Find the transfer function for this signal flow graph

[dat]

Homework Statement

Homework Equations

Manson method

The Attempt at a Solution

I used Manson method. I am not sure this is the best result. can someone use MATLAB or some software to solve this quickly ??

 

[Hesch]

I think the man is called Mason, and sorry: I think you are your method is wrong.

Now, if you number the points from x to y: 1 . . 6, the transfer function from 1 to 2 seems to be 1. But later you will have a problem with the W4 from 1 to 3. You must move this W4 connection from 1-3 to 1-2. You can do this if you substitute the W4 by W4/W1, so that the new 1-2 function becomes 1 + W4/W1.

In the same way you must move the W5 function from 3-5 to 4-5, so that the new 4-5 function becomes
1 + W5/W2. So now the 2-3 and 3-4 loops in series have been made nice and clean.

You will have to do some more movements, to unfasten the loops, but I hope you understand the "system". Having done so, the rest of the problem is Mason's.

 

[FactChecker]

My general comment is that the first thing to do is to label the edges so that all forward paths and loops can be clearly identified. Then do the substitutions in each clearly identified path. As far as I can see, the forward path gains and the loop gains make sense. But it is very difficult to identify the paths being calculated and I got tired of looking at it.
I am not aware of any software package that helps these calculations except one called freeMASON by Nikolai Schwerg https://www.radioeng.cz/fulltexts/2012/12_03_0892_0897.pdf The formula manipulations are equivalent to some standard matrix calculations, so there may be some software like Mathematica or Maple that would help.

 

[dat]

I think the man is called Mason, and sorry: I think you are your method is wrong.

Now, if you number the points from x to y: 1 . . 6, the transfer function from 1 to 2 seems to be 1. But later you will have a problem with the W4 from 1 to 3. You must move this W4 connection from 1-3 to 1-2. You can do this if you substitute the W4 by W4/W1, so that the new 1-2 function becomes 1 + W4/W1.

In the same way you must move the W5 function from 3-5 to 4-5, so that the new 4-5 function becomes
1 + W5/W2. So now the 2-3 and 3-4 loops in series have been made nice and clean.

You will have to do some more movements, to unfasten the loops, but I hope you understand the "system". Having done so, the rest of the problem is Mason's.

I understand what you mean, your method is the first method I learned. I can solve this problem by only doing your method, not using Mason method. But Mason method I had used is the faster way to solve and it assume that you don't have to simplify the graph.

 

[dat]

I think the man is called Mason, and sorry: I think you are your method is wrong.

Now, if you number the points from x to y: 1 . . 6, the transfer function from 1 to 2 seems to be 1. But later you will have a problem with the W4 from 1 to 3. You must move this W4 connection from 1-3 to 1-2. You can do this if you substitute the W4 by W4/W1, so that the new 1-2 function becomes 1 + W4/W1.

In the same way you must move the W5 function from 3-5 to 4-5, so that the new 4-5 function becomes
1 + W5/W2. So now the 2-3 and 3-4 loops in series have been made nice and clean.

You will have to do some more movements, to unfasten the loops, but I hope you understand the "system". Having done so, the rest of the problem is Mason's.

oopss

 

[dat]

My general comment is that the first thing to do is to label the edges so that all forward paths and loops can be clearly identified. Then do the substitutions in each clearly identified path. As far as I can see, the forward path gains and the loop gains make sense. But it is very difficult to identify the paths being calculated and I got tired of looking at it.
I am not aware of any software package that helps these calculations except one called freeMASON by Nikolai Schwerg https://www.radioeng.cz/fulltexts/2012/12_03_0892_0897.pdf The formula manipulations are equivalent to some standard matrix calculations, so there may be some software like Mathematica or Maple that would help.

can you just put the graph in the software and find the tranfer funtion to get the result ?? I only want to know the right answer

 

[FactChecker]

can you just put the graph in the software and find the tranfer funtion to get the result ?? I only want to know the right answer

Sorry, I have never used that software and don't have it.

 

[dat]

Sorry, I have never used that software and don't have it.

thank you for your concern