[MUSIC] >> Welcome back to Linear Circuits. This is Dr. Ferri. This is our module summary. We'll be reviewing the basic methods that we've introduced, and then we'll be doing an exercise on which method, and why. First of all, we introduce the Phasor to represent a cosine. We introduce it in terms of the Polar form as well the Rectangular form. The other thing we did is look at common signals and just so that you get a better feel for what the Phasor looks like when it relates to signal. For example, in this particular one 360 degrees corresponds to one cycle right there. So this one right here is off by half of a cycle, so that's why it's 180 degrees. This one right here, if this is 360, this one is off by a quarter of that amount, so that's why it's 90. And the angles are negative right here, because this is shifted to the right from one that would have zero degrees. We introduced the impedance for resistors, capacitors and inductors. We also introduced a circuit analysis method, solution method using impedances. Three step methods. First of all we draw the circuit replacing The sources with their phasors and components with their impedances. The next is to use the methods that we did in module two which were just like all the resistor methods, KBL, KCL, Thevenin-Norton, Mesh Node. Any of those methods that we're familiar with to solve this. The key was to treat the impedances as if they were complex resistors. And then the last step was to convert from the phasar form back to the cosine. We introduced transfer functions. Our motivation was to find an expression to solve for the output given an input. In other words,find a functional relationship for a function that relates the input to the output. And we want to be able to solve for various frequencies, various angles and various amplitudes of the input, and that function, in kind of a generic form, allows us to do that. The transfer function we define as the output phasor over the input phasor, in other words, the output is equal to the transfer function times the input. And then we use this relationship In particular, to solve for the output amplitude and the output angle in this form right here. Now let's look at which method and why. So if I look at a circuit like this, the first step would be to convert it to its impedance form. And I look at this and say, okay, which method do I want to use to solve for Vo In this particular case, we're going to look and say, let's combine these two resistors in parallel, and then I want to use the voltage divider law. On this particular one, once I convert it to its impedance form, I'll look at this and say well, I know this current source right here, I'm trying to solve for that current right there. So in this particular case I'm going to use mesh analysis. Now in this last example here, suppose I'm trying to solve for V out. Well once I convert it to its impedance form, I look at this and say, I need to solve for V out. This is an unknown node. If I could choose my ground node right here, this node is node that node is node I'm going to use node analysis. Alright that's it on this particular summary. I encourage you to go to the forums and ask and answer questions. All right, thank you. [MUSIC]
