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.

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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.



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Let's get started. Can you hear me back there? Loud and clear. OK. Let's get started. Before I begin, just a couple of announcements. Brad Buren is one of our students here and he needs a note-taker.

It's a paid position. So if you are interested you can stop by after class and see him. He's sitting right here out there, OK? Second, just a reminder that 6.002 does have prerequisites. And the prerequisites are 8.02 and 18.03.

So with that let me start off with the usual. Do a quick review of what we've done so far. So we started out life looking at the laws of physics and Maxwell's equations and so on. And those were way too hard so we said let's make life easy for ourselves.

So we chose to play in this playground in which we said we shall adhere to the lumped matter discipline. OK? The LMD. So we are in that playground. So this entire course, and for that matter large parts of EECS are within that playground, within which the lumped matter discipline applies.

So as soon as we jumped into the playground, the LMD playground, we could take Maxwell's equations and abstract them out into two very, very simple rules. And the very simple rules were KVL and KCL.

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KVL simply said that I can sum the voltages in any loop in a circuit and the result then would be zero. Similarly, I can sum the currents that enter or exit any node and the sum will also be zero. So what you can now do is, if you feel like, you can go around and brag.

Oh, yeah, we use Maxwell's equations in everyday life and, yeah, it's good stuff. And the key is that this is really an encapsulation of Maxwell's equations within this playground that we are in. So I talked about the first method of circuit analysis in the last lecture.

And that method simply took the, wrote KVL for all the loops, wrote KCL for all the nodes and wrote element vi relationships. And together gave you a big bunch of equations. And you sat down and grunged through the equations and you solved for branch voltages and currents.

So we reviewed a second method of circuit analysis. And I'll simply call it circuit composition. The basic idea behind this method was to learn some simple rules of how resistors add and conductances add and so on and so forth and look at a circuit and simplify the circuit by making series simplifications when the resistors are in series and so on and so forth, and compose it and play around with it till we end up with the current, the voltages that we are looking for.

This is the intuitive method. And so a section in Chapter 2, I believe, of the course notes discusses several examples using this method and attempts to make a little bit formal the intuitive approach that is applied in this method.

So we then looked at the node method. And the node method was simply a particular way of applying KVL and KCL. Node method, remember? We took a ground node. Then we labeled the nodes of the remaining voltages with respect to that ground.

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Let's get started. We have one handout today. That's your lecture notes. There's some copies still outside for those who haven't picked one up. In general, what I do is, in the lecture notes, I leave out large amounts of material.

So, this will enable you to keep your hands busy while I'm lecturing and take down some notes and so on. So, don't assume that everything that I talk about is on here. Please follow along. OK, so as is my usual practice, let me start with a quick review of what we covered so far.

So what we did primarily was looked at this discipline that we call the lump matter discipline, which was very similar, very reminiscent of the point mass simplification in physics. And this discipline, this set of constraints we imposed on ourselves, allowed us to move from Maxwell's equations to a very, very simple form of algebraic equations.

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And specifically, the discipline took two forms. One is, we said that we will deal with elements for whom the rate of change of magnetic flux is zero outside of the elements, and for whom the rate of change of charge I want to charge inside the element was zero.

So, if I took any element, any element that I called a lump circuit element, like a resistor or a voltage source, and I put a black box around it, then what I'm saying is that the net charge inside that is going to be zero.

And this is not true in general. We will see examples where, if you choose some piece of an element for example, there might be charge buildup, but net inside the, if I put a box around the entire element, I am going to assume that the rate of change of charge is going to be zero.

So, what this did was it enabled us to create the lump circuit abstraction, where I could take elements, some element of the sort, this could be a resistor, a voltage source, or whatever, and I could now ascribe a voltage, some voltage across an element, and also some current, "i," that was going into the element.

And as I go forward, when I label the voltages and currents across and through elements, I'm going to be following a convention. OK, the convention is that I'm going to label, if I label V in the following manner, then I'm going to label "i" for that element as a current flowing into the positive terminal.

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So, one question to ask ourselves is, what is engineering? How do we define, what is engineering? Well, the definition I like to use is one put forth by Steve Senturia, one of our professors who is now retired.

He defined engineering to be the purposeful use of science. All right, so what is 6.002 about? So, 6.002 is a first course in engineering. And I like to view 6.002 as the gainful employment of Maxwell's equations.

Many of you have seen Maxwell's equations before. Most of you should have. And they are hard stuff. 6.002 is all about teaching you how to simplify our lives, make things simple. So, if you can gainfully employ Maxwell's equations, gainfully employ the facts of nature to build very interesting systems.

So let me show you how the transition is made. So, there's a world around us, nature, so we made some observations in nature. We make measurements, and we can write down large tables of measurements.

So, for example, we can take objects and measure the voltage across them, and look at the resulting current through the elements. So, we may end up getting a bunch of values such as [CHALKBOARD]. So, we start out life with making measurements on what exists.

And we build a bunch of tables. Now, we could directly take these tables, and based on observations of these tables, we could go ahead and build very interesting engineering systems that help us out in day-to-day lives.

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But that's incredibly hard. Imagine having to resort to a set of tables to do any kind of useful work. So what we do as engineers, we first layer a level of abstraction. We look at all the data, and somehow layer abstraction such that we can simplify or much more succinctly put in a simple equation or a simple statement what these numbers are telling us.

OK, so for example, our physics laws, so laws of physics for example are simply abstractions, the laws of abstractions. So, these sets of numbers can be codified by Ohm's law, for example, V is equal to RI, the voltage current, relates to the resistance of the object.

So, V is equal to RI is a law that succinctly describes a set of experiments, and replaces a large number of tables with a very simple statement. You could call this the law, or you could call it an abstraction.

OK so you see laws of physics, call them abstractions of physics if you like. Similarly, there are Maxwell's equations and so on and so forth. So, this is what is. This is what's out there. OK, and a law as an abstraction describe the properties of nature.......

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