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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 dvout , 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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