Welcome to the 22nd lecture in the course Engineering Electromagnetics. For the last few lectures we have been discussing the propagation of uniform plane waves in homogeneous media and then we have considered their reflection, refraction etc. In this work we have found that the behaviour of the plane waves is quite similar to that of the waves on a transmission line and at various points during these last few lectures this similarity has been pointed out to you. The topic for today therefore is the transmission line analogy for plane waves where we will try to formalize the similarity between the behaviour of the plane waves and that of the waves on a transmission line. The similarity between these two types of waves is quite striking particularly if we consider the reflection coefficient on a transmission line or the reflection coefficient related to plane waves travelling from one medium to the other and we find that the expressions for the reflection coefficient v- by v plus for the transmission line and E r by E i for the plane waves have a striking resemblance. Also the formation of standing waves etc are quite similar in the two cases. Now actually this similarity is not a coincidence and if one looks at the evolution of the waves on the two media one finds that there is a basis for fairly rigorous formal analogy or correspondence between these two situations. So we try to recapitulate the various expressions, mathematical expressions that lead us to the waves in these two cases and we consider a uniform transmission line on one hand and we consider a wave propagation or a uniform plane wave in a homogeneous medium and we consider what are the various equations and expressions that hold good in the two cases. For example on the transmission line considering the distributed parameter equivalent circuit for a small section of the transmission line we wrote del v by del z equal to minus l del i by del t minus r i where symbols carry their usual mean. Also del i by del z is equal to minus c del v by del t minus g times v. These are the equations governing the behavior of v and i in terms of the primary constants r l c g of the transmission line. On the other hand what equations do we start with for the plane waves we start from the Maxwell's equations and we write del cross e for example equal to minus mu del h by del t and the second equation is del cross h equal to epsilon del e by del t plus sigma e in the case of conducting media. And we are making the usual assumptions that we are dealing with a homogeneous medium so that these are constants the constitutive parameters mu epsilon sigma are constants and we are not restricting it to a dielectric medium or a perfect dielectric medium. Also we are considering that the medium is source free so that the source term does not complicate the situation. Now these we specialize so that they become simple and it is possible to see the correspondence between the two situations separately. For example if we consider a plane wave propagating in z direction and now recalling the properties of the uniform plane waves the field vectors will be normal to this direction of propagation so that let us say that we have an x component of the electric field somebody please close the door and there is a y component of the magnetic field. And then looking at these two components and considering that there is only spatial variation with respect to the z direction we are going to get one can write out the cross product in terms of the Cartesian coordinates and see that we will get del e x by del z equal to minus mu del h y by del t. On one hand corresponding to the first equation and similarly del h y by del z equal to minus epsilon del e x by del t plus sigma e x on the other hand. And the analogy or the correspondence between these equations representing the plane wave in a homogeneous medium and these equations representing the wave propagation on a transmission line is quite clear. For example one can identify the various quantities which behave similarly or which are analogous on the two sides of the white board. We can see that we have a correspondence between v and the electric field vector say the x component one has units of volts the other has units of volts per meter. Then we have l which has the same role or the same behavior as mu l is the inductance per unit length so has units of henry per meter mu is the permeability of the medium. This one no please correct this should be a negative sign here this one is alright. Thanks for pointing it out anyway. Now so mu has the units of henry per meter and therefore it is it has correspondence with the parameter l and then we do not have something corresponding to the resistance per unit length which exists in the case of the transmission line but right now is absent from the right side of the board. We can consider the reasons for this a little later. We go on to find out the analogous quantities and we see that i has the same role as h y i has the units of amperes h y has the units of amperes per meter then c and epsilon are analogous they both have units of farads per meter and then finally we have the conductance g which is analogous to the conductivity sigma both having units of most per meter therefore one can see there is a almost one to one correspondence between the various quantities on the two sides and the equations are almost identical in nature. We can consider the equations now written for this special case of sinusoidal time variation and assume that these equations were written in phasor notation and then we get del v by del z equal to minus r plus j omega l into i here and del i by del z equal to minus g plus j omega c into v here and what we get here is similarly del e x by del z equal to minus j omega mu h y and del h y by del z equal to minus j omega epsilon minus or plus sigma into e x one can combine these couple partial differential equations using the standard procedure to get let us say an equation in voltage variable as del 2 v by del z squared equal to r plus j omega l into g plus j omega c into v or simply gamma squared v with gamma squared having the expression r plus j omega l into g plus j omega c and similarly on the other side we are going to get del 2 e x by del z squared equal to j omega mu into sigma plus j omega epsilon e x and this also can be written say as gamma squared e x where gamma squared here is j omega mu into sigma plus j omega epsilon a similar equation will be obtained in h y here and in i here and considering this final result that we have got we can see that we can write either v or i as a result which reads as let us say a times e to the power minus gamma z plus b times e to the power plus gamma z here and similarly we can write either e x or h y as a e to the power minus gamma z plus b e to the power plus gamma z and therefore we find that it was not just a coincidence that we got some two isolated results which was similar in these two cases the entire mathematics is quite parallel and there is a one to one correspondence in these two situations. One also has the expression for the impedance for example the characteristic impedance here is going to be r plus j omega l upon g plus j omega c and similarly we have the expression for the intrinsic impedance here eta which is j omega mu upon sigma plus j omega epsilon whole square root z naught is the ratio of the voltage and current in one particular way and the sign is chosen appropriately depending on the direction of propagation. Same is the case with eta the intrinsic impedance it is the ratio of the fields electric field and the magnetic field in one particular wave with an appropriate sign and we have also used the specialized results for the lossless case where we have r and g as equal to 0. So, that z naught becomes simply root l by c here and beta becomes omega times square root of l c and here for the lossless case we will have sigma equal to 0 and then eta will specialize to square root of mu by epsilon and beta will become simplified to omega times square root of mu epsilon. Now one can comment for a short while on something on this side missing corresponding to the resistance per unit length in the transmission line. One could look at it from two points of view. First point of view would be that here the transmission line is constructed out of two materials one is the conductors constituting the conductors of the transmission line a good conductor the other is the dielectric medium filling the region between the two conductors or supporting the conductors. In practice both are going to be lossy and therefore r and g cater to the loss caused by the conductor and the dielectric material respectively. For plane waves we do not really need two separate media they can propagate in free space or in one single homogeneous medium and therefore only one loss mechanism is present and therefore we have a term corresponding to the r missing here that is one way of looking at it. Alternatively we have seen that particularly when we use the phasor notation we can incorporate sigma in the complex permittivity of the dielectric medium. Similarly if in addition to dielectric losses what does the complex permittivity actually signify signifies that there are losses present in the dielectric medium. Similarly if it is not a dielectric medium if it is a magnetic medium magnetic material which also has some losses the losses can be accounted for at least mathematically by replacing the real mu real permeability by a complex permeability in which case we will find immediately that a term corresponding to r will appear in the simplified Maxwell's equations. And therefore we do not pay much attention to this fact that for this simple case there is no term corresponding to r present in the case of the plane waves. This homework should put the analogy between the transmission lines or the wave phenomena on transmission lines and the wave phenomena in homogeneous media on a very formal and rigorous footing. It is not a coincidental similarity between one or two results. The entire body of results that we have derived for the transmission lines or that are available for the transmission lines can now be so to say lifted and applied to these situations which can cause a considerable amount of simplification in the work that one has to do. This formal correspondence or analogy was first noticed and brought to light by S. A. Shalkunov. Now what is it that we want to really gain out of this formal analogy or correspondence between the two situations? We can gain in two ways. One is that we gain a better understanding of the plane wave phenomena. Plane wave phenomena are usually more complex because the three dimensional media are involved. On the other hand transmission lines are a single dimensional entity. On the other hand there are certain topics for example impedance matching where large amount of work has been done in the context of the transmission lines, switch chart etc. have been developed they can be utilized. That entire work can be utilized for work with plane waves. A single example should suffice to convince us of the utility of this analogy. In the last lecture you would recall that we considered the behavior of a plane slab. A plane slab inserted between two different media and we analyzed the behavior by considering multiple reflections at the two interfaces of the plane slab. And you found that the expressions were fairly tedious. However if we consider the transmission line equivalent of the problem you can visualize already that the work can be considerably simplified. So it is this that we shall attempt to do in the rest of the time. Before we do that we are going to require the definition of impedance. This is the characteristic impedance. This is the ratio of the voltage in current for one particular wave. If it is a uncorrupted propagating wave then this is the ratio of the voltage in current. However if it is a combination of an incident wave and a reflected wave then we know that the impedance behaves in a different manner. And that impedance can be written as let us say z as a function of z and it is equal to the total voltage at that location divided by the total current at that location and we have got expressions for this impedance at different distances from a certain load impedance on the transmission line. In a similar manner here also we could say that the wave impedance or the field impedance which in the general situation that is when we are considering a superposition of an incident wave and a reflected wave is not the same as the intrinsic impedance can be written as z as a function of z equal to E x upon H y. Whatever is the total E x at a certain distance from an interface and whatever is total H y at that distance we take the ratio and that we use as the field impedance or the wave impedance. Using this concept we first take a very simple situation and then consider the plane slab problem once again. Now while we have tried to establish an exact analogy when there is just one kind of propagating wave for example in the positive z direction or in the negative z direction what happens to this analogy when there is a discontinuity either in the path of the transmission line or in the path of the plane wave. We have seen recently that in the case of the plane waves the reflection, refraction etcetera take place and these are governed by the boundary conditions which have to be satisfied by the field components at the interface. Now how does the analogy hold between these two situations at that time when there is a discontinuity and there is an interface of two different media or there is a joint between two different transmission lines. Our experience with the expressions for the reflection coefficient shows that the analogy should hold good. The reflection coefficient that we have got in the two cases virtually has the same form. So one would for example be curious how this analogy is holding good even when a discontinuity is there. So actually the problem is straight forward. We consider the boundary conditions for the case of the plane waves we have the tangential electric field at the interface continuous and the tangential magnetic field also continuous. Now we just have to realize that is there something corresponding to these boundary conditions or these continuity relations which applies to the transmission line situation as well. And actually it does if there is a joint let us say between two different transmission lines there must be the voltage must be the same on the two transmission lines at the joint. Similarly the current that is coming out of one transmission line at the joint should have the same value as the current that is going into the other transmission line at the joint. And therefore in effect these boundary conditions are identical and therefore it should be of no surprise that the behavior the analogy between the transmission lines and the plane waves is maintained even in the presence of discontinuities. We consider reflection at a perfect conductor for the purpose of demonstrating this analogy even in the presence of discontinuities. Let us say this is the perfectly conducting interface existing at z equal to 0 and let this be the normal. And therefore we are considering wave propagating in the positive z direction and impinging on this interface at z equal to 0. We will have let us say the x directed electric field and the y directed magnetic field. Now with our experience we can write down the total fields in a fairly straight forward manner. We will have e x equal to say e plus into e to the power minus j beta z minus e to the power plus j beta z. Taking care of the direction of propagation of the incident wave and the reflected wave and the fact that the tangential field at the interface must be 0 which is equal to minus 2 j e plus and then sin of beta z. Similarly h y is going to be e plus by eta eta being the intrinsic impedance of the medium into e to the power minus j beta z and plus e to the power plus j beta z. Taking care of the fact that the relationship between the field components changes sin depending on the direction of propagation which simplifies to twice e plus by eta cosine of beta z. Therefore what is going to be the value of the field impedance or the wave impedance at some distance z from the interface? We will have z as a function of z equal to total e x by total h y and it is going to be minus j eta times tan beta z. And for the case of the transmission line what is the input impedance at different distances from the short circuit from a short circuit termination that is z i equal to j z naught tan beta l where l was taken as minus z and therefore if we do that substitution that for l equal to minus z this is going to be simply j eta tan beta l where l is the distance from the interface. So we started with the field description. We arrived at some wave impedance result which is identical to what we would have arrived had we just used the transmission line analogy. Just a simple demonstration of the analogy and therefore one can use the results that we have got for the transmission line for input impedance under different situations straight away for the plane waves situation. We have got the input impedance in the general case as z i equal to z naught times z l cos beta l plus j z naught sin beta l divided by z naught cos beta l plus j z l sin beta l. You can write this in different alternative forms that does not matter so much. Now it is this input impedance expression that we shall try to use for the problem of the plane slab. Let us make space here. We consider a plane slab and we have three regions. Let us say this is medium one with intrinsic impedance eta 1 this is medium two with intrinsic impedance eta 2 and this is medium three with intrinsic impedance eta 3. Let the slab thickness be l or let us just use l. Let this interface between the two media media 1 and 2 be located at z equal to 0. And let us say that we want to calculate the reflection coefficient for a wave impinging on this plane slab from medium one. Using the transmission line analogy all that we need to do is to consider the input impedance at this point. Let us call it z l 1 which can be calculated if we know let us say the load impedance at this point which we may call z l 2. Now if there is no other discontinuity in medium three in the path of a wave which is transmitted through the plane slab then what would be z l 2 then z l 2 would be simply eta 3. So, making that assumption we can write z l 2 equal to eta 3. The other quantities in this case for example, z naught will go to eta 2.    Almost in a minute you are in a position to write down the reflection coefficient if we draw upon the transmission line analogy for the plane waves. Now there were two results of general significance that we had derived that we had stated last time. For example, one was that the reflection coefficient can be eliminated if eta 2 is equal to the geometric mean of eta 1 and eta 3. And if beta l is equal to an odd multiple of lambda by 4. Now, to make sure which lambda we have in mind we should put proper subscripts here for example, this is beta 2 it is the phase shift constant of a plane wave in medium 2 that will be involved here. And similarly this will be the wave length in medium 2 which should be utilized for deciding the thickness of the plane slab. Such a slab was given the name a quarter wave plate or a quarter wave coating. Similarly we had results for a half wave plate. Actually it is possible to derive those results in a rigorous mathematical manner which is we will attempt here just a minute. Yes please I think you are right this is how it will be. This is the process result what we need is beta 2 l equal to an odd multiple of pi by 2. Thank you. And when we substitute for beta 2 in terms of 2 pi by lambda 2 then we get this. Thank you. Let us consider the expression for Z l 1 and in terms of this the reflection coefficient. Let us say we require that the reflection coefficient should be 0. That requires that Z l 1 should be equal to eta 1 and this is the condition we use for no reflection. We put the condition that Z l 1 should be equal to eta 1. And therefore, we have eta 2 into eta 3 cos beta 2 l plus j eta 2 sin beta 2 l divided by eta 2 cos beta 2 l plus j eta 3 sin beta 2 l on the left hand side. And let us rationalize the denominator. So, that we multiply by eta 2 cos beta 2 l minus j eta 3 sin beta 2 l divided by the same quantity. So, eta 2 cos beta 2 l minus j eta 3 sin beta 2 l which entire expression should be equal to eta 1. And now we get eta 2 into eta 3 squared sorry eta 2 eta 3 on one hand. The product of these two terms they simplify to this eta 2 plus eta 3 and the other terms give us plus j sin beta 2 l cos beta 2 l into eta 2 squared minus eta 3 squared divided by eta 2 squared cos squared beta l plus eta 3 squared sin squared beta 2 l which should be equal to eta 1. Now, assuming that eta's are all real the imaginary part on the left hand side must be equal to 0. And therefore, we say that sin beta 2 l cos beta 2 l into eta 2 squared minus eta 3 squared should be equal to 0. Now, one can see that if we choose the option that eta 2 is equal to eta 3 one lands into a trivial situation. And then there will be no interface between these so called 3 different media. So, leaving aside that we have two possibilities one is that either sin beta 2 l is equal to 0 or cos sin beta 2 l is equal to 0. Considering the second possibility first the other one will also be considered this tells us that the simplest solution is that beta 2 l is equal to pi by 2 or in general an odd multiple of pi by 2. We make this substitution in the expression and then we find that the imaginary part is already 0. And we are left with eta 2 squared by eta 3 equal to eta 1 you just substitute beta 2 l equal to pi by 2. So, only this term will remain in the denominator and this will be the final result that is eta 2 should be equal to the geometric mean of eta 1 and eta 3. And the other condition that we got is exactly corresponding to the general condition that we had stated earlier. Similarly, one can see that the first choice sin of beta 2 l equal to 0 which will translate into let us say the taking the first solution beta 2 l equal to pi this will lead to the general result that eta 1 is equal to eta 3 and that there is no reflection if beta 2 l is equal to pi. So, this corresponds to lambda by 2 plane slab and the other choice that we have discussed is the lambda by 4 plane slab. Now, supposing we are interested in eliminating reflections over a broad range of frequencies then we are aware of the limitations of a single coating. For example, here it will have a limited bandwidth beyond the design wavelength or the design frequency the reflections are bound to increase and only where such a relation is satisfied the reflection will be eliminated. And as a solution to this problem we had stated that one can use multi section quarter wave coatings or in transmission line terminology multi section quarter wave transformers. And one can now see how one is going to analyze this kind of multi junction or multi interface problems using the multiple reflection point of view that we had adopted earlier. It will be virtually impossible to do that but using the transmission line analogy one can handle that kind of situation without much difficulty. So, that brings the power of the transmission line analogy into focus.


Hi everyone, Sean with jaspyscasebrakes.com here doing 2021 Panini Select basketball four box one third case break pick a team number three where this is the last four boxes of the first case of the day so pick a team is one through three all from the same case these last four boxes here followed up with pick a team number one and number two earlier all card ship and here is our list of customers and respected teams from Atlantic cards in the Hawks down to Darren Porter and the Washington Wizards no randomized to figure out which boxes we're doing these are the four you can see on here I originally wrote on there two three obviously we already did pick a team two so I slashed out the two once we figured out which boxes we're doing for that one these are your boxes here for pick a team three here is our final list good luck to everybody and find something crazy kind of bum I wasn't there for that Adam I almost went to the went to the camp today I think the dual camp that the chargers have this here is at the 49 correctly yeah how's your uh so in MLB the show you make your own team right Adam like that's the whole thing like you play the longer you play like you customize your team and get like legendary players and stuff right yeah you should play I've never played it yeah are you do you play it oh honestly Tom I respect you highly so you build it from scratch so is it like do you start like an expansion team and you draft or what do you how do you do diamond like you come into like a an existing team with an existing like staff and you just start you know making trades developing players drafting and stuff like that I know a lot of my friends play it players have to build it up by playing online and doing missions so I think we've seen a Weissman silver maybe at Edwards tricolor I don't think we've seen any uh any uh no we haven't seen any color from the mellow yet I want to see we saw an ant man tricolor perfect good luck guys box uh one pick a team number three 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Krista Domsik and James Weissman for the Warriors Shawn Mattick Carl Anthony Towns for the Timberwolves Alex Fogel Patrick Williams rookie tricolor for the Bulls Eric Ainge Ant-Man Anthony Edwards Timberwolves Alex Fogel Last Spot Mojo Sadiq Bay rookie Silver for the Pistons Jimmy Stratton Steph Curry Warriors Shawn Mattick and Alexi Pokhagesky rookie Relic for the Thunder Jens McLeese Facundo Campazo rookie lime green for the Nuggets that is for David Chan numbered out of 75 Luca Donchich for the Mavericks and Shull Kessler Killian Hayes Silver for the Pistons and Jimmy Stratton Tyrese Halliburton for the Kings Jose Arias and Isaiah Ryder to 249 in-flight auto for the Dallas Mavericks and Shull sorry that's Minnesota Timberwolves my apologies Timberwolves and Alex Fogel Last Spot Mojo Steph Curry Silver Scope for the Warriors Shawn Mattick Patrick Williams for the Bulls Eric Ainge Isaiah Stewart for the Pistons Jimmy Stratton and Gorin Dragich Silver for the Heat Austin Holmesy Peyton 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the Lakers and John Reeder Cole Anthony for the Magic and Matt Daniels Onyeka Kongwu Rookie Relic for the Hawks that is Atlanta Cards and Denny Avdija team color matching red to 199 for the Wizards and Daren Porter and Emmanuel Pickley for the Knicks that goes to Eric Ainge as I mentioned before we did this four boxes I think out of the top pigs he was the only one we didn't have color yet for us so glad we found it in here last half of box four good luck everybody Zach Levine Silver Scope for the bowls Eric Ainge and Isaac Acoro Rookie die cut red to 175 for the Cavaliers and Roger Hoynes Andre Drummond to for the Lakers Silver John Reeder Anna Ron Harper auto 20 out of 249 for the Cavaliers in-flight Cavs Roger Hoynes CJ LB tri-color for the Blazers Chris Adamsik Lamello base for the Hornets Matthew Beninato Bojan Bogdanovich for the Jazz Silver Kihun Kim Patrick Williams courtside for the bowls Eric Ainge Tyrell Terry Blue for the Mavericks and Shull Kessler to 299 and there you go guys that finishes it we got one randomizer which is the Kevin Garnett dual relic between the Timberwolves and the Nets that'll wrap it up for us very nice first case pick your teams one two and three finished up so that's going to be between the Timberwolves and the Nets we're going to pop over here to do our randomizer on that there's the Timberwolves there's the Nets what's up jack how are you man dice roll team on top after snake eyes two times one and a one I'm not no the big the big guys are and it's going to go to the Timberwolves two times on the randomizer two times on the dice Timberwolves on top and there you go guys that is 2020-2021 Penini select basketball four box one third case break pick your team number three from jasperyscasebreaks.com I'm Sean jasperyscasebreaks.com thanks for hanging out we'll see you next time


And I was dumb to let her do that am I a slot maker? Yeah My opinion the sluts are self-made mostly like a self-made millionaire self-made slut But I do have yeah, I don't I don't take responsibility for the actions of women They're responsible for their slut in my opinion. I know the women a slut, but men are slot makers Sometimes yeah, so sometimes you could you know, some people would say yeah, I'm an expert slot maker top you are up notch Sometimes yeah, if that's how you want to frame it, but I don't in my opinion strongly You know sluts are mostly self-made like self-made millionaire. Will you say stuff me? What do you mean? I mean, I'm not responsible for them having sex with 40 men before me So if I'm number 41, I don't understand how she wasn't a slut at number 39 number 40 number 30 and all these things So women I think I support your message very strongly, but most of it But with sluts, I think mostly they're self-made they did this to themselves They did it many many times before me and other men that have sex out of wedlock But I'm careful and I don't help women cheat. That's the one thing I don't do. I'm very very opposed I Refuse to help them in cheat adultery any kind of cheating and fidelity. I hate it. I think it's very very evil and abusive So that's one thing I don't do. That's too much slut. That's super slut I don't do that Men were not slot makers women could not be sluts because the man is over the in reality The man is the head of the woman.  I believe I agree with that the men are Enables this but it's a woman who are the primary drivers of it I think because they don't listen to the mother. They don't listen to their father There's no father around and they self they self make into slut. They they morph Uh over time like a caterpillar into a slut butterfly slut. Yeah I absolutely agree. I'm not taking responsibility from the woman because she's a spot of our own action, right? Yeah, because if she wasn't a slut, she couldn't become a slut if she wasn't You know, she has to control of that and if she gave into it, there's no one else's fault but her own That she became a slut. Absolutely. Even though man is not makers. That doesn't mean she got to be a slut Yeah, yeah, it's also like the dinosaurs like the dinosaurs life will find a way So the drastic sluts that the sluts will find a way if they want to be a slut Absolutely, they're always going to find a man.  I really think need to stop being sluts. I agree But if they want to be a slut and also there's always been sluts, I think throughout history Yeah, a little bit a little bit of women and I think always going to be falling prostitutes and strippers and these things That's been around for thousands and thousands of years So I don't think it'll it'll It's just most women are being sluts today. That's a big problem. Most women should not be sluts very bad for them There's nothing new under the sun Yeah Well, I think we have well hang on though. I think what's new under the sun is that we have a lot of sluts today And that's we have more sluts than ever since the 1960s of birth control and feminism And you got word man. It's out of control. Yeah, it's wild.  I think with a single motherhood and all these Broken families and it's it's very bad. It's bad for women. It's bad for kids bad for men It's worse that I ever I knew things would get bad if they didn't and we didn't turn it around But I never imagined how bad It would get right and if it doesn't turn around soon, we haven't seen anything yet. It gets worse


So when Jamie pointed, we sort of understand why you may have had some difficulty seeing at last night. What would have been a difficulty seeing the Southern Cross last night? Absolutely. Who has a house that looks, has a higher vantage, higher up? Hands up. Okay. Can you see south? You obviously identified where south is. You know where south is from your house? Yeah? Okay. So that's the, so here we have the one that I put on the learning center and Southern Cross all the way down here. Very similar to the positioning that you have on that one.  There might be some clouds. You might have a lot of homework and you can't go outside, etc. So over the next week, I'd like you to have another look. And if you look closely, we have Alpha and Beta Centauri. These two quite bright stars that we can use as pointers. And sometimes it's easier to find the two pointers and then look for the Southern Cross. And remember, we need to go through the middle of this one here, but then at a right angle. So this line has to go out. Remember to get that right angle, girls. That's a tricky part. How did you go? Well, there. So where is it? Yeah. Very good. Now I need you to draw, is your stylus working? Draw the lines as we described before. First, you've dropped down before those two are joined together. So have a look at this one. That's correct.  Does that make sense? So if you're easily able to find South doing that, and if you find it like that, can't you do that and that's North? Absolutely. Of course. And what would you do with East and West? Once you have South, you then have North, North, East and West. Make sense? So once you have one, you can get the other three. Yeah.  I had to find a way in the road where they dropped us, but actually no. That would be interesting. How did you go? Did you find your way back? Yeah, we did. It was very cold. Which you were with your parents? Yeah. I was with my dad and I took a lot of the friends that we were doing, and they also dropped a man, and one of the instructors who had to follow us and try to do a lot of the three bells on us, so we had to be moving and find our way back to camp. That sounds like a lot of fun. A little bit nerve-racking, but a lot of fun. You've almost got it. Remember between these two, we want a straight line, and then we want to go at a right angle, so this line joins with that line, and South is directly from that point. Does that make sense? Yeah. This is the second one, and that's the Southern Cross, and these are the two points, but we don't know how to explain it. From here, you've got the correct intersection perfectly. You just go straight towards the horizon from the point that you've identified there, so that everything is correct, except this. Straight down, so South is there. So this is our activity. I would like you, I'm going to divide you up into groups, you're going to make a model of the solar system, and what I would like you to do is make it to scale, which means that probably in this lesson we will plan it, we will get our materials ready, but next lesson, I will give you opportunity to be outside in the room. We're not going to do the scale so that we have the sun here and earth over on Corinda Station, but you will be able to use some free space, maybe out in the foyer, hopefully it won't be raining, or we can go outside have usual size, so we're considering two things. How big do you want your model to be? So picture you might be in here, next lesson we'll do it, we don't have time to do it now, or you might be out in the auditorium foyer, you might be out on the concrete.  What else would we think about? And it also needs to relate directly to those numbers of distances. What trend have we got in those numbers? Absolutely, is that what we expect as we go from the sun out towards the edge of the solar system? Yeah, of course. So quite a large number though and we're going to need to know how many kilometers for each sheet.


Namaste. In last few sessions, we are studying the analysis of statements, so we have in detail studying the shipping corporation case, calculating the comparative common size as well as trend and then we went for calculation of ratios. So for Havels Ltd, we have calculated first the balance sheet ratios, three important ratios, one was current ratio, quick ratio and the third one was debt equity ratio. Then for P&L, we have calculated profitability as net profit after tax, popularly known as NP ratio, net profit before tax ratio and also EBITDA or cash operating profit ratio. Is it clear to you? Now we will continue the case and try to calculate return and activity related ratios which pick up one figure from P&L and one figure from balance sheet. So you have to keep both the sheets ready now. Now first of all, this profitability which is calculated as a percentage to sales, naturally we would be interested in knowing profitability on their investment which is called as return ratios. So we would try to calculate return on equity, popularly known as ROE. Do you remember the formula? Let us check from the sheet. So this is the return meant for the equity shareholders which is profit after tax. So we will take the final profit and divide it by from the balance sheet, we take the total shareholders funds, I will just do it again. So profit after tax divided by shareholders funds. So you get 0.27 as a percentage it is better understood, it means 27 percent is the profitability with respect to owners or shareholders. There has been a good change from 22 it has improved to 27, you can easily compare with normal returns which you get from bank FD which is 8 or 9 percent. So definitely it is a good return but there can be scope for even higher return. Now the other measure is ROI also known as return on investment or return on invested capital. So what is the formula? Instead of taking profit after tax we will take profit before tax and to this we are going to add the interest income if any, sorry interest expense if any. Now here again should we take PBT or should we take profit before exceptional items? Maybe it makes more sense to take profit before exceptional item because you are trying to calculate profitability of the business, exceptional items are not regularly going to recur, you can see it is a big amount 202. So we will go for 711 which is in the numerator, we will put it in bracket because this is a profit before tax and before exceptional items to this add finance cost which is interest and such types of costs. This is the numerator and divide it from the balance sheet we have to take shareholders funds plus borrowings. So what we are doing is in the numerator we are going to take profit before exceptional items before taxes add finance cost and in the denominator we have taken owner's fund plus debt. So we got 27 percent and in all the 3 years it is more or less constant at 27 percent. You can see here mainly it is only because of effects of taxes that there was a slight change. So this was ROE and ROI. Now let us try to calculate activity ratios. So to know how efficiently the company is using its assets. So we will go to balance sheet. In balance sheet you are having fixed assets, we will compare them with sales. Maybe from P&L it is easier because we have got a sales figure here. This is fixed asset turnover ratio as it is known as. So normally we will go for operating revenue, total operating revenue and divide it by total fixed assets. So you are getting it 5.02. Can we convert it into percent? Actually no it does not make sense because this is number of times. That means you are using your assets to generate revenue 5 times in the year. Over the period of time you will find it is more or less constant although their profits the revenues are increasing slowly the fixed assets are also increasing slowly. So more or less steady fixed asset turnover ratio. Now we can also calculate other type of turnover ratios so I will just keep them here. One is TAT that is total asset turnover ratio. So let us compare the total revenue and divide it by total of all the assets. Now naturally the ratio has gone down because in the first ratio that is FAT we had taken in the denominator only fixed assets. Now we have taken all the assets. So you can see there is a compare it to FAT this is lesser ratio it is slightly going down but it is more or less constant. So this is how now going for little bit of working type capital types of assets we can calculate inventory turnover ratio. So for inventory turnover total operating revenues divided by the value of inventory which is 6.93 or 0.7, 0.5 and 6.91. So it is more or less constant the efficiency of use of inventory had increased a bit now it has fallen. Now would you like to convert it into number of days it is known as inventory velocity. Let us try to do that what is the formula we can just transpose this take 1 upon the given inventory turnover and then multiply it by 365. So this is in terms of days so it was 52 days then it came down to 42 days now again it is 52 days. So that means any inventory which comes in remains with the company for 52 days. Same way it can also be done for daters and for other assets. Now we can calculate more ratios but we will not go into that depth we are going to consider two more cases of different companies where we will calculate much more variety of ratios. But now let us understand two other important ratios which are already calculated. One is EPS what is the formula we have discussed it earlier do you remember that is earning per share. So we take profit or loss for the period and divided by number of shares. So here you can see there was a fall in EPS from 38 to 7 and then it has increased now to 11.45. You can check the share capital which is more or less constant. So you can see here that this is the EPS as calculated by the company. There are no pending warrants etc. So diluted EPS and basic EPS is more or less same. Equity share dividend for first two years was constant in the current year they have increased the dividend to 374 and this is the tax on dividend. So they have also calculated equity dividend as a percentage to their nominal value of capital. So earlier it was 300 percent now they have increased it to 600 percent. We can also calculate their dividend their EPS which is already given and we can go for their payout ratio dividend payout ratio. Now there are two ways of doing it either we can go for DPS by EPS but right now we do not have the figure of DPS but we know the total dividend. So what we can do is take the total dividend and divide it by the available profits which is equity dividend of the company divided by the profit for the period. So you are getting 52 converted into percentage. So you can see earlier company was distributing 40 percent of their profit. Now since the profits have increased but they have doubled the dividend. So the percentage of distribution has gone to 52 percent. Is it good to have higher or lower ratio? There is nothing good or bad but higher ratio signifies that company is able to company has decided to distribute more profits. A lower ratio will mean that company is distributing less but retaining the profit for own growth. So it depends on the strategy of the company and on the opportunities which they have. So we have just calculated few important ratios here. Now in the next problem we will go for more detailed ratio taking out a particular company and looking for variety of aspects of that company. In the meantime I will request you to go through the ratio sheets which are given to you and also variety of problems which we have already discussed. Having calculated variety of ratios of profitability, return as well as the activity. Let us have a look at expense ratios. So this is our profit and loss account. We have got number of expenses particularly the larger expenses cost of material consumed. So it will be of interest for us to know cost of material consumed is what percentage of the revenue. So the formula for expense ratio is that particular expense ratio divided by sales. In this case since we know the revenue from operations and we have also been given other operating revenue we can also take total operating revenue in the denominator. So let us find the cost of material consumed as a percentage of total operating revenue. We are calling it cost of material consumed ratio. Like that you can give it any suitable name. So it is 0.52 it is better understood if we convert it into percentage. So you can see it is more or less stagnant 52.89 then 53.15 and 53.95. There is no other major expense item in the P&L the largest expense was material consumed. So that is what is required that is the way we can also link other items. But still let us link one more item that is employee benefit expense ratio. So you can see over the period of 3 years it has increased it is almost 7 percent now earlier it was 5.28 percent. So these were important expense ratios. Now let us go to cash flow statement. In cash flow we have got cash flows categorized into 3. So the most important of that is cash from operating activities. Let us see what percentage of revenue it is. So cash from operating activities as a percentage of revenue. Now it is logical for us to take revenue from operations or total operating revenue. So let us take total operating revenue we get 0.09. So total operating revenue was 5.436 and the cash from that revenue of course we have incurred variety of expenses. The final cash which came into hand of business was 0.09. As a percentage it becomes 9.64. So you can see a slightly worrisome figure here. What was 13 percent in March 14 became 11 percent and now it is about 9.6 percent. So there is a fall in the ratio of cash from operations as a percentage of operating revenue. One can also link the net cash from operating revenues to the operating profits. So if you go to PNL we have got profit before exceptional and extraordinary items to that if we add finance costs we will get profit before interest and taxes. So we get 72 percent. So out of the profits which we are reporting 72 percent is available as cash from operations for the business. Here also you see a drop earlier it was more than 100 percent then it became 90 and now it is 72 which means that lesser amount is now getting realized as a cash which is not a very positive value for the business. Like that you can calculate a few cash flow ratios of course most of the important ratios are on the side of PNL where a different type of ratios can be calculated on PNL. So we will stop here. Namaste. Dhannevar.


Hey everybody, welcome, welcome, welcome. We are live from ITW 2023. This is JSA TV, ITW Extra, powered by JSA TV, the official broadcast of ITW 2023. Again, we are here National Harbor, Maryland, right outside of DC. And I will tell you the buzz on this floor, guys. You can feel it. You can feel it. And I'm joined here, so excited to say by Mr. Juan Salazar, of course, the CEO of MDC Data Centers. Juan, welcome back to JSA TV. Thank you for having me again. We are so honored, so excited, and the news keeps coming from MDC. You guys are rocking it, but for our viewers who may not already know, and we should correct this instantly, tell us a little bit about MDC. Sure, glad to. So MDC is a data center provider. We're really focused on a particular niche, which is the US-Mexico border. And that's all we do. We're on the border, all the key locations. Right now, we're in McAllen, Laredo. We just turned up Eagle Pass, which we announced here at your show last year. And then El Paso, Nogales, Arizona, and also the newest facilities in San Diego, California. So essentially, now we're from the Gulf of Mexico to the Pacific Ocean. It's amazing. Amazing. And I don't know if there's a better partner out there to make US companies feel so comfortable going into Mexico and, of course, vice versa. So incredible job, what you guys are doing. But do tell our audience here, how does the MDC border connect platform concept and its components, and the, of course, the MDC value proposition, how does that all facilitate more connectivity on the US-Mexico border? Sure. So what we call the MDC, the border connect platform, is really two parts to it. One of the components is the physical layer, which are actually the data centers all along the border, US-Mexico border. But then there's a, I guess the sort of GUI, if you will, that allows you to turn up locations, get business for those locations. And that's just part of the whole, what we call the border connect platform. So it's the physical layer, establishing connectivity, and then helping our customers find success in those data centers and not just leaving them to fend for themselves once they've signed out as a client. That's a big part of what MDC does. Really proud of it.  But we, we, I like that play on, on active and neutral. Yeah, I love that. Actively neutral. And, you know, you mentioned neutrality, being so critical into your data centers, a platform, getting those customers to really market themselves.  So tell us specifically, how does, and in what ways does this platform really benefit carriers? And how can MDC assist in growing businesses in Mexico? Yeah, so I think the best way it does is you mentioned the marketplace, which is something that we do. It's a, I guess, a marketplace in a sense, like you normally see, but ours is different in the fact that we actually put people together, we find business, so helping our customers make their business case.  But there are no, there's no agent agreements. We don't charge any commission. We don't get in the middle. We just do the presentation. And, and we let people, you know, win the business. So people can log on, say, Hey, I need, you know, 100 gigs in El Paso or something. Then all the carriers who are customers of MDC, they get notified of that. And then they're able to bid for that project and, you know, may the best man win or the best woman win. So yeah, that's kind of it. And we, we stay out of it, just try and add value. I love that though, you're enabling business growth within your, your data centers, and it's beautiful. And it's pure clean. That's our purpose, by the way, it's to create connections that empower people to thrive. Yeah, I love that. I love it. So we spoke a little bit about it, but can you tell us a little bit more about the positive impacts on the platform, on the communities along the border, particularly, and what your future plans might be to go ahead and meet this evolving need of the telecom community. Yeah, so I'm from the border. I'm from McGowan, born and raised. So I think the impact that it has on the low communities, normally border communities aren't, we always say that we don't, we don't get the news until a week later. So I'm really proud that we're bringing like these high tech jobs to the border. And we partner with the different cities where we're at on the border, McGowan, of course, but we do things with the Boys and Girls Club, and all of that to try and promote growth in our communities. So we, we call that, you know, making a difference on the border. So I think it, and it, by the way, it works straight into our purpose. That's how we also empower people to thrive.  You're really making a mark not here, not just here in our telecom community, but within the border communities. I just, I'm such a big fan of MDC. I don't know if you could tell or not, but where can our viewers who don't know already, they can go and learn more information. Well, like I said last year, I think the JSA website, you know, your newsletter is always a good place to start. But you can find us all the usual places, right? mdcdatacenters.com, LinkedIn, I think we have a Twitter. I'm not a Twitter guy, but I think we have, right, Julio? Yeah, we're good. Yes, yes. mdcdatacenters.com for sure. Thank you so much, Juan for taking time here. It's a busy, busy day for you. We appreciate you. And thank you viewers for tuning in to ITW Extra, powered by JSA TV. Happy networking.


New York will require state employees to be vaccinated against COVID-19 or get tested by September 6. And according to Governor Andrew Gommel, health care workers who directly interface with patients at state hospitals will have to be vaccinated. The court has upheld and the Department of Justice just did a memo that says an employer can mandate an employee get vaccinated. We're taking the first major step down this road. We're saying in state hospitals where the state is the employer, the frontline workers must be vaccinated, period. Not vaccinated or you have to have a test once a week. We're taking that position like other state governments, the federal government is supposed to take that position for normal public employees. But for the public employees, the hospital workers who are front facing, we are mandating vaccinations bill. And you're right. It is an aggressive step. And there will be pushback. And I'm going to be having more conversations with the unions about it. But we know what we're dealing with, right? You have a public facing person who the public must by definition be exposed to. That person has an added responsibility of not transmitting the virus.


You just need to point your life in the general direction of where you think you need to be going next. You don't need coordinates yet. You know, when they launched the space shuttle, I watched a masterclass of an astronaut who was talking to us about space, and he said that the shuttle, the space shuttle, has a phenomenal state-of-the-art guidance system, which you can imagine it must have. But the guidance system doesn't even kick in till the rocket has left the Earth's atmosphere. Why is that? I'll tell you why, because the moon is up. That's it.