 Hence, today we are going to study condition of reciprocity in two port parameter representation. Learning outcome at the end of this session students will be able to describe condition of reciprocity in two port parameter representation. So, in today's lecture we are going to study what is the condition of reciprocity in two port parameter like z parameter, y parameter, h parameter or a b c d parameter. So, from this today we are going to see what is the condition of reciprocity for z parameters. But before starting with the derivation or condition of reciprocity you have to pause this video here and you should recall the equations which are to be related to z parameter and which are dependent and independent variables used while writing the equations for z parameters. We will start the condition of reciprocity in two port parameter representation for z parameters. While studying this we have to write down the equations related to z parameters. But before that we will see what is the condition of reciprocity. Basically a network is said to be reciprocal if the ratio of excitation variable and response variable of a two port network is same even if we interchange the excitation as well as response of a two port network ok. So, first we will draw the diagram related to that excitation variable as well as response variable and this is two port network. Here it is the excitation voltage V1 current I1 and we have to short circuit the output this is current I2 and this is minus I2 because the direction is opposite. So, conditions in this case are V1 should be considered as a Vs current I1 is I1 current V2 is equal to 0 and current I2 is equal to minus I2 ok. So, first we will write the equation of z parameters and the equations are V1 is equal to z11 I1 plus z12 I2 and second equation is V2 is equal to z21 I1 plus z22 I2 is it. Now, we will put the values of these four variables in these two equations ok. So, now V1 is Vs. So, Vs is equal to z11 I1 minus z12 I2 because value of I2 is minus I2 because of this opposite direction and value of V2 is 0 because output port is short circuited. So, value of V2 is 0. So, 0 is equal to z21 I1 minus z22 I2 ok. So, from this second equation we will get the value of I1 as I1 is equal to z22 I2 upon z21 ok. So, we will call it this as a equation 1, this as a equation 2, this as a equation 3 and this as a equation 4 ok. Now, we will put the value of I1 in equation number 3 Vs is equal to z11 z22 into I2 divided by z21 minus z12 I2 is it. Now, Vs is equal to z11 z22 I2 minus z12 z21 into I2 and when this term goes to the left side that should be multiplied. So, it is z21 is it. So, z21 Vs is equal to I2 into z11 z22 minus z12 z21 is it. So, from this we can find out the value of current I2 as z21 Vs upon z11 z22 minus z12 and z21 is it. So, this is the value of current I2 and for the circuit to be reciprocal the condition is I1 by V1 at V2 is equal to 0 should be equal to I2 by V2 at V1 is equal to 0 ok. So, we have to check for this condition. So, presently we get the value of I2. So, ratio I2 by Vs is z21 by this is mod z mod z means determinant of that z z matrix ok. So, determinant of that z matrix is z11 z22 minus z12 z21 is it. So, similarly we will go for the second condition and for that we have to draw the diagram. So, again this is 2 port network. Now, we have to short the port 1 this is current I1 this is minus I1 and here we have to give the excitation plus minus voltage V2 current I2 and now here conditions are voltage V1 is 0 because port 1 is short circuited current I1 is equal to minus I1 because of the direction change current I2 is equal to I2 and V2 we will consider it as a Vs that is source voltage is it. Now, we derive for this. So, equation for z parameters again we have to write V1 is equal to z11 I1 plus z12 I2 V2 is equal to z21 I1 plus z22 I2 these are the equations related to the z parameter equation 1 equation 2. Now, we will put the conditions in this case in these 2 equations. So, 0 is equal to minus z11 I1 plus z12 I2 equation 3 and Vs is equal to minus z21 I1 plus z22 I2 we will make this as a equation number 4. So, from equation number 3 we will get the value of I2 as z11 I1 upon z12 is it. Now, we have to put the value of I2 in equation number 4 is it. So, we will get the ratio. So, Vs is equal to minus z21 I1 plus z22 instead of I2 we have to write z11 I1 upon z12 is it. So, next step Vs is equal to if we simplify this, this will be minus z12 z21 I1 plus z22 z11 I1 and this term will go to left hand side. So, it is to be multiplied with Vs is it. So, after this next step we will directly write the value of current I1 as I1 is equal to z12 Vs upon z11 z22 minus z12 z21 is it. So, I1 by Vs is equal to z12 by mod z is it. So, this is a ratio of V1 sorry I1 by Vs. So, for the condition of reciprocity we have to go for this I1 by V1 at V2 equal to 0 should be equal to I2 by V2 at V1 is equal to 0. So, if we compare this with the resultants we are getting that I1 by Vs should be is equal to I2 by Vs. So, this is the condition of reciprocity. So, from this z12 by mod z is equal to z21 by mod z. So, this mod z get cancelled and we get the condition of reciprocity as z12 is equal to z21 ok. So, this is the condition of reciprocity. So, like this we can find out the condition of reciprocity for y parameter g parameter h parameter or a Vs parameter. While preparing this video lecture I have used circuit theory analysis and synthesis by A Chakravarti. Thank you.