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All right. Good morning, all. You have two handouts, lecture notes and an article on mixed signal chips. A mixed signal stands for circuits that have both analog and digital components to them. The reason I am giving you the handout is that Lab 4 and also your last homework involve designing and building a mixed signal circuit.

It's a real fun exercise. And I just wanted to tell you that from past experience people who have taken 6.002 often view the last lab as the single most fun thing they did in all of 6.002. So, as you go into Lab 4, you should be telling yourself I should be having fun, I should be having, I should be having fun.

You have to positively psych yourself. Otherwise, it's going to go by. And then you're going to say boy, that was fun, I wish I had savored the moment as I was doing it. All right. Let's see. What do we do today? Today's lecture is actually going to be a fair amount of fun.

We are going to blast through a bunch of fun things. And some things that you will be quite unprepared for. Until now, in the last two lectures with op amps we talked about negative feedback. That is applying some portion of the output voltage to the negative input so that I could control this high strung device, my op amp.

Today, what we are going to do is try to get a handle on what happens if we use positive feedback. It's the usual curious child. You tell them to do this, and of course they're going to try to do this as well.

And we are going to try to do that and see what happens and look to see if we can build some useful circuits. Today — As motivation, let me do a quick review of a circuit that should now become affixed in your brains in a standard pattern.

This is a circuit that gives you negative feedback. R1 and R2. And I apply a vIN. By now you should be able to look at this pattern. And this is your inverting amplifier pattern. So, you should be able to write down by inspection this is simply vIN or the minus vIN times R2 divided by R1.

This is an amplifier whose gain is controlled by the ratio of R2 and R1. This is a negative feedback circuit because it is always fun to do the intuition thing and say that look, if this voltage tends to go more positive than I care then this negative input goes more positive than I care.

If that goes more positive then the negative input v minus becomes more positive in the plus input which yanks the output down. So, there is a nice counteracting force that keeps the output stable.

Let's look at this circuit. Being curious engineers, let's look at the opposite here where I give myself some positive feedback in this op amp. And it is going to be interesting to analyze this because what we find out on the face of it is not quite actually how it behaves.

We are going to spend most of the lecture today on understanding the dynamics of circuits that look like this and to see if we can build some fun and interesting circuits and systems based on this kind of positive feedback.

It is positive feedback because I am feeding back a portion of the output to the positive input. And you should be able to stare at this and already begin to intuit what should happen to this. Let's think about it.

This is zero. Remember, with positive feedback, the famous v plus is equal to v minus method doesn't apply anymore. Let's apply very simple analyses. If this is zero, let's say for example that this output tends to go a little bit more positive.

This output, due to some noise or perturbation, tends to go up a little bit.

It's a real fun exercise. And I just wanted to tell you that from past experience people who have taken 6.002 often view the last lab as the single most fun thing they did in all of 6.002. So, as you go into Lab 4, you should be telling yourself I should be having fun, I should be having, I should be having fun.

You have to positively psych yourself. Otherwise, it's going to go by. And then you're going to say boy, that was fun, I wish I had savored the moment as I was doing it. All right. Let's see. What do we do today? Today's lecture is actually going to be a fair amount of fun.

We are going to blast through a bunch of fun things. And some things that you will be quite unprepared for. Until now, in the last two lectures with op amps we talked about negative feedback. That is applying some portion of the output voltage to the negative input so that I could control this high strung device, my op amp.

Today, what we are going to do is try to get a handle on what happens if we use positive feedback. It's the usual curious child. You tell them to do this, and of course they're going to try to do this as well.

And we are going to try to do that and see what happens and look to see if we can build some useful circuits. Today — As motivation, let me do a quick review of a circuit that should now become affixed in your brains in a standard pattern.

This is a circuit that gives you negative feedback. R1 and R2. And I apply a vIN. By now you should be able to look at this pattern. And this is your inverting amplifier pattern. So, you should be able to write down by inspection this is simply vIN or the minus vIN times R2 divided by R1.

This is an amplifier whose gain is controlled by the ratio of R2 and R1. This is a negative feedback circuit because it is always fun to do the intuition thing and say that look, if this voltage tends to go more positive than I care then this negative input goes more positive than I care.

If that goes more positive then the negative input v minus becomes more positive in the plus input which yanks the output down. So, there is a nice counteracting force that keeps the output stable.

Let's look at this circuit. Being curious engineers, let's look at the opposite here where I give myself some positive feedback in this op amp. And it is going to be interesting to analyze this because what we find out on the face of it is not quite actually how it behaves.

We are going to spend most of the lecture today on understanding the dynamics of circuits that look like this and to see if we can build some fun and interesting circuits and systems based on this kind of positive feedback.

It is positive feedback because I am feeding back a portion of the output to the positive input. And you should be able to stare at this and already begin to intuit what should happen to this. Let's think about it.

This is zero. Remember, with positive feedback, the famous v plus is equal to v minus method doesn't apply anymore. Let's apply very simple analyses. If this is zero, let's say for example that this output tends to go a little bit more positive.

This output, due to some noise or perturbation, tends to go up a little bit.

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