Given a Schmitt trigger with Vout_high = +Vsat, Vout_low = -Vsat and a divider ratio α = R2/(R1+R2), what are the upper and lower switching thresholds?

Given a Schmitt trigger with Vout_high = +Vsat, Vout_low = -Vsat and a divider ratio α = R2/(R1+R2), what are the upper and lower switching thresholds?

• A. Vth+ = α Vsat; Vth− = −α Vsat.
• B. Vth+ = α (−Vsat); Vth− = α Vsat.
• C. Vth+ = −α Vsat; Vth− = α Vsat.
• D. Vth+ = Vsat/α; Vth− = −Vsat/α.

Answer: (A)

Schmitt triggers use positive feedback to create two distinct switching thresholds. The resistor divider that feeds the noninverting input sets a reference that equals a fraction α of the output voltage, where α = R2/(R1+R2). When the output is high, this reference is +α Vsat. The op-amp switches when the inverting input (the signal being tested) reaches that reference, so the input must rise to +α Vsat to cause a transition from high to low. After switching, the output is low and the reference becomes -α Vsat. Now the input must fall to -α Vsat to cause the opposite transition back to the high state. Hence the upper switching threshold is α Vsat and the lower switching threshold is -α Vsat, i.e., the thresholds are ±α Vsat.

Schmitt triggers use positive feedback to create two distinct switching thresholds. The resistor divider that feeds the noninverting input sets a reference that equals a fraction α of the output voltage, where α = R2/(R1+R2). When the output is high, this reference is +α Vsat. The op-amp switches when the inverting input (the signal being tested) reaches that reference, so the input must rise to +α Vsat to cause a transition from high to low. After switching, the output is low and the reference becomes -α Vsat. Now the input must fall to -α Vsat to cause the opposite transition back to the high state. Hence the upper switching threshold is α Vsat and the lower switching threshold is -α Vsat, i.e., the thresholds are ±α Vsat.