Schmitt trigger
In electronics, a Schmitt trigger is a comparator circuit that incorporates positive feedback.
When the input is higher than a certain chosen threshold, the output is high; when the input is below another (lower) chosen threshold, the output is low; when the input is between the two, the output retains its value. The trigger is so named because the output retains its value until the input changes sufficiently to trigger a change. This dual threshold action is called hysteresis, and implies that the Schmitt trigger has some memory.
The benefit of a Schmitt trigger over a circuit with only a single input threshold is greater stability (noise immunity). With only one input threshold, a noisy input signal near that threshold could cause the output to switch rapidly back and forth from noise alone. A noisy Schmitt Trigger input signal near one threshold can cause only one switch in output value, after which it would have to move beyond the other threshold in order to cause another switch.

# Invention
The Schmitt trigger was invented by US scientist Otto H. Schmitt in 1934 while still a graduate student, later described in his doctoral dissertation (1937) as a "thermionic trigger". It was a direct result of Schmitt's study of nerve propagation in squid nerves.

# Symbol
The symbol for Schmitt triggers in circuit diagrams is a triangle with a hysteresis symbol:

# Comparator implementation
Today Schmitt triggers are typically built around comparators, connected to have positive feedback instead of the usual negative feedback. For this circuit the switching occurs near ground, with the amount
-f hysteresis controlled by the resistances of R1 and R2:
The comparator simply gives out the highest voltage it can, +VS, when the positive input ("+" on the above diagram) is at a higher voltage than the negative input ("-" on above diagram), and then switches to the lowest output voltage it can, VS, when the positive input drops below the negative input.
For instance, if the Schmitt Trigger is currently in the high state, the output will be at the positive power supply rail (+VS). V+ is then a voltage divider between Vin and +VS. 
The comparator will switch when V+=0 (ground). Current conservation shows that this requires:
Vin/R1 = VS/R2
so Vin must drop below (R1/R2)VS to get the output to switch. 
Once the comparator output has switched to VS,  the threshold becomes +(R1/R2)VS to switch back to high.
So this circuit creates a switching band centered around zero, with trigger levels (R1/R2)VS. 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 and then back off. If R1 is zero or R2 is infinity (an open circuit), the band collapses to zero width, and it behaves as a standard comparator. The output characteristic is shown in the picture on the right. The value of the threshold T is given by (R1/R2)VS and the maximum value of the output M is the power supply rail.
A possible structure of a more realistic configuration is the following:
The output 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: this way the output can be modified and it is much more stable. The resistor R3 is there to limit the current through the diodes, while R4 is there to minimize the input voltage offset caused by the op-amp's input bias currents (see Limitations of real op-amps).

# Schmitt trigger with two transistors
A Schmitt trigger is still frequently made using two transistors as shown. The chain RK1 R1 R2 sets the base voltage for transistor T2. This divider, however, is affected by transistor T1, providing higher voltage if T1 is open. Hence the threshold voltage for switching between the states depends on the present state of the trigger.
For NPN transistors as shown, when the input voltage is well below the shared emitter voltage, T1 does not conduct.  The base voltage of transistor T2 is determined by the mentioned divider. Due to negative feedback, the voltage at the shared emitters must be almost as high as that set by the divider so that T2 is conducting, and the trigger output is in the low state. T1 will conduct when the input voltage (T1 base voltage) rises slightly above the voltage across resistor RE (emitter voltage). When T1 begins to conduct, T2 ceases to conduct, because the voltage divider now provides lower T2 base voltage while the emitter voltage does not drop because T1 is now drawing current across RE.  With T2 now not conducting the trigger has transitioned to the high state.
With the trigger now in the high state, if the input voltage lowers enough, the current through T1 reduces, lowering the shared emitter voltage and raising the base voltage for T2. As T2 begins to conduct, the voltage across RE rises, further reducing the T1 base-emitter potential and T1 ceases to conduct.
In the high state, the output voltage is close to V+, but in the low state it is still well above V. This may not be low enough to be a "logical zero " for digital circuits. This may require additional amplifiers following the trigger circuit.
The circuit can be simplified: R1 can be omitted, connecting the T2 base directly to the T1 collector, and the connection of the T2 base to V-  via R2 can be completely omitted. When T1 conducts, it connects the T2 base to the T2 emitter so that T2 does not conduct. When T1 does not conduct, RK1 pulls up the T2 base and T2 conducts.

# Use as an oscillator
Schmitt triggers are sometimes used to implement a simple type of relaxation oscillator, or multivibrator. This is achieved by connecting a single resistor-capacitor network to an inverting Schmitt trigger  the capacitor connects between the input and ground and the resistor connects between the output and the input. The output will be a continuous square wave whose frequency depends on the values of R and C, and the threshold points of the Schmitt trigger. Since multiple Schmitt trigger circuits can be provided by a single integrated circuit (e.g. the 4000 series CMOS device type 40106 contains 6 of them), a spare section of the IC can be quickly pressed into service as a simple and reliable oscillator with only two external components.

# Devices that include a built-in Schmitt trigger
The following 7400 series devices include a Schmitt trigger on their input or on each of their inputs:
- 7413: Dual Schmitt trigger 4-input NAND Gate
- 7414: Hex Schmitt trigger Inverter
- 7419: Hex Schmitt trigger Inverter
- 74132: Quad 2-input NAND Schmitt Trigger
- 74221: Dual Monostable Multivibrator with Schmitt Trigger Input
- 74232: Quad NOR Schmitt Trigger
- 74240: Octal Buffer with Schmitt Trigger Inputs and Three-State Inverted Outputs
- 74241: Octal Buffer with Schmitt Trigger Inputs and Three-State Noninverted Outputs
- 74244: Octal Buffer with Schmitt Trigger Inputs and Three-State Noninverted Outputs
- 74310: Octal Buffer with Schmitt Trigger Inputs
- 747541 Octal Schmitt Trigger Buffer/Line Driver
A number of 4000 series devices include a Schmitt trigger on inputs, for example:
- 14093: Quad 2-Input NAND
- 40106: Hex Inverter
- 14538: Dual Monostable Multivibrator
- 4020: 14-Stage Binary Ripple Counter
- 4024: 7-Stage Binary Ripple Counter
- 4040: 12-Stage Binary Ripple Counter
- 4017: Decade Counter with Decoded Outputs
- 4022: Octal Counter with Decoded Outputs
Dual Schmitt input configurable single-gate CMOS logic, AND, OR, XOR, NAND, NOR, XNOR
- NC7SZ57 Fairchild
- NC7SZ58 Fairchild
- SN74LVC1G57 Texas Instruments
- SN74LVC1G58 Texas Instruments