How is hysteresis implemented in a Schmitt trigger using positive feedback, and how do you compute the upper and lower thresholds in a common configuration?

• A. Positive feedback creates two switching thresholds; with Vin at the inverting input and a portion of Vout fed back to the noninverting input via resistors, thresholds: Vth+ = α Vsat, Vth− = −α Vsat where α = R2/(R1+R2)
• B. Positive feedback creates two switching thresholds; with Vin at the noninverting input and feedback to the inverting input via R1 and R2, thresholds are zero
• C. Negative feedback creates switching thresholds; thresholds: Vsat and −Vsat
• D. No hysteresis; single fixed threshold at ground

Answer: (A)

Hysteresis in a Schmitt trigger comes from positive feedback that shifts the reference voltage at the noninverting input depending on the output state, creating two distinct switching points for rising and falling inputs. In the common inverting configuration, the input is applied to the inverting input while the output is fed back to the noninverting input through a resistor divider. The node at the noninverting input sits at a fraction α of the output, where α = R2/(R1 + R2). When the output is saturated high, that node equals α Vsat, so the input must rise above α Vsat to flip the output low. When the output is saturated low, the node equals −α Vsat, so the input must drop below −α Vsat to flip the output high. Therefore, the upper and lower thresholds are Vth+ = α Vsat and Vth− = −α Vsat, with α between 0 and 1 setting the hysteresis width. This configuration produces two distinct switching points; configurations that place the input at the noninverting input or rely on negative feedback would not produce hysteresis with two thresholds, and a setup with no hysteresis would have a single fixed threshold.