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All right. Let's get moving. Good morning. Today, if everything works out, we have some fun for you guys. I hope it works out. We'll see. What I am going to do today is a very major application of the frequency response and the frequency domain analysis of circuits.

And this application area is called filters. The area of filters often times demands a full course or a couple of full courses all by itself. And filters are incredibly useful. They're used in virtually every electronic device in some form or another.

They're used in radio tuners. We will show you a demo of that today. They're also used in your cell phones. Every single cell phone has a set of filters. So, for example, how do you pick a conversation? You pick a conversation by picking a certain frequency and grabbing data from there.

They are also in wide area network wireless transmitters. Do we have an access point here? I don't see one, but you've seen wireless access points. Again, there they have filters in them. So, virtually every single electronic device contains a filter at some point or another.

And so, today we will look at this major, major application of frequency domain analysis. Before we get into that, I'd like to do a bit of review. The readings for today correspond to Chapter 14.4.2, 14.5 and 15.2 in the course notes.

All right. Let's start with the review. We looked at this circuit last Friday — — where I said that for our analysis, we are going to focus on this small, small region of the playground. And what's special about this region of our playground is that I am going to focus on sinusoidal inputs.

And, second, I am going to focus on the steady state response. How does the response look like if I wait a long, long time? And then we said that the full blown time domain analysis was hard. This was, remember, the agonizing approach? And then I taught you the impedance approach in the last lecture, which was blindingly simple.

And, in that impedance approach, what we said we would do is — I will apply the approach right now and in seconds derive the result for you. But the basic idea was we said what we are going to do is assume that we are going to apply inputs of the form Vi e to the j omega t.

Wherever you see a capital and a small, there is an implicate e to the j omega t next to it. I'm not showing you that. And what I showed last time, and the class before that was once you find out the amplitude — Once you find out the multiplier that multiplies e to the j omega t, it's a complex number, you have all the information you need.

And once you have this, you can find out the time domain response by simply taking the modulus of that, or the amplitude and the phase of that to get the angle. And that gives you the time domain response.

So, our focus has been on these quantities. The impedance method says what I am going to do is replace each of these by impedances. And then the corresponding impedance model looks like this. Instead of R, I replace that with ZR.

And instead of the capacitor, I am going to replace that with ZC. And this is my Vc. ZR is simply R and ZC was going to be one divided by sC where s was simply a shorthand notation for j omega. Based on this, once I converted all my elements into impedances, I can go ahead and apply all the good-old linear analysis techniques.

I will discuss a bunch of them today. As an example, I could analyze this using my simple voltage divider relationship. Vc is simply ZC divided by ZC plus ZR times Vi.

And this application area is called filters. The area of filters often times demands a full course or a couple of full courses all by itself. And filters are incredibly useful. They're used in virtually every electronic device in some form or another.

They're used in radio tuners. We will show you a demo of that today. They're also used in your cell phones. Every single cell phone has a set of filters. So, for example, how do you pick a conversation? You pick a conversation by picking a certain frequency and grabbing data from there.

They are also in wide area network wireless transmitters. Do we have an access point here? I don't see one, but you've seen wireless access points. Again, there they have filters in them. So, virtually every single electronic device contains a filter at some point or another.

And so, today we will look at this major, major application of frequency domain analysis. Before we get into that, I'd like to do a bit of review. The readings for today correspond to Chapter 14.4.2, 14.5 and 15.2 in the course notes.

All right. Let's start with the review. We looked at this circuit last Friday — — where I said that for our analysis, we are going to focus on this small, small region of the playground. And what's special about this region of our playground is that I am going to focus on sinusoidal inputs.

And, second, I am going to focus on the steady state response. How does the response look like if I wait a long, long time? And then we said that the full blown time domain analysis was hard. This was, remember, the agonizing approach? And then I taught you the impedance approach in the last lecture, which was blindingly simple.

And, in that impedance approach, what we said we would do is — I will apply the approach right now and in seconds derive the result for you. But the basic idea was we said what we are going to do is assume that we are going to apply inputs of the form Vi e to the j omega t.

Wherever you see a capital and a small, there is an implicate e to the j omega t next to it. I'm not showing you that. And what I showed last time, and the class before that was once you find out the amplitude — Once you find out the multiplier that multiplies e to the j omega t, it's a complex number, you have all the information you need.

And once you have this, you can find out the time domain response by simply taking the modulus of that, or the amplitude and the phase of that to get the angle. And that gives you the time domain response.

So, our focus has been on these quantities. The impedance method says what I am going to do is replace each of these by impedances. And then the corresponding impedance model looks like this. Instead of R, I replace that with ZR.

And instead of the capacitor, I am going to replace that with ZC. And this is my Vc. ZR is simply R and ZC was going to be one divided by sC where s was simply a shorthand notation for j omega. Based on this, once I converted all my elements into impedances, I can go ahead and apply all the good-old linear analysis techniques.

I will discuss a bunch of them today. As an example, I could analyze this using my simple voltage divider relationship. Vc is simply ZC divided by ZC plus ZR times Vi.

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