Материал готовится,

пожалуйста, возвращайтесь позднее

пожалуйста, возвращайтесь позднее

So today we are going to talk about another process of lumping or another process of discretization what will lead to the digital abstraction. So today's lecture is titled "Go Digital." So let me begin with a usual review.

And so in the first lecture we started out by looking at elements and lumping them. For example, we took an element and said for the purpose of analyzing electrical properties let's lump this element into a single lumped value called a resistor, R.

And this led to the lumped circuit abstraction. The lumped circuit abstraction says let's take these elements, connect them with wires and analyze the properties of these using a sort of analysis technique.

So a set of a methods. We've looked at the KVL, KCL method. Another example of a method we looked at was the node method. And of this category there is one method you should remember, which you can apply to every single circuit and it will simply work, is the node method.

For linear circuits other methods also apply, and these include superposition, Thevenin method, and in recitation or in your course notes you would have looked at the Norton method. So that's what we did so far.

So this is a toolkit. So now you have a utility belt with a bunch of tools in it, and you can draw from those tools. And, just like any good carpenter, you know, the carpenter has to cut a piece of wood.

He could use a chisel. He could use a saw. He could use an electric saw. And the reason you pay carpenters $80 an hour in the Boston region is because they know which tool to use for what job. So what we'll learn today is, so this was one process of discretization.

We discretized matter. This gave us the discipline here that we decided to follow, lumped matter discipline, that moved us from Maxwell's equations into this new playground called EECS. Where all elements looked like these rinky-dinky little values like resistors and voltage sources and so on.

What we'll do today, if that wasn't simple enough, let's simplify our lives even further. What we're going to do is lump some more. So what else can we lump? We've lumped matter, so all matter is taken care of.

So what can we lump to make life even easier? When in doubt, if things are complicated, discretize it or lump it, right? So what do you think? What we will do today is lump signal values. So we'll just deal with lumped values.

And this will lead to the digital abstraction. And the related reading is Chapter 5 of the course notes. So before we do this kind of lumping, let me motivate why we do this. One reason is to simplify our lives, but there is no need to just go around simplifying things just because we can.

Let's try to see if there are other reasons motivating the digital abstraction. So what I would like to start with is a simple example of a analog processing circuit that you should now be able to analyze.

So I'm going to be motivating digital. So let's start with an analog circuit that looks like this, two resistors, R1 and R2. And what I'm going to do is apply a voltage source here, V1, apply another one here, V2, and make this connection.

And let me call this voltage V nought and call this my output. This voltage with respect to ground node, rather than drawing this wire here, I often times draw a ground here and simply throw ground wherever I want.

This symbol simply refers to the fact that the other terminal is taken at the ground node. So here is my V nought. Now, let's go and analyze this and see what it gives us.

And so in the first lecture we started out by looking at elements and lumping them. For example, we took an element and said for the purpose of analyzing electrical properties let's lump this element into a single lumped value called a resistor, R.

And this led to the lumped circuit abstraction. The lumped circuit abstraction says let's take these elements, connect them with wires and analyze the properties of these using a sort of analysis technique.

So a set of a methods. We've looked at the KVL, KCL method. Another example of a method we looked at was the node method. And of this category there is one method you should remember, which you can apply to every single circuit and it will simply work, is the node method.

For linear circuits other methods also apply, and these include superposition, Thevenin method, and in recitation or in your course notes you would have looked at the Norton method. So that's what we did so far.

So this is a toolkit. So now you have a utility belt with a bunch of tools in it, and you can draw from those tools. And, just like any good carpenter, you know, the carpenter has to cut a piece of wood.

He could use a chisel. He could use a saw. He could use an electric saw. And the reason you pay carpenters $80 an hour in the Boston region is because they know which tool to use for what job. So what we'll learn today is, so this was one process of discretization.

We discretized matter. This gave us the discipline here that we decided to follow, lumped matter discipline, that moved us from Maxwell's equations into this new playground called EECS. Where all elements looked like these rinky-dinky little values like resistors and voltage sources and so on.

What we'll do today, if that wasn't simple enough, let's simplify our lives even further. What we're going to do is lump some more. So what else can we lump? We've lumped matter, so all matter is taken care of.

So what can we lump to make life even easier? When in doubt, if things are complicated, discretize it or lump it, right? So what do you think? What we will do today is lump signal values. So we'll just deal with lumped values.

And this will lead to the digital abstraction. And the related reading is Chapter 5 of the course notes. So before we do this kind of lumping, let me motivate why we do this. One reason is to simplify our lives, but there is no need to just go around simplifying things just because we can.

Let's try to see if there are other reasons motivating the digital abstraction. So what I would like to start with is a simple example of a analog processing circuit that you should now be able to analyze.

So I'm going to be motivating digital. So let's start with an analog circuit that looks like this, two resistors, R1 and R2. And what I'm going to do is apply a voltage source here, V1, apply another one here, V2, and make this connection.

And let me call this voltage V nought and call this my output. This voltage with respect to ground node, rather than drawing this wire here, I often times draw a ground here and simply throw ground wherever I want.

This symbol simply refers to the fact that the other terminal is taken at the ground node. So here is my V nought. Now, let's go and analyze this and see what it gives us.

Загрузка...

Выбрать следующее задание

Ты добавил

Выбрать следующее задание

Ты добавил