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Filter Design



                                                                                  Filter Design  305

                          Figure 6.53 is a common RC active low-pass filter, and functions so: C
                                                                                                2
                        passes the higher frequencies to ground, while  C sends a degenerative
                                                                          1
                        feedback to the noninverting input as the frequency increases. This is
                        caused by the capacitor’s decreasing capacitive reactance at increasing fre-
                        quencies. Thus,  C , C , R , R , and the op-amp efficiently form an active
                                          1   2  1   2
                        low-pass filter.
                          An active high-pass filter is shown in Fig. 6.54, with R , C , and C forming
                                                                             2  1       2
                        a simple high-pass filter that is used to send the higher frequencies to the op-
                        amp’s input with little attenuation. At the lower frequencies, however, the
                        increasing capacitive reactance of C and C attenuates, decreasing their sig-
                                                          1      2
                        nal at the filter’s output.
                          The active bandpass filter of Fig. 6.55 employs a feedback network that
                        readily passes all frequencies back to its input that are not within the filter’s
                        passband and, since this feedback is degenerative, all but a narrow passband
                        of desired frequencies will be attenuated.


            6.5.2 Active filter design
                        All of the active filters below have a Bessel response, and are meant to be driv-
                        en from a low-impedance source that is significantly below R in value.
                                                                                 1
















                        Figure 6.53 An active low-pass filter.


















                        Figure 6.54 An active high-pass filter.


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