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

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

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.

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.

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.

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.

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.

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

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

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.

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.

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

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

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.

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.

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.