 So, today we are going to study interconnection of two port network. Learning outcome at the end of this session students will be able to use series connection of two port networks for matching of networks. So, before starting with interconnection of two port network in different cases you should pause this video here and you should know what are the equations related to the two port network parameter as well as different connections like series connection, parallel connection, cascaded connection of two port networks. So, now we will start how two port networks are connected in series and what are the equivalent values of particular variable that we can find out by deriving it. So, first we will draw the series connection of two networks. So, first network is to be represented by later a and then we will draw the series. Second two port network is to be represented by network B. So, this is the input part and input voltage is represented by V 1 input current represented by I 1. Similarly, this is the output voltage represented by V 2 plus minus plus minus current represented by I 2. Now, these two connections are connected in series here is the current flowing through network B and here it is current flow through network A. So, current are to be represented by I 1 A and I 2 A here it is I 1 B and here it is I 2 B voltages V 1 A V 2 A here it is V 1 B and here it is V 2 B is it. So, this is series connection of two port networks. Now, we will write the equation for this. So, equation is to be represented by I 1 once R V 1 A is equal to Z 1 1 A into I 1 A plus Z 1 2 A into I 2 A. Similarly, V 2 A is equal to Z 2 1 A into I 1 A plus Z 2 2 A into I 1 A plus Z 2 2 A into I 1 A plus Z 2 1 A into I 2 A. So, these are the two equations related to network A. Similarly, we can write equations for second network that is B network. So, V 1 B is equal to Z 1 1 B I 1 B plus Z 1 2 B into I 2 B and I 2 B is equal to Z 1 1 B plus Z 1 2 B V 2 B is equal to Z 2 1 B I 1 B plus Z 2 2 B into I 2 B is it. So, these are the two equations related to those two port network. Now, think is in this diagram I 1 is total current V 1 is input voltage I 2 is current at the output side of the two port network and V 2 is the total output voltage. So, from this we can say that current I 1 is equal to I 1 A is equal to I 1 B. Similarly, current I 2 is equal to I 2 A is equal to I 2 B is it and total voltage V 1 at the input side is addition of these two voltages. So, V 1 is equal to V 1 A plus V 1 B and V 2 is equal to V 2 A plus V 1 B and V 2 is equal to V 1 A plus V 2 B. So, these are the relations we are getting for this particular series connection of two port networks. So, from this we will simplify the equations. So, again we write the value of V 1 is equal to V 1 A plus V 1 B and we know the value of V 1 A and V 1 B from the equations for those two port networks. So, we have to put the values respectively. So, V 1 A can be replaced by Z 11 A I 1 A plus Z 12 A into I 2 A plus value of V 1 B is Z 11 B into I 1 B plus Z 12 B into I 2 B. Now, we have to simplify this and we have to put value of I 1 A and I 1 B as a current I 1 and value of current I 2 A and I 1 B as a current I 2 B as current I 2. So, this can be simplified as Z 11 A plus Z 11 B into current I 1 plus Z 12 A plus Z 12 B into I 2. So, this is the value of voltage V 1 is it. Similarly, we have to solve for V 2. So, value of V 2 is V 2 A plus V 2 B. So, we have to put the respective values of V 2 A and V 2 B. So, value of V 2 is Z 21 A I 1 A plus Z 22 A I 2 A. This is the value of V 2 A plus. Now, we have to put the value of V 2 B. So, value of V 2 B is Z 21 B I 1 B plus Z 22 B I 2 B is it. Now, again for I 1 A plus Z 12 B I 2 B is it. Now, I 1 A I 1 B we have to put it as the I 1 and for I 2 A and I 2 B we have to replace this by current I 2. So, this can be solved as or simplified as Z 21 A plus Z 21 B into I 1 plus Z 22 A plus Z 22 B into current I 2. So, this is the value of voltage V 2 is it. So, this can be written in matrix form as V 1 V 2 is equal to Z 11 B plus Z 22 A plus Z 22 B plus Z 11 A plus Z 11 B Z 12 A plus Z 12 B Z 21 A plus Z 21 B and Z 22 A plus Z 22 B and this multiplied by this I 1 I 2 is it. So, from this we have to put the value of we can say that when two port networks are connected in series then to find out resultant value of that matrix Z matrix. So, that time we have to add the Z parameter values of those two port networks as Z 11 A plus Z 11 B and Z 12 A plus Z 12 B third one is Z 2 A plus Z 21 B and fourth value is Z 22 A and Z 22 B is it. Similarly, for interconnection of two port networks we can solve for parallel connection of two port networks as well as cascade connection of two port networks and we can derive it and we will get the value of that voltages as well as currents and we can find out the resultant matrix from the derivation. So, this is all related to series connection of two port networks. While preparing this video lecture I have used circuit theory analysis and synthesis by a Chakravarti.