 I am Priyanka Bidla and today we will see about signal flow graph. This is the learning outcome of this video lecture. At the end of this session, students will be able to represent a given physical system into the signal flow graph, that is, SMG. These are the contents of this video lecture. First, we see signal flow graph representation. The graphical representation of the variables of a set of linear algebraic equations representing the system is called signal flow graph representation. Signal flow graph shows the flow of signals from one point of system to another point and which gives the relationships among the signals. It consists only of branches and which represent signals and nodes. Consider a simple equation V equal to IR, where V is the voltage, I is the current and R is the resistance. This is nothing but a simple Ohm's law. Now, the signal flow graph of the equation is shown below. Here, the current I and the voltage V are the nodes and these two nodes are connected by the branch. The voltage V depends on the value of current I and the relationship between them is through R. It represents I gates multiplied with R to generate V. All the dependent and independent variables are represented by the nodes and the relationship between nodes are represented by joining the nodes. As per the equations, according to equations, we have to connect the nodes. Now, we see the definitions of node and branch. So here, signal flow graph represents by small circles. So here, I and V are the nodes. These two circles are nothing but these are the nodes. And branch are nothing but line joining two nodes is called branch. So this is a branch and the branches are always unidirectional. Now, we see the terminologies related to signal flow graph one by one. So first, input node, output node and the chain node. Input node is nothing but a node has only outgoing branches is known as input node or source node. Then output node, it is also called as sync node. A node has only incoming branches is known as output node. Then chain node. A node has incoming as well as outgoing branches is known as chain node. The next terminology that is path. A path is defined as a traversal of connected branches in the direction of branch arrow. So this is a path from X1 to X3. Here X1, X2 and X3 are the nodes. Then we have to calculate the path gain. Path gain is nothing but it is defined as the product of all branch gains while going through the forward path. So forward path is nothing but from X1 to X3. So calculate the path gain is equal to A12 into A23. Then next, dummy nodes. In this, X1 and X2 are having incoming as well as outgoing branches. So according to definition, X1 and X2 are called as chain nodes. In such a case, a separate input and output nodes can be added by adding a branch with gain 1. These nodes are called as dummy nodes. Means here R and C are the input and output nodes. Means what? Here X1 and X2 are the chain nodes. Then there is no input node and output node according to signal flow graph. So the nodes R and C having branch 1 can be added at input and output respectively. These nodes are called dummy nodes. And remember signal flow graph must have at least one input node and one output node. Then forward path. A path from input to the output node is called as forward path. So here R is the input node and C is the output node. So the path from R to C is nothing but forward path. And it is represented by P. So P1 is equal to G1, G2, G3. And P2 is equal to G1, G4. Next terminology is loop. A closed path from a node to the same node is called loop. So here there are total four loops. A loop starts with the same node and ends at the same node. That is nothing but this is L1, L2, then L3 and this is L4. Now we have to calculate the loop gain. This is nothing but the product of all the gains forming a loop. So first you have to identify the loop and then you have to multiply all the gains of that loop. That is nothing but this is a loop. For that loop you have to calculate the loop gain is equal to A23 and A32. The next self-loop. A feedback loop consisting of only one node is called as self-loop. A33 at x3 is a self-loop. Now consider one example. Consider the signal flow graph and identify the following terms. That is forward path loops and loop gain. So here r of s is the input node and c of s is the output node. First we have to calculate the forward path. So first forward path is nothing but G1, G2, G3, G4, G5, G7. And the second forward path will be G1, G2, G3, G4, G6, G7. So there are two forward paths. Now we have to identify the loops and find out the loop gain also. So first loop this one. So calculate the loop gain is nothing but G2 of s into H1 of s. Then I will calculate the loop gain for that G4 of s into H2 of s. Then third loop this one. So again calculate the loop gain. L3 is equal to G4 of s into G5 of s into H3 of s. And the next loop that is L4 is equal to G4 of s into G6 of s into H3 of s. In this way you have to calculate the loop gains also. And these are the loops, non-touching loops. If the loops are not having any common node between them, then those loops are called as non-touching loops. Here there are the two loops. Loop 1 and the loop 2. So here first loop flowing through the X2 and X3 nodes and the loop 2 flowing through the X1 and X4 nodes. So these two nodes are not having any common node. Then non-touching loop to forward path. The meaning of this is if there is no node common in between a forward path and a feedback loop, a loop is said to be non-touching to that forward path. So here this is a loop. And there are the two forward paths through nodes X1, X2, X3, X4 and the another is through X1, X4 nodes. So here this loop represents it does not touch to that forward path. So this is a non-touching loop to forward path. Next self-loop non-touching to forward path. So this is self-loop. Now there are again two paths through nodes X1, X2, X3, X4, X5 and the another from X1 to X2 and then X5. So this is a self-loop does not touch to that forward path. This is a self-loop. It does not touch to that forward path. These are the terminologies of signal flow graph. These are the references of this video lecture. Thank you.