Welcome back to Electronics. We're starting module two, which is on Op Amps. Lor lesson objectives here are first to introduce operational amplifiers, to describe their ideal behavior, and then to introduce two particular circuits. An, a comparator and a buffer circuit, which use Op Amps. So operational amplifiers, or what we call Op Amps, are specialized circuits made up of transistors, resistors, capacitors, and are fabricated on an integrated chip. They're actually fairly complicated, internally. But the nice thing about Op Amps is that they've got a fairly easy input to output sort of behavior. So, if I look at this as being my input to my circuit. V sub n. And then this being the output, V out. The, I can come up with a fairly simple expression relationship for the input to output behavior. So the uses of. Op Amps is ann amplification. So I can amplify a voltage signal, make it larger, or I might be able to boost the power from the input to the output. We typically use Op Amps in active filters. What do I mean by active? Active, an active device is something that has its own power supply. So if I'm looking at this right here, V sub s and, you know, I've got V sub s and minus V sub s gives me a power supply. So any active element is one that has its own power supply to it. Now in another use of Op Ampsers in Analog computers, and this is the old style computers that we used years and years ago before they had digital computers. They had Op Amps in them. And that was one of the basic components of them. Lets look at Op Amps in circuits. And as I mentioned this is the power supply. These don't actually have to equal each other. I might have a, a different plus value and a diff with a different minus value. And then I've got my output and my two input terminals. So actually I've got five inputs to this circuit. Now this circuit is, in, is fabricated on this integrated chip and I have pins to this integrated chip that allow me to connect to the internal circuitry of it. Now common values of power supply the V sub s is 10 volts to 15 volts. Now a symbol, a circuit symbol for an Op Amp looks like this. Now, notice that I dropped the power supply. The reason I dropped the power supply in this symbol is because the power supply is what makes it work, but it does not affect the circuit equations that we use in analyzing Op Amps in circuits. So again, the power supply doesn't affect our circuit equations. In most circuits. As I mentioned, it's an active element, because it has its own power supply. And the other thing is that we're ignoring that, V sub s in the symbol of it [SOUND] Lets first examine open loop behavior of this. So I've got my op app here and I'm going to have a value a which is a scaler of v plus minus v minus. The difference in other words between these two input terminals. So, this A is actually the slope. And typically, A is really large, say on the order of like, you know, 10,000. And we often tall, call that the open loop gain [SOUND] And with that being very large and it doesn't take very much for this to do what we call saturate. When a difference, this difference, doesn't get very large before it reaches this value here where it's constant. We call that saturation. [SOUND] And often times, we look at the input to this circuit as Vin, and it's a difference between these two values, so this would be called Vin. So with a very small value of Vin, it saturates. Now let's do a quiz on that value. Now in the quiz we had to 10,000 and we had v of s is equal to ten, and so what value of this of the voltage input before it saturated it was one milliamp minus one milliamp. So in other words, very small value of V in made this saturate. So we'd have what we'd say, a very small range of operation for the linear range. This is the linear range right here, very small range of operation, when we've got what we call, the Open Loop Behavior. A comparator circuit is one that utilizes an Op Amp in its open loop configuration. So we've got the open loop configuration here, and we've just repeated what this value looks like. In this particular circuit, we're assuming that for the most, most of the time we are operating not in a linear region, but in a saturation region. So in other words, if vin is greater than 0. In other words, v plus is greater than v minus, we have a value of vs. If v plus is less than v minus, we have a value of minus vs. So, that gives us an indication whether these root, we are looking at a difference really between these two voltages. If one, if V plus is greater than V minus, we have got a positive value out of our comparator. And if V minus is, if V plus is great less than V minus, we have got a negative value. So, it's an indicator, which of these is larger than the other. As an example of a comparative circuit, let's assume that we've got a sine wave voltage going into V plus, whereas C is just some constant. And we connected V minus to ground. So our input voltage is actually some constant times the sine of omega t. Now this is our comparator circuit right here. And we're assuming that C is a fairly large value. So that we're into the saturation region almost immediately, as we go through 0. So if this is our sine wave, of our input. Voltage. That we're in the linear region very, very small amount of time. So that means we're almost always in saturation. So my output will actually have a value of vis of s anytime I've got a positive value of vn. And then when I go through ze, the 0 crossing, it becomes negative. It goes to minus Vs. And it stays that way as long as we're on the negative cycle of this sin wave. And then when we go positive again, it goes positive. So, in other words, we've converted our sin wave into a square wave. By sending it through a Comparator. Let's examine a model, or different models for Op Amp behavior. Now as I mentioned before, what's internal to an Op Amp is a lot of transistors, capacitors, it's rather complicated, but we can come up with a fairly simplistic model of it. That looks like this over here. And in this model we've got an, what we call an input impudence, R sub i. And R sub i is actually very large. And because it's large, the current running through it is very small. So this current i, is very small. And we have this dependent source right there, and that dependent source gives us the output, A times Vm, which we've already seen before. For ASM gain. Now this is a model for an We wanted to come up with this simpler model. And this is what we're going to call the ideal model here. Now, in the ideal model. Instead of saying i is very small, we're going to say it's zero. The input current at both of these terminals, we're going to set equal to zero. And since that current is zero, another words this current going through this resistor zero then this voltage is going to be equal to zero, the voltage across these terminals is equal to zero. So this right here is equal to zero. And we've also got this equal to zero and that equal to zero. So that's my ideal model. We're going to use that in analyzing op amp circuits. The simplest circuit we're going to examine is what's called a buffer circuit. A buffer circuit is made by just connecting the output back to the negative terminal. And this is what we call a feedback loop. And because it's a feedback loop we often call that closed loop and that's the difference. Before I used the term open loop. Now this is called a closed loop or a closed loop around here. A lot of the op ant circuits we're going to be looking at. Actually have a resistor in this. But all of the other Op Amps circuits re, we'll examine aside from the Comparator all have this feedback loop, with our without a resistor in there. Now the buffer circuit has this relationship between the output to the input. V in is equal to V out. We want to examine how you would come up with that, equation. And is, it, to examine that, it's actually easier to re-draw this circuit, showing some sort of reference ground. because this V in is a node voltage, and it's with respect to some ground. So, let me, go ahead and re-draw the input, and the output voltage is this way, because I want to do a K-V all around this. I'm going to do a K-V-L from the ground, up across the input, across the input of the up amp and then back to the output. So this is back to ground, so I've done a complete loop there, and I, I want to show these equations. The way I do a KBL is, I will go to here. When I see a ne, negative sign on an element, I negate, I add in it, minus voltage and go in Now actually, when I go from here to here, I'm gaining potential. And I come around here, I'm losing potential, but just for my sake and a lot of student sake, it's just easier whenever to use the convention. Whenever you come a minus sign, subtract it. Whenever you come to a plus sign first, you add it. So coming across here, I have the minus V n and I've got the voltage drop across this input. Well with the ideal. Die ideal op amp behavior that would be zero volts. And then coming around here, I get to the plus V out is equal to 0. And that gives me the equation back for buffer circuit. So in summary, we've shown that op amps are active devices. Active again, meaning they've got their own power supply. And they can be used to filter or amplify signals, linearly. Just to comment about linear, what I mean by linearly. We've got an input and output characteristic. And in the open loop, we show that we've got this range right here, before we saturate. This range right here, is what we call, the Linear Range. So if we stay in that range, we stay in what we call linear range. Now we looked at ideal op amp models, in particular, the model required this assumption. So any of the following lessons, we will be developing a lot of op amp circuits, and we will always go back to this model right here. Where these assumptions are, are true. We looked at two particular types of circuits. A comparative circuit, and a buffer circuit. So the remainder of module 2, we will go in more depth in the buffer circuit, we will cover a number of different amplifier configurations with op amps, and we'll look at differentiators and integrator circuits. And then we'll go on to look at active filters. Now 'd like to encourage you again to go to the forums and ask and answer questions. We really appreciate your participation, especially those of you who are on there answering questions. You do a, a great favor to us and to the rest of the class. Thank you.
