Investing differentiator circuit resistor

For each individual case the designer must decide which parts of a circuit are best implemented by analog circuitry, which by conventional digital circuitry and which sections could be microprocessor controlled. In order to facilitate this decision for the designer who is not familiar with all these subjects, we have arranged the book so as to group the different circuits according to their field of application.

Each chapter is thus written to stand on its own, with a minimum of cross-references. To enable the reader to proceed quickly from an idea to a working circuit, we discuss, for a large variety of problems, typical solutions, the applicability of which has been proved by thorough experimental investigation. Our thanks are here due to Prof. Let me do this first one, this one right here first. In this particular one, this voltage drop is 0. And this is the ground so, this actually is the ground right here.

This is, this is equal to zero potential, that means that Vn is equal to the voltage across that capacitor. And we'll define the current. Is going in this direction so that voltage drop is plus minus V sub c. Now, my second KVL is around this outer loop right here, and writing that I get minus Vn plus V sub c plus R times i, because all the current going through that capacitor must go in this direction, since this current is zero in this little branch there. Plus V zero is equal to zero.

Now these first two, this first equation still holds. In other words, these are equal, that means that this cancels out. And what I'm left with, is V0 is equal to minus R times i. While i is up here, C dvc dt. Well Vc, V sub c is equal to Vn. So that's where we get this equation right here. So this is now the equation that governs this circuit, the differentiator circuit. I want to show you an example of a real circuit that we've built to, to demonstrate this.

And we're using real Op Amp chip right here. And that Op Amp chip has eight pins to it. And if you can look carefully right here there's, there's a little indent right up here and where those indents are, that shows you that the one-pin is going to be just to the left of it. It gives you the orientation. And there's a 1 pin 2, 2, 3, 4, 5, 6, 7 and 8. That's how I know how to hook things up. In the 2 pin we're going to be hooking up to V minus.

Well V minus is right here, so let me show that as the 2 pin right here. Where is that over here? Well, the indent is right here, so the 2pin right there. We count 1, 2, and that's V minus. So actually let's start looking at this circuit right from the beginning. So we've got V in, goes into the capacitor. So V in comes in. That's from my function generator goes into one side of the capacitor.

The other end of the capacitor goes into these V minus, which is right there the two pin. The other, the capacitor also goes into the resistor, And the resistors connected over to V sub 0. So v sub 0 is a 6 pin, I'm going to mark it as a 6 right there. So we should have a resistor going between the two pin and the six pin. So that's the two pin there, and there's a 6. So that's 1, 2, 3, 4, 5, 6. So that's the 6 pin right there. And that is connected to V0. Now the voltage source to power this, we've got minus 15 volts connected to pin four and plus 15 volts connected to pin seven.

We can see V sub s here. And minus V sub s there. So this is now my circuit that implements this schematic. Let's look at the results here for this osiliscope. If V in, Is this voltage right there And V out is this voltage. So if we look at this voltage here, V out, and V in, so it does differentiate. If V in is a triangular wave, then if I take the derivative of it, I get a constant, and I'm actually going to get a positive constant, but then I negate it. So that's why it goes this way.

So my output is equal to the derivative of the input. And I have a scaling factor in there of gain, which is equal to minus RC. Now let's take a look at the integrator circuit. The integrator circuit, again, uses the IV characteristics of a capacitor. But this time we're going to integrate this equation and get the integral form of the eq, form of the IV characteristics here.

And that's what we'll exploit.

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