[User] Please transcribe this text

[Assistant] You're not going to buy a mansion. You'll probably just have a nice house. You might have a big house. But if you are a multi-millionaire, that means you have more than a million dollars. You have


[User] Please transcribe this text

[Assistant] 20 million or 30 million or 50 million dollars, you might buy a mansion. Certainly if you are a billionaire,


[User] Please transcribe this text

[Assistant] You will most likely own a mansion. So again, a mansion is just a really, really, really big house. A gigantic house.


[User] Please transcribe this text

[Assistant] So in the United States and in Canada, most farms are now gigantic.


[User] Please transcribe this text

[Assistant] Here's a term for you. Many years ago, there were a lot of family farms. A family farm is a small farm, maybe 100 acres, maybe 200 acres. I know that might seem big to you, but uhm, when I was a kid, almost all of my friends lived on a farm.


[User] Please transcribe this text

[Assistant] There were a lot of family farms, so the parents and the kids


[User] Please transcribe this text

[Assistant] Uhm, had cows or pigs or chickens and the farm was just big enough for a family to do all the work.


[User] Please transcribe this text

[Assistant] Now a lot of farms are gigantic. They are actually called agribusinesses. They are enormous farms. Thousands of acres. And there's more than just a family working there. Sometimes a gigantic farm will be three or four families, like


[User] Please transcribe this text

[Assistant] So the one gigantic farm I know, uhm, one brother and his wife have four kids.


[User] Please transcribe this text

[Assistant] Other sister and her husband have three kids. The other sister and her husband have two kids and they all run a gigantic farm. Uh, and some are just businesses. They're just owned and run by, um, by a, by a boss who hires lots of employees.


[User] Please transcribe this text

[Assistant] Signs and billboards. So this is the Hollywood sign. Apparently it's, I'm not sure I'm allowed to show this, but I found a royalty free picture, so I will.


[User] Please transcribe this text

[Assistant] Uhm, the Hollywood sign is gigantic. I think if you were up close, the letters are way bigger than you are as a person. Uhm, but a sign, and then the signs you see along a highway are called billboards.


[User] Please transcribe this text

[Assistant] So this is a billboard and some billboards are definitely gigantic. Uhm, I see more billboards when I'm in Michigan.


[User] Please transcribe this text

[Assistant] Then I do in Canada. I'm not sure if we have


[User] Please transcribe this text

[Assistant] Stricter laws in Canada about billboards, but when I'm in Michigan there are a lot of billboards along the highway. Not as many in Canada, for some reason.


[User] Please transcribe this text

[Assistant] So, there's something called a roadside attraction or a tourist attraction and different cities in the world have decided to build extra big things.


[User] Please transcribe this text

[Assistant] So this is called an Adirondack chair. This is what we call this type of chair. Normally it's human size, but this one is extra big.


[User] Please transcribe this text

[Assistant] Uhm, so some places have decided to build a really big pencil. There's a place in Canada where they mine nickel, and so they have a gigantic, sorry, this isn't a nickel, but this is some money, uhm, they have a gigantic nickel, uh, in Sudbury, Ontario.


[User] Please transcribe this text

[Assistant] So a tourist attraction or a roadside attraction, uh, these are sometimes gigantic. They decide to build something gigantic, uh, for people to look at and for people to see.


[User] Please transcribe this text

[Assistant] So spiders and bugs are actually quite small, but we use the word gigantic when we see one that's extra scary and bigger than you would expect or bigger than normal. So uhm, just last night,


[User] Please transcribe this text

[Assistant] Which wasn't nice, but I laughed because I knew I was going to talk about gigantic spiders today. People who are afraid of spiders when they see a big spider will often say, ah, there's a gigantic spider.


[User] Please transcribe this text

[Assistant] Uhm, don't go in that room, there's a gigantic spider. And sometimes when we are sitting around a campfire, mosquitoes will bite us, and sometimes there will be a really big mosquito, and we'll say, oh, that was a gigantic mosquito.


[User] Please transcribe this text

[Assistant] Malls. So I believe this is the Mall of America. There's also in Canada something called the West Edmonton Mall in Edmonton. I think it's still called that. I'll have to check.


[User] Please transcribe this text

[Assistant] Enormous, it's not gigantic. There is a mall though in Toronto and I can't remember the name and it's gigantic. You could literally


[User] Please transcribe this text

[Assistant] If you track your steps, you could get your 10,000 steps just by shopping in that mall because the mall is gigantic. So again, a mall is a shopping mall.


[User] Please transcribe this text

[Assistant] It's a collection of stores, um, usually indoors, like 99% of the time a mall is something where you are indoors. We do have outdoor malls in this part of Canada though. There's one in Niagara Falls.


[User] Please transcribe this text

[Assistant] But a mall, uh, depending on where you are could be described as gigantic.


[User] Please transcribe this text

[Assistant] So if you go watch soccer, or what most of you call football, you probably go to a gigantic stadium. Uhm, I think soccer stadiums are the biggest stadiums in the world.


[User] Please transcribe this text

[Assistant] Uhm, they're definitely bigger than a hockey arena, uhm, or a basketball arena. Uhm, football stadiums though, in America,


[User] Please transcribe this text

[Assistant] Might also be, I think maybe the biggest stadium in the world is in Texas.


[User] Please transcribe this text

[Assistant] Everything is gigantic in Texas. That's a little bit of a joke. If you're from Texas, I'm not trying to insult you, uh, but, uh, I should ask Brett about this sub day, but for some reason, the state of Texas in the US, um,


[User] Please transcribe this text

[Assistant] In North America, we always imagine everything in Texas is gigantic. Stadiums are gigantic. And etc. I don't know where that came from, but that's a common thing.


[User] Please transcribe this text

[Assistant] Auditoriums. So an auditorium is where you would go in order to hear a concert. Maybe you're going to, maybe you bought, you've bought tickets to the opera. Uh, you would go to an auditorium. That would be the place that you would go in order to


[User] Please transcribe this text

[Assistant] And so sometimes when you have a camera, I can't show you because my camera's right there, uh, when you have a camera, it has a little lens on it or a big lens on it, but sometimes it will have an enormous lens or a gigantic lens. Usually these lenses are used for sporting events.


[User] Please transcribe this text

[Assistant] If you were a wildlife photographer, you probably have a gigantic lens.


[User] Please transcribe this text

[Assistant] Because you want to be able to take pictures of the wild animals from far away especially if they're dangerous.


[User] Please transcribe this text

[Assistant] The same is true for, uhm, sports photographers. You want, you can't be on the field to take a good picture. You need to be far away, uhm, so that you don't disturb the game. So you most likely will have a gigantic lens.


[User] Please transcribe this text

[Assistant] And then I'm going to end with this slide. The universe. So all around us there are planets, there are stars, uhm, there are galaxies. All of those things are gigantic. But the universe is the word we use to talk about everything that exists. So the universe


[User] Please transcribe this text

[Assistant] Is the most gigantic thing in the world. There's nothing bigger than the universe because everything is part of the universe.


[User] Please transcribe this text

[Assistant] Why does she have to work overtime again? She is so busy.


[User] Please transcribe this text

[Assistant] Why does she have to work overtime again? She is so busy.


[User] Please transcribe this text

[Assistant] Why does she have to work overtime again? She is so busy.


[User] Please transcribe this text

[Assistant] Not yet. The light in his room is still on.


[User] Please transcribe this text

[Assistant] Not yet. The light in his room is still on.


[User] Please transcribe this text

[Assistant] I think so. We made a movie date last time, but he came in the middle of that movie.


[User] Please transcribe this text

[Assistant] I think so. We made a movie date last time, but he came in the middle of that movie.


[User] Please transcribe this text

[Assistant] I think so. We made a movie date last time, but he came in the middle of that movie.


[User] Please transcribe this text

[Assistant] If we don't finish today, we need to do it tomorrow.


[User] Please transcribe this text

[Assistant] If we don't finish today, we need to do it tomorrow.


[User] Please transcribe this text

[Assistant] If we don't finish today, we need to do it tomorrow.


[User] Please transcribe this text

[Assistant] I didn't bring my umbrella yesterday, so I was caught in the rain.


[User] Please transcribe this text

[Assistant] I didn't bring my umbrella yesterday, so I was caught in the rain.


[User] Please transcribe this text

[Assistant] I didn't bring my umbrella yesterday, so I was caught in the rain.


[User] Please transcribe this text

[Assistant] Not bad. She asked me so many questions.


[User] Please transcribe this text

[Assistant] Not bad. She asked me so many questions.


[User] Please transcribe this text

[Assistant] Not bad. She asked me so many questions.


[User] Please transcribe this text

[Assistant] Just cleaning my room, washing clothes, and watching TV.


[User] Please transcribe this text

[Assistant] Just cleaning my room, washing clothes, and watching TV.


[User] Please transcribe this text

[Assistant] Just cleaning my room, washing clothes, and watching TV.


[User] Please transcribe this text

[Assistant] He said it wasn't serious, and he gave me medicine for three days.


[User] Please transcribe this text

[Assistant] He said it wasn't serious, and he gave me medicine for three days.


[User] Please transcribe this text

[Assistant] He said it wasn't serious, and he gave me medicine for three days.


[User] Please transcribe this text

[Assistant] The weather forecast reports it will be cloudy to sunny.


[User] Please transcribe this text

[Assistant] The weather forecast report sunny.


[User] Please transcribe this text

[Assistant] Are tuition fees and living expenses very high in there?


[User] Please transcribe this text

[Assistant] Are tuition fees and living expenses very high in there?


[User] Please transcribe this text

[Assistant] Are tuition fees and living expenses very high in there?


[User] Please transcribe this text

[Assistant] I heard that she began to learn Latin dancing at the age of five.


[User] Please transcribe this text

[Assistant] I heard that she began to learn Latin dancing at the age of five.


[User] Please transcribe this text

[Assistant] I heard that she began to learn Latin dancing at the age of five.


[User] Please transcribe this text

[Assistant] That good? Let's go to that new restaurant.


[User] Please transcribe this text

[Assistant] That good? Let's go to that new restaurant.


[User] Please transcribe this text

[Assistant] That good? Let's go to that new restaurant.


[User] Please transcribe this text

[Assistant] I am so sorry. I didn't know what time it was.


[User] Please transcribe this text

[Assistant] I am so sorry. I didn't know what time it was.


[User] Please transcribe this text

[Assistant] I am so sorry. I didn't know what time it was.


[User] Please transcribe this text

[Assistant] Of course you will. You eat well, but don't exercise.


[User] Please transcribe this text

[Assistant] Of course you will. You eat well, but don't exercise.


[User] Please transcribe this text

[Assistant] Of course you will. You eat well, but don't exercise.


[User] Please transcribe this text

[Assistant] I promise to take my kid to the zoo this weekend.


[User] Please transcribe this text

[Assistant] I promise to take my kid to the zoo this weekend.


[User] Please transcribe this text

[Assistant] I promise to take my kid to the zoo this weekend.


[User] Please transcribe this text

[Assistant] I'm going on a run at 6, in about a half an hour.


[User] Please transcribe this text

[Assistant] I'm going on a run at 6, in about a half an hour.


[User] Please transcribe this text

[Assistant] I'm going on a run at 6, in about a half an hour.


[User] Please transcribe this text

[Assistant] There's both a coffee shop and bookstore on the top floor of that building. If you buy a book, you can go directly to the coffee shop and enjoy it.


[User] Please transcribe this text

[Assistant] There's both a coffee shop and bookstore on the top floor of that building. If you buy a book, you can go directly to the coffee shop and enjoy it.


[User] Please transcribe this text

[Assistant] There's both a coffee shop and bookstore on the top floor of that building.


[User] Please transcribe this text

[Assistant] If you buy a book, you can go directly to the coffee shop and enjoy it.


[User] Please transcribe this text

[Assistant] My friend invited me to have a hot pot tonight.


[User] Please transcribe this text

[Assistant] My friend invited me to have a hot pot tonight.


[User] Please transcribe this text

[Assistant] My friend invited me to have a hot pot tonight.


[User] Please transcribe this text

[Assistant] Really? After that, I will go there to buy something.


[User] Please transcribe this text

[Assistant] Really? After that, I will go there to buy something.


[User] Please transcribe this text

[Assistant] Really? After that, I will go there to buy something.


[User] Please transcribe this text

[Assistant] You have had a long day. Just go to bed early this evening.


[User] Please transcribe this text

[Assistant] You have had a long day. Just go to bed early this evening.


[User] Please transcribe this text

[Assistant] You have had a long day. Just go to bed early this evening.


[User] Please transcribe this text

[Assistant] I do not want to eat cheap food anymore, but I do not have the money to eat expensive food.


[User] Please transcribe this text

[Assistant] Me too. I do not want to eat cheap food anymore, but I do not have the money to eat expensive food.


[User] Please transcribe this text

[Assistant] Me too. I do not want to eat cheap food anymore, but I do not have the money to eat expensive food.


[User] Please transcribe this text

[Assistant] No, I've taken my child to go to the hospital several times, but he is still not well.


[User] Please transcribe this text

[Assistant] No, I've taken my child to go to the hospital several times, but he is still not well.


[User] Please transcribe this text

[Assistant] No, I've taken my child to go to the hospital several times, but he is still not well.


[User] Please transcribe this text

[Assistant] He just came to Japan recently, so he doesn't speak Japanese very well.


[User] Please transcribe this text

[Assistant] He just came to Japan recently, so he doesn't speak Japanese very well.


[User] Please transcribe this text

[Assistant] He just came to Japan recently, so he doesn't speak Japanese very well.


[User] Please transcribe this text

[Assistant] Yes, I've always wanted to visit the Sagrada Familia in Barcelona.


[User] Please transcribe this text

[Assistant] Yes, I've always wanted to visit the Sagrada Familia in Barcelona.


[User] Please transcribe this text

[Assistant] Yes, I've always wanted to visit the Sagrada Familia in Barcelona.


[User] Please transcribe this text

[Assistant] Yes, what about its taste? Is it good?


[User] Please transcribe this text

[Assistant] Yes, what about its taste? Is it good?


[User] Please transcribe this text

[Assistant] Yes, what about its taste? Is it good?


[User] Please transcribe this text

[Assistant] Phuket is so much fun that I want to go there again.


[User] Please transcribe this text

[Assistant] Phuket is so much fun that I want to go there again.


[User] Please transcribe this text

[Assistant] Phuket is so much fun that I want to go there again.


[User] Please transcribe this text

[Assistant] I think so. People behind him can't see anything when he gets up.


[User] Please transcribe this text

[Assistant] I think so. People behind him can't see anything when he gets up.


[User] Please transcribe this text

[Assistant] I think so. People behind him can't see anything when he gets up.


[User] Please transcribe this text

[Assistant] I usually go to the food court on the fourth floor of the department store. It's cheap and delicious.


[User] Please transcribe this text

[Assistant] I usually go to the food court on the fourth floor of the department store. It's cheap and delicious.


[User] Please transcribe this text

[Assistant] I usually go to the food court on the fourth floor of the department store. It's cheap and delicious.


[User] Please transcribe this text

[Assistant] I did it yesterday, so my sister should do it today.


[User] Please transcribe this text

[Assistant] I did it yesterday, so my sister should do it today.


[User] Please transcribe this text

[Assistant] I did it yesterday, so my sister should do it today.


[User] Please transcribe this text

[Assistant] No, I won't. They are still wearable after being darned.


[User] Please transcribe this text

[Assistant] No, I won't. They are still wearable after being darned.


[User] Please transcribe this text

[Assistant] No, I won't. They are still wearable after being darned.


[User] Please transcribe this text

[Assistant] I am feeling a little bit uncomfortable. Now, I want to go back.


[User] Please transcribe this text

[Assistant] I am feeling a little bit uncomfortable. Now, I want to go back.


[User] Please transcribe this text

[Assistant] I am feeling a little bit uncomfortable. Now, I want to go back.


[User] Please transcribe this text

[Assistant] I am fine, and I can leave the hospital next month.


[User] Please transcribe this text

[Assistant] I am fine, and I can leave the hospital next month.


[User] Please transcribe this text

[Assistant] I am fine, and I can leave the hospital next month.


[User] Please transcribe this text

[Assistant] That's enough. The shop has large portions.


[User] Please transcribe this text

[Assistant] Today, I already had a rest, and I want to get more sleep.


[User] Please transcribe this text

[Assistant] Today, I already had a rest, and I want to get more sleep.


[User] Please transcribe this text

[Assistant] Today, I already had a rest, and I want to get more sleep.


[User] Please transcribe this text

[Assistant] The food is cold. Heat it up in the microwave.


[User] Please transcribe this text

[Assistant] The food is cold. Heat it up in the microwave.


[User] Please transcribe this text

[Assistant] The food is cold. Heat it up in the microwave.


[User] Please transcribe this text

[Assistant] That's good. They are all my good friends. Let me introduce them to you.


[User] Please transcribe this text

[Assistant] That's good. They are all my good friends. Let me introduce them to you.


[User] Please transcribe this text

[Assistant] That's good. They are all my good friends. Let me introduce them to you.


[User] Please transcribe this text

[Assistant] Yes, I went to bed at 2 o'clock and got up at 5 o'clock.


[User] Please transcribe this text

[Assistant] Yes. I went to bed at 2 o'clock and got up at 5 o'clock.


[User] Please transcribe this text

[Assistant] Yes. I went to bed at 2 o'clock and got up at 5 o'clock.


[User] Please transcribe this text

[Assistant] Sorry, I have to work on my paper at home tonight.


[User] Please transcribe this text

[Assistant] Sorry, I have to work on my paper at home tonight.


[User] Please transcribe this text

[Assistant] Sorry, I have to work on my paper at home tonight.


[User] Please transcribe this text

[Assistant] Yes, it's next to the elevator on the ground floor.


[User] Please transcribe this text

[Assistant] Yes, it's next to the elevator on the ground floor.


[User] Please transcribe this text

[Assistant] Yes, it's next to the elevator on the ground floor.


[User] Please transcribe this text

[Assistant] I did not buy it. It was a gift from my friend.


[User] Please transcribe this text

[Assistant] I did not buy it. It was a gift from my friend.


[User] Please transcribe this text

[Assistant] I did not buy it. It was a gift from my friend.


[User] Please transcribe this text

[Assistant] I am so sorry. I was stuck in traffic.


[User] Please transcribe this text

[Assistant] I am so sorry. I was stuck in traffic.


[User] Please transcribe this text

[Assistant] I am so sorry. I was stuck in traffic.


[User] Please transcribe this text

[Assistant] It is not enough, but I don't have another choice.


[User] Please transcribe this text

[Assistant] It is not enough, but I don't have another choice.


[User] Please transcribe this text

[Assistant] It is not enough, but I don't have another choice.


[User] Please transcribe this text

[Assistant] It is a pleasant atmosphere and the food is great.


[User] Please transcribe this text

[Assistant] It is a pleasant atmosphere and the food is great.


[User] Please transcribe this text

[Assistant] It is a pleasant atmosphere and the food is great.


[User] Please transcribe this text

[Assistant] I am sorry. It was borrowed from the library.


[User] Please transcribe this text

[Assistant] I am sorry. It was borrowed from the library.


[User] Please transcribe this text

[Assistant] I am sorry. It was borrowed from the library.


[User] Please transcribe this text

[Assistant] Not sure. Some people will rest at home, and some people will go to travel.


[User] Please transcribe this text

[Assistant] Not sure. Some people will rest at home, and some people will go to travel.


[User] Please transcribe this text

[Assistant] Not sure. Some people will rest at home, and some people will go to travel.


[User] Please transcribe this text

[Assistant] I'm not tall like you, so your clothes may not fit me.


[User] Please transcribe this text

[Assistant] I'm not tall like you, so your clothes may not fit me.


[User] Please transcribe this text

[Assistant] I'm not tall like you, so your clothes may not fit me.


[User] Please transcribe this text

[Assistant] It doesn't matter, but you better rest up and take your medicine on time.


[User] Please transcribe this text

[Assistant] It doesn't matter, but you better rest up and take your medicine on time.


[User] Please transcribe this text

[Assistant] It doesn't matter, but you better rest up and take your medicine on time.


[User] Please transcribe this text

[Assistant] Read, study, watch movies, and have dinner and chat with my friends.


[User] Please transcribe this text

[Assistant] Read, study, watch movies, and have dinner and chat with my friends.


[User] Please transcribe this text

[Assistant] Read, study, watch movies, and have dinner and chat with my friends.


[User] Please transcribe this text

[Assistant] Of course. You can see it as soon as you get out of the station.


[User] Please transcribe this text

[Assistant] Of course. You can see it as soon as you get out of the station.


[User] Please transcribe this text

[Assistant] Of course. You can see it as soon as you get out of the station.


[User] Please transcribe this text

[Assistant] It was so boring. I fell asleep when it was showing.


[User] Please transcribe this text

[Assistant] It was so boring. I fell asleep when it was showing.


[User] Please transcribe this text

[Assistant] It was so boring. I fell asleep when it was showing.


[User] Please transcribe this text

[Assistant] Over one week. I have to give it back tomorrow.


[User] Please transcribe this text

[Assistant] Over one week. I have to give it back tomorrow.


[User] Please transcribe this text

[Assistant] Over one week. I have to give it back tomorrow.


[User] Please transcribe this text

[Assistant] Yes, but I haven't been to the Forbidden City.


[User] Please transcribe this text

[Assistant] Yes, but I haven't been to the Forbidden City.


[User] Please transcribe this text

[Assistant] Yes, but I haven't been to the Forbidden City.


[User] Please transcribe this text

[Assistant] The street is very busy. Let's take Boston Street.


[User] Please transcribe this text

[Assistant] The street is very busy. Let's take Boston Street.


[User] Please transcribe this text

[Assistant] The street is very busy. Let's take Boston Street.


[User] Please transcribe this text

[Assistant] I feel weak, and my head and throat have something wrong.


[User] Please transcribe this text

[Assistant] I feel weak, and my head and throat have something wrong.


[User] Please transcribe this text

[Assistant] I feel weak, and my head and throat have something wrong.


[User] Please transcribe this text

[Assistant] In 1997, and I have lived in Beijing for more than 20 years.


[User] Please transcribe this text

[Assistant] In 1997, and I have lived in Beijing for more than 20 years.


[User] Please transcribe this text

[Assistant] In 1997, and I have lived in Beijing for more than 20 years.


[User] Please transcribe this text

[Assistant] He is a swimming coach and has participated in many races before.


[User] Please transcribe this text

[Assistant] He is a swimming coach and has participated in many races before.


[User] Please transcribe this text

[Assistant] He is a swimming coach and has participated in many races before.


[User] Please transcribe this text

[Assistant] I'll go there by subway. It is quick and convenient.


[User] Please transcribe this text

[Assistant] I'll go there by subway. It is quick and convenient.


[User] Please transcribe this text

[Assistant] I'll go there by subway. It is quick and convenient.


[User] Please transcribe this text

[Assistant] Me too. So I have a good relationship with my grandmother.


[User] Please transcribe this text

[Assistant] Me too. So I have a good relationship with my grandmother.


[User] Please transcribe this text

[Assistant] Me too. So I have a good relationship with my grandmother.


[User] Please transcribe this text

[Assistant] Take two tablets three times a day. You'd better take it after meals.


[User] Please transcribe this text

[Assistant] Take two tablets three times a day. You'd better take it after meals.


[User] Please transcribe this text

[Assistant] Take two tablets three times a day. You'd better take it after meals.


[User] Please transcribe this text

[Assistant] If you come to London, I'll be your guide.


[User] Please transcribe this text

[Assistant] I also think it's better for you two not to work in the same unit.


[User] Please transcribe this text

[Assistant] I also think it's better for you two not to work in the same unit.


[User] Please transcribe this text

[Assistant] I also think it's better for you two not to work in the same unit.


[User] Please transcribe this text

[Assistant] No, my parents will come here for Chinese New Year.


[User] Please transcribe this text

[Assistant] No, my parents will come here for Chinese New Year.


[User] Please transcribe this text

[Assistant] No, my parents will come here for Chinese New Year.


[User] Please transcribe this text

[Assistant] I am glad to hear that. Where else would you like to go?


[User] Please transcribe this text

[Assistant] I am glad to hear that. Where else would you like to go?


[User] Please transcribe this text

[Assistant] I am glad to hear that. Where else would you like to go?


[User] Please transcribe this text

[Assistant] Turn right after you get out of the elevator on the third floor, and then go all the way to the end.


[User] Please transcribe this text

[Assistant] Turn right after you get out of the elevator on the third floor, and then go all the way to the end.


[User] Please transcribe this text

[Assistant] Turn right after you get out of the elevator on the third floor, and then go all the way to the end.


[User] Please transcribe this text

[Assistant] Go straight and turn left at the third signal.


[User] Please transcribe this text

[Assistant] Go straight and turn left at the third signal.


[User] Please transcribe this text

[Assistant] Go straight and turn left at the third signal.


[User] Please transcribe this text

[Assistant] He goes to the gym to do exercise in the morning and goes to the coffee shop to have a conversation with friends in the afternoon.


[User] Please transcribe this text

[Assistant] He goes to the gym to do exercise in the morning and goes to the coffee shop to have a conversation with friends in the afternoon.


[User] Please transcribe this text

[Assistant] He goes to the gym to do exercise in the morning and goes to the coffee shop to have a conversation with friends in the afternoon.


[User] Please transcribe this text

[Assistant] Don't be nervous. You are so hardworking. There'll be no problem.


[User] Please transcribe this text

[Assistant] Don't be nervous. You are so hardworking. There'll be no problem.


[User] Please transcribe this text

[Assistant] Don't be nervous. You are so hardworking. There'll be no problem.


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[Assistant] No. I called ten times in a row, but nobody answered.


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[Assistant] No. I called ten times in a row, but nobody answered.


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[Assistant] No. I called ten times in a row, but nobody answered.


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[Assistant] I just finished my class. There was no time for me to read it.


[User] Please transcribe this text

[Assistant] I just finished my class. There was no time for me to read it.


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[Assistant] I just finished my class. There was no time for me to read it.


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[Assistant] Definitely. I feel really upset if I forget it.


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[Assistant] Definitely. I feel really upset if I forget it.


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[Assistant] Definitely. I feel really upset if I forget it.


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[Assistant] Yes, we will meet at 3pm in Starbucks.


[User] Please transcribe this text

[Assistant] Yes, we will meet at 3pm in Starbucks.


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[Assistant] Yes, we will meet at 3pm in Starbucks.


[User] Please transcribe this text

[Assistant] Unfortunately, I'm busy tonight. Let's do it another day.


[User] Please transcribe this text

[Assistant] Unfortunately, I'm busy tonight. Let's do it another day.


[User] Please transcribe this text

[Assistant] Unfortunately, I'm busy tonight. Let's do it another day.


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[Assistant] No, I want to eat first before I do it.


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[Assistant] No, I want to eat first before I do it.


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[Assistant] No. I want to eat first before I do it.


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[Assistant] You have had too much. Don't drink anymore.


[User] Please transcribe this text

[Assistant] You have had too much. Don't drink anymore.


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[Assistant] You have had too much. Don't drink anymore.


[User] Please transcribe this text

[Assistant] My father forced me to practice calligraphy for several years when I was young.


[User] Please transcribe this text

[Assistant] My father forced me to practice calligraphy for several years when I was young.


[User] Please transcribe this text

[Assistant] My father forced me to practice calligraphy for several years when I was young.


[User] Please transcribe this text

[Assistant] Don't wait for me. You can go first.


[User] Please transcribe this text

[Assistant] Don't wait for me. You can go first.


[User] Please transcribe this text

[Assistant] Don't wait for me. You can go first.


[User] Please transcribe this text

[Assistant] No, my friend painted it and gave it to me.


[User] Please transcribe this text

[Assistant] No. My friend painted it and gave it to me.


[User] Please transcribe this text

[Assistant] No, my friend painted it and gave it to me.


[User] Please transcribe this text

[Assistant] Have you ever watched a baby learning to crawl? Because as any parent knows, it's gripping.


[User] Please transcribe this text

[Assistant] First they wriggle about on the floor, usually backwards. But then they drag themselves forwards. And then they pull themselves up to stand. And we all clap.


[User] Please transcribe this text

[Assistant] We tell it in our story of evolution as well. From our lolloping ancestors, to Homo erectus finally upright, to Homo sapiens depicted, always a man, always mid-stride.


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[Assistant] That need to grow, whether or not they make us thrive.


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[Assistant] And what we need, especially in the richest countries


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[Assistant] Yes, it's a little flip in words, hiding a profound shift in mindset.


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[Assistant] But I believe this is the shift we need to make if we, humanity, are going to thrive here together this century. So where did this obsession with growth come from?


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[Assistant] In the richest of countries, governments think that the solution to their economic problems lies in more growth. Just how that happened.


[User] Please transcribe this text

[Assistant] Is best told through the 1960 classic by W. W. Rostow. I love it so much. I have a first edition copy.


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[Assistant] Where compound interest is built into the economy's institutions, and growth becomes the normal condition.


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[Assistant] Well, you can hear the implicit airplane metaphor in this story, but this plane is like no other, because it can never be allowed to land.


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[Assistant] What to do when the increase in real income itself loses its charm?


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[Assistant] He asked that question, but he never answered it, and here's why. The year was 1960, he was an advisor to the presidential candidate John F. Kennedy, who was running for election on the promise of five percent growth.


[User] Please transcribe this text

[Assistant] So Rosto's job was to keep that plane flying, not to ask if, how or when it could ever be allowed to land.


[User] Please transcribe this text

[Assistant] Putting publicly traded companies under constant pressure to deliver growing sales, growing market share and growing profits. Because banks create money as debt bearing interest, which must be repaid with more.


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[Assistant] We're politically addicted to growth because politicians want to raise tax revenue without raising taxes. And a growing GDP seems a sure way to do that.


[User] Please transcribe this text

[Assistant] But if their economy stops growing while the rest keep going, well, they'll be booted out by the next emerging powerhouse.


[User] Please transcribe this text

[Assistant] And we are socially addicted to growth, because thanks to a century of consumer propaganda.


[User] Please transcribe this text

[Assistant] Which fascinatingly was created by Edward Bernays, the nephew of Sigmund Freud, who realized that his uncle's psychotherapy could be turned into very lucrative retail therapy.


[User] Please transcribe this text

[Assistant] If we could be convinced to believe that we transform ourselves every time we buy something more. None of these addictions are insurmountable.


[User] Please transcribe this text

[Assistant] But they all deserve far more attention than they currently get. Because look where this journey's been taking us.


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[Assistant] And that increase has brought prosperity to billions of people. But the global economy has also become incredibly divisive.


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[Assistant] With the vast share of returns to wealth now accruing to a fraction of the global one percent.


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[Assistant] Rapidly destabilizing this delicately balanced planet on which all of our lives depend.


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[Assistant] Politicians know it, and so they offer new destinations for growth. You can have green growth, inclusive growth, smart, resilient, balanced growth. Choose any future you want, so long as you choose growth. I think it's time to choose a higher ambition, a far bigger one.


[User] Please transcribe this text

[Assistant] Within the means of this extraordinary, unique, living planet, so that we and the rest of nature can thrive.


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[Assistant] Progress on this goal isn't going to be measured with a metric of money. We need a dashboard of indicators.


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[Assistant] But let me introduce you to the one doughnut that might actually turn out to be good for us. So imagine humanity's resource use radiating out from the middle. That hole in the middle is a place where people are falling short on life's essentials. They don't have the food, healthcare, education, political voice, housing that every person needs for a life of dignity and opportunity.


[User] Please transcribe this text

[Assistant] We want to get everybody out of the hole, over the social foundation and into that green doughnut itself. But, and it's a big but,


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[Assistant] We cannot let our collective resource use overshoot that outer circle, the ecological ceiling, because there we put so much pressure on this extraordinary planet that we begin to kick it out of kilter. We cause climate breakdown. We acidify the oceans, a hole in the ozone layer.


[User] Please transcribe this text

[Assistant] So this double-sided challenge to meet the needs of all within the means of the planet, it invites a new shape of progress. No longer this ever-rising line of growth, but a sweet spot for humanity.


[User] Please transcribe this text

[Assistant] And I was really struck once I'd drawn this picture to realize that the symbol of well-being in many ancient cultures reflects this very same sense of dynamic balance from the Maori takarangi.


[User] Please transcribe this text

[Assistant] Well, that's a key question, because as these red wedges show, right now we are far from balance, falling short and overshooting at the same time.


[User] Please transcribe this text

[Assistant] Risking irreversible impacts of climate breakdown and ecosystem collapse.


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[Assistant] This is the state of humanity and our planetary home. We, the people of the early 21st century, this is our selfie.


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[Assistant] We need ideas of our own, because we are the first generation to see this.


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[Assistant] You see, 20th century economics assured us that if growth creates inequality, don't try to redistribute, because more growth will even things up again. If growth creates pollution,


[User] Please transcribe this text

[Assistant] We need to create economies that tackle this shortfall and overshoot together by design. We need economies that are regenerative and distributive by design.


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[Assistant] You see, we've inherited degenerative industries. We take us materials, make them into stuff we want, use it for a while, often only once, and then throw it away.


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[Assistant] And that is pushing us over planetary boundaries. So we need to bend those arrows around.


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[Assistant] Create economies that work with and within the cycles of the living world, so that resources are never used up, but are used again and again. Economies that run on sunlight, where waste from one process is food for the next. And this kind of regenerative design is popping up everywhere.


[User] Please transcribe this text

[Assistant] Over 100 cities worldwide, from Quito to Oslo, from Harare to Hobart, already generate more than 70 percent of their electricity from sun, wind and waves.


[User] Please transcribe this text

[Assistant] Cities like London, Glasgow, Amsterdam are pioneering circular city design, finding ways to turn the waste from one urban process into food for the next. And from Tigray, Ethiopia, to Queensland, Australia,


[User] Please transcribe this text

[Assistant] Concentrated wealth, knowledge and power in few hands.


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[Assistant] This century, we can design our technologies and institutions to distribute wealth, knowledge and empowerment to many. Instead of fossil fuel energy and large-scale manufacturing,


[User] Please transcribe this text

[Assistant] And corporations that still pursue maximum rate of return for their shareholders, well, they suddenly look rather out of date.


[User] Please transcribe this text

[Assistant] Next to social enterprises that are designed to generate multiple forms of value and share it with those throughout their networks. If we can harness today's technologies, from AI to blockchain,


[User] Please transcribe this text

[Assistant] To the internet of things, to material science, if we can harness these in service,


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[Assistant] Create extraordinary opportunities for the 21st century economy. So, why does this leave Rostow's airplane ride?


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[Assistant] Well, for some, it still carries the hope of endless green growth, the idea that thanks to dematerialization,


[User] Please transcribe this text

[Assistant] Yes, we need to dematerialize our economies, but this dependency on unending growth cannot be decoupled from resource use on anything like the scale required to bring us safely back within planetary boundaries.


[User] Please transcribe this text

[Assistant] I know this way of thinking about growth is unfamiliar, because growth is good, no? We want our children to grow, our gardens to grow.


[User] Please transcribe this text

[Assistant] It's a phase, but many economies like Ethiopia and Nepal today may be in that phase. Their economies are growing at seven percent a year. But look again to nature, because from your children's feet to the Amazon forest, nothing in nature grows forever. Things grow.


[User] Please transcribe this text

[Assistant] Because we intuitively understand that when something tries to grow forever within a healthy, living, thriving system, it's a threat to the health of the whole.


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[Assistant] So why would we imagine that our economies would be the one system that could buck this trend and succeed by growing forever?


[User] Please transcribe this text

[Assistant] ...that enable us to overcome this structural dependency on growth, so that we can instead focus on thriving in balance.


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[Assistant] And if the mere idea of boundaries makes you feel, well, bounded, think again. Because the world's most ingenious people turn boundaries into the source of their creativity. From Mozart on his five-octave piano, Jimi Hendrix on his six-string guitar, Serena Williams on a tennis court. It's boundaries that unleash our potential.


[User] Please transcribe this text

[Assistant] And the doughnut's boundaries unleash the potential for humanity to thrive with boundless creativity, participation, belonging and meaning.


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[Assistant] It's going to take all the ingenuity that we have got to get there. So bring it on. Thank you.


[User] Please transcribe this text

[Assistant] Hold on there! You can't throw a rock at a girl! Are you crazy or something? You can't hit a girl with anything!


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[Assistant] Alright, so what we've been doing up until now is creating these bit different building blocks and understanding them. These are basically just, you can think about them as Lego.


[User] Please transcribe this text

[Assistant] Blocks that you can use to make more complex circuits. And the first step, the next step you're going to take, and we've started taking, is basically building op-amps.


[User] Please transcribe this text

[Assistant] So we'll start building op amps and we'll try to come up and we'll see how the progression of that process.


[User] Please transcribe this text

[Assistant] What is an op-amp? But if you think about an op-amp, really, an op-amp is a device that has a differential input and a single-ended output. And it has some substantial gain, right? And you want, generally speaking, if it's a voltage amplifier, you want the input impedance not to be too low.


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[Assistant] The simplest stage that we had in terms of a differential to single-ended conversion was a stage that we extensively discussed, which was a stage like this.


[User] Please transcribe this text

[Assistant] So you have a differential pair, and we've looked at this extensively, with a tail current source, and then you have a current mirror, off the top,


[User] Please transcribe this text

[Assistant] That basically reflects this mirror. And we know exactly what the gain of this thing is. We've discussed this extensively multiple times. So that should not be a surprise. So what happens here is that you have this stage. So this is your differential input.


[User] Please transcribe this text

[Assistant] And that's your output. Now, we know the gain of this thing is basically the GM of one of these transistors times the RON and ROP. Those are the impedances you see across here.


[User] Please transcribe this text

[Assistant] And we have even calculated some of these numbers. I'm sorry, ROP and RON.


[User] Please transcribe this text

[Assistant] And it's driven by GM of these guys. We also know that if you have a fully differential signal, this is VID over 2, this is negative VID over 2, and what it does is that it induces a current GM VID over 2, and if you flip the sign,


[User] Please transcribe this text

[Assistant] This would be GMV ID over 2. This current would be reflected here by the current mirror if the ratio is 1 to 1, which typically is in this stage.


[User] Please transcribe this text

[Assistant] This becomes VID over 2. There are two that are injecting current into this node, and that current gets multiplied by the total resistance from this node to ground in differential mode, which is the parallel combination of those two. So the gain becomes GM, uh, RON, parallel ROP.


[User] Please transcribe this text

[Assistant] And say, okay, if I wanna make it really simple, I can even have something like this.


[User] Please transcribe this text

[Assistant] And if you want to make more sophisticated, which you will, uhm, you can have more sophisticated current sources here, references that are independent of things. But let's look at this from a slightly different perspective now. One of the things that we want to look at is, okay,


[User] Please transcribe this text

[Assistant] Is this, what is the range of operation in terms of voltages?


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[Assistant] That the, for example, the input of this thing can have. When I say range of operation, I mean in particular, common mode voltage. So let's say you are not applying any differential voltage. What is the range of common mode voltages where this is operational?


[User] Please transcribe this text

[Assistant] Well, we can find out. Basically, the requirement here is that you need to make sure, so let's say, for the sake of organics, it's a single supply, so let's say 0 and VDD.


[User] Please transcribe this text

[Assistant] It could be negative, positive, et cetera, et cetera. Doesn't matter right now. But, uh, for example, we want to see how low can this voltage, the common mode, be before things start going bad. And what do we mean by going bad? Meaning basically transistors leaving the pinch-off region going into trial.


[User] Please transcribe this text

[Assistant] And this is that we're not intended to be in triode region going into triode.


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[Assistant] And what's the problem, for example, if this transistor or that transistor goes into triode reach? What would happen?


[User] Please transcribe this text

[Assistant] Right, I mean, it becomes less dependent and it will exhibit itself, manifest itself as RON dropping significantly, for example. The output, because now you're seeing the channel.


[User] Please transcribe this text

[Assistant] You're seeing that resistance, right? You're seeing that that, this part of the slope, so if you look at the IV characteristic, there's this flatter part which has higher outputs and you're starting to see this part. And this is a low resistance, the gain will start dropping significantly.


[User] Please transcribe this text

[Assistant] So that's not a good thing. So obviously we want to maintain that in that region. So what is the range? So what is the, basically we have to see what, and if this for example starts crunching, meaning that essentially it goes into triode region, then the output resistance of this guy will start dropping, the common mode rejection ratio will start suffering and things will go back.


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[Assistant] So what is the lowest this can go? What is the minimum this can be?


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[Assistant] Gain overdrive, exactly, delta Vgs, right? Let's call it delta Vgs. I don't know, it's delta Vgs really, some 5. But, but, some delta Vgs, right? So this is the lowest it can be. So now, based on that, can we determine what is the lowest voltage this guy can be?


[User] Please transcribe this text

[Assistant] 2 delta, 2 delta VGS plus a VT, right? How did we get that? Because this voltage is gonna be a VT plus delta VGS of this guy. Right? Let's call delta VGS 1.


[User] Please transcribe this text

[Assistant] Okay, now therefore, this guy cannot go lower than VT plus some two delta VGS's or delta VGS1 plus delta VGS5.


[User] Please transcribe this text

[Assistant] Numbers, let's say, put some numbers. So let's say, let's say, your VT is 0.6 volts. And let's say, your delta VGS is 0.3.


[User] Please transcribe this text

[Assistant] Or .4, let's say .3 volts. And another .3 volts here. You're looking at what? You're looking at 1.2 volts.


[User] Please transcribe this text

[Assistant] So the input common mode of the common mode of the input or essentially the input voltage cannot go below that because if it goes below that essentially then for even one of the terminals if it goes a little bit below that then you can start crunching this guy.


[User] Please transcribe this text

[Assistant] Let's say you're running off of a 3V voltage or even worse, 1.5V voltage, right?


[User] Please transcribe this text

[Assistant] Then your range, your input range is very limited because you can't go down. But again, if you are a 3, the low end of this thing is limited.


[User] Please transcribe this text

[Assistant] Right, so that, that there's a limit set by this. Now, how about the high end? How high can it go?


[User] Please transcribe this text

[Assistant] So what is the V common mode maximum? What determines that?


[User] Please transcribe this text

[Assistant] What would happen? This voltage, this, remember, this voltage, this node voltage will essentially, primarily follow


[User] Please transcribe this text

[Assistant] Primarily follow the larger of these two voltages in large signal.


[User] Please transcribe this text

[Assistant] In large signal, if I grab one of these and start pulling it up.


[User] Please transcribe this text

[Assistant] But now if I take, grab both of them and pull them up, that's fine. This will pull this node up, so this guy will be happy. This will not, nothing will happen to this. This will actually get more and more headroom. Right?


[User] Please transcribe this text

[Assistant] And these guys are going pulled up, pulled up, pulled up. What happens? At some point, this will start conflicting with this. So one of these guys will start crunching.


[User] Please transcribe this text

[Assistant] So what is the lowest or what is the highest this voltage can be before this one crunches?


[User] Please transcribe this text

[Assistant] VDD minus delta VGS, right? Minus delta VGS. Let's call delta VGS free.


[User] Please transcribe this text

[Assistant] So if I pull this up, this will be delta Vgs. And this guy will be a V, delta Vgs above that. At that, at the verge, on the cusp of going into the triode region. So, this guy will essentially be what? A Vg, Vg, V in, minus Vt below.


[User] Please transcribe this text

[Assistant] At the, on the cusp, right? Because this is a VT plus delta VGS.


[User] Please transcribe this text

[Assistant] Delta vgs. And then this is a delta vgs. So this would be vgs, v in minus vt.


[User] Please transcribe this text

[Assistant] So basically, the constraints we have is that V in minus VT, this voltage has to be greater than V in minus VT.


[User] Please transcribe this text

[Assistant] In the ma- in the case of max it would be equality, comes in equality because it's maximum, uh, would be VDD minus, plus VT minus delta VGS3.


[User] Please transcribe this text

[Assistant] Room to operate in the common mode rate in the higher end. So for high voltages it's fine. But it's not good for low voltages.


[User] Please transcribe this text

[Assistant] What would be doing, what would be a good thing for low voltages? What kind of variations?


[User] Please transcribe this text

[Assistant] Remember this principle, that this is actually a useful and important principle, that you can take, essentially, if you have complementary devices, you can get, take any stage and flip it upside down and change the NMOS to FMOS.


[User] Please transcribe this text

[Assistant] And p-mouse to l-mouse. Or p-devices to n-devices. And vice versa.


[User] Please transcribe this text

[Assistant] But that relies on availability of complementary devices.


[User] Please transcribe this text

[Assistant] That may or may not be the case, depending on what technology you're operating in.


[User] Please transcribe this text

[Assistant] Right? This would be the current source. This, this guy will go there. You have that current mirror.


[User] Please transcribe this text

[Assistant] This is the resistor. Now you have a differential pair.


[User] Please transcribe this text

[Assistant] And then you have the current mirrors, now they're made out of NFETs.


[User] Please transcribe this text

[Assistant] And you can make this one, and this is your output, so this is your differential.


[User] Please transcribe this text

[Assistant] This is your differential input, right? And now you can imagine we don't need to, yes.


[User] Please transcribe this text

[Assistant] Why can't, why is this, right? You're asking about, where did this come from? Yeah, okay. So, think about it this way. If it, that happens, if it starts going, if it goes below that, this one will start going to triad reading.


[User] Please transcribe this text

[Assistant] Then you drop a VT plus delta VGS. In our example, we assume that VT plus delta VGS is 0.6 plus 0.3, so it's 0.9. So you go to 0.2, right? So this voltage would become 0.2 volts.


[User] Please transcribe this text

[Assistant] Right? But you need to be, we are, we are, made up example, we said we needed at least 0.3 volts for this to stay on. Because if the delta Vgs of this guy is 0.3, then you needed the 0.3. So you actually have gone below that, it pushes this guy into the triode region.


[User] Please transcribe this text

[Assistant] The delta Vgs is the, so you see, this is a capa, for, in this example, I mean, the MOSFET is even easier to see, I mean, it's true, but, well, bipolar things can happen if, because there can be current flowing through heat in this direction, but, uhm, what happens is that this voltage, this is a capacitor, there's no current flowing, right?


[User] Please transcribe this text

[Assistant] So, the only current that's flowing here is through here. If I remove this connection.


[User] Please transcribe this text

[Assistant] This voltage is whatever it is, set by this voltage source, this resistor, and this W over L of this transistor, right? So now if I connect it here, I'm not drawing any current. So it's not gonna change.


[User] Please transcribe this text

[Assistant] Even if it's in triode region. So this V delta Vgs is fixed. So this Vgs is fixed, which basically means that the delta Vgs is fixed. Because it's Vgs minus Vt, right?


[User] Please transcribe this text

[Assistant] So the minimum V, delta Vgs that you can maintain is fixed.


[User] Please transcribe this text

[Assistant] While you are in triad, while you are in pin shaft region. So if you go below that, you will end up in the triad.


[User] Please transcribe this text

[Assistant] What about the delta V juice of that? Well, the delta V juice of that is dictated by this current.


[User] Please transcribe this text

[Assistant] Right, so let's say if I make it common mode, which basically means that I've shorted these two to each other.


[User] Please transcribe this text

[Assistant] They both have, they both have the, they are connected to the same gate, the gate and source are the same.


[User] Please transcribe this text

[Assistant] So they're in parallel. So they will have to have, they will have the same delta Vgs. There is a current flowing through here. That current is gonna be, if they're matched, they will be, it will be equally divided between these two.


[User] Please transcribe this text

[Assistant] I mean, that will be maintained for that current. And assuming that this voltage is not too low, they are going to remain in the, uh, pinch-off region.


[User] Please transcribe this text

[Assistant] Let's look at some more examples, and if you are not convinced, feel free to ask more questions. So, here, how about this one?


[User] Please transcribe this text

[Assistant] What are the limits on this? Do you think, where would it be good at and where would it not be good at?


[User] Please transcribe this text

[Assistant] The common mode range that can go high, even above VDD, it has limit, it has problems if the common mode range is low. Right? And you can see this one is the opposite. So this one has no problem going down. This can actually go even below, the common mode can be even below the lowest potential here.


[User] Please transcribe this text

[Assistant] So each one of them has an advantage. And now, depending on what you're trying to design and what you're trying to do with the op-amp, you can actually make a choice.


[User] Please transcribe this text

[Assistant] Do you see any advantage other than that? Let's say, let's say you didn't care about that or you were both okay with both of them. Do you see an advantage to one over the other one if this was your entire op-amp? Yes.


[User] Please transcribe this text

[Assistant] Okay, faster, faster is one, yeaah. We'll talk about faster later, but other than faster, do you see any other advantage? Do you think that gains would be different?


[User] Please transcribe this text

[Assistant] The gain of this guy is gonna be G-M-P-R-O-N parallel R-O-P.


[User] Please transcribe this text

[Assistant] So what happens in gen- typically, because the mobility of the holes is smaller than the mobility of electrons, on the same W over L, on the same current, this would be about, this would be less than that. And therefore this would give you less gain. Now,


[User] Please transcribe this text

[Assistant] If this is your entire op-amp, obviously you wanna have, if you could operate under, I mean both of them are okay as far as the range of operation, voltage range of operation is concerned, this would have some preference, I mean there would be a preference for that, because that would give you more gain. So,


[User] Please transcribe this text

[Assistant] Again, so that's one of the things to think about. Now, of course, the next step is to increase the gain. And again, we talked about this before. So, how do you do, how do you increase the gain?


[User] Please transcribe this text

[Assistant] There are several ways. If you're trying to make a single-ended output,


[User] Please transcribe this text

[Assistant] And of course you have always differential input. But single-ended output, you can actually make a single-ended differential conversion with cascode. Right? And we did this last time quickly. But, so here, you could do that.


[User] Please transcribe this text

[Assistant] We'll do it in a second. Now, but in general, by the way, remember, there are op-amps that are differential output. And if they're differential output, you can always use just basically the active loads and have the two sides equal. But we are focusing on single-ended output op-amp because they're a little more


[User] Please transcribe this text

[Assistant] Interesting and complex, but again, there's nothing fundamentally


[User] Please transcribe this text

[Assistant] Different about them. So if you wanted to use the cascode, so this is the idea, right? I mean we've seen these stages, so we're gonna go through them quickly.


[User] Please transcribe this text

[Assistant] And then, starting with a current source.


[User] Please transcribe this text

[Assistant] You can actually have a, and then we have a cascode stage.


[User] Please transcribe this text

[Assistant] And then you can do something, the simplest form is this, you have the differential input, and


[User] Please transcribe this text

[Assistant] This guy is sitting here, so, so, you have two N monsters and two P monsters. If this were properly biased, so you need to provide some bias. Be bias.


[User] Please transcribe this text

[Assistant] Here, but if it's properly biased, then you can have the same operation. The same kind of calculations apply here, right? I mean, we did a little bit of that. You can actually try to kind of like reference this, for example, to this node.


[User] Please transcribe this text

[Assistant] There are different ways to do this. One of the things that you can do, for example, is you can have a diet-connected device here that's driven by a current source.


[User] Please transcribe this text

[Assistant] Yeah, and if you choose this W over L properly, we saw that you could actually make this W over L one quarter of that, etc., etc., or different values of this W over L.


[User] Please transcribe this text

[Assistant] And there's calculations you can make to make the DC operation properly working. So you will have something like this that's self-biased. Now of course this current should not be as large as that current, right? Because what happens if this current is as large as that current?


[User] Please transcribe this text

[Assistant] Now, this has to be a small fraction of that, I would argue. What happens if it's exactly the same?


[User] Please transcribe this text

[Assistant] There's no current left for the differential pressure. All the current goes through here, through this device, and through this here. Done. Right?


[User] Please transcribe this text

[Assistant] Why share I tell? Because if I don't share, so, so, so that's a good question. So what's the alternative? Let's think about. Again, there's no


[User] Please transcribe this text

[Assistant] Single correct answer in design, right? So this is the one pathway we've taken.


[User] Please transcribe this text

[Assistant] So if I were to do this and have a separate eye tail too, is that what you had in mind? Okay, so what would happen? How would I?


[User] Please transcribe this text

[Assistant] The purpose of this device was to establish a voltage here, right?


[User] Please transcribe this text

[Assistant] Yeah, I mean, by the way, so if that was the proposal, we don't really need one of, well, we have to get rid of one of them anyway. Right?


[User] Please transcribe this text

[Assistant] So let me ask you this question, what determines this voltage?


[User] Please transcribe this text

[Assistant] Well, right now the way I've drawn it, VDD determines the voltage, so that's not good, because it's shorter to VDD.


[User] Please transcribe this text

[Assistant] Do you see the problem there? Because now, if I do it this way, what is this voltage? It's reference to here. So this voltage is gonna be VT plus some delta VGS of this guy. So yes, I can establish some fixed voltage.


[User] Please transcribe this text

[Assistant] I can do it with the diode connector, I can even do it with the resistor, etc, etc. But then this voltage would be fixed. Right? Do you want this voltage to be fixed?


[User] Please transcribe this text

[Assistant] You want it to be moving, why? That's correct, why?


[User] Please transcribe this text

[Assistant] Because then, this voltage will dictate this voltage, right? And this voltage dictates how low this voltage can be. The drain can be here, right?


[User] Please transcribe this text

[Assistant] Because as I change my common mode, so if I go back to the original pathway, we were exploring.


[User] Please transcribe this text

[Assistant] And put some sort of a transistor here with some W over L that needs to be determined based on that current. And provide a current.


[User] Please transcribe this text

[Assistant] Then, this voltage is basically tracking this co- this lower source voltage. So as you increase your common mode and decrease, this voltage moves up and down with it because it's delta- it's a VGS below that, right? And then this guy will be above that by a certain amount.


[User] Please transcribe this text

[Assistant] That's determined by this current and the W over L of that pole, that transistor.


[User] Please transcribe this text

[Assistant] So it has the advantage of allowing this to be tracking the common mode of this thing as opposed to being pinned to a fixed point.


[User] Please transcribe this text

[Assistant] But it's really good that you're thinking about these alternatives.


[User] Please transcribe this text

[Assistant] That's really good. I mean you should be, that's exactly what you should be thinking about. Because that's how new designs are created.


[User] Please transcribe this text

[Assistant] So yeaah, we should continue thinking about them and seeing, okay, what does each one of them do? And you can actually propose, keep, feel free to propose, say, why aren't we doing this? Or what happens if you do this? If something that say, oh, we could do that instead. How about that? And that may be a valid answer.


[User] Please transcribe this text

[Assistant] But anyway, so if you do something like this, let's, let's try to kind of like push it a little bit farther and get a sense of what this op-amp looks like. So you can see that we are adding complexity to it. There are different ways to deal with this. Sometimes we would like to actually keep these abstract.


[User] Please transcribe this text

[Assistant] Right, this current source. Because we know how we are going to make it. You will see op-amps inside op-amps. Right? And, and, and, and,


[User] Please transcribe this text

[Assistant] It's not a, it's, it's the same deal as recursion. The op-amp inside the op-amp is simpler. It's a simpler op-amp than the full op-amp. So eventually that stops at some point. But, now here's the thing.


[User] Please transcribe this text

[Assistant] If, just for the sake of argument, let's make this full trans, fully based on transistors. So you, let's express every transistor in this example, just quickly. And see how it works, how it looks. So, how do we make it current source here? Well, this current source will have to be an NMOS transistor. You can actually make it out of some sort of a


[User] Please transcribe this text

[Assistant] Current mirror. And now you have to provide some pathway for this current mirror to be biased, right?


[User] Please transcribe this text

[Assistant] What would be a better thing that would not depend on the power supply, for example?


[User] Please transcribe this text

[Assistant] As a reference current. Let's make a reference current. We've built these things before, right?


[User] Please transcribe this text

[Assistant] A threshold reference, right? A reference, a volt, a voltage that's related to a threshold voltage may be a good thing. How do we do that? Well, to refresh your memory,


[User] Please transcribe this text

[Assistant] There are varying ways of doing it. A simple one would be to use a floating mirror.


[User] Please transcribe this text

[Assistant] And take a, you, there are many different ways to do this. This is a easier to see way of doing it.


[User] Please transcribe this text

[Assistant] So you basically take another transistor, you make it W over L.


[User] Please transcribe this text

[Assistant] And here, what the voltage you get here is VT plus delta VGS of this guy. And you make this W over L, and you make this W over 4L, or basically


[User] Please transcribe this text

[Assistant] One, well, W over four divided by L, that's a better way of saying it. And this is an R. And you remember why we did this, right? Because if this voltage was VT plus delta VGS, this voltage was what?


[User] Please transcribe this text

[Assistant] Right? VT plus VGS here, delta VGS here, VT plus delta VGS here, right? So it's the sum of the two, so you get twice as many.


[User] Please transcribe this text

[Assistant] And then if I make this W over LW, W over 4, what would happen to its delta Vgs for the same current?


[User] Please transcribe this text

[Assistant] The Delta VGS doubles, right? Because it's Delta VGS.


[User] Please transcribe this text

[Assistant] So if I make this W over 1 quarter, my gate overdrive for this guy has to be double.


[User] Please transcribe this text

[Assistant] And the reason we did that is that now here we just get the Vt. You get rid of the W, delta Vgs.


[User] Please transcribe this text

[Assistant] You get the VT without the delta VGSS. You cancel the delta VGSS.


[User] Please transcribe this text

[Assistant] And then you basically do this. Now depending on how much, if assuming that, well, if you have enough headroom for all of this stuff, then you will have headroom for a cascode.


[User] Please transcribe this text

[Assistant] The mirror forces the currents of the two branches to be equal. That's what it does, right?


[User] Please transcribe this text

[Assistant] And I gotta be careful here about how we do this. So I can put this, for example, on this side.


[User] Please transcribe this text

[Assistant] And those on that side. Why did I do, why didn't I put these on this side? You remember?


[User] Please transcribe this text

[Assistant] Yeah, I will have a low impedance path between VDD and ground. I will have like five diode connected transistors in series.


[User] Please transcribe this text

[Assistant] And you can make it so that it has the current that you want. I mean, and of course you make, usually make this much smaller than that because you don't want to be spending as much current on the reference brand as everything else, right?


[User] Please transcribe this text

[Assistant] So, and then you can copy it. You can replicate it here. You can take this, for example, if you want, and make a copy here that would go and drive this guy.


[User] Please transcribe this text

[Assistant] Okay, and I s- and we need to make this one too. Right?


[User] Please transcribe this text

[Assistant] Now of course this W over L, uhm, I don't know.


[User] Please transcribe this text

[Assistant] It's gonna be different from that W over L. Much smaller probably. Cause you are trying to produce a current that's much smaller than that.


[User] Please transcribe this text

[Assistant] And you can go and adjust the W over L to get the DC level right, and then you will have something that will have gain as long as there is no resistive load.


[User] Please transcribe this text

[Assistant] So this is gonna be Ro4. This output resistance is roughly gm3 Ro3, which is the intrinsic, maximum intrinsic gain of this guy, times Ro4.


[User] Please transcribe this text

[Assistant] So the RO4 gets multiplied by that. Same deal here, this is gonna be differentially RO1, and this is gonna be


[User] Please transcribe this text

[Assistant] The maximum intrinsic gain of this guy, which is gm2 ro2 times ro.


[User] Please transcribe this text

[Assistant] We can actually calculate it. Let's just put some numbers down, just to get a feel. So let's say, let's say mu and cox.


[User] Please transcribe this text

[Assistant] Now, this translates to certain numbers, right? I mean, so, so, we need to pick some sort of a current. Let's make, let's try to make these branches, and let's say VT, the threshold voltage is, I don't know, uhm, 0.5 volts. Uhm, I think those are the things that we need for this calculation. So, first we need to establish a reference branch here, right?


[User] Please transcribe this text

[Assistant] How do we establish the reference branch? Well, we are trying to find something that works, that produces some current, and it depends on what kind of current we are trying to determine, because in this case, this current is going to be VT divided by R.


[User] Please transcribe this text

[Assistant] Uhm, let's say we make a reference branch that's let's say at 10 microamps.


[User] Please transcribe this text

[Assistant] So we're trying to make it a 10 microamps. So we are trying to make this number 10 microamps. So let's see if we can do that. So for this to be 10 microamps, and VT of 0.5, what do we need to have?


[User] Please transcribe this text

[Assistant] So it's 0.5 volts divided by 10 microamps. What do we get in terms of resistance? If it was 1 volt divided by 10 microamps, it would be 100 kilo ohms, right? So this would be 50 kilo ohms.


[User] Please transcribe this text

[Assistant] And here you can do the same thing, or you can have actually something a little bit larger to make up for the smaller mu and cox.


[User] Please transcribe this text

[Assistant] Something like that. Again, this is not optimized or something like that.


[User] Please transcribe this text

[Assistant] Oh, you're right, this should be one quarter of that. So, you're absolutely right. So this should be 2.5 divided by 1. Thank you.


[User] Please transcribe this text

[Assistant] Uh, to make, to get rid of that extra delta Vgs. So, this is some sort of a set of numbers. And then, we don't, we still want this reference branch to be one-to-one with that. Now we are trying to see, we are starting to see something interesting. So we can actually see, for example, that this reference branch would be also, uh, at what? Let's say 20 over 1.


[User] Please transcribe this text

[Assistant] So, you get the same amount of current. You get the 10 microamps here. Now, here, you're trying to basically get probably more than 10 microamps. Let's say you wanna have


[User] Please transcribe this text

[Assistant] Right, roughly. So to get 200 microamps here, you're trying to get 200 microamps here. It means that this ratio, and if this branch is still carrying 10 microamps,


[User] Please transcribe this text

[Assistant] This ratio needs to be what? The ratio of this W over L to that W over L needs to be


[User] Please transcribe this text

[Assistant] 20, exactly. Now, you could, for example, depending on what you're trying to do. So the simplest thing you could do is say, look, you know what, this, I can make this still a 10 to 1, and this becomes 200 to 1.


[User] Please transcribe this text

[Assistant] That's a possibility. It's, may have, so here's what the trade, one of the trade-offs there involve.


[User] Please transcribe this text

[Assistant] But, if it's 200 microns, you may say, this is quite large, this capacitance may become large, this may affect, have some effect in the, effect on the, uh,


[User] Please transcribe this text

[Assistant] Instead of 200 over 1, you can have a 100 over half. Depending, assuming that what your process allows you, what the minimum channel length is. But when you do that, you're compromising something, right?


[User] Please transcribe this text

[Assistant] And you need to do the same thing here too, right? You need to make this, whatever, 5 over 1.5 or something like that.


[User] Please transcribe this text

[Assistant] What is the trade-off? What happens if I make this L shorter?


[User] Please transcribe this text

[Assistant] What does this L determine? The output resistance of this guy, right?


[User] Please transcribe this text

[Assistant] Common mode rejection, exactly, because your output resistance is going to reduce and your common mode rejection is compromised because of that. So there's a trade-off there. Sure. Let's keep it the way it is right now. It's fine.


[User] Please transcribe this text

[Assistant] Now, you are talking with something like this and then you, but these guys now here is where you need your GM. The GM here matters, right? Yes.


[User] Please transcribe this text

[Assistant] Like, like, let's say, let's say for the sake of argument, if I make them 1 and 20. That's an extreme version, right?


[User] Please transcribe this text

[Assistant] You don't need to. You don't need to cut this one, right? This needs to be matched with that, right? What you suggested is sound, but it's another trade-off. Let's see what that trade-off is. So if instead of 10 to 200, I go to 1 to 20, what would happen? What's the thing? What am I trading with? What? Right? What is the trade-off now?


[User] Please transcribe this text

[Assistant] I didn't change the L, so my output resistance should not change. Right? So output resistance is not affected. But something else will be affected.


[User] Please transcribe this text

[Assistant] Delta Vgs, right? So now, when this could, for example, go down to 0.3 volts, now it now needs to go to like 0.7 volts before it crunches. I mean, so it's, so now you're losing headroom here. You're trading with headroom.


[User] Please transcribe this text

[Assistant] So there are trade-offs here. So I'm just gonna keep some numbers. I mean, these are, like I said, there's nothing optimum about anything you're doing here. Just some set of numbers to get you a sense. And of course, they need to be looked at and optimized. And if you plug this in, it may not be very good anyway.


[User] Please transcribe this text

[Assistant] Uhm, but let's start with something. You have to have a starting point, right? Usually that's the hardest part when you're designing or creating in general, right? Creating from clean slate and blank sheet is usually the hardest thing.


[User] Please transcribe this text

[Assistant] Right? So once you put something down, you can say, okay, I can work with this, it has this problem, I can change it and it evolves into whatever that final thing is. Okay, so let's go through this process. So,


[User] Please transcribe this text

[Assistant] And you want to have a large ratio of W over L, which basically means that use the smallest product


[User] Please transcribe this text

[Assistant] And largest ratio that you can use. Now, for every process there's a minimum channel length that you can use here. You may not want to be at minimum minimum, for example, depending on what your other requirements are in terms of noise and all those things, but let's just say this could be like, I don't know.


[User] Please transcribe this text

[Assistant] I mean, it depends on the process. So this can be a pretty small number, right? Let's say, let's make it a, I don't know, .1. Micro, 100 nanometer. Right? And then you might make this probably a 10 over 1.


[User] Please transcribe this text

[Assistant] With relatively low capacitance. And if you're using things like that, you're probably not going to be deviating too much over those. So you probably may end up having the same dimensions or slightly different dimensions here. And then h-


[User] Please transcribe this text

[Assistant] Here, I have to be careful though, right? Because now, if you do just that, if I make it that small, what am I gonna compromise now? Are we gonna gain necessarily?


[User] Please transcribe this text

[Assistant] Not necessarily, right? If I just use it. Why? Because, now, what happens to my RO? Let's calculate our RO. For 1 micron and 0.1 micron, based on the numbers we have. So the RO's, let's say ROA, well, ROA and ROP would be the same.


[User] Please transcribe this text

[Assistant] And we are making the currents to be 100 microamps each in the balance case. So RO is gonna be L divided by I.


[User] Please transcribe this text

[Assistant] Inverse. So you're getting, for one micron,


[User] Please transcribe this text

[Assistant] Micrometers. This cancels that, this over that. Basically you get, uh, what do you get?


[User] Please transcribe this text

[Assistant] So that becomes 5 microamps, so it becomes 1 over 5 microohms, which basically becomes 200 kiloohms, right?


[User] Please transcribe this text

[Assistant] So for these guys, this is going to be 20 kilo ohms.


[User] Please transcribe this text

[Assistant] And that's gonna be 200, oh no, sorry, but this output for example is gonna be 200 kilo ohms. The output resistance, right? Roughly.


[User] Please transcribe this text

[Assistant] So, let's see, what do we get? Let's go through the process a little bit more. Yes.


[User] Please transcribe this text

[Assistant] That's a great point. This doesn't need to be this small. Right? Another trade-off though. If you make this very large, if you, so because you need to, so,


[User] Please transcribe this text

[Assistant] Can I just scale, what happens, so let's go two directions we can go. I can just scale this guy. Let's say make the L one. Back to one.


[User] Please transcribe this text

[Assistant] It would improve it because then this term is gonna improve, right?


[User] Please transcribe this text

[Assistant] But it's gonna reduce as a square root, but this is gonna grow as a linear, so it's still an advantage.


[User] Please transcribe this text

[Assistant] So, but what else do I compromise if I just do this? My W over L has become smaller. For the same current, with smaller W over L,


[User] Please transcribe this text

[Assistant] My delta vgs is gonna be larger, so I'm losing range of operation. Right? Now, you may say, okay, how about, well, you increase the w2, make this 100.


[User] Please transcribe this text

[Assistant] But L is larger, so you get the same GM.


[User] Please transcribe this text

[Assistant] What did I lose in the process of doing that? What did I compromise? Of course you have to do it on both sides, right?


[User] Please transcribe this text

[Assistant] What did I compromise? What did we compromise right now? Speed.


[User] Please transcribe this text

[Assistant] Which we haven't talked about, but then you're making this capacitance on this node larger, and you're losing on that. So,


[User] Please transcribe this text

[Assistant] If you feel that something is just like, oh, this is like a free knob, I can turn it. Nine out of ten times you're missing something. Right? There's something else you're compromising when that happens. And that's the way it should be. That's the way it actually is.


[User] Please transcribe this text

[Assistant] But anyway. So, I mean, yeah, you're right. I mean, this may, so there may be a compromise here. So this may end up being 0.5.


[User] Please transcribe this text

[Assistant] 50 over 0.5 or something like that. And these are the things that you need to do quantitatively when you calculate the speed and all those things. And the same thing here, you can basically do similar things here, so you probably want to have a 50 over 0.5.


[User] Please transcribe this text

[Assistant] As a for example, I mean again, there's nothing magical about the numbers I'm putting down here. And probably they're not optimum.


[User] Please transcribe this text

[Assistant] Definitely not optimal, not probable. Okay, something like that.


[User] Please transcribe this text

[Assistant] And then you have to also, last time we talked about, we have to think about the startup, so you may need to create a branch here to kind of like make sure that this turns on because this has a stable state at zero volts, at zero current.


[User] Please transcribe this text

[Assistant] Uhm, so that you need to make sure that that's stuck. But this is an example, right? This is a simple example.


[User] Please transcribe this text

[Assistant] So now if I ask you, come and quickly ask you guys, what do each one of these transistors do? What is the role that they play? You should be able to tell me, right? So let's do it. So, what is the role of this transistor?


[User] Please transcribe this text

[Assistant] It's part of the current mirror here, right? That guarantees the equality of the branches of these two. So, so these four really are a combination. What is the role of these guys? It's just forming a cascode with that, right?


[User] Please transcribe this text

[Assistant] Or if they were equal. So now we also kind of like modified it a little bit, so we kind of made it to a tweak, so it gets rid of this voltage too, as well. But if they were equal, then it would be flowing. Uhm, what role does this transistor play?


[User] Please transcribe this text

[Assistant] Put that gate, right? Uh, what role do these transistors play?


[User] Please transcribe this text

[Assistant] What's, what are they doing? They're part of the cascode. Why did we use cascode? Increase the gain by this factor, right? Uhm, what role do these guys play? They're the cascode part of the mirror, right? Right. So, and what are these two doing?


[User] Please transcribe this text

[Assistant] So we can actually even calculate the gain, right? So let's see what the gain of this thing would be. So we didn't do that calculation. So what we have to calculate is gm. So gm, n.


[User] Please transcribe this text

[Assistant] We'll get, so I get 100 microamps out.


[User] Please transcribe this text

[Assistant] Uh, over volts. And then I have a square root of 200. So it's like 10 times 10 times square root of 2.


[User] Please transcribe this text

[Assistant] So that becomes 1 milliamps per volt times square root of 2, so it's 1.4 millisiemens. That's your GM.


[User] Please transcribe this text

[Assistant] Right? And if I ask you what's the gain, so now let's calculate it. Uhm, and the GM of this guy is gonna be the same.


[User] Please transcribe this text

[Assistant] And same here because the W over L is the same and the current is the same. Right? So it's gonna, this factor is going to be what?


[User] Please transcribe this text

[Assistant] Let's calculate this factor. This factor is gonna be 1.4 millisiemens times...


[User] Please transcribe this text

[Assistant] Oh no, I have to calculate the new RO. So RO of this guy.


[User] Please transcribe this text

[Assistant] This is going to be 1.4 millisiemens times 100 kilo ohms. So kilo and millisiemens and kilo ohms cancel, so you have 140, so this factor is 140.


[User] Please transcribe this text

[Assistant] Times RON, which is 220 kiloorbs, that's a pretty large number, right?


[User] Please transcribe this text

[Assistant] That's basically you're looking at, uhm, 2.8 mega ohms.


[User] Please transcribe this text

[Assistant] Now what we know is it's going to be a factor of 2 smaller here, which basically gets rid of this factor of square root of 2, so it becomes just 1 millisiemens. So this is 1 millisiemens times 100 kilo ohms times 100 kilo ohms.


[User] Please transcribe this text

[Assistant] So this is a 1 milli, the 100 times 1, so that becomes like 10 mega ohms. So you have 2.8 mega ohms in parallel with 10 mega ohms. I'd have 2 mega ohms, roughly. 2 mega ohms times


[User] Please transcribe this text

[Assistant] And this is a very rough calculation. So if you put this in SPICE, you can get, you may get something like


[User] Please transcribe this text

[Assistant] You know, 3,500 or you may get like 1,800, 1,900. So, so, but it's the ballpark of it that you're calculating, right?


[User] Please transcribe this text

[Assistant] So, and that's what matters. So you're getting in the range of a thousand or a couple of thousands. A gain of a couple of thousands, right?


[User] Please transcribe this text

[Assistant] So this is as far as you freely can go. I mean, you may say, okay, well, I do a triple cascode, and I get another factor of this. But at that point, when you're going above mega ohms,


[User] Please transcribe this text

[Assistant] A few mega ohms. Your leakage current and second order things that you've ignored in your simplified model will come and kick in. And you, you may calculate something that's like 100 mega ohms. It's not 100 mega ohms because there's, that leakage current is going to dominate.


[User] Please transcribe this text

[Assistant] So what if you need more gain? Well, you can deal with that stuff. We'll deal with that in a sec. But now, let's talk about variations on this.


[User] Please transcribe this text

[Assistant] That may also be helpful before we try to get more game. We also saw that we have these limitations on the headroom. We can imagine that the headroom limitations actually are


[User] Please transcribe this text

[Assistant] More pronounced here, right? Because now you have five transistors stacked.


[User] Please transcribe this text

[Assistant] And we've seen folded cascode. You've seen folded cascode in some of the problem sets. The idea of a folded cascode is that, yea, cascode is great because it gives you gain. Why does cascode give you gain? Because it has higher intrinsic, uhm,


[User] Please transcribe this text

[Assistant] Output resistance, right? Now, that's good.


[User] Please transcribe this text

[Assistant] And also cascode has a second advantage, which we haven't talked about in significant. When we talk about high frequency, we'll see that it's actually from a frequency response perspective, it has a certain, quite a bit of advantage actually.


[User] Please transcribe this text

[Assistant] But the concept of folded cascode itself is a simple concept. So you're saying that if I have


[User] Please transcribe this text

[Assistant] The regular cascode, which looks like this, so this is the input, this is the bias, and this is the load resistor, and this is your output.


[User] Please transcribe this text

[Assistant] Right? You now have two transistors stacked plus some sort of a load.


[User] Please transcribe this text

[Assistant] The idea here is that you actually turn one of these guys, the common gate transistor, and use the PFET.


[User] Please transcribe this text

[Assistant] Of course, since this draws current, we've seen this before, and this draws current, you need to have a current source flowing into both of them, so you have to provide some sort of eye bias.


[User] Please transcribe this text

[Assistant] Now what is the disadvantage of casc- folded cascode compared to the regular cascode?


[User] Please transcribe this text

[Assistant] Let's say this one, if it wants to operate, it needs to be drawing current 2. You want to do the same thing?


[User] Please transcribe this text

[Assistant] But here, if you, for example, were to divide it equally, if you have one milliamp here, half a milliamp would go here and half a milliamp would go there.


[User] Please transcribe this text

[Assistant] So, you are basically, yes, you are gaining in headroom, because now you have really one transistor, well really you have two, because this is another transistor, and you have, you have had to have two if you were to do it this way, but this is, this can be crunch, this can be close to, this can be a small overhead, because this can only go down to delta VGS,


[User] Please transcribe this text

[Assistant] So there's a price. But, if your voltage range is a problem, you have to deal with it, right?


[User] Please transcribe this text

[Assistant] Now, there's an equivalent, there's a differential equivalent of that thing, so you can actually take that for example, or any kind of things like that, and then you can flip the input. So the folded, there's a folded cascode variation of these op amps, right? So the folded cascode variation looks like this. So you can have, you have your branches,


[User] Please transcribe this text

[Assistant] And this time I'm going to show it, for example, as a fully differential output. So this is, these are called telescopic cascodes, by the way. Because, because they're like the old telescopes, the old that they used to just extend it out and in, they can actually compress.


[User] Please transcribe this text

[Assistant] That is coming in and driving these guys. Like that.


[User] Please transcribe this text

[Assistant] Does everyone see that this is the flipped version of that? Right? The inverted version of that.


[User] Please transcribe this text

[Assistant] This guy corresponds, these are the input transistors, so from a single-ended, from a half-circuit equivalent perspective, you get that. It looks like that, right? And then, these two are, correspond to this. Again, in half-circuit, you will get one of them. Right? And what is the role of these guys?


[User] Please transcribe this text

[Assistant] Right? So, let me show it one more time.


[User] Please transcribe this text

[Assistant] Right? Now you have to have a reference branch of course here.


[User] Please transcribe this text

[Assistant] Are, correspond to that, and that, corresponds to this.


[User] Please transcribe this text

[Assistant] This is just the equivalent half circuit. The one on the left is the half circuit equivalent of the one on the right.


[User] Please transcribe this text

[Assistant] Cascade, well, cascade op amps, right? Just basically put them in, basically make a two stage op amp. Two game stages. So let's do that. Let's go here. And try to do that.


[User] Please transcribe this text

[Assistant] Let's start with a very basic stage, very basic single ended to, differential to single ended converter stage.


[User] Please transcribe this text

[Assistant] My, this is our single-ended to differential, uh, differential single-ended, sorry, conversion, converter stage.


[User] Please transcribe this text

[Assistant] We know whatever gain we get from this one, and this can be cascoded or not, let's just deal with the simple one, because we don't want to make it too complicated right now. But, now I want to add a second game stage. Right?


[User] Please transcribe this text

[Assistant] What kind of stage can I use? The most, the basic gain stage is the common source, right? So


[User] Please transcribe this text

[Assistant] Don't take notes yet, with an active load, because there's a problem with what I'm drawing.


[User] Please transcribe this text

[Assistant] If this current source has some output resistance, some sort of an ROP, and then this is the RON,


[User] Please transcribe this text

[Assistant] And then there's a gm, so this current is gonna be whatever, that's v1. This is gonna be gm v1, so it's gonna be gmn times ron rop. ron parallel rop, right?


[User] Please transcribe this text

[Assistant] 100, 100 around there, so I get 100 squared. So I get 10,000.


[User] Please transcribe this text

[Assistant] And if we go to cascode, you can get to a thousand times a thousand, presumably, and make this cascode and all. But there's a problem with this, the way I've drawn it. Can anyone identify a problem? Yes.


[User] Please transcribe this text

[Assistant] So, so, so, you, you, you identify the source of the problem. Let's talk about the source of the problem, then talk about solution. So,


[User] Please transcribe this text

[Assistant] What voltage is this, let's say if this was balanced, if this were balanced, what voltage do you expect this to be roughly at? When the input is balanced, there's basically no differential input.


[User] Please transcribe this text

[Assistant] Right, more or less. Then, this vgs, delta vds has to be the same as this vds, so this would be roughly around a vgs below, or vt plus delta vgs below vt. Vdd, right? So it's gonna be a little bit below. So it's gonna be around the same point this guy is. Mostly. So,


[User] Please transcribe this text

[Assistant] If I put some numbers, let's say this is 5 volts and this is 0. Now, and let's say,


[User] Please transcribe this text

[Assistant] Then the Vgs, so what did we say? We said 0.6 plus 0.3 volts, let's make it 0.6 plus 0.4, so 0.6 for Vt and delta Vgs of 0.4. So that's gonna be a volt below that, that's gonna be around 4 volts. Right? Nominally. When the stage is balanced.


[User] Please transcribe this text

[Assistant] And this guy wants to be what? It's gonna be VT plus delta VGS above zero, so it's gonna be, it wants to be around one volt.


[User] Please transcribe this text

[Assistant] So this one cannot pull that down, essentially, right? Because it has no influence backwards in the MOSFET. Because it's not drawing any current.


[User] Please transcribe this text

[Assistant] So it will be pushed way up to 4 volts.


[User] Please transcribe this text

[Assistant] This guy goes into, this one starts crunching, this one goes into triad region. Because it has a large VGS.


[User] Please transcribe this text

[Assistant] And it basically just starts pulling this node down, it will go to ground and will not produce any gain. Because GM would be lower, but more importantly output resistance would be very low. So it's not gonna work.


[User] Please transcribe this text

[Assistant] So Alex suggested something interesting, said that look, you know, put some sort of a follower to adjust these voltages. So let's say, how much, what do I need to adjust it by? Let's go down that route.