 Welcome to the video lecture on Z-parameters. Myself Prachisha working in Varshan Institute of Technology will be taking up video lecture based on this. At the end of video lecture, student will be able to investigate and analyze two port network parameters. Also, they will be able to analyze Z-parameter of the given two port network. A port is basically defined as those pair of terminals from where you can give the input supply or supply the energy or you can withdraw some amount of energy. Also, port can be defined as the pair of terminals where you can measure the network variables. The figure represents a standard configuration of two port network. V i and I 1 are nothing but the voltage and current at port 1 and V 2 and I 2 are nothing but the voltage and current at the port 2. The ports can be active as well as passive. So, if you are considering any kind of transmission lines, those represent passive ports. So, if we take the corresponding input voltage current and output voltage current keeping two at a time as independent, then six type of network equations can be formed. All of these network equations have been represented over here. So, the first one represents impedance parameters. The second one represents admittance parameters. The third one are known as hybrid parameters which relate the relation between input voltage and output current. While as the inverse hybrid parameters give the relation between input current and output voltage. Transmission parameters can be used for transmission lines. Those basically give the relation in terms of input voltage and currents and output voltage and current. Similarly, we can have inverse transmission parameters where the relation between the output values that is nothing but output voltage and current is given in terms of input voltage and current. Let us look at the first type of parameters which are called as open circuit impedance or Z parameters. So, again the figure represents a linear 2 port network without any independent sources. So, here the network equations can be represented as here. So, the input voltage it is nothing but response of currents, two currents flowing at input port 1 and output port 2. Similarly, we can have an equation for voltage at port 2 which is nothing but it is response of because of two voltages at because of two currents flowing at input port i1 and input output port i2. The Z parameters can be represented over here in terms of these matrices where this particular matrix it represents the Z parameters. So, the individual Z parameters can be defined by setting each of these ports equal to 0. Let us first of all calculate or discuss about two parameters that is nothing but Z11 and Z21. To find out Z11 and Z21 we need to make the port 2 as an open port which indicates that current i2 is 0. Hence Z11 is called as driving point impedance of port 1 while at Z21 it is called as transfer impedance. It is the ratio of the voltage at port 2 to the current at port 1 when we have kept the port 2 as an open. Similarly look at the figure 3b. Here from here the corresponding current i1 is made equal to 0 which indicates that port 1 is kept open. So, we can find out values Z22 and Z12. Z22 is called as driving point impedance of port 2 and Z12 is called as transfer impedance. It is the ratio of corresponding voltage V1 to the corresponding current i2. So, by making the currents equal to 0 which indicates that we have kept some of the port as open these Z parameters can be found out. So, hence these parameters are called as the open circuit parameters. So, at 2 port network it is said to be symmetrical if the input and output ports can be interchanged without altering the port voltages and currents. What will be the open circuit impedance parameters if the given circuit is symmetrical? Pause the video for a moment and think about it. So, at 2 port network where it can be said as symmetrical when the corresponding impedance parameters are that is nothing but the condition is Z11 is equal to Z22. Also for a reciprocal network the relation between Z parameters can be given as Z12 is equal to Z21. Let us look into one example based on this 2 port network where we need to calculate the Z parameters. Observe the given Z network carefully. So, for finding out the Z parameters of this particular network we can utilize these equations given over here. In the first two equations we have put i2 is equal to 0 which indicates that port 2 is left open while as for the second that is nothing but third and fourth equation we have kept i1 value is equal to 0 which indicates that port 1 has been kept open. When we say that current i2 is equal to 0 then the circuit can be redrawn as in this passion. So, the parameters Z11 and Z21 can be calculated as below. So, Z11 as we have said that it is driving point impedance of the port 1 so which is nothing but the total impedance of port 1 so which can be calculated as taking 20 and 10 ohm in series and the equivalent resistance is in parallel with the 20 ohms that the corresponding resistance is it is in the series with the final resistance. So, we can find out Z11 value as 20 ohms. Similarly, we can calculate the of Z21 by using current division rule. So, according to the equation that we have Z21 is nothing but ratio of V2 upon i1. So, voltage V2 is nothing but the corresponding current flowing through 20 ohm is will be the V2 voltage. So, the current can be found out by using current division rule which can be calculated as current i1 multiplied by resistance 20 ohms and divided by total resistance is 20 plus 30. So, this iA is nothing but the current flowing through the 20 ohm resistance which gives us the value as 8 into i1. Hence, ratio of V2 upon i1 gives us the value as 8 ohms. Therefore, value of Z21 comes out to be 8 ohms. Now, let us calculate the rest of the parameters that is nothing but Z12 and Z22. As said before, Z22 is nothing but the driving point impedance of the port 2. So, which can be calculated as ratio of V2 upon i2. So, which is nothing but the total resistance of the network. So, 20 plus 10 in series. So, which is nothing but 30 ohms in parallel with 20 ohms. So, Z22 comes out to be 12 ohms. Also, again by using current division rule, we can calculate Z1 to value. So, Z12 is ratio of V1 upon i2. So, voltage across 20 ohms has to be calculated for that we need to calculate current flowing through 20 ohms. So, by using current division rule current through 20 ohms is nothing but i2 multiplied by 20 divided by the total resistances 20 plus 10 plus 20. Hence, Z12 comes out to be 8 ohms. So, the total solution of this example can be given us. Now, if you look carefully at this particular example, we see that Z12 and Z21 are same, which indicates that the given network is reciprocated. This particular video lecture is used created by using the following references. Thank you.