# 1 z v dt vout rc in and for a single fourier component

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Unformatted text preview: f an active lter. In practice, one may need to supply a resistor in parallel with the capacitor to give a DC path for the feedback. !RC C R - IN OUT + Figure 33: Op-amp integrator or low-pass lter. 6.5.2 Di erentiator The circuit of Fig. 34 can be analyzed in analogy to the integrator. We nd the following: vout = ,RC dvin dt G! = ,!RC 40 41 So this ideally represents a perfect di erentiator and an active high-pass lter. In practice, one may need to provide a capacitor in parallel with the feedback resistor. The gain cannot really increase with frequency inde nitely! 6.6 Negative Feedback As we mentioned above, the rst of our Golden Rules for op-amps required the use of negative feedback. We illustrated this with the two basic negative feedback con gurations: the inverting and the non-inverting con gurations. In this section we will discuss negative feedback in a very general way, followed by some examples illustrating how negative feedback can be used to improve performance. 39 R C - IN OUT + Figure 34: Op-amp di erentiator or high-pass lter. 6.6.1 Gain Consider the rather abstract schematic of a negative feedback ampli er system shown in Fig. 35. The symbol is meant to indicate that negative feedback is being added to the input. The op-amp device itself has intrinsic gain A. This is called the op-amp's open-loop gain since this is the gain the op-amp would have in the absence of the feedback loop. The quantity B is the fraction of the output which is fed back to the input. For example, for the non-inverting ampli er this is simply given by the feedback voltage divider: B = R1=R1 + R2. The gain of the device is, as usual, G = vout=vin. G is often called the closed-loop gain. To complete the terminology, the product AB is called the loop gain. v in a v out A + - B Figure 35: General negative feedback con guration. As a result of the negative feedback, the voltage at the point labelled a" in the gure is va = vin , Bvout The ampli er then applies its open-loop gain to this voltage to produce vout: vout = Ava = Avin , ABvout Now we can solve for the closed-loop gain: vout=vin G = 1 +A AB 42 Note that there is nothing in our derivatio...
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## This note was uploaded on 01/14/2014 for the course AEI 601 taught by Professor Soujanu during the Fall '12 term at Bingham University.

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