Use Mason's rule to find the transfer function of the signal-flow diagram shown. R(S) V₁(s) G₁(s) V3(s) -H{(s) G₂(s) -H₂(s) 1 V4(s) V5(S) G3(s) -H3(s) C(s)

Question

Follow the instructions. Kindly provide a COMPLETE and CLEAR solution. Answer it ASAP because I really need it right now. Answer should be typewritten.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

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Step 1: Find forward path gains and loop gains

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Step 2: Find non-touching loop gains and determinants

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Step 3: Apply Mason's Gain formula to find transfer function

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Follow-up Questions

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Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 18

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Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 19

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Answer 20

Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 21

Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 22

Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Answer 23

Follow-up Question

Answer 24

Follow-up Question

Answer 25

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Answer 26

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Answer 27

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Answer 28

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Answer 29

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Answer 31

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Answer 32

Follow-up Questions

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Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 33

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Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 34

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Answer 35

Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 36

Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Solution

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Answer 37

Follow-up Question

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Answer 38

Follow-up Question

Answer 39

Follow-up Question

Answer 40

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function

Answer 41

Can you redo this again? The answer should be typewritten, thanks.

Provide the following:
Step 1. Solve for k
Step 2. Solve for T_k (forward path gain)
Step 3. Identify the loop gains (T_L)
Step 4. Identify the nontouching loops taken two at a time T_NL_{(2 time)}
Step 5. Identify the nontouching loops taken three at a time T_NL_{(3 time)}Step 6. Identify the nontouching loops taken four at a time T_NL_{(4 time)}
Step 7. Solve for component ∆
Step 8. Solve for component ∆_k (Note: We form ∆_k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function