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Good morning. OK. The topic for today is Energy and Power. Most of the time this semester, up to now at least, we focused a lot on speed. We have been truly speed freaks looking at how fast can we switch the signal, what does a time domain waveform look like? We also looked at frequency responses of circuits.

This week we will spend on something a little bit different, and that relates to energy and power. Energy and power is gaining a lot more importance in certainly this decade, and will do so in the future.

And I am going to work out a little example towards the end of the lecture. And there you will see that if you do things naively, your handheld devices, your cell phone, laptops and so on will just up and explode.

You have got to be a little bit careful in terms of how to manage energy and power. Before I get into that, I just want to wrap up with a quick review of what we covered last week. We ended last week by looking at positive feedback in analog circuits using an op amp.

And, in particular, we built an oscillator. We built an oscillator that allowed us to charge a capacitor. And when the voltage across the capacitor equaled that at the minus terminal it would flip and keep doing so.

And at the output you would get a waveform that looked like this. You would get a square wave output. Now, throughout the course we have talked about getting square wave inputs. And this is one example of how you can actually produce a square wave pretty much from first principles using a capacitor, resistors and an op amp.

Now, I just wanted to wrap up this little item here by talking about one application of an oscillator. And this application of the oscillator really nicely closed the loop on the body of knowledge relating to digital circuits that we have covered in this course.

What I want to talk about briefly is a small digital system with a sender and a receiver. And the sender is sending a signal, the receiver receives a signal, and in this course we have talked about senders sending a sequence of ones and zeros.

Say, for example, the sender wants to send some sort of a signal like this. We have seen that this is quite a legitimate signal. We get some kind of oscillatory behavior because of the inductance and capacitance associated with the wire.

And what you have done is that you pretty much believed me when I said that this really corresponds to a one, one, zero. The sender wants to send a one, one, zero signal to the receiver, and the receiver gets it.

So this is a one, this is a one, this is a zero. But if I am a receiver, I am going to look at the square wave. There is no such thing as sending a one on a wire. You cannot send a one on a wire.

You send a voltage signal or a current signal on a wire. So, the receiver receives a voltage signal. It is going to be zero for some time and then maybe 5 volts or 3 volts or whatever is your high and then zero again.

How does my receiver know it's a one, one, zero? Why can't it be a one, one, one, one, zero, zero, zero? It doesn't know. How does the receiver know it's a one, one, zero sequence and not 50 ones followed by 40 zeros? It doesn't know.

What we need is — For senders to be able to communicate with receivers, we need some kind of agreed upon time when receivers sample the signal coming in and decide whether it's a one or a zero. They both have to agree on certain time bases when to look at the input.

This week we will spend on something a little bit different, and that relates to energy and power. Energy and power is gaining a lot more importance in certainly this decade, and will do so in the future.

And I am going to work out a little example towards the end of the lecture. And there you will see that if you do things naively, your handheld devices, your cell phone, laptops and so on will just up and explode.

You have got to be a little bit careful in terms of how to manage energy and power. Before I get into that, I just want to wrap up with a quick review of what we covered last week. We ended last week by looking at positive feedback in analog circuits using an op amp.

And, in particular, we built an oscillator. We built an oscillator that allowed us to charge a capacitor. And when the voltage across the capacitor equaled that at the minus terminal it would flip and keep doing so.

And at the output you would get a waveform that looked like this. You would get a square wave output. Now, throughout the course we have talked about getting square wave inputs. And this is one example of how you can actually produce a square wave pretty much from first principles using a capacitor, resistors and an op amp.

Now, I just wanted to wrap up this little item here by talking about one application of an oscillator. And this application of the oscillator really nicely closed the loop on the body of knowledge relating to digital circuits that we have covered in this course.

What I want to talk about briefly is a small digital system with a sender and a receiver. And the sender is sending a signal, the receiver receives a signal, and in this course we have talked about senders sending a sequence of ones and zeros.

Say, for example, the sender wants to send some sort of a signal like this. We have seen that this is quite a legitimate signal. We get some kind of oscillatory behavior because of the inductance and capacitance associated with the wire.

And what you have done is that you pretty much believed me when I said that this really corresponds to a one, one, zero. The sender wants to send a one, one, zero signal to the receiver, and the receiver gets it.

So this is a one, this is a one, this is a zero. But if I am a receiver, I am going to look at the square wave. There is no such thing as sending a one on a wire. You cannot send a one on a wire.

You send a voltage signal or a current signal on a wire. So, the receiver receives a voltage signal. It is going to be zero for some time and then maybe 5 volts or 3 volts or whatever is your high and then zero again.

How does my receiver know it's a one, one, zero? Why can't it be a one, one, one, one, zero, zero, zero? It doesn't know. How does the receiver know it's a one, one, zero sequence and not 50 ones followed by 40 zeros? It doesn't know.

What we need is — For senders to be able to communicate with receivers, we need some kind of agreed upon time when receivers sample the signal coming in and decide whether it's a one or a zero. They both have to agree on certain time bases when to look at the input.

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