Non-inverting Schmitt Trigger
In this circuit, the two resistors R1 and R2 form a parallel voltage summer. It adds a part of the output voltage to the input voltage thus "helping" it during and after switching that occurs when the resulting voltage is near the ground. This parallel positive feedback creates the needed hysteresis that is controlled by the proportion between the resistances of R1 and R2. The output of the parallel voltage summer is single-ended (it produces voltage in respect to ground); so, the circuit does not need an amplifier with a differential input. Since conventional op-amps have a differential input, the inverting input is grounded to make the reference point zero volts.
The output voltage always has the same sign as the op-amp input voltage but it not always has the same sign as the circuit input voltage (the signs of the two input voltages can differ). When the circuit input voltage is above the high threshold or below the low threshold, the output voltage has the same sign as the circuit input voltage (the circuit is non-inverting). It acts like a comparator that switches at a different point depending on whether the output of the comparator is high or low. When the circuit input voltage is between the thresholds, the output voltage is undefined; it depends on the last state (the circuit behaves as an elementary latch).
For instance, if the Schmitt trigger is currently in the high state, the output will be at the positive power supply rail (+VS). The output voltage V+ of the resistive summer can be found by applying the superposition theorem:
The comparator will switch when V+=0. Then (the same result can be obtained by applying the current conservation principle). So must drop below to get the output to switch. Once the comparator output has switched to −VS, the threshold becomes to switch back to high. So this circuit creates a switching band centered around zero, with trigger levels (it can be shifted to the left or the right by applying a bias voltage to the inverting input). The input voltage must rise above the top of the band, and then below the bottom of the band, for the output to switch on (plus) and then back off (minus). If R1 is zero or R2 is infinity (i.e., an open circuit), the band collapses to zero width, and it behaves as a standard comparator. The transfer characteristic is shown in the picture on the right. The value of the threshold T is given by and the maximum value of the output M is the power supply rail.
A unique property of circuits with parallel positive feedback is the impact on the input source. In circuits with negative parallel feedback (e.g., an inverting amplifier), the virtual ground at the inverting input separates the input source from the op-amp output. Here there is no virtual ground, and the steady op-amp output voltage is applied through R1 - R2 network to the input source. The op-amp output passes an opposite current through the input source (it injects current into the source when the input voltage is positive and it draws current from the source when it is negative).
A practical Schmitt trigger with precise thresholds is shown in the figure on the right. The transfer characteristic has exactly the same shape of the previous basic configuration, and the threshold values are the same as well. On the other hand, in the previous case, the output voltage was depending on the power supply, while now it is defined by the Zener diodes (which could also be replaced with a single double-anode Zener diode). In this configuration, the output levels can be modified by appropriate choice of Zener diode, and these levels are resistant to power supply fluctuations (i.e., they increase the PSRR of the comparator). The resistor R3 is there to limit the current through the diodes, and the resistor R4 minimizes the input voltage offset caused by the comparator's input leakage currents (see Limitations of real op-amps).
Read more about this topic: Schmitt Trigger, Implementation, Op-amp Implementations