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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: Opamp integrator or lowpass 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 highpass 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 opamps required the use of
negative feedback. We illustrated this with the two basic negative feedback con gurations:
the inverting and the noninverting 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: Opamp di erentiator or highpass 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 opamp device itself has intrinsic gain A. This is called the opamp's openloop gain since
this is the gain the opamp 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 noninverting
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 closedloop 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 openloop gain to this voltage to produce vout:
vout = Ava = Avin , ABvout
Now we can solve for the closedloop gain: vout=vin G = 1 +A
AB 42 Note that there is nothing in our derivatio...
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 Fall '12
 Soujanu

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