 This is the video on smith chart part 2 here I will be telling you about how to use a smith chart. Learning outcomes at the end of the video you will be able to locate the impedance on the chart, you will be able to determine the VSWR and reflection coefficient for a given load, you will be able to determine the admittance, you will be able to determine the Zmax that means maximum impedance and the minimum impedance along the transmission line, you will be able to determine the distance or from voltage maximum and voltage minimum from load or towards generator and these all you can do using the smith chart. These are the contents of the video. Let us first revise what is a smith chart. The smith chart is a graphical aid designed for electrical and electronic engineers for assisting in solving the problems with transmission lines and matching circuits. What it consists of? It consists of X in and R in circles. On smith chart the impedances are normalized impedances, smith chart can be used simultaneously to display the multiple parameters such as impedances, admittances, reflection coefficient, VSWR, wavelength towards load and wavelength towards generator and for impedance matching purpose also. Let us go further. Let us consider one example. Let us consider the example. The transmission line has characteristic impedance of 50 ohm and it is terminated in the load impedance ZL. So we can take different values of ZL but here I am assuming that the I am considering the fixed characteristic impedance of 50 ohm and for given load impedance calculate the following parameters using smith chart. The parameters are reflection coefficient, VSWR, impedance at V min and V max that is maximum voltage and minimum voltage, distance at which V min and V max occurs, admittance and calculate the maximum impedance and minimum impedance values. Let us do all those using smith chart. Locating impedance on smith chart. To locate the impedance on smith chart as I said we work on smith chart with normalized impedances. So for that first of all find out the normalized load impedance ZL where I shown Z as small and this capital ZL indicates the actual impedance, actual load impedance. Let me assume the actual load impedance I assumed here 5 plus J25 and I should normalize it so I divide it by Z0 which is 50 ohm. So I will get 5 by 50, 25 by 50 so ZL normalized impedance is 0.1 plus J 0.5. How to locate it on the smith chart? To locate it on the smith chart Rn should be taken as 0.1 and Xn should be considered as 0.5 and locate the coinciding point on the chart. Let us see here. Here you can see the Rn equal to 0.1 and this well this point Rn equal to 0.1 and Xn is equal to 0.5. Here Xn is 0.5. The coinciding point is nothing but this point which is the impedance point ZL which is 0.1 plus J 0.5. Determining the reflection coefficient? To determine the reflection coefficient it is a complex quantity. It consists of magnitude as well as angle. So for that join the impedance point P. Let me name the point as P the impedance point to the center of the chart O and extend the line outward and mark the point Q on Xn circle. So let us see that and by this I can do it by two methods. In the first method when after joining the line I measure the length OP and I measure the length OQ using my centimeter scale and I will take the ratio that is length of OP to length of OQ will give me the magnitude which in this case I got as 0.855 and angle can be directly read from the circle which is named as angle of reflection coefficient circle. The value in this case is 1.26.5 degrees. Here you can see this is the center of the chart O, this is the impedance point P, I extend this line outward and I mark the point the Xn's last Xn circle that at that circle I mark the point Q and this length of OP upon length of OQ will give me the magnitude of reflection coefficient and here as I already talked in the video first there is an angle of reflection coefficient circle and on this circle if I read the value of the angle it is 126.5 degrees. So my reflection coefficient is 0.855 and angle is 126.5 degrees. This is by method one. If I do by method two, in the method two I can directly read the value of magnitude from the scale given below and theta v angle can be read from the circle marked as angle of reflection coefficient. So you can see here, here is the circle, here is the scale where VSWR reflection coefficient different values with different parameters are written. So I can measure this length OP and the same length I can mark at the respective scale if I want the reflection coefficient I will mark it on the reflection coefficient the length of OP and at this length whatever is the reading that is nothing but the magnitude of reflection coefficient. If I want to find VSWR same length I need to mark but on the VSWR scale and read this value I get VSWR. So this is the method two for finding VSWR the method one I will show you further how to find VSWR without using this lower scale. So determination of VSWR for that I will draw a circle from impedance point P with the center as O and radius as OP. Center as O, radius and OP draw a circle complete circle and read the value of Rn these are all Rn values on the real axis. So read the value of Rn which Rn value which is towards open circuit side as I said this is the open circuit side and this is short circuit side. So read the value of Rn on the open circuit side this is nothing but the VSWR value. So in my case this is my VSWR value. Locating the impedance on smith chart already we have located now let me show you locating the impedance point which has a negative imaginary part or reactance part. Let me consider this as ZL and Z0 if I normalize I get 0.2 minus j 0.2. Let me locate Rn 0.2 Xn 0.2 but this 0.2 Xn is on the lower half of the circle why because the sign is negative. So I can locate this 0.2 and 0.2 here and this coinciding point 0.2 and this 0.2 this is coinciding point 0.2 minus j 0.2 why lower half because the X reactance is negative. Using this load impedance point or this is point P I can find different parameters that I want to show for further. So determination of admittance if this is my impedance point how I can find the admittance. So for that extend this line OP in the opposite direction and locate a point where the line touches the constant VSWR. So this is my which center as O radius is OP if I draw a circle it is a constant VSWR circle here only arc is shown but you can draw a complete circle and diametrically opposite point will give me the admittance. If I how to find this value this point lies on one circle of Rn and one circle of Xn. So read the Xn value here read the Rn value here. So in this case these values are 2.5 plus j 2.5 y plus because X is on the upper side not on the lower half of the circle. So it is 2.5 plus j 2.5. The given ZL is 10 minus j 10 ohm and Z0 is 50 ohm which we are considered the example and while obtained using graphical method is 2.5 plus j 2.5 but this is normalized admittance this is not the actual admittance. To find the actual admittance as I shown for actual as capital Y capital YL can be given as the normalized admittance small YL divided by Z0. In many cases we are multiplying with Z0 but here we are dividing it by Z0 because it is the admittance. So the value is 2.5 plus j 2.5 divided by 50. So I get actual admittance YL as 0.05 plus j 0.05. This is the actual admittance for the given impedance 10 minus j 10 ohm with characteristic impedance of 50 ohm. Let me find out Zmax and Zmin and Vmax and Vmin points. Point A that means when I draw a constant VSWR circle with center as O radius as OP the point towards the open circuit side is point A and this point is Zmax or Vmax point and the point towards the short circuit side that is a point B which is the Zmin and Vmin point. How to find Zmax and Zmin? The VSWR red here or the Rn value red here is multiplied with Z0 which will give me Zmax. So here if I read the value of Rn which is 5.3 when it is multiplied by 50 I get 265 ohm as my Zmax and same is the case with B if I read the value here and multiply with Z0 I get 9 ohm which is Zmin, minimum impedance of the transmission line. Determination of distance from load at which Zmax and Zmin occurs Zmax and Zmin are the points where impedance is purely resistive Zmax is the point where voltage Vmax occurs and Zmin is the where Vmin occurs to determine the distance the follow the circle marked wavelength towards generator from point P. Point P read the values of the circle and Zmin point is marked as a 0 it means that there the impedance there the value is 0.5. That means from P if I want to find out this distance if I want to read this distance I should read the circle wavelength towards generator or wavelength towards load circle and that value if I read here this value here is 0.467 and when I come back here the value is 0 but actually it is not 0 because it starts from 0 and again when it returns back the value here is 0.5. So, it is a 0.5 lambda minus 0.467 lambda so it is 0.337 lambda is the Z where Zmin occurs. Similarly to find Zmax and you should move from point P up to point A. So, when I move from point P up to point A for that this to this distance opposite diametrically opposite distance which is 0.25 lambda and I need to read from this point to this point this distance is 0.033 lambda. How it is calculated? It is 0.25 here here it is 0.217 so difference is 0.33 so it comes to be 0.283 lambda. These are the references used for preparing this video. Thank you.