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                                  V                              V
                                   C1                              C1
                              R
                               1
                                     V                               v
                                      ref                     R       in            v
                                            -       v 0        1            -       0
                                           +                               +
                              R
                               2     v in                             V  ref
                                                              R
                                                               2

                                         v
                                          in










                                         v
                                          0
                                        v
                                         sat



                                       - v
                                         sat


                                         v
                                          0
                                        v
                                         sat



                                       - v
                                         sat

                              FIGURE 5.29: Open loop op-amp used as a comparator: V ref  reference voltage and V in  input
                              voltage (i.e., voltage from a sensor) are switched at the op-amp terminals between the two
                              cases. The net result is the output polarity change.



                              Op-Amps with Positive Feedback       Modifications to the op-amp feedback loop
                              on the non-inverting terminal can provide hysteresis in the comparator to implement
                              ON/OFF relay control with hysteresis, such as is used in home temperature control. A
                              well-known circuit with this function is the Schmitt trigger (inverting and noninverting
                              types, Figure 5.31). The op-amp uses positive feedback which results in a hysteresis rela-
                              tionship between input and output. Positive feedback is the key to the hysteresis function
                              realization. Such circuits are not only used in ON/OFF control systems with desired hys-
                              teresis, but also reject undesirable noise in the signal provided the noise magnitude is
                              smaller than the hysteresis magnitude (Figure 5.31). A more general form of the Schmitt
                              trigger op-amp circuit allows adjustment of both the hysteresis magnitude and center input
                              voltage value about which the hysteresis is designed. Schmitt trigger circuits are also used
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