An Introduction To Signal Flow Graph .

* Draw back of the block diagram reduction techniques :

--- Draw back of the block diagram reduction techniques is that it is a lengthy method.

And this type of drawback is not present in the another method of obtaining the transfer function which is known signal flow graph method.

* Signal flow graph method :

Signal flow graph method is discovered by S.T. MASON .

--- Signal flow graph method is also regarded as a modification of the block diagram.

* Basic modification in the signal flow graph method :

--- In signal flow graph there are following modification from block diagram reduction techniques :

I . Take off point: Take off point in signal flow graph method is represented as :

II . Block: Block in the signal flow graph method is represented as :

III . Summing point: Summing point in the signal flow graph method is represented as :

* Terms used in the signal flow graph method :

I . Loop gain: Loop gain is defined as’ the multiplication of the branch transmittance of the different loops'.

II . Forward path: Forward path is defined as ‘ path which is starting from one node and end to another node in the forward direction without crossing any node.

III . Forward path - gain : Forward path gain is defined as ' the multiplication of the branch transmittance of the different forward path '.

* Mason ‘ s gain formula :

--- Mason ‘s gain formula is written as :

Where,

- T = Transfer function .

.

- Mk = Gain of the forward-path.

-   🔺 = Signal flow graph determinant .

-🔺k = The value of the signal flow graph determinant ‘🔺 ‘ for which part of the graph not touching the forward path .

---  🔺  is given by the formula :

  🔺 = 1 - ( sum of gain of the individual loop ) + ( sum of gain product of two non - touching loops ) - ( sum of gain product of four non - touching loops ) - ……..  .

* Procedure to solve the signal flow graph by mason ‘s gain formula :

--- The procedure to solve the signal flow graph by mason ‘s gain formula is given as :

I . Find out the total no. of the forward path .

II . Find the product of the gain of the different forward path .

III . Find the total no. of individual loop ( closed path ) .

IV . Find out the total gain of the individual loops .

V . Find out the total no. of the non - touching loops ( Those loops which are not in touch with the other loop i.e., which are not joint to any common node with different loop) .

VI . Find out the total gain of the non - touching loop ( product of the gain of the non - touching loop ).

VII . Find out the’  🔺 k ‘ of the non - touching loop.

Where,

 

 🔺1 = 1 - ( sum of the gain of the loop non - touching the 1^st forward path ).

Similarly ,

  

  🔺 k = 1 - ( sum of the gain of the loop of the non - touching kth forward path ).

VIII . Find out the value of 🔺.

Where ,

 🔺 = 1 + ( sum of the gain of all the non - touching loops ) - ( sum of gain of all single loop ) .

XII . Find out the transfer function where transfer function is given as ,

Mk = Gain of the forward path .

 🔺 K = The value of the signal flow graph determinant ‘🔺  ‘ for which part of the graph which is non - touching the forward path .