One day one of their babies grew up and like almost had all its feathers and they were taking care of it and they were doing so good and then the baby died. Hello my fellow snippers, flighters, and hatchlings. My name is Marlene McCown. Welcome to my channel. I can't wait for you to see who's going to be in the video today. None other than my little Finch. I call Finch Finchy and why I came up with such a generic boring name. I'll tell you in a second. But anyway, if you guys are new to the channel don't forget to subscribe, put on those notification buttons. I love sharing my life with birds and you know just kind of educating you guys and showing you guys through entertainment how to live with birds in your house. If you love animals then you're really gonna like this channel. But before we go on for all of our new hatchlings here on this channel I just want to go into real quick what Engage Not Caged is. It is my platform, my hashtag, my slogan, what I believe in. Engage Not Caged is living in a house with birds and not specifically not caging them. My birds have cages that they love to sleep in but my birds kind of have the choice to go in their cage or not. Like their cage is like their bedroom. They enjoy it. They like to play with toys in there. But I honestly like know how to live with them free and they're flighted and so I try to show you guys that on the channel like my real life with them and how I manage that because we have to do better for birds. I mean there's a lot of people that are good at working with birds, training birds but do you know how to live with a bird? Like do you know how to live with a bird? The way you live with a dog where they can go in the cage themselves in or out however they want. It's so funny like my Gala Kakatu Vinny puts himself to bed at the end of the day. You know that kind of independence is just so entertaining. So let's get on to the story of Finchi. A lot of you have seen Finchi on my channel and I'm sure you guys have a lot of questions and you guys have asked me a lot of different things about Finchi that I always wanted to cover but I never really dedicated a video to Finchi until a few weeks ago when Finchi got a girlfriend. We are choosing a mate for our handsome bachelor Finch. We would appreciate it if one of you would come forward and announce yourself as the shooter which I'll give you guys an update on that soon. Oh my god. Okay here's the story of Finchi real quick. I went to a bird mart and when I wasn't looking my dad came back with two Finches. Okay male female and he was like they were two lonely Finches I had to get them. I was like oh my god no. What? Oh you bought them? You bought them dad? God why did you get two Finches? Because they were two lonely Finches. Because one I don't set out to get birds like I prefer to have rescue birds except for my baby Brando which you guys know the whole emotional story behind that. Why did you do this to me right now? It's like baby Picasso. I'm not sure if you don't go back and watch. Also like small birds like Finches and I just like I never was into having them because I just believe in general that all birds should be outside flying around and to have a Finch it's like ah but he came back with this Finch and then it was too late so he yeah I was like oh great then he went got the Finches like this rounded cage which a lot of you guys have questions about and saw a lot in my channel sitting on the counter which we're going to address in a second. Finchy and his girlfriend came home with us and my sister named them Atticus and Jem Finch and honestly I just could not remember which was which like which was the female name and which was the male name. The more Finchy and I bonded the more I just kept going Finchy Finchy and like I know it's not the most creative name but it just like started and I loved it. He's got a lot of personality so like he literally could be like I don't know a Stephen or something but he's Finchy so in the beginning real quick Finchy and Jem Finchy and Atticus or Atticus and Jem whatever it was they made it and started laying eggs like right away so all the improvements that I wanted to do to this cage like I couldn't do it they had literal like eggs in the nest and they were like taking care of them and hanging out with them so I did not want to interfere and to be honest I didn't have any experience with Finches. Did you do? What did you do? No. Finchy's not potty trained and Finchy wet potty in my hand. We have to take a break. Do we have to take a break and clean this Finchy? Yes we do yes. Okay we're back so basically all the improvements that I had dreamt of making for the birds now that they were basically my responsibility did not happen because they were laying eggs like laying eggs they would sleep in their nest together and then these babies would hatch real fast and basically they kind of failed at being parents for a little bit like they just like did not have the care to take care of the birds and a lot of them were duds and they'd like kick them out of the nest and I would like be so nervous I'd be like what the heck happened like this was a little baby and then like after some research and some investigation with some Finch experts I realized that young Finches they kind of like they need a few attempts to learn how to take care of their babies and then one day one of their babies grew up and like almost had all its feathers and it was the cutest baby and they were taking care of it and they were doing so good and then the baby died and I wasn't interfering with this at all so like George was heartbroken he buried the birdie baby like right next to our african gray George he was very very upset I was too it was really heartbreaking and then in the same month Finchy's wife had some seizures and I tried to do everything and I couldn't get her to the vet in time because she had like a few quick seizures and then she died and so I gave Finchy some time to grieve and um then I said when when you know he's had enough time to grieve we're gonna get him like a friend because he he doesn't want to be alone you know I didn't think he wants to be alone I know you guys probably want to see how cute Finchy is I thought about bringing Finchy's tree over so that you guys could see Finchy in the background no no come here Finchy come here yeah Finchy landed right here I gotta show you yeah Finchy you like that Finchy smiles it's so amazing do you want to sit right there you can sit right there what's on my shoulder it was heartbreaking and then I decided okay well now I can at least move Finchy into a better cage because these birds it's not even seasonal or it wasn't they just laid eggs every single day just like busy busy new eggs they would lay eggs on top of like the hatched birds so the hatched bird or baby or whatever so it was it was uh pretty impressive I realized pretty quickly that if they kept going and they were successful at it I would have a lot of Finchy's and uh as you guys who know I never want to breed birds that's not something I want to get into so basically then what happened was I got a bigger cage for Finchy but every time I got Finchy a bigger cage he would act so depressed and be on the bottom of the cage and the reason was because that small cage would be in the center of everything like if you guys saw it was on our island it was in the center and Finchy has a really big personality and I learned really quickly how to like engage with Finchy and understand like his vocals and what they meant so like when he'd see me eating he would like demand to eat whatever I was eating like like obviously vegetables and greens and such so he would like scream for it and then I would give it to him and then I'd hear him after he ate do like a little song of thank you so I really started picking up on like his behavior and so we really started bonding that way but every time I put him in another cage that was bigger he couldn't be in the middle of the island so he would get like depressed quiet and sit on the bottom of the cage and then another problem would happen that because he was on the bottom of the cage he would get like first I thought it was like bumblefoot I'm like oh my god something's wrong with him but he literally would get like his feet dirty because he would like step in his you know feces no matter how many perches I would put there for him and he loves his nest and he loves his like little nest house but like basically he would get himself like all dirty so if that happens to any of your birds I could do a video on how to fix it but in case you're wondering right now then I would have to kind of like give him a bath and like have some like hot water not not like too hot and not boiling but like and kind of like dip his foot in and then like kind of clean it and then he'd get a blow dry and all that and actually I think through all that that's how he got like pretty tame I never did any like treat training with him um that would be a really good and easy way to get smaller birds to come your way like budgies finches birds that are a little more fidgety pigeons outside as you guys know like I really just gain a bird's trust by the way that I bond with them and it works really well for me I'm not so technical about how I work with birds my whole thing about engage not caged is them being part of the family and I think that's what I'm trying to promote and that's the difference here and that is going to make your bird come such a long way and have such a good personality that's what finchy has so yeah I kept putting finchy back in that small cage because like he was comfortable there and then he fly all around and like anytime I switched it out he'd get all depressed so I was like okay but at the same time like obviously he would come out and like be where it's safe and like like in this room specifically but a lot of you would notice the small cage and be like why don't you let your bird out this isn't like what you promote engage not caged and I'd be like no guys you don't understand like one just what I told you is like that I would have him there so he could be in the middle of the interaction and two you don't really get to see him out with me like this because whenever we're filming a video we're so focused on the story of the other big birds and I don't really have him like in a situation where he could just get lost among all of the birds there is lots of opportunity for finchy to always be included like he is now when I'm up here in my office so yeah we have a good time and I want to tell you some really cute things about finchy finchy is to be upstairs in my bedroom and every morning I used to like obviously have this task of feeding finchy and cleaning out his water and doing all these different things and it gave me like that first task of the day and it made me really motivated to feel like whoa I did something today and then I would just get going with the rest of my day it was just this kind of weird small bonding thing that I had with them that I you know really appreciated but I think the overall thing I want you guys to realize is that like there is so much to building up trust with an animal and sometimes people make things very technical and very this is what you have to do to train a bird and this is what you have to do to get them to come to you that stuff will honestly work but there is another way there is just like kind of letting your bird know that it is not going to be in a cage situation let's not forget these are birds they want to fly and and by the way he's flighted as you guys saw like they want to fly they want to experience life and then we take that away from them so there is a lot of trust when they learn that you're not going to do that especially if they are a rescue and they came from somewhere else where they're always locked up in the cage I really want to stress on that because um I really want you to when you work with a bird come from the place of this is a family member I do see a lot of times people try to take away that guilt of like well I spent a good enough amount of time with a bird or maybe quality time so they could go back in the cage no one's against cages but why not let them kind of make that choice themselves if you're good with your animals and you're good with your birds and you have a real gift with them and if you're really doing the work you will be able to have a cage that the bird can go into itself and be free in your house because you have a sense of control you know what I mean birds are difficult because they'll chew up things they'll destroy things they'll damage things and if you guys watch my instagram you'll see a lot of that rambunctiousness but also like I know what's entertaining so I know what's going to happen because I literally know everything they're going to do before they do it and I'll be like this will be entertaining I will let it happen it just about like really being in tune with your animals and always striving to be better I'm always striving to be better like you know recently I found out that Fanchie loves to be on the tree in my office and so like it's part it's an idea like okay like let's get Finchie a tree that Finchie can sit on all the time that Finchie feels comfortable in and I don't know how it's gonna work with Finchie's girlfriend because Finchie's girlfriend is a very rambunctious breed and I don't know how it's gonna work when Finchie has the girlfriend and they're together and maybe he won't be like a mommy's boy anymore but I wanted to address some other questions and also I'm realizing that I didn't ask you guys on Instagram what you might want to know about Finchie so if there's anything you want to know then maybe we'll do another video please let me know in the comments and I'll collect it and I'll do another video for you I know some of you are going to ask why I got Finchie a friend that he couldn't mate with why not just not have like the nest because if the nest isn't there they're not going to breed and my answer to that is that Finchie was used to his nest and that's like where he sleeps and he likes it so I'm not gonna take that away from him that's like his little place that he loves to sleep in at night so I want him to have that his wife was the one that kind of like did all the foraging with all of the nesting materials let's talk about Finchie's personality guys if you saw did you guys watch the video where we went to get Finchie a girlfriend and we took Finchie out and like the carry on Finchie was so happy Finchie was on his tippy toes looking out the window and my cousin Mandy would hold Finchie up so he could see and then we did some videos like on Instagram and stuff so you guys could see and we took Finchie some other places that day and he was just so happy and that makes me really happy just to be able to give him that kind of entertainment that also just kind of like solidified to me like how much he wants to see and why he liked that smaller cage like right now he's in a bigger cage and he's just not happy like he won't even fly up and perch on the purchase like so I have to put everything super low because he's just like just not happy I'm hoping that when he gets his girlfriend then maybe the two of them can like be more excited together because they're like you know she's still in quarantine but it's about time for them to be together I am thinking about kind of bringing his other cage back a little bit again so that like maybe I can move him in and out like hey if I want him to see what we're doing and let's say there's too many animals like running around or whatever or too many doors opening he'll be in that little cage sometimes I don't know we'll see what happens the other day he was hanging out outside in a cage like I rolled the whole thing outside he loved that like he loved to have like his bath he has a little bath he's just an amazing bird he's got a very strong personality just the way he would boss me around I love those kind of birds you know when you give them a little bit of like control they have so much to say to communicate and like it's all about listening you really got to listen to the animals so that's like my answer to how to tame a fish just kind of bond to hang out with them when you include a bird like inclusion is so important for birds I'd love to know what else you guys want to know about Finchi I'm happy that you guys like Finchi soon when we do their introduction I'll reveal the name of Finchi's girlfriend I hopefully they will be in a relationship you guys let me know what you think what do you think Finchi this is Finchi up close do you see how he smiles you guys have any questions let me know I love you guys so much thank you so much for watching this video enjoy this pick me Marlene submission don't forget to submit yours on instagram follow my instagram to be always up to date with what is happening with me bye guys by the way don't forget if you guys are looking for an amazing bird food brand for your bird that is healthy organic and not full of food colorings and sugar and peanut smash check out Marlene's signature blend I did this along with tops parrot food I encourage you guys to check out my feathered fun box it's a passion project it's a subscription box that comes with parrot toys for your bird and also special merch kind of like my dream box honestly I put so much into it I love that there's something like this for birds out in the world that's why I created it www.featheredfunbox.com I love you guys so so much thank you for listening


In this video, we provide the solution to question number six for practice exam number three for math 12 10 And we're asked to compute the derivative of the function f of x equals e to the x over x squared plus two This because our function is a fraction. We're going to use the quotient rule to calculate its derivatives So remember our poem here. We're going to get low D high take the derivative e to the x minus high d low Square the bottom here we go some things to remember about the quotient rule is don't try to do too much at once use some scratch paper Or use the margins in the page to write it out if you need to Also, don't actually multiply out the denominator leave it factored. That should be a square not a prime there And so now let's try to simplify these remaining derivatives here.  I It turns out we need to simplify things a little bit So let's factor out the e to the x and then see what polynomials left behind x squared plus 2x We get a minus 2x minus 2 remember this negative sign will distribute on to both of these pieces And this sits above the denominator x squared plus 2x quantity squared Notice now once you've explained once you factor out the e to the x the 2x is cancel out You're left with x squared minus 2 you have an e to the x you have this is all above x squared plus 2x squared x squared over 2x squared that's right So we see that the correct answer would be a using the quotient rule


Miki you made it look easy today with the white pieces two out of two pleased with the way things are going Well my game yesterday was ridiculous, but Yeah, I don't know. I don't think the game is that impressive, but he sort of gave way a little material at the end and made it quite easy for me Right now of course starting in an open tournament yesterday. We had a few casualties amongst the top players Is that something? You guys being the world's best players think about or worry about in the opening rounds at an open like this No, not so much. I was surprised how many surprise results they were yesterday and I moved up a couple of ports So yeah, I wasn't really expecting that. I thought there would be more Some more winners, but they look like they were pretty good games actually the games that were upset skies just played well Right now Mickey a lot of your colleagues refer to you as the spider talking about your style of play Which is a lot about weaving this web around your opponents and before they knew they know it They're helpless and it seemed like something like that happened today. Your opponent collapsed quickly. Tell us a little bit about this spider technique Okay, but this was a vigorous attacking game by my standards No, I don't know. I I think I played a bit more aggressive today trying to castle queen side in this line in the tarash is But okay, I don't really know I mean, I didn't think he would play this Queen D7 move. It's quite rare and he never played before so and Anyway, this line was far off my radar, but I don't know. I mean I had the impression We got a original position kind of quickly, but I managed to get through the game without blundering anything So that was good start. All right And if I absolutely insist on you breaking down the concept of weaving a web again around your opponent What would you say to that? I Don't know. It wasn't my idea, but Sometimes sometimes you can get a grip on the position, which is nice All right. Thank you very much and good luck for the remaining tournament. Okay. Thank you


तुके जहां लोग, जहां आबादी कुशाल होगी, वहां पर उस्मूल की जु सुसाटी है, उसका अपनी रयासत के साथ तालुक भी बहतरीन पुम में होगा. तुनाचे हम ये कै सकते हैं, that through out the old human history, the world's population had grown slowly. By the beginning of the 20th century it was only 1.6 billion people. But today after only 110 years the world's population has surpassed 7.5 billion people. And during this time the world has witnessed tremendous development including innovation in health care, education, infrastructure and technology. But more than 2 billion people still live in poverty and remain left out of this progress. With the passage of time, in the world, there is a lot of progress in every aspect of health. The government is trying to invest more in the field of health so that they can facilitate the basic health matters. So that if people are healthy, then the country will be healthy. Similarly, education, infrastructure and technology. These are all the fields in which there is a lot of development in the passage of time. But along with that, the reality and the reality of the future is that the world still has a large number of population throughout the world which is below the poverty line. These are the people whose basic needs are not the same. And this is a very big question, a very big challenge for the world and for the people in the world. And the biggest challenge is that the leaders of the world face today is to reduce poverty and inequality and improve people's life without compromising the environment and the well-being of the future generations.  They should improve their situation. But how? That the environment in the world should not be damaged, that is, the parallel of technology and development, which is developed by the situation, if they will also put up projects like unplanned, just to bring their people up from the poverty line, then the environment in the world will deteriorate. So, it is better to keep the environment in the best condition and also keep the environmental issues in mind while planning. At this time, every country has a big challenge for leadership. Because at the same time, world population continues to increase by more than 80 million people a year with most of the growth occurring in the world's least developed countries. And by 2020, as per the UN estimation, world's population will increase to 9.6 billion people and will continue to grow to 2100.0. Now, this is the situation. If we look at the kind of effects and figures that are giving different examples of the world and in which the provided data is provided by the UN, it is very alarming that the population is increasing from the speed of the world. The majority of the population in the world is still the country that is increasing by more than 80 million people a year. The country that is still the country of progress, where the situation is still not very good. If the population is increasing by more than 80 million then the increase in the population by more than 80 million people can lead to a better situation in the world. If the population and population are not in a good condition and the population is increasing, then the developed countries and the world will become a big challenge because this continued growth has strong implications for health, well-being and economic development. Definitely, the biggest challenge that is being created by the population is how the requirements of health will be matched with that. Along with that, well-being and the overall situation will be improved. If well-being is not consistent with that, then certainly, the situation will continue with music. Along with that, the disturbance is the package of economic development in the world. Similarly, how does population growth affect national development and what must be done to make the challenges of population growth? Now, one of the most important issues that we are discussing here is how the national development of the population growth can be made with the help of national development. Along with that, the challenges that are being faced by the population growth can be tackled. The understanding of the population development connections, as well as the right investments, nations can ensure a better life for the people today and future generations. Now, where can the people invest properly in such a way that they can benefit their people by investing in it? There are long-term planning for proper policy-making and policy-making is the fundamental responsibility of every government to ensure that the two concepts of population and development can be made in such a way that the government can manage the short-term long-term planning for the long-term planning of the political sociology in many areas. Rather, it is very important for the students to find their suitable answers for the political sociology.


Ukraine sends Western tanks into battle for the first time to bolster counter-offensive. Ukraine appears to have deployed Western battle tanks into combat for the first time. Analysts tell NBC News as Kyiv launches its long-awaited counter-offensive against Russian occupying forces. The counter-offensive has been months in the planning, and Ukraine's military has been holding back fresh troops, as well as recently supplied Western weapons for what may be its best opportunity to make significant gains on the battlefield. Russian officials and military bloggers reported heavy fighting along the war's southeastern front lines. Ukraine has remained officially silent on the subject, but a senior officer and a soldier near the front lines said that the wave of attacks represented a significant new push to break through Russian defenses, and that efforts appears to be bolstered by heavy armor. Analysts say that the opening stage of the counter-offensive has seen the combat debut of German-made Leopard 2 battle tanks, which were supplied to Kyiv after months of diplomatic wrangling with its NATO backers. Russia's military released drone footage of what it said was an attack by Ukrainian armoured units in the southeastern Zaporizia region. Michael Horowitz, Head of Intelligence at Lebeck International, a risk management consultancy, reviewed the footage and said he was confident that it showed Leopard tanks in action. This would be the first time Ukraine deploys Western battle tanks, which is a sure sign that this is serious, Horowitz told NBC News.


تفوته آدك الأيام فتا الحمد لله رب العالمين له الحمد الحسن وثاناء الجميل وأشد أن لا إله إلا الله وحده لا شريك له يقول الحق وهو يهد السبيل وأشد أن سيدنا ونبينا محمد صلى الله عليه وعلى آله وأصحابه والتابعين لهم بإحسان إلى يوم الدين أما بعد إن شاء الله تعالى today سوف نأخذ رسالة رسالة لطيفة جامعة في أصول الفق المهمة للعلامة عبد الرحمن ابن ناصر السعودي رحمه الله تعالى سوف نأخذ رسالة لطيفة وعندما أخبره عبد الرحمن ابن ناصر السعودي ألمام السعودي رحمه الله هذا ألو رسالة لطيفة هو ألو رسالة لطيفة رسالة لطيفة وقدمنا وقعنا وقواعد الفق هو في الذي أخبره وقدمنا ألو رسالة لطيفة وقدمنا وقعنا هذا الأمو هو compared with our subject وأخبار دائم أصول الفق أصول الفق is from the important sciences it is from the knowledges which are important and it is from the knowledges important and it's from the fields which are high and it's from the fields which are high because it is what طريق a way to stop the law it is a way that allows a person to extract rulings from the sharia من الدلتها التفصيلية from its detailed evidences this book that we have with us insha'Allah that we're going to be taking today it is a bridged summarized book and it's a book which we could say it's a مدخل it's an introduction to أصول الفق it's an introduction and this book it brings a lot of principles قواعد جامعة principles which are comprehensive which benefits every student of knowledge who reads it and I personally believe anybody who understands this book who implements the things that are in it he will have a good portion a good amount of understanding of أصول الفق he still hasn't entered into the field very well but he has some form of understanding he has some form of understanding and one of the things that is his methodology his methodology which is unique which is praiseworthy in writing a book in a field which is complicated he will come he will write a book in it in that field and he will summarize it بالإيجاز والاختصار he will summarize it he will abridge it and even then in the way he does it is what مع جودة الترتيب والإتقان the way his words are and the terminologies that he uses and the way he organizes it it's so amazing and this is what مما ميز الله المؤن مصنف one of the things that Allah specifically gave to sheikh abdulhaman ناصر السعدي and because of that in which he had الله تبارك وتعالى he made him that his works in which and the books he authored the students of knowledge they didn't attack on it they sat over his books and they benefited from it so insha'Allah تعالى we will take a lot of benefit from this book insha'Allah تعالى this book that we have with us the author who wrote it his name is and this is a summary of the book written by sheikh عبد الرزاق عبد المحسن العباد عبد الرزاق عبد المحسن العباد رحمه الله رحمه حفظه الله he's still alive حفظه الله وما يالله تبارك وتعالى protect him وما يالله تبارك وتعالى protect his father عبد المحسن العباد المحدث العالم الزاهد عبد الرزاق the obedient son of عبد المحسن he wrote a book where he called it الشيخ عبد الرحمان ابن سعدي وجهوده في توضح العقيدة he wrote a book where he talks about the efforts of عبد الرحمان ناصر السعدي his efforts and how he clarified عقيدة a big book masha'Allah and he spoke about his life in that book his name is العلمة الورع الزاهد الفقيه الأصولي علامة القصيم وشيخها عبد الله عبد الرحمان ابن ناصر ابن عبد الله ابن ناصر وهي من قبيلاء عبد الرحمان عبد الرحمان ابن ناصر عبد الرحمان الشيخ رحم الله بانه يبون عونيزا في قصيم عندما كانت تاريخ محرم 1307 وانه يتعب يتعب يتعب يتعب وانه يتعب يتعب في حول عبار عبارة عبارة عبارة عبارة Before he passed away he passed over the responsibilities to his older brother his brother Hamad and his brother Hamad stood up for the raising of very well خير قيام his best way he made sure that the environment and the surrounding which the sheikh رحم الله كانت جيدة في العلم.  فهينزل قاعدة وقت ما بين العلم والتعلم. قاعدة وقت العلم وقت العلم وقت العلم. و هذا هو فقط المتعلم. و هذا هو المشاكل that many students of knowledge have. عندما تبدأ العلم ينزلوا بحيث أن تتعلم نفسه. ينزلوا بحيث أن تتعلم نفسه. فهي يتعلم و لا تنزل. وما يحدث؟ الناس who are studying with you reach you and they even pass you أو not only that but what even happens is that your knowledge becomes less and less because you're only tackling the matters that are needed by that the crowd you're teaching so that shouldn't be the way you are you should educate yourself even more and learn even more so the sheikh he was like that فكان يقضي بعض أوقاتي في القراءة على العلمة he used to spend some of his time going to the scholars and reading on them and others he used to what يجلسوا الى تلاميذي ويعلمهم and other times he would sit with the students and he would educate them and teach them and some of it he used to what he used to revise his books in which he and also research matters he would research وَلَا يُفَوُّتْ مِنْ أُوقاتي شَيْئَنْ إِلَّا وَقَتَرَتَبَةَ and none of his time will go by except he organized those time he had something to do and he carried on like that الشيخ رحمه الله until he became what حس حتى صار التدريس ببلده راجع عن إلي until the city in Qasim and the people they made to him the reference point every seeking everyone would come and benefit from him take from him from the sheikhs that he took from and his teachers وَالشيخ إبراهيم ابن حمد ابن وجاسر and he's the first man man lastly said I read on he took a Tafseer from him he took a Hadith from him and he took a Ossol Al-Faq and he also took from him Ossol Al-Mustahlah Al-Hadith he took Ossol Al-Faq Mustahlah Al-Hadith and he also even took from him Ossol Al-Tafseer he also took knowledge from الشيخ محمد ابن عبد الكريم الشبل he took from him Faq Ossol Al-Faq he took from him علوم اللغة العربية the Arabic language he also took knowledge from him الشيخ محمد ابن الشيخ ابن عبد العزيز المحمد المانع he took from him the Arabic language he studied and he took knowledge from الشيخ محمد الامين الشانقيطي he took from him Tafseer he took from him Hadith he took from him Mustahlah Al-Hadith and he also took from him the Arabic language I've seen some scholars they said that this محمد الامين الشانقيطي isn't the Sahb Al-Adha Al-Bayan I saw some scholars say that and I've seen others who said it was so I don't know I'm confused in regards to that matter his students that took knowledge from him are from them الشيخ محمد ابن صالح العثيمين who rather took the position of his teacher خالف الشيخه في إمامة الجامعة بعونيزة the sheikh's chair الشيخ ابن عثيمين took off when the sheikh died and he took over teaching reminders and everything that the sheikh used to do also from his students عبدالله ابن عبد الرحمن الباسم sorry عبدالله ابن عبد الرحمن الباسم and I know you should know عبدالله ابن باسم he's very well-known he's the author who done the شرح of عمدة الاحكام the one volume عمدة الاحكام or sometimes published as two he also even has a شرح on بلو والمرام he's from the teacher's students of the sheikh نعم ام also الشيخ عبدالله عزيز ابن محمد السليمان who used to teach in what who used to teach in what في محدي إمامة دعوة بالرياض in the ma'ad of إمامة دعوة in riad and he took the way of his teacher in how he authed the books and he wrote he took from his teacher الشيخ عبدالله عزيز ابن محمد السليمان he has books which are heart softening as a book I remember is called اقتنام الأوقات benefiting from your time very nice book and he also even has a book in which he talks about Ramadan the things that you need to do within those days heart softening books and his books الشيخ عبدالله عزيز ابن محمد السليمان are not what his books are not published the reason why they're not published is because he made his books مجانن free so his books won't carry on for long because who's really going to take that initiative to carry those books and publish it properly people want to make money out of the books that they publish so his books are really rare to find them نعم الشيخ عبدالله عزيز ابن محمد السليمان he had a lot of books that he authored and he used to give a lot of consideration دع عناية بالغة بالتأليف he gave a lot of consideration to authoring and he has a lot of مقلفات on different fields from his books أعدلة القواتع والبراهين في إبطال أصول الملحدين he refutes atheists has a little aesal on it and he has a book called الإرشاد إلى معرفة الحكام which this book الإرشاد is a question and answer إنفق question and answer that's how he صلاح he does question and answers question and answers he also has a book called بهجة قلوب الأبرار وقرة عيون الأخيار في شرح جوامع الأخبار he wrote a book himself he wrote a book called جوامع الأخبار he wrote a book called what جوامع الأخبار where he brought a large number of hadiths صلاح فوت حديث من نووي he brought them together and then what he did was he these hadiths he said that they're the most comprehensive جوامع الكلب they're the smallest hadiths but the meaning are so fast so vast and they deal with matters which are قواعد and you take from them so he brought those hadiths and he tells you the قواعد that are taken out of it and what not so he himself explained a book so he wrote it he called it جوامع الأخبار and then he done a شرح on it he called it بهجة قلوب الأبرار وقرة عيون الأخيار في شرح جوامع الأخبار he explained his own book he has a book which he called توضيح الكافية الشافية إمامه بن القيّم الكافية الشافية للإنتصار للفرقة الناجية which is well known as نونية he put a little explanation on it not full but a little تعليقات a little explanation here and there نعم he also has a book التوضيح والبياء لشجرة الإيمان where he talks about الإيمان وبيضعوا وسبعون شعباء أعلاها قولوا لا إله إلا الله وإذنها إيمان والله it's very beneficial very beneficial he also has a book التنبيهات اللطيفة في محتوى عليه الواسطية من المباحث المنفية sorry he put it التنبيهات اللطيفة في محتوى عليه عقيدة الواسطية في محتوى عليه الواسطية من المباحث المنيفة صمف الله يتعى which is basically a little explanation on عقيدة الواسطية بايمونتينيا he also has a تفسير بوك تيسير الكريم الرحمن في تفسير كلام المنان and he explained the Quran and it's so simplified the words are very easy no tekeluf no hardship علماء praised that book ابن عثيمين praised it ابن الشيخ محمد ناصر دينا ألباني praised it and others they praised that book he has another book قول الدورة المختصرة في محاسن دينا الإسلام and he talks about الإسلام and the good things about Islam he also has a book تقول رسالة في قواعد الفقية which we have studied previously he also has another book وهي كولد طريق الوصول إلى العلم المأمول بمعارفة القواعد والضوابض والأصول he also has a fatawat دية two volumes where he gives fatawat he also has القواعد الحسان لتفسير القرآن he made principles of how to do تفسير of the Quran principles رحمه الله he also has a book القول السديد في مقاصد التوحيد where he speaks he does explanation of كتاب التوحيد by محمد عبد الهاب he also has a book منهج السالكين وتوضيح فقوا في الدين which this call is Outs to explain فقبك وكونت الحمب المدهب نعم and last but not least he also has a book الوسائل المفيدة للحيات السعيدة means to get a beneficial life do you want to live a good life? he has a book on it how to gain happiness those who are looking for it those who are depressed and sad اله الحمد لله قطر they published all of his books الشيقات الحمد للسعيدة all of his published الحمد لله وزارة الأوقاف they've published it all so all of his مؤلفات are published best publication نعم الشيق رحمه الله إتعالى when the year was 1376 1371 the sheikh which remained for what? for five years five years the sheikh was ill he had an illness which basically was blood pressure blood to dim his blood pressure went up and it got serious as time went by and the sheikh was very patient very very patient he refused medication he refused medication رحمه الله إلا انتقل إلى ربه until he went and died رحمه الله he died on a fajar on a Thursday on the 22nd of جماد الأولى آخر جماد الآخرة he died when the year was 1376 غفر الله له ولي ولي دي ولي ولي دي ولي ولي دينا وجميع المسلمين may Allah forgive him his parents and our parents and all the Muslims إن شاء الله إتعالى I'm going to go through with you all أصول الفق a bit about brother's what I want you to all know is that the علامة who have authored books who have spoken about any field they've all made 10 مبادئ to عرفوا بهذا العلم 10 matters that allows this person who is studying that field for him to comprehend what that field is about what's this field about why do I have to study this there are 10 points or 10 questions a student of knowledge has to have answers for once he gets these 10 points answered for him he is what he is able to understand what that field is about those 10 are brought in these lines of poetry إن مبادئ كل فن عشرة الحد والموضوع ثم ثمرا ونسبة وفضله والواضع والاسم الاستمداد وحكم الشارع مسائل والبعض بالبعض اكتفا ومن در الجميع هاذ الشرف those 9 those 10 so based on that فسيرا مني على طريقتهم me treading on the path of my previous scholars and my our teachers وسلوكا لدربهم وتشبهم بهم I will say the following إن مصول الفق إن شاء الله تعالى follow the path of our scholars we have to go and say because what did the poet said say إن لم تكونوا مثلهم فتشبه إن تشبه بالكرام يفلاحوا if you can't be like the ulama imitate them for verily imitating the scholars is an honor in and within itself so إن شاء الله تعالى I'm going to speak about those 10 points number one إن شاء الله تعالى what's the definition of أصول الفق what's the definition of أصول الفق أصول الفق the definition of it is علمون it's a knowledge يبحاثوا you can say يبحاثوا or you can say يبحاثوا both are not wrong if you say يبحاثوا مبنين المجهول the person who's researching is anyone who studied this field or it's a field in which you study in it if you say يبحاثوا you're making this you're ascribing this verb to the fun itself the field itself the field's researchers يبحاثوا means the person the مجتهد does the researching so علمون a subject يبحاثوا which inside it is it's reached searched so in this field you research القواعد والأدي الله principles and evidences which are comprehensive المصلة للفق that will allow you to reach فق that's number one I want you to all understand as it's important that we understand the definition لأن الحكم على شيء فرق العم تصوري to give a ruling on a matter you have to have perception for you to even understand what the word is about and what it's going to deal with or what it if you don't even understand what it means then you're not going to the word only means three things only three things if you learn these three you'll understand it very well first one is it is that's the first one it is comprehensive evidences or even if you want to say this comprehensive principles that allow you to reach فق it allows you to reach فق with these comprehensive evidences you'll be able to reach فق that's the first point the second one is وكيف يتل استفادة تيميلها and how to benefit from it how to benefit from the evidences how to what? to benefit from this evidence and that deals with this word shows this is this is this is this is this is this is this is this is this is this is all of these are that's the second how to benefit from the text the third one is how to benefit is what? the مجتهد this book would teach us teach us the مجتهد شوروطر اجتهاد the مجتهد who is the مجتهد what are the conditions to be a مجتهد and etc that's the first point the definition the second thing that it is this topic and again the topic is the same as the definition the topic as I said it deals with comprehensive evidences in understanding jurisprudence rulings also how to benefit from the text at last but not least the مجتهد the مستفيد the مستدل the مجتهد matters pertaining to him number 3 is what number 3 is what it is تمرته تمره means what تمره means how to benefit from أصول الفق sorry تمره means the benefits that are in أصول الفق the benefits are in أصول الفق what will I benefit by studying أصول الفق the ثمر is as follows that comes from أصول الفق it's basically the benefits there are many benefits these are just some of them شاء الله يتعالى the first one is ضبط أصول الإستدلال وذلك ببيان الأديلة الصحيحة من الزائفة you will narrow down the أصول the fundamental استدلال the fundamental ways of taking evidences and it will also clarify for you what is a correct evidence and that which is not correct evidence you will narrow yourself down you will be able to understand that the second one is the correct way إضاح الوصح الصحيح للستدلال the second thing that it teaches you is what the second thing that it teaches you is how to use something as evidence the correct way to use it is an evidence because not every evidence that's authentic is the way that you use the evidence is going to be authentic so you got the evidence how are you going to use it in your advantage or how are you going to use it to prove your points number the third benefit or the third ثمر that it gives you is تيسير عمالية الاجتهادي وعطاع الحوادة الجديدة ما يناسبوها من الأحكام it makes it easy for you to do each tihad it makes it very simple very easy for you to give to do each tihad and also it gives situations that occur the befitting ruling to give it the right ruling it will make it easy for you in that way the fourth إن شاء الله تعالى is بيان الضوابط والفتوة it will give you the ضوابط dealing with Fatwa the ضوابط pertaining to Fatwa and the conditions to it and the etiquettes the ضوابط, the شروط the adab of Fatwa يولاني أصول فق the fifth one إن شاء الله تعالى you will come to know the reasons معرفة الأسباب التي أدت إلى وقوع الخلاف بين العلماء والتماس الأعدال لهم في ذلك you will come to know the reasons that led for scholars to differ on this matter and you will also be able to find excuses for them because you know where things went wrong or where they differed on نعم that was five right six number six to call to what to call the people to follow the correct evidence wherever it is or to call the people to the correct stance there is and and to leave off fanaticism and blind following of individuals سول الفق will take you out of the shackles of blind following and it will free you from that also the seventh is حفظ العقيدة it will safeguard the عقيدة how بحماية أصول الإستدلال by safeguarding how the evidences rulings are extracted from it ورد على شبه المنحرفين and it will refute the doubts that are brought forward by who those who deviated like those who say تأويل for the characteristics and the attributes of Allah if you study سول الفق you will know what is تأويل ها how does تأويل occur and إن شاء الله تعالى we're going to be taking that here إن شاء الله تعالى also the benefits that it teaches you is what ببط قواعد الحواري والمناظرة you will know how to narrow down when you're having a dialogue a debate with a person you will know how to bring them back to what by bringing them back to the correct evidence that are out there وذلك بالرجوع للأديلة الصحيحة المعتبرة and last but not least the last last but not least the other benefit that it has is that الوقوف على سماحة الشريعة الإسلامية it will teach you how Islam that kindness the simplicity the ease that lies within Islam and you will come to know والطلاع على محسين الدين how good this religion is perfected no one can tamper with it it's well organized نعم that is نسبته which is the fourth one so when we finished the definition we took what it deals with we now we also took the benefits that lie within now we're moving on to the fourth one which is نسبته where does أصول الفق lie in comparison to the other fields that's the fourth one when we compare it to the other fields now this brings us to a point which we're going to have to speak about later إن شاء الله إتعالى but I want you to all pay attention which is the knowledge is categorized and the knowledge is categorized into two علوم which are known as علوم الوسائل their means and علوم which are غاية their objectives علوم which are وسائل means and there are علوم sciences which are what غاية objectives أصول الفق falls under the instrumental knowledge علوم which are وسائل their means so if it's a means which fields will it be in the same category as it will be with مصطلح الحديث علوم اللغة like نحو بلاغة صرف it will be in the same so نسبت to who means what when we look at the other fields it is part of the علوم الوسائل means so anyone who doesn't understand أصول الفق will struggle in understanding what فق the same way anyone who struggles to understand مصطلح الحديث will struggle to understand حديث and also the person who struggles to understand نحو will struggle to understand أربك language because these are what the instrumental knowledge that allows the person to understand الكتاب والسنة to understand the Kitab of Allah and the Sunnah of the Messenger صلى الله عليه وسلم so the field أصول الفق it falls under علوم الوسائل what is the virtue of what is the virtue in it what virtue do I gain in learning it not benefits but virtue do I get from it that's the fifth point the virtue that you get is these three points point number one شرف العلم من شرف المعلوم the virtue of a knowledge is attached to what you're learning the virtue of what you're learning and since أصول الفق is dealing with the book of Allah and the Sunnah of the Messenger صلى الله عليه وسلم then the question is what is the book of Allah and the Sunnah what status do those two knowledges have then learning أصول الفق has that virtue because it's a means for you to understand Allah his words and the Messenger صلى الله عليه وسلم his traditions then the virtue of it goes high


lecture before doing that let me quickly recapitulate the things that we did in the last class. We discussed the fly back converter wherein I am using though I am using a transformer only one coil is carrying current at a time. The transfer function to the fly back converter is given by V naught is equal to N 2 by N 1 into V in or V dc d divided by 1 minus d. One point to be remembered is that provided flux is continuous, flux is continuous this is a transfer function, but I also told you that generally fly back converter is operated in discontinuous maximum value is around 0.5 or so. So, at that time what could be the output voltage 1 has to derive 1 has to derive please remember this function this transfer function is valid only if only if flux in the core is continuous. See how did it derive this equation we used volt second per turn balance volt second per turn balance. So, I said primary voltage applied to the primary is V dc for d t seconds and number of turns is N 1 and we equated this equal to volt second volt second per turn of the secondary I said V out 1 minus d into t divided by N 2. See I am assuming that I am assuming that voltage applied to the secondary is V 2 for 1 minus d into t seconds that can happen only when diode is conducting in the secondary see in this circuit dot current enters the dot current should enter the dot now this is how it is. So, switch is on for d into t seconds and switch is turned on only after t seconds is like you know this is what I am trying to tell you d into t and this is t second time is being turned on. So, one from d t to t voltage applied to the secondary is V naught provided this diode is on. If the current becomes 0 in the secondary before t then this transfer function is not valid this function transfer function is not valid remember I will repeat voltage applied to the secondary is V naught only when diode d 2 is conducting and in case diode turns of before t then volt second per turn for the secondary is not V naught into 1 minus d into t divided by N 2. So, you have to find out where the diode turns off. So, if it turns off somewhere here then volts second per turn is beta into t minus d into t remember. So, this is this trans equation I have derived neglecting the winding resistance device drop. So, if this device drop is comparable or comparable to the input voltage say I have 12 volts solar panel and device drop is 2 then the 2 is comparable to 12. So, we have to take care of this 2 volts similarly here in the secondary. So, all the idea non idealities we need to take into account while determining the turns ratio. So, if time permits we will take one design problem all those issues will be discussed. Similarly, for a forward converter as well forward converter as well. So, in both forward converter as well as in fly back converter I am using a transformer, but then if I see the BH characteristics we are operating in the first quadrant itself. So, in other words the magnetics are not utilized fully can I use bidirectional core excitation something similar to AC. So, if I use bidirectional excitation is something similar to AC therefore, voltage induced in the secondary will have both positive half as well as negative half finally, we require a DC. So, what we need to do the voltage induced in the secondary we need to rectify it and filter it to get a DC. Please try to understand the moment I am using bidirectional excitation voltage induced in the secondary is going to be AC because it will have positive half as well as a negative half I want finally I want a DC I have to rectify it and filter it. So, why are we doing this first we are converting this DC to AC and again again to DC. I did say that I am using a bidirectional excitation, but one thing that I did not tell you is the switching frequency is very high or the frequency of the voltage induced in the secondary is very high. So, as the switching frequency increases. So, frequency of the voltage induced in the secondary also increases. So, there are two advantages one is size of the magnetics the inductor or the transformer reduces as the frequency increases number of turns come down. Second I have to rectify this AC to DC as the frequency increases the ripple frequency also increases see what I mean is if I take say full wave rectifier single full wave rectifier it looks something like this. What is this? This is T by 2 and this is T by 2. So, if I do if the frequency is very high. So, this the frequency of this pulses also increases. So, my filtering requirement comes down. So, if I have a three phase six pulse conversion what will happen? I will have something like this. So, my filtering requirement in this case is much less compared to filtering requirement here. So, what I will do is I will convert this DC to high frequency AC magnitude is determined by the application. So, number of turns will be magnitude will be determined by the application frequency is very high I will convert it to DC then I will use a very small filter to filter out the ripple and get a constant DC that is the philosophy. So, first one in this class is push pull converter push pull converter the circuit configuration is here. See the secondary sorry see the transformer connection I have a center top and at the secondary you just see it is nothing but a center top full wave rectifier is with this circuit would have seen in while fabricating a regulated power supply in the lab something like this. It looks something like this what we did to get a 5 volt DC in the lab what we did a diode and diode capacitor this what we did and we connected to AC. So, the secondary here what this does it rectifies this is a filter something similar one here there is no difference at all see the secondary there is a filter where did we see this stage this filtering stage in buck converter. See in the primary side I have two switches and see the connections a center top primary center top secondary even in T 2 or two switches V DC is the supply voltage here it could be voltage from the solar panel through a capacitor filter or whatever. See the dot conventions let us see how it works now from 0 to DT by 2 the first half T 1 is on when I close T 1 this is the path positive the direction of current. Current enters the dot let us see what happens in the secondary current enters the dot current can leave the dot. So, yes current can leave the dot D 1 can conduct can D 2 conduct no. So, when T 1 is turned on current enters the dot current can leave the dots therefore, D 1 conducts. So, what is the path D 1 secondary the filtering stage back to. So, what is the voltage applied to the N 1 turns it is V DC. So, what the corresponding there will be voltage induced in the secondary with the dot as positive and that will that will force the current in the secondary after sometime open T 1 here voltage across N 1 is equal to V 1 1 that is nothing but V DC with the dot as positive. Now, this dot is positive and this dot also will be positive. So, what is the voltage rating of T 2 you just stress the circuit V DC positive of the V DC is connected to 1 terminal T 2 negative here to the positive of the voltage source which is induced a positive voltage source which is induced in N 1 2 with the dot as positive I am calling that voltage as V 1 2 if N 1 1 is equal to N 1 2. In fact, they are the same the voltage induced here will be V DC itself. So, this is the voltage. So, similarly what is the voltage induced in D 2 when D 1 is conducting same concept we need to see this is positive this is positive voltage induced in N 2 1 is proportional to the number of turns in the supply voltage similarly N 2 2 stress the circuit positive positive D 1 is on the entire voltage D 2 has to block. So, voltage across D 2 is 2 V DC N 2 by N 1 voltage across D 2 is 2 V DC. So, voltage rating of the switches is 2 V DC after sometime open T 1. Now, what happens in the secondary the moment D 1 is on D 1 is positive after sometime open T 1 what will happen. So, this is the duration from 0 to T is equal to 0 to T T by 2 T 1 is on T 2 is off from D T by 2 to T by 2 see here D T by 2 to T by 2 I am saying T 1 and T 2 I am saying T 1 and T 2 are off I am not saying anything about the secondary from D T by 2 to T by 2 both T 1 and T 2 are off what happens in the secondary we will see from T by 2 to 1 plus D into T into T by 2 T 2 is on T 1 is off and from this period to T both T 1 and T 2 are off nothing has been mentioned about what happens in the secondary N 1 1 is equal to N 1 2 and N 2 1 is equal to N 2 2. So, when I close T 1 current enter the dot current can leave the dot in the secondary. So, therefore primary current I 1 has 2 component 1 is the magnetizing current plus the equivalent secondary current. Now, when I open T 1 what happens 1 there should be a path for for the magnetizing flux or the magnetizing current and there should be a path for the inductor current as well I L while discussing forward or fly back what we found that when the if the current enters the dot the correct direction the polarity for the magnetizing flux to be continuous is current should enter the dot in some other winding I will repeat the correct direction is for the magnetizing current if current enters the dot current should enter dot dot dot even in the secondary or even whichever winding same thing is in forward as well this what we did V D C current current enters the dot current leaves the dot. So, these 2 windings carry current simultaneously. So, the the source current or the primary winding current has 2 components magnetizing current plus the equivalent secondary current. So, when I open S if current enters the dot current can enter the dot here. So, this is the correct direction or direction for the magnetizing current current should enter the dot something similar same principle is applicable everywhere even here if current enters the dot current should enter the dot even in some other winding by the way T 2 is not closed. So, what happens in the secondary you just see see in the second half. So, current can enter the dot if current enters the dot D 2 it can flow through D 2, but then here if the moment D 2 starts conducting D 1 also starts conducting D 1 also starts conducting see the what will happen to the flux linkages in this 2 windings you need to check the moment D 2 starts conducting D 1 also will start conducting D 1 also starts conducting. So, this is the equivalent circuit I 2 enters the dot I D 1 can leave the dot if D 2 conduct D 1 also can conduct see I 2 enters the dot these 2 are mutually coupled can if I 2 whatever I D 2 can enter the dot some current can leave the dot I D 1 can leave the dot yes D 1 can leave the dot see it is bit tricky here just try to understand in this circuit nothing no current can flow in the primary, because both the switches are off when I close the switch no current can flow through D 2 because dot is positive dot is positive dot is positive voltage twice the supply voltage appears twice the supply voltage into the number of turns will appear across D 2. So, D 2 has to block that voltage when I open the switch correct direction for the magnetizing current is since this enter the dot in the primary it should enter the dot enter the dot in any winding which is mutually coupled yes it can enter the dot here, but then if it enters the dot here it can leave the dot can leave the dot here because of D 2 1. So, therefore, both D 1 and D 2 are on and this is the equivalent circuit both D 1 and D 2 are on now see this is what this is the equivalent circuit N 2 2 into D 5 by D t is the is the voltage here similarly N 2 1 D 5 by D t is the voltage here R is the winding resistance of this 2 coil this is the equivalent. Now, can we write the voltage equations this are the 2 volt N 2 1 D 5 by D t minus I D 1 I D 1 into R 1 is equal to V o 1 this is the voltage V o 1 and that voltage is also equal to N 2 2 D 5 by D t plus I D 2 into R is equal to minus V o 1 voltages are same and if I voltages are same therefore, if I equate it equate it I get this equation if I D 2 minus I D 1 of course, I D 2 should be greater than I D 1 why entire the magnetizing current current can flow only through this. So, I D 2 should be greater than I D 1. So, this is the voltage average voltage across L equal to 0 V o 1 is equal to 0. So, voltage induced this how it looks T o T 1 on T 1 on for D into T D T D into T by 2 in this period both are off. So, if the flux is continuous both T 1 and T both D 1 and D 2 are on here both the diodes are on both the diodes are on that is the reason see here I D I L 1 is the inductor current when T 1 is on I L is the current that is flowing through D 1 same current. The moment you turn of T 1 T 1 current become 0 current flowing through D 1 also falls by falls to approximately 50 percent. And correspondingly current through D 2 also rises this how at T by 2 to. So, what happens after T by 2 I will turn on T 2. So, when I turn on T 2 what happens in the primary this is the path current leaves the dot current leaves the dot if current can leave the dot current should enter the dot not possible here this is the path. See please do not get intimidated only principle that you need to understand is you need to know is mutually coupled circuit. Yes it is not very straight forward, but then if you can understand this dot convention the it is becomes relatively simpler. So, if current enters the dot current should leave the dot if there is a path if there is no path when I open the switch if current enter the dot current should enter the dot in some other winding that is all only those concepts one need to remember. When I close the switch current leaves the dot N 2 2 when I open T 2 I am not close T 1 we have to wait for some time I said in this period none of the switches T 1 and T 2 are off 1 plus D into T by 2 2 to T T 1 and T 2 are off something similar to D T by 2 to T by 2 both T 1 and T 2 are off the transfer function is you can derive it as 2 V D C N 2 divided by N 1 into D. So, this is I said this is nothing, but a forward buck converter when T 1 is on D 1 is on. So, this is a buck converter with the forcing function of V D C into N 2 1 N 2 1 divided by N 1 1 when I open the switch we proved that this voltage is 0. So, this is nothing, but the output stage or this is nothing, but the equivalent circuit of the buck converter when you open the switch. So, the transfer function is only for one winding is V D C into N 2 1 divided by N 1 1 into D something similar happens for these two winding as well. So, a factor 2 2 V D C N 2 divided by N 1 into D nothing, but an isolated buck converter isolated buck converter quite popular if the power rating is around 1 to 1.5 kilowatt or 2 kilowatt or so. So, above 700 to 800 watts one has to go in for the push pull converter wherein I am using both of the magnetic circuit. So, what are the limitations of the push pull converter see I said I need I told you both windings are number of turns in both the halves is the same N 1 1 is equal to N 1 2 N 2 1 is equal to N 2 2 what will happen if they are not the same they change by a fraction primary winding may differ by a fraction of a turn what will happen here switches may have a fine circuit switches may have a slightly different saturation voltage. So, this is the equivalent circuit when I close T 1 a dot is positive. So, may be we are in the first half of the V H loop increasing flux, but then I said N 1 1 is not equal to N 1 2 there could be if both the there could the number of both the windings could change by a fraction or device drop may not be the same if device drop is may not be the same voltage applied to N 1 1 is equal to V D C minus the drop across T 1 that is being applied to the coil which is having a small or a small resistance plus the leakage, but then N 1 2 voltage applied to N 1 2 is V D C minus the voltage drop across T 2. So, if there is a difference in the magnitude of the voltage applied to the coil. So, therefore if there is a difference in the voltage applied to this coil. So, what will happen d phi by D T I will write this I have something like this magnitude of voltages are not the same they change there is a small difference plus there is a number of turns also may not be the same if they could change in a small by a small fraction if that is the case what will happen when I am here I am the first half here I am the third quadrant. So, what will happen B H curve may not be travels symmetrically B H curve will not travels symmetrically if that is the case a D C flux will exist in the core average is going to be finite average is going to be finite the positive half is not equal to the negative half now there is average is finite average is nothing but the D C flux. Now, if there is a D C flux what may happen assume that there is a small d by D C flux and in second or third cycle load has changed also load has increased now the control is trying to increase D. So, as D increases time for which T 1 is on also increases now instead of starting from 0 since there is a D C flux it starts from a finite value switch is on for a longer time. Therefore, a D C voltage is applied to a winding for a longer time flux and current increases they cannot go on increasing linearly after some time core may get saturated or so that is one core may get saturated second is I have a core imbalance and what is known as a flux walking in one direction there could be gradual increase in flux. So, that is also known as a flux walking in one direction. So, these are the limitations of of push ball you need to ensure that both the winding should have both the winding are same number of turns and third one is if there is no dead time between these two dead time in a sense there is before T 1 turns of you are turned on D T 2 what may happen the flux produced by I 1 opposes the flux produced by I 2 number of turns is the same. So, the current is so the number of turns is the same L 1 is equal to L 2 I am neglecting the leakage of that is equal to the mutual they cancel out and now I is limited by the internal resistance itself that is a dead short circuit current is limited by a small r. So, there has to be a dead time between T 1 and T 2. So, these are the limitations of the push pull converter load and I am assuming the current in the inductor is something like this. So, under this condition how does the current through S look like D into T this is T at this point again you are increasing. So, whatever the current that was flowing through the diode just prior to T starts flowing through S. So, current through S looks something like this see the D I by D T of the current that is flowing through S there is a large D I by D T we all know that in the initial when the device is getting turned on the entire area is not available for conduction. So, you if the D I by D T exceeds a rating because the hot spot device may fail. So, a D I by D T is very high also if I see the voltage across the device when I turn on it gradually falls. So, therefore, during on time voltage and current flowing through the device voltage across the device and current flowing through the device are finite and that is good the product is nothing, but the power loss that is taking place. So, as the switching frequency increases losses that are occurring the device also increases. So, therefore, the efficiency point number 1. So, as the losses increases your junction temperature also increases and in a safe operation setting area there is one area is always is limited by or one of the boundaries is the junction temperature that one has to consider. Second is the D I by D T and D I by D T through the device is very high therefore, there will be a E M I electromagnetic interference it will produce its own field try to effect the nearby the control circuit. Can I try to address this limitations? So, this set of a switching is also known as hard switching why hard I am just I am not bothering about what is the current flowing through the device at the instant of turn on. The whatever the pulses that are coming out from the controller are just passed on to this switch. So, depending upon the current that is flowing through the inductor the switch starts taking the current starts carrying the current. So, therefore, D I by D T is very high plus the voltage the product of V and I during conduction is during the turn on is high losses are high. So, that is so losses that are taking place in the device is one of the it puts one of the limit on the switching frequency. So, if I am doing a hard switching if I am doing a hard switching it may not be possible to switch this device at a very high frequency though it is capable of switching at a very high frequency. See I will repeat if I am doing hard switching in other words I am just not bothered about what is the current that is flowing through the device at the instant of turn on due to the power loss that is taking place and other effects I may not be able to increase the switching frequency beyond a certain value. So, if I am in a hard switch converter there is always in a hard switch converter switching frequency is generally low. See one of the question that was asked in one of the centers sir what is the switching frequency in a fly back converter? How am I supposed to answer that? I cannot answer I do not know what sort of a switching is being used are you doing this hard switching? What is the power rating? What is the voltage rating? What sort of a device based on that you can decide? So, if you are using a fly back converter power is of the order of 100 watt also safely for hard switch converter I can say around 25 kilo hertz. First you try to operate at 25 kilo hertz you may not be able to do because all the non idealities that parasitic capacitors inductance all those issues will come. It is very easy to make the circuit to work on a breadboard or on a table the moment you start integrating it the moment you start integrating it the because of this EMI it will affect the control circuit. So, you may not be able to increase beyond a certain value. So, please when I say that I do not know you need to try to understand it may not be possible to often tell you what could be the switching frequency? It all depends on what sort of a switching that you do what sort of a device that you use what is the voltage and power. Fine if you want to start off with any design take one assemble the circuit start with a very conservative figure if you are able to operate it is fine. There are no problem then go on increasing the switching frequency do not have to take that value from me I am no god please that is about it. Second is now coming to the hard switching because of this hard switching there are losses that are taking place. If the losses that are taking place since I have to control the junction temperature I have to use a bigger heat sink therefore, my size increases plus my cooling requirement I may have to use a force cooling as well. Because of this hard switching I cannot increase the switching frequency though in principle this device is capable of operating at a high frequency. I will repeat because of this hard switching we may not be able to it may not be possible to switch this device at a high frequency though this device is capable of switching at a high frequency. Switching frequency may not be governed by this switch switching frequency may be limited by the way you are switching the way you are switching. Can I try to address this issue? Yes it is possible yeah I will try to cover in my next lecture is 9.50 for 10 minutes or so I will take up few questions. Last three minutes you Tanjavur over to you. Secondary of the push pull amplifier behave like say full wave midpoint converter. In midpoint converter at a time the two switches are not conduct but after that you told here at a time d 1 and d 2 conducts how its possible sir please explain. Please try to understand in what context that I have said. See what is this tell me secondary what is this? It is the rectifier circuit sir. Why am I doing this? Why am I using rectifier circuit in DC to DC conversion? So, I am here when I turn on both t 1 and t 2 what happens direction of flux here increase in the positive direction this was positive now the dots are negative I am using the both after the magnetic circuit. So, what will happen? Voltage induced in the secondary has a positive half as well as a negative half. Finally, I want to have a DC to DC I want to have a DC voltage here what do I do filter it? Now your question is yes both the diodes are not conducting in full wave rectifier. Yes here also it happens in the sense when I open when I close when switch s 1 is on only one diode is on when both are off both are off primary is completely cut off do not come do not directly relate to what happens in full what center type transformer in AC to DC converter that you use in the lab. Now when both the diodes are conducting here neither t 1 and t 2 are on both these two are off and if it so happens that in this case if d 1 starts conducting d 2 also will start conducting you need to write the circuit I wrote the circuit equation and that showed you please in the sense I explained to you because this why did I why did I say that this looks like a center type transformer is yes it looks does in the sense secondary is there are it is a center type a full wave rectifier center type transformer why am I using this looks like looks like voltage induced here is AC I want to have DC looks like. Now I have told you the principle of operation now you go back understand in your own way is that ok. Sir thank you sir no problem. Government college Salem over to you. Sir good morning say if I say what do you mean if you can say sir what do you mean by high power density converter high power density DC to DC converter if it means what what it means sir high power density converter. What is a what is a foot area a foot print area foot print area to the other rating I have a huge converter power rating is very small density is very small 75 ampere device full bridge 3 3 legs of a voltage source 30 ampere 30 ampere this is 75 ampere ok 3 legs I need to have a separate now this I do not have 4 ampere now you convert now you try to make a converter with where in you require 75 ampere device you design the converter using this this and this now you try to find out the foot print area the entire area of the size of the converter bit will have a smaller size. So, therefore, do not you think the power density in this case will be higher. So, the overall size the foot print area the ratio of the output power to the foot print area I can say the power density. Thank you sir. Thank you. Hello sir can we have normal primary without tapped primary normal primary in the sense without center tap where will I connect where will I connect T 1 and where will I connect T 2 and where is the supply voltage you tell me can we have a normal primary without center tap somehow I have to reverse the direction of flux both the halves of the entire BH loop in the both half positive first quadrant both I need to use. If you do not have a center tap then I may not be able to use with two switches I may have to change the device configuration. I may have to use the device configuration so with normal winding in principle yes, but not with two switches alone not with two switches alone you have to change the input stage because if dot is positive after sometime I have to make dot as negative I have one source. So, what will you do here it can be done think it over R C P S the question is fine the what is method to reduce I think dead time of switches in circuit method to use a dead time of switches I think I expect this what you mean if I have a input as a voltage source something similar happens in the so on. So, if I these two switches are complementary only one of them can be on if both are on yes there could be a short circuit. So, in other words having turned off having turned off T 1 T 1 is turned off T 2 should be turned on after sometime this is known as a dead time this depends on the type of device. Once upon a time I have to use a dead time when we are using d j t this could be of the order of 10 microsecond. Now, if I am using I G B T of a much higher rating then it could be of the order of the type of device it depends on the type of device that is in a multi stage is boosting if you are increasing the number of stages the efficiency becomes efficiency reduces what is the maximum number of stages we can apply for boosting the voltage level. I think this is what he means I have a d c source boost 1 boost 2 and boost n and finally, he gets a higher voltage this is V d c this could be 7 to 7 7 times V d c this is a given by V d c this could be again whatever getting boosted finally, he will get the required voltage. Now, one is not only the efficiency one is the number of component count as the component count increases reliability may come down reliability one fails everything gone there reliability comes down space size cost and efficiency. Now, instead you can use a transformer and depending upon the power levels choose a suitable power configuration. Now, which one will you use how many number of stages frankly I have no answer you what is the efficiency that you can get here what is the efficiency that you efficiency are not the only issue the component count reliability cost I would like to refrain from answering this question of how many stages I would encourage you to try yourself it is not only the efficiency there are other issues as well as as well size should be as small as as low as small as possible hello sir which range of inductor gets quickly saturated what does it what do you mean by which range of inductor gets quickly saturated g c t s which range of inductor gets quickly saturated what does it mean what do you how to select the range of inductor how to select the range of inductor what do you mean by how to select the range means what in converter, what do you want to ask? So, whether low range or high range. Value of L you mean? Yes sir, value of L. Yes sir. So, it all depends on the ripple. You have to say ripple on the current and the flux and the voltage, that will determine the value of C and value of L. These are the design parameters, sir. These are the design parameters, I will say 5 percent ripple. So, depending upon the voltage and current gets fixed, D i ripple in the current, that is allowed determines the value of L, delta i ripple. Current ripple will determine the value of L and again of course, please in flyback value of L 1 will determine the peak current. I p is given by V dc divided by L 1 into t. This is what we derived in expression. Manipal, what do you? Sir, about the switching frequency I already answered sir. I think few minutes I spent when I was talking about hard switching. Switching frequency to adopted. And as it got bearing on the transform on core material selection in this. Sir, say may be around depending upon depends on the power level sir, up to say 100 kilo hertz also you can go for ferrite core. As the frequency increases, it all depends on what sort of a what type of switching that you apply. Are you doing hard switching or soft switching? I just discussed about hard switching. We will see what happens in short switching, what exactly you win by short switching and can or is it possible to increase the switching frequency as well we will see in the next lecture. But often if you ask me what is the switching frequency that I can choose? Sir, I am bit hesitant to answer this question. So, the simple reason that if I say some figure it may be possible, it may not be possible. It all depends on how well you going to integrate. See if you keep the devices I told that is how I told you when you assemble the converter or when you want to operate when you are working on a table everything works fine. As you try to integrate things are not as straight forward whatever the due to EMI your base drive may get effected. It will show some spikes here and there. So, product integration is not very simple. So, my best my my my advice is you start from a low frequency say a conservative figure of 10 kilo hertz. If you can work at 10 kilo hertz gain sufficient confidence then gone increasing the frequency. All of a sudden if you say start with a 25 kilo hertz it may not be you may not be able to design and integrate it. Let us start with a conservative figure of 10 kilo hertz find your product one cannot be say in a sense your prototype one cannot be the final product. There will be three four stages. So, first you gain enough confidence by fabricating the first prototype start with a conservative figure of 10 to 15 kilo hertz not more than that then slowly slowly you increase. I cannot I can tell you from my experience we have achieved as high as 75 kilo hertz. Now, if I say operate at 75 kilo hertz and you go back to your lab saying that once serve from IITS told me to operate at 75 kilo hertz I will operate it you may not be. So, start with a very conservative even we have started sometime back when we started we started with the 10 kilo hertz also we learnt from our experience. So, that is my sincere request to you please I do not want to throw some figure it just does not make sense. Sir, you want to design a control circuit sir. So, what is the procedure sir because power circuit it is not much difficult to understand sir, but how to design a control circuit easy there in this particular topic or what is and one more doubt regarding control circuit sir. Suppose, if we design for a let us say power circuit can we use the same control circuit for higher rating the power circuits also sir. Sir, I would think that designing a control circuit is simpler than power circuit anyway what exactly even by control circuit is the driver circuit or overall closed loop control. Yes sir, to turn on the switches MOSFET and IGBT what to turn on and turn on the switches. You need to have a control circuit and gate drive circuit I am talking about this is a gate drive circuit BJT gate the philosophy that I used to sir fine I can understand your problem my I will tell you two steps one is the philosophy that we use to design the gate drive circuit for a BJT I would explain almost the same philosophy for MOSFET and IGBT. I will give you I will tell you the design procedure I will tell you the design procedure for a gate drive circuit for MOSFET as well as IGBT I will tell you they are not very difficult making a digital and analog circuit work is not very difficult I am telling you you can incorporate all the protections my worry is here you may be able to may be able to operate it or you may be able to work on a breadboard or on a simple PCB when you try to integrate it you may face some problems my sincere request there are dedicated chips available gate drive circuits use them wherein they are worried about taking care of all this EMI issues interference issues. So, main problem comes in operating DC to DC converters as not the device or not something like that the external interference to the control circuit if your gate drive is very stable take it from me you have achieved 90 percent success 10 percent only remains the only problem is your gate drive works sufficiently reasonably at low frequencies as to increase because of the external interference gate drive starts misbehaving if there are no hardened parts so it comes through experience the integration. So, best thing is I encourage you need to know the philosophy you need to know the philosophy what is being done there are people have spent lot of time on designing and addressing all these issues why not use that same expertise. I would encourage you to use that gate drive circuits that are available I can suggest the suppliers please I do not use the various vendors you can get them and try to operate and I will assure you that it will work, but then you need to know what what may be inside that is all that is all close look control I will try to explain see close to the structure will remain the same structure will remain the same only the gains will change gains will change and the question to another question that you are asked is I have designed the gate drive circuit control circuit for low power what will happen for high power. See as the power rating increases your device also will change now if there is a MOSFET and gate to source voltage is the same in principle you may be able to use the same thing you may be able to use the same thing. So, it all one has to first choose the devices what sort of a control circuit you want from based on the parameters you have to choose the control is not very difficult sir, but one we have to take first step then things go on one or twice device may fail let them fail we have to learn from a failure that is my sincere request to you and my suggestion I would encourage you to instead of using discrete components to make a gate drive circuit I will repeat instead of using discrete components to make a gate drive circuit there are dedicated chips are available s x which is s x circuits are available use them, but understand or know the know the principle or whatever things are there you may use it as a black box, but you need to know what exactly is there inside the black box that is all yeah. Sir where can we get this control circuit sir and suppose if suppose if I have my own problem related to the power circuit suppose I have own design my own control power circuit. So, will be dedicated if I have say my problem will the vendors can design the control circuit accordingly sir. Which vendors which vendor no no sorry sir I did not get your question you say that again. I think you are going to suggest some vendors to move. No no no these are dedicated chips dedicated chips are available dedicated chips are available already existing power existing power circuits. Existing gate drivers gate drivers see gate drivers I said if you use say for IPM you do not need to use external gate driver IPM you do not need to use external everything is built in now for this also there is no I need to have external gate drive, but then dedicated dedicated circuits are available I will bring it those dedicated circuits may be in the next class not today on Monday I will bring and I will show you what I mean. I can directly use them to drive this or use transistors, diodes, resistors and other components capacitors to drive them. So, gate drive is very important if a gate drive is stable I am telling you you have crossed a major hurdle and in principle do not get intimidated take a first step and start assembling things may not work things will not work, but they have to work they have to work take it from me. How will you ensure a symmetrical how will you ensure a symmetrical flux in the core? No no no I will you need to ensure you need to ensure number of turns is the same almost same device drops see small changes here and there should not affect see even if there is a DC flux there is there are issues there are ways to address them there are ways to address them flux working can be addressed it is there in half bridge by putting a capacitor all those things can be addressed they are not a problem at all are you with me if there is a DC flux or the flux the so called flux working can be addressed literature is available I just told you the limitations I may not have suggested the solutions solutions are there see the problem here today I see major the big thing is to find out the problem having found the problem solution can be found out not a issue not a issue. Super what are you? Sir regarding that dead time of the circuit is it any current flowing through the circuit hello. Dead time of the circuit any. Sir please go to the slide sir the practical aspects of the push pull amplifier. What is the push pull? Dead time I mean T 1 and T 2 closing simultaneously or T 1 is not turned off T 2 is on that is what I am trying to tell. Since we have to close the T 1 sorry we have to open the T 1. Open T 1 wait for some time. Sir the case when the both switches T 1 and T 2 will be on. If they are on no no no no no if they are on you are in trouble I am not telling you that when they are on that is known as a dead time no no if both are on you are in trouble current will be limited by the internal resistance that is very small because these are tightly coupled I need to you operate a very high frequency and ensure that T 1 and there is both of them do not they both of them are not on and see these are the timings D T by 2 to T by 2 both T 1 and T 2 are off. At that time these two diodes D 2 starts conducting this I D 2 is the correct direction for the magnetizing current because magnetizing current enter the dot here. So, magnetizing current has to enter the dot N 2 2. So, magnetizing current will flow through magnetizing current will flow through entire magnetizing current through will flow through D 2, but then the remaining I L by 2 will flow through D 1 and the other I L by 2 will flow through D 2 entire magnetizing current has to flow through D 2 because that magnetizing current had had enter the dot. So, magnetizing current has to enter the dot here. So, at that time both T 1 and T 2 are off now it is so happened that D 2 as you are switching for duty cycle has increased and accidentally if you close T 1 and T 2 you are in trouble current is limited by the internal resistance R is that ok see I do not sir it is possible to use a full bridge circuit in the primary coil of a push pull converter that is what I meant yes. See this is the push pull the so called the original push pull converter see the question is instead of using a center tap and two devices in this fashion can we use only one winding and modify the power circuit answer is yes. That is what I told you in the beginning answer is yes, but I did not name the type of power circuit. So, in the literature if you see the conventional push pull this what it is now instead of having two switches and a center tap winding I can have I can have a bridge and connect them accordingly now you require four switches now you require a four switches of course you can further modify it go back and check can I use half bridge it is possible, but then now you require four switches whether now you decide what you want a center tap two switches or four switches see that you need to decide I am just telling you the various possibilities the final decision is going to be yours in principle yes it is possible I can still call this as a push pull I do not know, but then original push pull if you see the text books or something they name push pull as center tap with two switches whatever people have modified it this is one such modification.