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Good morning. All right. Today we are going to take a fresh look at some of the stuff we covered in the last two lectures. And the graph I want you to keep in mind as we go through this lecture in terms of what to expect.

This was time. And last Tuesday's lecture we covered some stuff. I talked about a method for the sinusoidal response which was agony, I warned you it will be agony, and then towards the end I showed you another method that was quite a bit easier but still pretty hard.

And I promised you that today there will be a new method which is going to be so easy , actually almost trite. Just imagine. I am going to make a statement right now that I think you will all find hard to believe.

What I am going to say is just imagine your RLC circuit, your resistor, inductor and capacitor, a parallel form or series form. Imagine that you could write down the characteristic equation for that by observation in 30 seconds or less.

Just imagine that. By observation, boom, write down the characteristic equation for virtually any RLC circuit or RC circuit or whatever. And we all know that once you have the characteristic equation you could very easily go from there to the time domain response intuitively or to the sinusoidal steady-state response, too.

So just keep that thought in mind. Imagine 30 seconds. And that is what you should expect in today's lecture. Students often ask me, if this stuff is actually so easy why do you take us through this tortuous path? Are we just mean? Do we just want you show you how hard things are and then show the easy way? I have argued with myself every year as to whether to just go ahead and give the easy path and that's it.

But I think the reason we cover the basic foundations is that it gives you a level of insight that you would not have otherwise gotten if I directly jumped into the easy method. So you need to understand the foundations and you need to have seen that at least once.

And second, once you do something the hard way, you appreciate all the more the easy method. All right. Today we cover what is called "The Impedance Model." First let me do a review just because of the large amount of content in the last two lectures.

I did them using view graphs. I usually don't like to do that, but even then it was quite rushed. So let me quickly summarize for you kind of the main points. We have been looking at, on Tuesday, the sinusoidal — — looking at the sinusoidal steady state response.

Also fondly denoted as SSS. And the readings for this were Chapters 14.1 and 14.2. what we said was if you took this example circuit and we fed as input cosine of omega t, we have an R and a C, and let's say we cared about the output response and we cared about the capacitor voltage.

What we talked about was focused on the sinusoidal steady-state response. And what that meant was first of all focus on steady-state. In other words, just to capture the steady-state behavior when t goes to infinity after a long period of time.

And for most of the circuits that we consider, because of the R or presence of any resistance, the homogenous response usually would die out because the homogenous response is usually of the form minus t by tau.

And as t goes to infinity this term tends to go to zero. We are just looking at the steady-state. And therefore, because of the circuits we looked at, we can ignore the homogenous response. All we are left to do is to find the particular response to sinusoids of this form.

This was time. And last Tuesday's lecture we covered some stuff. I talked about a method for the sinusoidal response which was agony, I warned you it will be agony, and then towards the end I showed you another method that was quite a bit easier but still pretty hard.

And I promised you that today there will be a new method which is going to be so easy , actually almost trite. Just imagine. I am going to make a statement right now that I think you will all find hard to believe.

What I am going to say is just imagine your RLC circuit, your resistor, inductor and capacitor, a parallel form or series form. Imagine that you could write down the characteristic equation for that by observation in 30 seconds or less.

Just imagine that. By observation, boom, write down the characteristic equation for virtually any RLC circuit or RC circuit or whatever. And we all know that once you have the characteristic equation you could very easily go from there to the time domain response intuitively or to the sinusoidal steady-state response, too.

So just keep that thought in mind. Imagine 30 seconds. And that is what you should expect in today's lecture. Students often ask me, if this stuff is actually so easy why do you take us through this tortuous path? Are we just mean? Do we just want you show you how hard things are and then show the easy way? I have argued with myself every year as to whether to just go ahead and give the easy path and that's it.

But I think the reason we cover the basic foundations is that it gives you a level of insight that you would not have otherwise gotten if I directly jumped into the easy method. So you need to understand the foundations and you need to have seen that at least once.

And second, once you do something the hard way, you appreciate all the more the easy method. All right. Today we cover what is called "The Impedance Model." First let me do a review just because of the large amount of content in the last two lectures.

I did them using view graphs. I usually don't like to do that, but even then it was quite rushed. So let me quickly summarize for you kind of the main points. We have been looking at, on Tuesday, the sinusoidal — — looking at the sinusoidal steady state response.

Also fondly denoted as SSS. And the readings for this were Chapters 14.1 and 14.2. what we said was if you took this example circuit and we fed as input cosine of omega t, we have an R and a C, and let's say we cared about the output response and we cared about the capacitor voltage.

What we talked about was focused on the sinusoidal steady-state response. And what that meant was first of all focus on steady-state. In other words, just to capture the steady-state behavior when t goes to infinity after a long period of time.

And for most of the circuits that we consider, because of the R or presence of any resistance, the homogenous response usually would die out because the homogenous response is usually of the form minus t by tau.

And as t goes to infinity this term tends to go to zero. We are just looking at the steady-state. And therefore, because of the circuits we looked at, we can ignore the homogenous response. All we are left to do is to find the particular response to sinusoids of this form.

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