Page 160 - Op Amps Design, Applications, and Troubleshooting

Zero-Crossing Detector with Hysteresis 143

Upper Threshold Voltage. The upper threshold voltage is the value of volt-
age that appears across Rj when the output is at its maximum positive level. In
our present circuit, the maximum output is essentiaEy +V SAT. We will use the low-
est value given in Appendix 1 (10 volts) for + V SAT. The value of threshold voltage
is computed by applying the basic voltage divider formula.

where V T is the total voltage across the series resistors RI and R F. In our case, we
have

This calculation reveals a significant limitation for this circuit. The value of thresh-
old voltage is directly affected by the value of V SAT. That value, however, is far
from constant. Appendix 1 indicates that V SAT can vary from a low value of 10
volts (with a heavy load) to as high as 14 volts when lightly loaded. The resulting
variation in threshold voltage may be objectionable in some applications. If so, the
feedback voltage can be regulated (e.g., by using a pair of zener diodes) for more
consistent performance.

Lower Threshold Voltage. The lower threshold voltage for the circuit shown
in Figure 3.7 is computed using the same method, Equation (3.5), discussed for the
upper threshold. The value is computed as

The lower threshold suffers from the same variations described for the upper
threshold. Also notice that in this particular circuit, the upper and lower threshold
voltages are equal in magnitude and positioned on either side of 0 volts. Other cir-
cuits may have dissimilar magnitudes for the two thresholds. Additionally, the
thresholds are not necessarily centered around 0 in all detector circuits.

Hysteresis. The hysteresis of the circuit shown in Figure 3.7 is simply the dif-
ference between the two threshold voltages. That is,