

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 13

Explanation: Use mason’s gain formula to solve the signal flow graph and by using mason’s gain formula transfer function from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

Test: Signal Flow Graphs - 1 - Question 14

A node having only outgoing branches.

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 14

Nodes are the point by which the branches are outgoing or ingoing and this can be input or output node and input node is the node having only outgoing branches.

Test: Signal Flow Graphs - 1 - Question 15

Use mason’s gain formula to find the transfer function of the given figure:

Detailed Solution for Test: Signal Flow Graphs - 1 - Question 15

Explanation: Using mason’s gain formula transfer function from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

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## GATE Electrical Engineering (EE) 2024 Mock Test Series

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