Page 180 - Op Amps Design, Applications, and Troubleshooting

Voltage Comparator with Output Limiting 163

Some algebraic manipulation gives us the expression for v t at the moment it
reaches the upper threshold:

In the present example, v 0~ equals the voltage of D 3 (-5.6 volts as listed in Appen-
dix 5) during this period of time. The reference voltage is 6.2 volts (see Appendix 5).
Substituting values enables us to calculate the value of the upper threshold voltage:

This value can be made slightly more accurate by including the effects of the for-
ward voltage drop of D 2 (about 0.7 volts). That is, v 0~ will equal the voltage of D 3
plus the forward voltage drop of D 2, or -6.3 volts. If this effect is included, the
threshold is computed to be 11.2 volts.

Lower Threshold Voltage. A similar application of basic circuit theory
when the output is at the +V SAT level and the input is approaching the lower
threshold voltage yields the following expression for the lower threshold volt-
age:

Recognizing that v 0* will be equal to the voltage of D 2 (3.3 volts) during this time,
we can calculate the value of lower threshold voltage:

If the forward voltage drop of D 3 is included in the calculation, the threshold volt-
age will be computed as 7.07 volts.

Hysteresis. Hysteresis is simply the difference between the two threshold volt-
ages. In our present case, hysteresis is computed as shown in Equation (3.6):