To understand the mechanics of sediment transport, it's really important to understand the fluid dynamics of the flows and the behavior of those flows. And so what I want to talk about in this video is the difference between a laminar flow, a turbulent flow, and then there's this transition in between, of course. So when we have water or any fluid, we can track a little bit of that fluid as it moves downstream in the flow. So we have a flow in this direction. And in the case of a laminar flow, the individual particles move downstream parallel to each other. So in a laminar flow, this would be a particle and it would move downstream. So if we have another particle here, it would move downstream in a parallel way. And there's actually no mixing of these particles. And I'll share a video that shows how that works. In contrast, if we have a flow with turbulence, the particles move in response to that turbulence and they don't move parallel, they end up getting all mixed up. So our black particle might move something like this. Our purple particle would have a different path and our red particle here would have a third path. And so this turbulent comes from the extra energy in the flow and bursts the flow that are at different speeds that cause this mixing. In contrast, a laminar flow is all parallel and going downstream. So like everything, most things in nature, there's not a strict division between laminar and turbulent flow. And we have between these two transitional flows. And these have characteristics of each of them. So if it's a transitional flow that's close to laminar flow, you might have your particle moving downstream but not in a straight line. So the paths aren't exactly parallel, maybe something like that. And there can be maybe a little bit of mixing, something like that. If you have a transitional flow that's really close to a turbulent flow, you'll end up with a lot more mixing. But maybe not as much as a fully turbulent flow. So you end up with these different possibilities and the behavior of a particle. This could be, for example, a particle of water that you're tracing or maybe a particle that's suspended in the fluid. These characteristics strongly affect sediment transport. Thanks for watching.


And it is the 2 p.m. Update with David White here at TFN and of course we're all holding our breath as we wait for the Fed minutes to come out we'll see what they have to say a lot of reading the tea leaves anyway other than that we've got just about what you would expect for a day before Thanksgiving and that is ultra low volume we're doing about four point excuse me five point six billion shares on the CBOE volume we did almost ten billion yesterday so with two hours left to go you got only about sixty percent I mean yeah you got about sixty percent of the time gone out of six hours so yeah maybe get eight and a half maybe nine billion shares my guess though is we'll get a little bit of a kick I don't see anything getting the wires just yet so maybe that'll happen here in a minute or two but that's kind of it we're waiting for that we've gone up on very light volume over the last couple of days only open a half day on Friday for trading TFN is closed but that's kind of it we've got a market that's kind of flat ish got pushed down a little bit not a lot of volume one of the things I pointed out in the newsletter this morning was the preponderance or huge percentage or bigger percentage let me say of Wall Street being part of the volume the dark pool which is generally what the big guys trade with is up about four or five percent higher than it generally is on average over the last few years and that says that either the pros are trading a lot more or the retail trader is not that enthused to buy highs especially going into a weekend of course I can expect that probably Monday or maybe even Sunday night we're going to have some fairly brisk action that's going to be on the early reads for the retail numbers and what people are doing for Christmas so I get ready get a lot of sleep probably going us in the den Sunday night we'll be back in a minute with the show the reality is that navigating


This is Bill Doyle and, for my knowledge, along with Sophie, who's known so for being a student in my class and a very fine student. We became very interested in Catherine Patterson's book. And why did this strike take place, Catherine? Well, the strike in Lawrence in 1912 took place because the conditions were absolutely measurable for the workers. They had come from many countries, speaking many languages, because the mill owners thought if they spoke that many languages, they couldn't possibly talk to each other and start a strike, but they were wrong because they did start a strike and they did communicate with each other because the conditions were so terrible. And they were working many hours every week and not making enough to – it was really pretty – starvation wages.  So they decided they had to strike for better working conditions, better – Oh. I told Sophie one of the reasons I became interested in your book and what you're good at in thinking. We appreciate the work that you have done, not only this book, but all the books that you have published and your credit to this – Well, you're kind. Thank you. Good to watch it. Anyone who lives in Washington County or the state of Vermont, but I became interested because my senior thesis at college was the other side, Cold Strike of 1902. And some of the things, the themes that ran through the Strike of 1902 books were so intense that it had to be settled by the President of the United States, Wilson. And so I – and some of the things that you write about in your book about conditions between labor and industry are very much today and being thought of today. And we both thank you so much for the book that you've written. Well, thank you so much. And I think what they have in common is the greed of the wealthy. You'd think they had plenty that they could spare some to pay their workers proper wages, but no, no, they needed more and more and their greed was what defeated them really. You have some great examples of that in your book. One of them is the discussion of Rosa, the lead character talking to her teacher. And her teacher says, oh, well, you know, the boss thinks his workers are good people and he's going to try and support them. And she says, well, mama makes $35 a month and 25 cents and he charges $30 for the rent.  You're living in a single flat with another family and nobody's got bread and you describe it so beautifully. It's really touching in this book about, you know, when the children arrive in Barry, the you know, the gentleman who meets them at the train station says, well, where are the children's bags?   Their shoes aren't going to work here. They don't have socks. And it was beautiful, too, that in the story there was a Jake or Jack, the boy lead. He has worked in the mills as a 14-year-old boy, maybe. And he's never had a pair of socks, wool socks. And so when he comes to Barry, he gets this pair of wool socks. And I think that's very, you know, explanatory of a lot of the experience of young American workers these days. And I think this book is totally relevant in that because these old Italians had this incredible wisdom about the heart and the beauty of humanity being stronger than the force of capitalism. And that was, I think, in the end, the only thing that gave them actual strength because they so obviously had nothing. I mean, did you feel that there was a turning point where they realized their desperation was, you know, in vain if they didn't take it seriously? Well, of course, to give up your children to someone else of care, somebody you don't know, somebody in a distant city shows how desperate they were. And I think they did it because they cared about their children and the fact that their children were cold and hungry, but also because they knew that if they were that desperate that the newspapers would get involved. And they needed the newspapers to see how desperate the situation was because they newspapers could tell the world that what was happening in Lawrence. So they were media savvy. It seemed like there was real national recognition of this. There finally was, yes. And it was because of the case that that was being experienced across the nation or was it because Lawrence was really an example of how bad it could get? I think Lawrence was an example of how bad it could get. And the turning point for the strike was that they had already sent children to New York and to Barrie, but they were going to send children to Philadelphia. And so the parents brought the children to the train station and the police and the guards, national guards, confiscated the kids, right? Yeah, took the kids away and beat up the parents and put them in jail. And that just exploded all over the national press. It's like something we've seen recently in this country. Well, you know, it just sort of breaks your heart that a book like this written about something that happened in 1912 could be relevant for today. We, you know, we hope we've gotten better. We hope we don't treat children this way anymore. We hope that we're humane towards those who work for us and on whom our life depends. In livelihood, I mean, we all need each other, right?  Well, there were other strikes in 1912. One of them was one that I studied at college, just to think. And there was so much violence and national concern that it finally was settled by the president of the United States, Deirdre Roosevelt. And but for that intervention, no one knows what would have happened. Yeah, well, and Taft, who was president at this period, he invited, and this is maybe a question you were going to ask me later, but he invited representatives from among the strikers to come to Washington and testify about the conditions. And one young girl whose hair had been, you know, she'd been scalped by the machine. She was scalped, right. Yeah, was among the young people who went down to testify. And they testified for Congressional Committee, and then Mrs. Taft invited them to the White House for tea. Amazing, right? Right, these tatters. In about 1960, a reporter began to get interested in the strike and wondered why we didn't know more about the strike. And he heard that the daughter of the young woman whose hair had been pulled out was still alive, and he was thrilled. So he went to Lawrence to interview her, and she had never heard the story of her mother's injury or of her mother going to Washington. Oh, my goodness. Now, I'm a parent. I cannot imagine that if I'd been scalped by a machine and had been taken to Washington to testify before Congress and to have tea at the White House, I cannot imagine that my children would not know that story.   So the fact that after the strike, which was one of the most successful strikes, if not the most successful strike, they got everything they asked for. It lasted for months, right? Yeah, four months. Yes, almost between three and four months. And the dead of winter, of course. Yeah. It was over in March. In March. Towards the end of March. So, and it started before Christmas, I think. But even though it was successful, they got everything they asked for. They should have asked for more, but they got everything they asked for. But the church said those leaders were communists and anarchists. Marxists. Marxists and atheists. So your anti-church, if you were for the strike, and the government said, well, no real American would go on strike and disobey the law and not obey the police. And so therefore, you're anti-American. And they had this big, all-American parade to shame the workers who had won the strike. And so the workers didn't talk about the strike. They didn't even tell their children about their success. So Catherine, earlier in the program, you talked about Lawrence, Massachusetts. And they sent children away from Lawrence, explained the circumstances why a city would ask children to leave. Well, the city didn't do it. The strikers did it. One, so that the kids would be warm and have food, which they certainly did, when they came to. In fact, after the strike was over, it was said that the parents who met them at the train didn't recognize their own children because they were rosy cheeks. They looked beautiful. And beautifully dressed. Thank you, Barry. Thank you, Barry. It's such a wonderful job. I mean, the generosity, I lived in Barry for 28 years. I never lived anywhere. You grew up traveling, right? After that long. Yes. I lived in many, many places. I will always think of Barry as my hometown because I've lived there so long. And I'm so proud of Barry and Barry history. Oh, it's gorgeous. We're all proud of Barry. Yeah. And I just, you know, I want all of them. I brought the whole world to know the generosity of those Italian stone workers. They didn't have to be good to the poor, ignorant, southern, Italian, emerald children. But they, you know, they took them into their own homes and treated them as though they were their own children. So how many children did Barry take? 35. And did any of those at 35 stay? None of the 35 stood. And in my book, which is fiction, Senator Joy, in my book, there's a boy who stays. And I wanted somebody to stay in Barry. I mean, that's as a writer and as a person who loves Barry, I wanted one of those children to be able to live out their lives in Barry. So I had to invent a child that nobody would miss if he didn't go home. Now those actual 35 children were going back to loving homes. And they would certainly have been missed if they hadn't shown up. So I had to invent somebody who stole away on the train, so nobody knew he was there, who kept himself out of sight of people who were counting heads and who somehow would remain in Barry and belong to Barry after the strike was over. That was just my privilege as the writer of work of fiction. So how was the strike finally settled? Strike was finally settled because the owners were brought to the table. And I mean, they weren't making any money when those mills were closed. How does that line go? The sound of silence, right? They will understand the sound of silence. I love that. When there's no hurrying in the mills. Yeah. And there's no change in their pockets. Then there will be brought to. And I think they thought, you know, it's dead or winter. These people aren't going to last. Yeah. And they did last. And partly they lasted because of the generosity of workers from our home. They were sending soup. They were sending food. I have a list of the articles in the Barry newspaper. They're having all these activities at the Socialist labor hall to earn money to send to the striking workers in Lawrence. The family in Lawrence. So, you know, there was a cooperation all around you, England, among other workers, to help the workers and strike the workers. So what's happening in the mills and the mills where people work, the working conditions and so on? I'm sorry? Can you say anything about the working conditions? Yes. Go ahead. Oh. They were pretty awful. I mean, there was not much safety. They weren't worried about the safety of the workers. Workers got killed. Right. You had the example of a fire breaking out in the woolen mill. Yes. And the main lead character's father was killed in that fire. And left a single mother with four children. Yeah. And there wasn't any compensation. Right. Insurance policies or... We have done better about compensating people for deaths at work or injuries at work. That's one thing we've done better at because in those days you get killed.  That's it. That's it. Right. Well, it was... Super damages. Similar in Barry, right? A lot of... I mean, the life expectancy was like 40 years old at that time in 1912 or 1918. No. And of course the stone workers. Right. They all got silicosis. Some got silicosis. But it... You died young. Yeah. I loved your tribute to the carvers. I, you know, enjoy the stone a lot. Just even the closing line of your book is so beautiful about... You know, well, I'll read it because it really is... The English... Oh no, that's the historical note. Ah, I should have marked it. And Jake Beale began to run even though his new boots sometimes slipped on the icy cobbles. He did not stumble. How strange. How wonderful it seemed to be running not away from petty crime or deadly fear, but toward a new life where bread was never wanting and roses grew on stone. In stone. And roses grew in stone. And I thought that was really beautiful because that was, you know, the whole beauty of their message of the humanitarian aspect of workers and their need for bread and their need for warmth and their need for wool socks. And, you know, it's been an issue for the labor movement always to be seen as human. And to have those parts of our, you know, experience really recognized beyond, okay, well, the boss can afford five cars and whatever about the rest of us, you know. So I really appreciated your writing about Barry, too, because I think it was important to recognize that individuals in Barry had taken the opportunity coming to a new country, learning new skills, participating in a new economy, and actually owning small businesses themselves. And so this was a major step that a lot of Americans in more industrialized areas like Lawrence, I suspect, didn't understand they had the right to participate in. So that was beautiful. Yeah, you really blended things so well in this book. I am thrilled that you wrote it. Thank you, Sophie. Thank you. Who took the lead in settling this great? Well, the wobblies, you know, the workers. The workers. Had come in and helped organize these disparate languages and nationalities and religions and everything that the workers represented and helped them plead for what they wanted. There was a local man who had actually started the strike, but he knew that he didn't have the skills to organize it in a way that it would be lasting and it would really make a difference. And he was arrested early on, right? Yeah, yeah. And so, you know, the three leaders of the strike were arrested for the death of the woman that had been killed by the National Guard. And that was in the first week, right? Something like that. Yeah. But they kept sending messages from jail. Telling people what to do. And one thing that's kind of wonderful is the singing. Oh, well, yes. And of course, this was very much of the women, because many of the workers, of course, were women. Interesting. In the pictures of the strike, you don't see so many women. You see the men. Oh, interesting. But more of the workers were women. So I don't know why. You know, maybe men always get the attention. I don't know. But anyhow, they sang. And somebody said, I don't know whether it's Helen Gerlachlan or who it was, said, you can't defeat a movement, a singing movement. Right. And I think about that in the civil rights movement. My husband was in jail during the civil rights movement. And he said they crowded them all into this big cell. And there was not room to lie down or even sit up. So they just sang all night. And he said, it ran the jailers crazy.  And they were just singing and singing. And you know, there is something rather wonderful about people who are singing. Was it Estonia that separated from Russia through the Singing Revolution? Oh, really? Yes. There's a movie made about it. It's a documentary. Oh, I haven't seen that. And when Russia started to become, you know, different countries again instead of the USSR, Estonia was, I think, the first country to initiate that with the Singing Revolution where, at their main yearly gathering, there were something like 25,000 people singing the national anthem, a new national anthem together. And the Russians literally started like freaking out and leaving the country by foot. You know? It was fabulous. Explain who the presidents were at the time. Well, Taft was the president in 1912. And you know, I remember Taft even when I forget his name because I was part of a book on the White House. And he couldn't get out of the bathtub in the White House because he was too fat. So they had to build a new bathtub in the White House that would accommodate his body. But he was, and Mrs. Taft, I think, was very instrumental in bringing the strikers to Washington to tell about the conditions in the mills. So the president, to some degree, played a role in the second. Yes. He did play a role in it. And I think this is still happening where you have major discrepancies within the union or corporate entities where you have a town like Lawrence where maybe people don't know what the laws are and who cares.  And they're not going to let you mess with them. And that's it, you know? It's like, these are the laws. No, you abide by them, so do we. Period. And that was also very well described in your book because Berry really didn't see that kind of poverty. No. We've asked you a lot of questions. I don't know any questions we should have asked you. Oh, Kevin, I'm always hoping people will ask me questions because when they say, what questions should we have asked you, I think, I don't know, what questions should they have asked me? Is there another question that I should have been asked? Well, I don't know. Was there, I guess this here it says, what was the outcome of the strike? What happened after the strike? That's what I was saying, that they were made ashamed of what they accomplished. And do you have an example or two maybe where the people were... The girl who didn't know that her mother... Oh, right, that was a perfect example, sure.  It sort of dropped out of the history books. We don't do a lot with labor history in our history books. No, we really don't. I mean, when I was being taught history was there was this war and then nothing happened. And then Goody, another war. In like 1970, right? So what's happening to the ordinary people gets dropped out of the history books, I think. And it wasn't until the 60s and 70s that people began to think, why don't we know about the large strike? Because it was a very important strike in labor history. Huge. And they began nosing around. And when I was working, I started writing about it because I saw the picture of the children standing on the steps. Which is a beautiful picture. You know, I just... But here's the old one. I had chills going down my spine. I said, there's a story in that picture. I've got to find out what the story is because I didn't know the story. You mentioned people not being taken out of history. These days, some prominent people are being dropped from being in history. And that's just some more reason. So it's imperative that the press and all the people involved should reason why history shouldn't be kept alive. History should... We've got to learn from our history, don't we? And it really bothers me that this book is so relevant for today. Yeah, it's stunningly relevant. Yeah. And a lot of... It's interesting to me how you've tucked in these little pieces of wisdom that are very... This book was written for young adults, right? And so it has a lot of wisdom. Like, I'm not a parent, but if I were a parent, I would want my child to understand that their thoughts are where their life is going to go. And that their camaraderie with their family is really the most important thing, even if circumstances are difficult and your education also is imperative. And it will be sought after by many groups who need your assistance as either smart or crafty or capable or whatever the different talents individuals have. And so I just really appreciate you putting this beautiful book together for young adults to learn from the history, but also from somebody who's experienced a lot of life's quirks and curves and been able to describe them, you know, in a very helpful way. Well, I love your... Well, the follow-up was what Sophie just said. So some things that we've talked about that we should have brought up in this interview. I don't know anything... One thing I did think about while Sophie was talking was that two years ago, I think it was, I was chair of the National Book Award Jury for Young People's Literature and the winner was Senator... I mean, Congressman who went through the civil rights movement and he got up there with his acceptance and he said... He said, do you know what it means to me to win this award? I was a sharecropper's son and I went to the local library and they said, it's for whites only. You can't come into the library. My teacher told me that books were important and so I read everything I could. Right. And here's a man who's changed the... The face of the demographic of writing. Yeah, he's changed the course of our country in many ways. Sophie, I should thank you for writing the beautiful book. Oh, well, thank you for appreciating my book.  I'd like to think that historians would approve of my fiction. Yes, we like it. Thank you for joining us. Oh, well, thank you so much, Sophie. Thank you so much for coming. Thank you so much, Stephanie. Oh, thank you. I want to see...


The Floyd County Fiscal Court kicked off their annual spring cleanup this Monday, April 15th. The cleanup allows all Floyd County residents to dispose of trash for free all week long at Waste Connections in Martin, and pickup is also available. So, uh, the dump at Garth is taken, any and everything, except tires, appliances that has free on, nothing with oil in it. But household goods you can take, and if you can't bring it yourself, then we have a crew. A mattress, have a crew, or have a litter maintenance crew, that we'll pick it up for you. But you have to have it out in your yard, you know. We can't go in your house, uh, uh, and get it. But if you will bring it outside and put it in a pile, we will pick it up for you. At Audiology Associates of Prestonsburg, you can live your life the way you want and find the freedom of better hearing. With 40 years of being in the hearing care industry, you'll experience patient care that is specific to you with exceptional follow-up care that ensures your hearing and balance needs are being met. Audiology Associates at 1428 Northlake Drive in Prestonsburg. In addition to biannual cleanups, the county offers free dumping once a month. In March, the county collected nearly 91 tons of garbage, completely free to Floyd County residents. We're just trying to clean our community up, you know, and get people to have some pride about what they're doing, and this cleanup helps the folks that really need that can't get it out, can't haul it. This helps them. You know, we're never going to grow if we can't change. We're wanting tourism, we're wanting to invite businesses in our county, but you know when they come in, they say, gosh, it needs cleaned up. So Judge Williams took that ball and run with it, and we haven't looked back since then. I know it's nothing that's happened overnight, but we are, we're having a lot of success with it. For dumping hours or to schedule a pickup, call<PHONE_NUMBER>. Reporting for Mountaintop News, I'm Brianna Robinson.


the question from there, if you could please ask the question. Sir, from Kakinata, go ahead. Second order differential equation using op-amps is accurate, which gives full explanation about all these things. How to solve second order differential equation using op-amps? This is our question, sir. Yeah, a differential equation essentially has various terms which are second order, first order, constants and so on. The equation says that the sum of these quantities must be equal to some forcing function. So, we know that how to produce an output such that the two inputs are equal. So, finally, if you give two inputs to an op-amp, its output will change in such a way that the two inputs must be equal. That is equivalent to the equal to sign in the differential equation. Now, all the terms on the left hand side and the right hand side of the differential equation can be implemented using the kind of circuits that I had. So, to give you an example, suppose you have a very simple equation saying that this second order differential is equal to some positive or negative. So, you will take the second order difference, create the second order differential equation and put it equal to a constant and put the feedback such that the two must be equal. Now, the voltage at which it settles, you will notice that in order to use these differential equations, you will have to use c and r. Suppose the value is positive, in that case you will get a voltage which is exponentially varying because the solution to a second order differential equation with a positive value is indeed exponential. If the value, if the constant is negative, then you will find that you will get an oscillatory circuit. So, the output voltage will then be a solution to this differential equation. Indeed, any old equation differential or otherwise can be solved. There is a left hand side, each term can be implemented using op-amp. There is a right hand side and each term can again be implemented using op-amp and now we want to force them to be equal and therefore, you use a feedback which will ensure that the two are equal and the voltages which satisfy this equality is indeed the solution to this. So, by constructing a circuit where each term is represented by an op-amp circuit and by forcing the two outputs to be equal using feedback, we can construct a differential equation or any equations. Sir, thank you. SVNIT Sura, we are connected to you, we can see you there. Could you please go ahead with your question please. Hello sir, my question is related to the morning session, FET characteristic, wherein it has been said that at the pinch of condition, the effective channel width at the drain and almost touches. Now, if it is so, then there is no path for the carrier to flow from source to drain, so the current has to be zero, but rather it is seen that it is almost remain constant. So, I just want to get the idea that how it is possible, over. Yeah, let me answer this question. In fact, we had a slide on this. Let us take two situations and this is your P plus which is the gate and of course, it is symmetric, so there is a gate at the bottom as well. So, let us say you are at V D sat and the depletion region looks something like this and here is the pinch of condition. Now, at this point and if you make V D greater than V D sat, what happens is this pinch of region extends just a little bit, not too much compared to the channel length. So, let us plot, let us sketch that as well. So, what has happened is the most of this channel is not really, there is no real difference between these two situations except at the drain end. Now, although it looks like these two regions have touched and it looks like there are no carriers there. If you expand this region, you will see that there is actually the electron density is not exactly zero, but there is a small opening there and then there are electrons going from this channel all the way to the drain. Now, this is something that you, it is difficult to understand analytically. So, what people do is they have numerical solution, numerical packages to solve these problems and then you can get a more clear picture, but this region which we call the pinch of region is not completely devoid of carriers. Otherwise of course, as you said the current will actually drop to zero, that does not happen. So, what happens is there is a very high field region here. So, any additional voltage like V d minus V d sat will in fact, just drop across this region and most of this channel will remain the same as before and therefore, the current really does not change. So, the key is that this although we say that it is a pinch of region, the number of carriers there is not exactly zero and then there is a small, there is a small region where you have carriers and which are going from the channel region to the drain at high speed, because the field is high. I would like to add just a little bit of point. This is of course, an excellent explanation that has been given, but we should ask a more fundamental question from ourselves. What is a depletion region? What causes the depletion region to be there? It is because of the p n junction effect, the field have removed the carriers from that region. Now, this depletion region is caused by the vertical junction. What it means is that the average concentration of carriers in this region is exceedingly small. However, in this little tip here, carriers are coming in here, in this tip carriers are coming from the left. What it means is that it is depleted because of the vertical field. That means no carriers are left from the original semiconductor, but there are carriers arriving here. Because the field is very high, they will be swept across very quickly indeed. Therefore, the net concentration of remaining electrons in this region continues to be very small. That means it is still depleted. However, the current is kept constant because the velocity is very high. Remember, the current is given by the product of the number of carriers and their velocity. The number of carriers continues to be extremely small, which is characteristic of depletion region. Notice even in the regular depletion region, this value is not 0, it is extremely small. However, the field is so high, the voltage drops across such a small region that the velocity is extremely high. That is what makes the current continuous. It is continuous at the value at which it was just before arriving at this tip. That value is the id set. Therefore, the current remains constant at id set rather than dropping to 0. In fact, this is exactly the same thing which happens in MOSFET devices as well. Thank you, sir. It is over. Go ahead with your question. Sir, what is the virtual ground concept? Can you explain? I think we did it briefly, but let us look at it again. Here is the op-amp. Suppose the voltage at this end is some v. Call it v1. And you have some negative feedback here in the general case. Let us not talk it, talk the other case I had worked out in full detail. But let us say some general case in which the output has a connection to this inverting input. Now, we know that no current can flow into this op-amp. Therefore, whatever current is coming in here must be carried out and this output itself must adjust itself to carry this current out. Now, should there be any voltage difference? So, let us take a numerical example which will make it quite clear. Let us say this is 1.0 volt. Suppose this was 1.01 volt. Now, the gain of this is very high. Rather than infinite, let us take some 1,000 or 10,000 which is typical of op-amp that you will get. This means that the output starts going towards minus 10 volts from 0 and that because it is connected through some negative feedback. As the output starts going towards large negative values, it pulls this voltage down because these two points are connected through some network. And it will pull it down till this point reaches exactly 1.0 volts. Once it reaches 1.0 volts, the output is 0 and there is no need to pull it down any further. Similarly, was it 0.99, then the output will go positive, pulling it up and it will pull it up till it is exactly equal to the input. So, in short what it says is that if there is a negative feedback, the output adjust itself in a direction such that it brings the voltage at this point equal to the voltage at this point. This is called a virtual short. These two points are not connected directly to each other. They are not shorted. However, the output is guaranteed to behave in such a way that it brings the potential at this point exactly to the potential at this point. That is called a virtual short. If you help for op-amp, you can able to amplify tc signals also, but is it does not affect the biasing circuits? In the initial stage of differential amplifier, we will have dual input, balanced output and dual input and unbalanced output. Yeah, it is clear that we can amplify dc inputs, but the point is because of the virtual short, these two inputs are at equal value and differential amplifiers are indeed designed to be tolerant of changing the bias potential as long as the two potentials are equal. So, if there is no differential voltage, but the common mode voltage varies all over the place. The circuits inside the op-amp are so designed that they are tolerant to this. The details of this we will probably do in one of the lectures where we see how differential amplifiers are made, but just because you have raised this question, consider this configuration which is quite often used where there is a current source in common of the two emitters. Now, as long as these two voltages are equal, it does not matter what their absolute values are. If they are equal, then both will both branches that means this branch and this branch will carry equal current. So, therefore, their biases will continue to be i by 2 where i is the current drawn by this irrespective of the actual voltage here. So, circuits like this are used inside the op-amp even though the absolute bias voltages change, but the amplification of the op-amp is unaffected. Therefore, an op-amp has to be carefully designed so that it is tolerant of changes in the common mode voltage. The feedback ensures that the differential voltage is kept to a very small value because of the virtual shock. So, the bias does change, but the circuit configuration is such that it is tolerant of changes in voltages, their current bias normally and the amount of current remains the same irrespective of the common mode voltage as does this. To a logarithmic amplifier, how to analyze the sort of circuit? We have not done non-linear amplifiers. A later lecture will take care of these, but the way of analysis is no different. You just have to assume, if there is negative feedback, you just have to assume virtual shock and equalize the input current to the output current. These will now be non-linear functions, but when you equate the current, then you will get the expression of output voltage versus input voltage. Gallium arsenide with silicon or germanium, what kind of bonding it is difficult to understand? So, these are called amphoteric dopants and if silicon replaces gallium, then it has a valency which is higher and now it will become a donor. On the other hand, if it replaces arsenic, then it will become acceptor. So, silicon has the capability of being both a donor and an acceptor in gallium arsenide. Such dopants are called amphoteric dopants and the actual technological process favors depending on the temperature and other conditions. It favors the replacement of either gallium only or arsenic only with silicon and the result is that silicon will show up either as a donor in the previous case or as an acceptor in the latter. We are connected to Jaipur college. Could you please ask your question? Sir, my question is from semiconductor physics. Sir, according to Hall, the holes are not vacant spaces but individual particles which have mass and the positive charge. So, when a p-type specimen is there and a hole travels around the circuit and it reaches an ohmic contact, how does it enter a metal because metals don't have holes? So, that is my question. The answer is simple. You have not understood Hall properly. You can explain the situation by an equivalent one where the hole is considered as an actual particle. It is not an actual particle. In the beginning of this class, if you had seen, I had explained what the situation is. Let me just hark back to that just a little bit. Essentially, you have a whole network of silicon atoms. Now, suppose you have made, you have created an electron hole pair. That means, one electron from here, let's say, has gone away as a free electron. This leaves this region electron deficient and therefore, there is a net positive charge at this location. No physical particle, the nucleus has a certain amount of charge and the net negative charge in the electron cloud is less by one electron charge. If I now apply a field, then these electron clouds will all be deflected. They will be attracted towards the positive plate and repelled away from the negative plate. As a result, if this was the original, if this one was the original electron deficient atom, electron cloud will be deflected this way and as a result, this will now become the electron deficient atom whereas, this will have a full quota of electron. Now, this is a bit of an oversimplification. I am talking of a transfer only between nearest neighbors, but the wave function in the valence band is actually spread over many, many atomic sites. That means, an electron does not belong to one silicon atom, but it belongs over a very wide region. Its wave function is spread out. As a result, what moves is the deficiency of electrons in position because it moves it is not an ionic charge, it is a hole and the hole itself is not a particle. It is the absence of an electron from a particular position. You have this interesting question of what happens when it reaches a metallic contact. Essentially, what happens is that this silicon in touch with this metallic contact is now electron deficient. There are lots of electrons in this metal and an electron, the potential is such that an electron from the metal now drops into this. That means, the electron deficiency is now over. There is no atom which is electron deficient. The electron deficient atom was here and the deficiency moved in this direction because the electrons moved in this direction and now this was the electron deficient atom. There are zillions of electrons in this metal and you have applied a potential which means that this is negative and you had positive here. That is how the positive charge has moved in this direction. Now, an electron will come from the metal and fall into this electron deficient location. Therefore, it will appear as if the hole has moved away out of the semiconductor and into the metal. That is how the conduction will take place at the quantum. Sir, my question is again that a vacant space, that is a hole, can be replaced by two kind of electrons. One is a mobile electron that is free in the specimen and another is a bound electron that is coming from a nearby bond. That means, it will have to break the bond and replace the hole. So, now these two kinds of electrons, the quantum physics cannot be applied. Similarly, to a free electron and to a bound electron. A bound electron has a different application on the quantum physics. So, that is my question. Again, the same way I am just… Indeed, the two cases are widely different. In one case and let me go back to the picture that I had drawn earlier. This was the situation and let us say this silicon atom is electron deficient. If a free electron happens to wander here and is captured here, the free electron has vanished and the electron deficiency has vanished. This is called recombination. This is the reaction we started with. That is to say an electron and a hole have recombined. The electron is not there anymore. The hole is not there anymore. I notice from your question that you keep on talking of vacant spaces. It is not a question of vacant space. It is a question of charge deficiency, negative charge deficiency. It is not a special, it is not a mechanical factor, but the charge density factor. Now, this atom is no more electron deficient and this free electron is not available anymore. It has got bound. This is a case of recombination. The electron and the hole have recombined and because this is a more stable configuration, it will give off some energy which will appear as added vibration in this lattice. The other case is that the electron was not free, but bound and that is the case that I was talking of earlier. This is an electron bound to this atom and it has moved from here to here. As a result, this position is no more electron deficient and this position is now electron deficient. That is therefore, an electron movement from here to here is equivalent to a hole movement from here to here. That means, when a bound electron moves, that is exactly equivalent to a hole movement. Whereas, when a free electron moves into a hole, that is a recombination. So, always we treat them differently. We are not saying the two are different. Two are the same. Thank you very much. Do I see Srinagar, could you please ask your question? Yes, good afternoon. My question is to Professor Patil. I would like to know about, in case you are increasing your drain source voltage excessively, means it is greater than the V D set. If you once again look into the pictures you mentioned, where you represent picture A, B, C and D for different characteristics, for different behavior of JFET at different drain source voltage for constant gate voltage. So, if we exceed the pinch of voltage and we move further with drain source voltage high, would you expect eventually it would break down or would it continue to have a constant current over to user? The question is what happens when you keep increasing the drain voltage? Doesn't the junction break down? We had actually discussed this a little bit in the morning. Let me repeat this. So, let us say your gate voltage applied is, let us say minus 2 volts. And for minus 2 volts, your characteristics, the IV curve looks like this. I D versus V D and let us say eventually the drain junction, drain voltage becomes so high that this, let us say the breakdown voltage is 12 volts. So, when the drain voltage is 10 volts, this 10 minus, 10 minus minus 2 will give you 12 volts and then this junction will break down. So, at this point what happens to the IV characteristics is the current, the drain current, very large current will flow because the junction is not insulating anymore. I am going off. So, what happens is the drain current starts rising and in fact, it rises without, almost without any control and that is the manifestation of the breakdown process. And of course, this area is to be avoided. We do not really operate the device in this region and if you continue to increase the drain voltage, the current will eventually become so high that the device will just burn, melt away or something. Okay, over to you. I am related to this. If we go on changing the gate voltage, would you expect that this breakdown voltage would also change with gate voltage? Okay. All right. The question is what happens if I change the gate voltage? Let us say instead of minus 2 volts, what happens if I change the gate voltage? So, instead of minus 2 volts, let us say I have minus 3 volts, right? So, in that case, what will happen is the I V curve will now be another one. Bike is... Can you hear? Can you hear now? Okay. So, if I change the gate voltage, let us say from minus 2 volts to minus 3 volts, I am now on another I V curve, I D V D curve and now this same breakdown voltage will reach at V D equal to not 10 volts, but 9 volts. So, when I reach 9 volts, now it will break down. We will see these little differences in the breakdown with respect to gate voltage. Okay. My question is related to the placement of pin 741 operational amplifier wherein we use pin number 2 and 3 for the input and pin 6 for the output. My question is that is there any reasoning in picking up 2, 3 for input and 6 for output? I mean why not 1, 2 for input and 3 for output? Over to you, sir. The reasons for this are rather mild. Indeed, there are op-amps in which other pins are used. You are talking only of one op-amp. So, there are, for example, quad op-amp packages in which very different pins are used for input and output. So, there is nothing holy about pins being 2 and 3 for input and 6 for the output. However, there are a few considerations which apply to the choice of input and output pins. And some of these, if they can be met, are indeed observed. We would like a balance as far as possible between the inverting and non-inverting input that keeps essentially the symmetry and therefore, the common mode rejection ratio high at all frequencies. As a result, you would like a, as far as possible, a symmetric placement of the circuit with respect to the positive as well as the negative input. Therefore, in the early designs, it was put on the middle somewhere on pin 2 and 3 because on the die itself, the connection is not linear. As you see in dual inline packages, the pads are actually surrounding all around a chip and these are towards the center of one of the arms of the chip. The output is generally kept far from the input to avoid any inadvertent feedback so that it does not start oscillating at high frequencies due to some parasitic feedback. So, the general consideration is that the two inputs must be symmetrically laid out and the output should be reasonably well separated from the two inputs. Now, whether it is exactly fulfilled by pin number 2 and 3 and 6 or any other pin, that will vary and indeed if you look at some more modern integrated circuit, then you will notice that it does not always follow these pinouts. However, because 741 was the first widely used op-amp, many of the circuit use that layout and if you wanted to make a replacement op-amp in which you can just pull out the 741 and put in the new IC and now have better performance in frequencies, flow rate or what have you. Therefore, it was important to keep the same pin out and therefore, a large number of modern ICs have also mimicked that same layout, but that is not a fundamental consideration. The fundamental consideration is that the inverting and non-inverting inputs must be symmetrically placed and the output should be well separated from this. Thank you sir. Another question is related to the operation amplifier. We understand that this slew rate is an inherent property. Would you suggest something that this slew rate can be increased while putting some external circuits around this like we do in transistor biasing. So, is there any alert net for that? Over to you sir. Actually this question requires discussing the circuit on the inside of the op-amp which we have not yet done. However, just to give you a brief answer since you have raised it, the easy way to increase the slew rate is to increase the bias current of the differential stage because the output is then charged by this bias current. The maximum current that you can get out of a differential amplifier is the tail current since the total current is limited by the tail current. So, by increasing the tail current you can increase the slew rate. However, this will increase the power dissipation as well. So, there is a tradeoff between slew rate and power. There are some dynamic slew rate compensation schemes and so on, but I think really that we have not yet reached a level in our discussion where we can meaningfully describe those circuit tricks. There are circuit tricks which allow you to temporarily increase the slew rate when it is required. Thank you sir. Thank you very much.


This is the animation minute as always let's start with jobs this time. It's Super Spline Studios They have a third annual paid games animation internship program. We'll check it out on that link and They're also looking for a super technical animator Half mermaid productions is looking for a lead animator to work on their third-person horror game Blizzard is looking for a mid-level gameplay animator Warner Brothers animation is looking for an animation lead for the wings of fire adaptation Do you know spine and are you a 2d animator? Then this is for you Wild brain is looking for 2d harmony animators Good post about creators pitching for animated shows now off to art This is awesome. I love this. It's a great cycle and you know and we can't go by without pixel art And this is about retro point-and-click adventure game called Lucy dreaming go check out the Kickstarter And yes, I'm the pixel art post this is 16 minutes of Rick and Morty in a pixel art fashion It's really really cool. Check it out That's right another one. Come on. This mock-up is fantastic. Love the colors. I would totally play this Here it just says design variations for bunny, but I thought they are so cute. I wanted to include those They're so cute. Love them And as for someone who can't draw I'm always fascinated by thumbnails and quick sketches These are great just telling you exactly what you need to know You can see how the quality and the detail has advanced there And that is that the short and sweet animation minute and you can find it every Monday on my channel