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In this case one would put a resistance from the

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Unformatted text preview: igate o set currents. In this case one would put a resistance from the , input to ground which is balanced by the R1 and R2 in parallel see Fig. 30. It is important to note that, just as we found for transistor circuits, one shpould always provide a DC path to ground for op-amp inputs. Otherwise, charge will build up on the e ective capacitance of the inputs and the large gain will convert this voltage = Q=C  into a large and uncontrolled output voltage o set. However, our modi ed designs to ght IOS have made our op-amp designs worse in a general sense. For the non-inverting design, we have turned the very large input impedance into a not very spectacular 10 k . In the inverting case, we have made the virtual ground into an approximation. One way around this, if one is concerned only with AC signals, is to place a capacitor in the feedback loop. For the non-inverting ampli er, this would go in series with the resistor R1 to ground. Therefore, as stated before, it is best, where important, to simply choose better op-amps! 6.5 Frequency-dependent Feedback Below are examples of simple integrator and di erentiator circuits which result from making the feedback path have frequency dependence, in these cases single-capacitor RC lters. It is also possible to modify non-inverting con gurations in a similar way. For example, problem 3 on page 251 of the text asks about adding a rollo " capacitor in this way. Again, one would simply modify our derivations of the basic inverting and non-inverting gain formulae by the replacements R ! Z , as necessary. 38 6.5.1 Integrator Using the golden rules for the circuit of Fig. 33, we have vin , v, = vin = i = i = ,C dvout , v, = ,C dvout R R in out dt So, solving for the output gives dt 1 Z v dt vout = , RC in And for a single Fourier component !, this gives for the gain G! = , 1 38 39 Therefore, to the extent that the golden rules hold, this circuit represents an ideal integrator and a low-pass lter. Because of the presence of the op-amp, this is an example o...
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